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JohnD.Sterman

MassachusettsInstituteofTechnology

SloanSchoolofManagement

幽腰閲脱水甘言告婁 Boston BurrRidge,lL Dubuque,lA Madison,WINewYork SanFrancisco St.Louis

Bangkok Bogota Caracas Lisbon London Madrid

MexicoCity Milan NewDelhiSeoulSingapore Sydney TaipeiToronto

McGraw-HillHigherEducation ADLmSLOnOfTheMcGraw-HillCompames

BUSINESSDYNAMICS SYsTEMSTHINKINGANDMoDELINGFORACoMPLEXWoRLD

Copyright㊨2000byTheMcGraw-HillCompaniesJnc.Allrightsreserved.PrintedintheUnited StatesofAmerica･ExceptaspermittedundertheUnitedStatesCopyrightActof1976,nopartof thispublicationmaybereproducedordistributedinanyformorbyanymeans,orstoredina databaseol-retrievalsystem,withoutthepriorWrittenpermissionofthepublisher.

Thisbookispnntedonacid-freepaper.

10QWV/QWVO987

ISBN-13:978-0-07-231135-8

ISBN-10:0-07-231135-5

Publisher:JejfreyJ.Shelstad

Seniorsponsorlngeditor:ScottIsenberg

Marketingmanager:ZinaCrqft

Seniorprojectmanager:GladysTrue Seniorproductionsupervisor:LoriKoetters Freelancedesigncoordinator:Ma7TLI.Christianson Freelancecoverdesigner:TheVl-sual Coverimage'.㊨SoniaDelaunay/i&MServices,AmsterdamuateGallery,London/ArtResoluCe,NY Compositor:GAC/Indianapolis Typeface:ll/13Tl'mesRoman Printer:QuebecorPrintingBookGroupWersailles

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Sterman,John.

Businessdynamics:systemsthinkingandmodelingfb∫acomplexworld/JohnD.Sterman. p･cm･

Includesbibliographicalreferencesandindex･ ISBN0-07-231135-5(礼lk.paper) ilIndustrialmanagement･ 2･Systemtheory. 3.Managementinformationsystems.I.

Title.

HD30.2.S7835 2000 658.4′038′011-dc21

99-056030

http:〟www.mhhe.com

ForCindy

ABOUTTHEAuTHOR

JohnD.Stermanis∫.SpencerStandishProfessorofManagementattheSloan SchoolofManagementoftheMassachusettsInstituteofTechnologyandDirector

ofMIT'sSystemDynamicsGroup.Hisresearchcentersonthedevelopmentof practiCalmethodsforsystemsthinkinganddynamicmodelingofcomplexsys-

tems,Withapplicationstoorganizationalleamlngandchange,operationsmanage- ment,corporatestrategy,andnonlineardynamicsinawiderangeofsystems,from supplychainstoscientificrevolutions.HehasplOneeredthedevelopmentofman-

agementflightsimulatorsofcorporateandeconomicsystems.Theseflightsimul latorsareusedinresearchtounderstandandimprovemanagerialdecisionmaking

incomplexdynamicsystems;moreimportantly,theyarenowwidelyusedbycor- porationsanduniversitiesaroundtheworldforteaching,problemsolving,andpol- 1Cydesign.ProfessorStermandiscoveredsystem dynamicsmodelinginhigh school,studieditasanundergraduateatDartmouthCollege,andreceivedhisPhD

fromMIT･HehasbeenawardedtheJayW ForresterPrize,glVenforthebestpubl lishedworkinthefieldofsystemdynamicsoverthepriorfiveyears,andhasfour timeswonawardsforteachingexcellencefromthestudentsoftheSloanSchool.

Acceleratlngeconomic,technological,social,andenvironmentalchangechallenge managersandpolicymakerstolearnatincreasingrates,Whileatthesametimethe complexltyOfthesystemsinwhichweliveisgrowlng･Manyoftheproblemswe nowfaceariseasunantlCIPatedsideeffectsofourownpastactions.Alltoooften thepoliciesweimplementtosolveimportantproblemsfail,maketheproblem worse,orcreatenewproblems.

Effectivedecisionmakingandlearninglnaworldofgrowingdynamiccom-

plexityrequiresustobecomesystemsthinkers-toexpandtheboundariesofour mentalmodelsanddeveloptoolstounderstandhowthestructureofcomplexsys- temscreatestheirbehavior.

Thisbookintroducesyoutosystemdynamicsmodelinglbrtheanalysisofpol- lCyandstrategy,withafocusonbusinessandpublicpolicyapplications･System dynamicsisaperspectiveandsetofconceptualtoolsthatenableustounderstand thestructureanddynamicsofcomplexsystems.SystemdynamicsisalsoarlgOr-

Ousmodelingmethodthatenablesustobuildformalcomputersimulationsofcom- plexsystemsandusethemtodesignmoreeffectivepoliciesandorganizations･ Together,thesetoolsallowustocreatemanagementflightsimulators-micro- worldswherespaceandtimecanbecompressedandslowedsowecanexperience thelong-termsideeffectsofdecisions,speedlearnlng,developourunderstanding ofcomplexsystems,anddesignstructuresandstrategleSforgreatersuccess.

Thefieldofsystemdynamicsisthriving.Overthepastdecade,manytopcom- panies,consultingfirms,andgovernmentalorganizationshaveusedsystemdy- namicstoaddresscriticalissues.Moreinnovativeuniversitiesandbusiness

schoolsareteachingsystemdynamicsandfindingenthusiasticandgrowlngen- rollments.Hundredsofprimaryandsecondaryschools,fromkindergartentohigh school,areintegratlngSystemsthinking,systemdynamics,andcomputersimula- tionintotheircurricula.Toolsandmethodsforsystemdynamicsmodeling,theli-

braryofsuccessfulapplications,andinsightsintotheeffectiveuseofthetoolswith executivesandorganizationsareallexpandingrapidly･

vii

viii Preface

FEATURESAh旧にoNTENT

Universltyandgraduatelleveltexts,particularlythosefocusedonbusinessand publicpolicyapplications,havenotkeptpacewiththegrowthofthefield.This

bookisdesignedtoprovidethoroughcoverageofthefieldofsystemdynamicsto- day,byexaminlng

｡Systemsthinkingandthesystemdynamicsworldview;

･Tわolsfわrsystemsthinking,Includingmethodstoelicitandmapthe

structureofcomplexsystemsandrelatethosestructuresto血eirdynamics;

･Tbolsformodelingandsimulationofcomplexsystems;

｡Proceduresfortestlngandimprovlngmodels;

｡Guidelinesfわrworkingwithclientteamsandsuccessfulimplementation｡

Youwilllearnaboutthedynamicsofcomplexsystems,includingthestructures

thatcreategrowth,goal-seekingbehavior,oscillationandinstability,S-shaped growth,overshootandcollapse,pathdependence,andothernonlineardynamics. Examplesandapplicationsinclude

･Corporategrowthandstagnation,

･Thediffusionofnewtechnologies,

｡ThedynamicsofinfectiousdiseasesuchasHIV/AIDS,

･Businesscycles,

｡Speculativebubbles,

｡Theuseandreliabilityofforecasts,

｡Thedesignofsupplychainsinbusinessandotherorganizations,

｡Servicequalitymanagement,

･Transportationpolicyandtrafficcongestion,

･Projectmanagementandproductdevelopment,

andmanyothers.

ThegoalofsystemsthinkingandsystemdynamicsmodelinglStOimproveour understandingofthewaysinwhichanorganization'sperformanceisrelatedtoits

internalstructureandoperatingpolicies,includingthoseofcustomers,competl- tors,andsuppliersandthentousethatunderstandingtodesignhighleveragepoli- ciesforsuccess.Todosothisbookutilizes

｡ProcessPointsthatprovidepracticaladviceforthesuccessfulapplication ofthetoolsinrealorganizations.

･CasestudiesofSystemDynamicsinActionthatpresentsuccessful

applicationsrangingfromglobalwarmingandthewarondrugsto reenglneerlngthesupplychainofamajorcomputerfirm,marketing strategylntheautomobileindustry,andprocessimprovementinthe petrochemicalsindustry,

Systemdynamicsisnotaspectatorsport.DeveloplngSystemsthinkingandmod- elingskillsrequlreStheactivepartlClpationofyou,thereader,via

Preface lX

･Challenges.Thechallenges,placedthroughoutthetext,glVeyouPractice withthetoolsandtechniquespresentedinthebookandwillstimulateyour

orlglnalthinkingaboutimportantrealworldissues･Thechallengesrange fromsimplethoughtexperimentstofull-scalemodelingprojects.

｡Sim111ationsoftwareandmodels.TheaccompanyingCD-ROMandweb

site(http:〟www.mhhe.com/sterman)includeallthemodelsdevelopedin thetextalongwithstate-of-the-artsimulationsoftwaretorunthem･There areseveralexcellentsoftwarepackagesdesignedtosupportsystem dynamicsmodeling.Theseincludeithink,Powersim,andVensim.TheCD andwebsiteincludethemodelsforthetextinallthreesoftwareformats.

Thediskalsoincludesfullyfunctionalversionsoftheithink,Powersim,and VensimsoftwaresoyoucanrunthemodelsusinganyOfthesepackages

withouthavingtopurchaseanyadditionalsoftware･

･Additionally,theInstructor'sManualandinstructor'ssectionofthe websiteincludesuggestedsolutionslbrthechallenges,additional asslgnmentS,Powerpointfileswiththediagramsandfiguresfromthetext

suitablefortransparencies,suggestedcoursesequencesandsyllabi,and othermaterials.

lNTENDEDAuDIENCE

Thebookcanbeusedasatextincoursesonsystemsthinking,simulationmodel-

1ng,COmplexlty,Strategicthinking,Operations,andindustrialenglneerlng,among others.Itcanbeusedinfullorhalf-semestercourses,executiveeducation,and

self-study.Thebookalsoservesasareferenceformanagers,englneerS,COnSul- tants,andothersinterestedindeveloplngtheirsystemsthinkingskillsoruslngSyS-

temdynamicsintheirorganizations｡

A NoTEONMATHEMATICS

Systemdynamicsisgroundedincontroltheoryandthemoderntheoryofnonlin- eardynamics.Thereisanelegantandrigorousmathematicalfoundationforthe theoryandmodelswedevelop.Systemdynamicsisalsodesignedtobeapractical

toolthatpolicymakerscanusetohelpthemsolvethepresslngproblemstheycon- frontintheirorganizations.Mostmanagershavenotstudiednonlineardifferential equationsorevencalculus,orhaveforgottenitiftheydid･Tobeuseful,systemdy-

namicsmodelingmustbeaccessibletothewidestrangeofstudentsandpractlClng managerswithoutbecomingaVagueSetOfqualitativetoolsandunreliablegener- alizations.ThattensioniscompoundedbythediversltyOfbackgroundswithinthe communltyOfmanagers,students,andscholarsinterestedinsystemdynamics,

backgroundsrangingfrompeoplewithnomathematicseducationbeyondhigh schooltothosewithdoctoratesinphysics.

X Preface

jFYouDoN'THAVEASTRONGMATHEMATICSBACKGROUND, FEARNo†

Thisbookpresentssystemdynamicswithaminimumofmathematicalformalism. Thegoalistodevelopyourintuitionandconceptualunderstanding,withoutsacri- ficingtherlgOrOfthescientificmethod.Youdonotneedcalculusordifferential equationstounderstand血ematerial.Indeed,theconceptsarepresenteduslngOnly text,graphs,andbasicalgebra･Mathematicaldetailsandreferencestomoread- Vancedmaterialaresetasideinseparatesectionsandfootnotes.Highermathemat- ics,thoughuseful,isnotasimportantasthecriticalthinkingskillsdevelopedhere.

fFYouHAVEASTRONGMATHEMATICSBACKGROUND,FEARNo†

Realisticandusefulmodelsarealmostalwaysofsuchcomplexltyandnonlinearlty thattherearenoknownanalyticsolutions,andmanyofthemathematicaltoolsyou havestudiedhavelimitedapplicability.Thisbookwillhelpyouuseyourstrong technicalbackgroundtodevelopyourintuitionandconceptualunderstandingof complexltyanddynamics.Modelinghumanbehaviordiffersfrommodelingphys- icalsystemsinenglneerlngandthesciences.Wecannotputmanagersuponthelab benchandrunexperimentstodeterminetheirtransferfunctionorfrequencyre- sponse.Webelieveallelectronsfollowthesamelawsofphysics,butwecannot assumeallpeoplebehaveinthesameway.Besidesasolidgroundinglnthemathe- maticsofdynamicsystems,modelinghumansystemsrequlreSuStOdevelopour knowledgeofpsychology,decisionmaking,andorganizationalbehavior･Finally, mathematicalanalysts,Whilenecessary,isfarfromsufficientforsuccessfulsys-

temsthinkingandmodeling.Foryourworktohaveimpactintherealworldyou mustlearnhowtodevelopandimplementmodelsofhumanbehaviorinorganiza- tions,withalltheirambigulty,timepressure,personalities,andpolitics.Through- outthebooklhavesoughttoillustratehowthetechnicaltoolsandma血ematical conceptsyoumayhavestudiedinthesciencesorenglneerlngCanbeappliedtothe messyworldofthepolicymaker.

FEEDBACK

Iwelcomeyourcomments,Criticisms,andsuggestions.Suggestionsforadditional examples,cases,theory,models,flightsimulators,andsoon,tomakethebook morerelevantandusefultoyouareespeciallyinvited.Iwillupdatethewebsite toincorporateuserfeedbackandnewmaterials･Emailcommentsto<BusDyn@ mit.edu>.

AcKNOWLEDGMENTS

Thisworkbenefitedimmenselyfromtheadvice,criticism,andencouragementof manycolleagues,students,andfriends.Ioweanimmeasurabledebttomyfirst systemdynamicsteachers,DanaMeadows,DennisMeadows,andJayForrester, fortheirintegrlty,highstandards,andpassionatecommitment.I'mparticularly indebtedtotheexceptlOnalstudentsoftheMITSloanSchoolofManagement. Theyconstantlychallengemetomakethedisciplineofsystemdynamicsrelevant,

Preface Xl

useful,andexcltlng;Ihopethey'velearnedasmuch丘.ommeasI'velearnedfrom them.Inaddition,IthankmycolleaguesattheSloanSchoolandinthesystem dynamicscommunltyaroundtheworld,whohelpedbyprovidingdataandexam- ples,reviewingthedraft,testlngearlyversionsintheircourses,andincountless otherways･Thisgroupincludes(butisnotlimitedto)thefollowingfolksand institutions:

TarekAbdel-Hamid(NavalPostgraduateSchool);DavidAndersen,George Richardson(SUNYAlbany);EdAnderson(Univ.ofTexas);CarlosAriza,Sharon

EIs,KenCooper,JimLyneis,HankTaylor(Pugh-RobertsAssociates);George Backus(PolicyAssessmentCorporation);BentBakken(NorwegianDefenseRe- searchEstablishment);YamanBarlas(BogaziciUniversity,Istanbul);Michael Bean(PowersimCorp.);EricBeinhocker,DamonBeyer,AndrewDoman,Usman Ghani,MauriceGlucksman,PaulLangley,NormanMarshall(McKinseyand

Company);LauraBlack,JohnCarroll,VanessaColella,ErnstDiehl,SteveEp- plnger,CharlieFine,MilaGetmansky,PauloGoncalves,JanetCouldWilkinson, JimHines,NanLux,BradMorrison,TimNugent,NelsonRepennlng,EdRoberts, ScottRockart,GeorgeRoth,EdSchein,PeterSenge(MIT);AllenandJane Boorstein;SteveCavaleri(CentralConnecticutStateUniv･);GeoffCoyle(Royal MilitaryCollegeofScience,UK,retired);BrianDangerfield(Univ.ofSalford); PalDavidsen(Univ.ofBergen);Jim Doyle,MikeRadzicki,KhalidSaeed (WorcesterPolytechniclnstitute);BobEberlein,TomFiddaman,DanGoldner, DavidPeterson,LauraPeterson(VentanaSystems);DavidFoleyandJudyBerk; AndyFord(WashingtonStateUniv.);DavidFord(TexasA&M University); NathanForrester(A,T.Kearney);RichGoldbach(MetroMachineCorp.);Chris- tianHaxholdt,HeatherHazard(CopenhagenBusinessSchool);JackHomer (HomerConsulting);JodyHouse(OregonGraduateInstitute);Billlsaacs(Dia- logos);Sam lsraellt(ArthurAndersen);NitinJoglekar(BostonUniv.School ofManagement);DrewJones(SustainabilityInstitute);ChristianKampmann, ErikMosekilde(TechnicalUniv･ofDenmark);DanielKim,VirginiaWiley (PegasusCommunications);CraigKirkwood(ArizonaStateUniv.);Elizabeth KrahmerKeating(NorthwesternUniv.);DonKleinmuntz(Univ.ofIllinois, Urbana-Champaign);DavidKreutzer(GKA,Inc.);RobertLandel(Dar°enSchool ofBusiness,Univ.ofⅥrginia);DavidLane(LondonSchoolofEconomics);Erik Larsen(CityUniversity,London);WinstonJ.Ledet,WinstonP.Ledet(TheMan-

ufacturingGame,Inc.);RalphLevine(MichiganStateUniv･);AngelaLipinski (SocietyforOrganizationalLearning);MartinGroJ3mann,FrankMaier,Peter Milling(Univ.ofMannheim,Germany);AliMashayekhi(SharifUniv.ofTech- nology,Teheran);NathanielMass(GenCorp);PaulMonus(BP/Amoco),John Morecroft,AnnvanAckere,Kin Warren(LondonBusinessSchool);Erling Moxnes(NorwegianSchoolofEconomicsandBusinessAdministration);Rogelio Oliva(HarvardBusinessSchool);MarkPaich(ColoradoCollege);StevePeterson, BarryRichmond(HighPerformanceSystems);GregPetsch(CompaqComputer); NickPudar(GeneralMotors);JackPugh,JuliaPugh,RobertaSpencer(System DynamicsSociety),JQrgenRanders(WorldWildlifeFundInternational);Nancy Roberts(LeslieCollege);JennyRudolph(BostonCollege);JorgeRufat-Latre (Strategos);AnjaliSastry,MarshallvanAIstyne(UniversityofMichigan);Bob Stearns;SusanSterman;JimThompson(GlobalProspectus,LLC);John帆)yer

xii Preface

(Univ.ofSouthernMaine);LyleWallis(Decisio,Inc.);JimWaters(WatersBusi- nessSystems);JasonWittenberg(HarvardUniv.);EricWolstenholme(Lee°sBusi一

messSchool,UK);PavelZamudioRamirez(MonitorCompany);theCopenhagen BusinessSchool,ThelnternationalNetworkofResourcelnformationCenters

(akatheBalatonGroup),McKinseyandCompany,theNorwegianSchoolof Management,Pugh-RobertsAssociates,theSocietyforOrganizationalLearnlng, theTechnicalUniversityofDenmark,and,ofcourse,theMITSloanSchoolof Management.

SpecialthankstoHighPerfわrmanceSystems,Powersim,SA,andVentana Systems-andtheirgreatpeople-forprovidingtheirsimulationsoftwareand translationsofthemodelsfortheCDandwebsite.

TheteamatIrwinMcGraw-Hilldeservesspecialmentionfortheirenthusiasm,

patience,andeditorialhelp,particularlyScottIsenberg,CarolRose,JeffShelstad, andGladysTrue.

CaraliarberandKelleyDonovanprovidedimportantsecretarialsupport. KathySullivanwentbeyondthecallofdutyonlibraryresearch,datacollec-

tion,editorialchanges,andgraphics, Finally,theloveandsupportofmyfamilyhavebeenconstantandessential.

Thanks,Cindy,David,andSarah.

Prefaee vii

PARTI PERSPECTIVEANDPROCESS 1

1 Learn1nglnandaboutComplexSystems 3 1.1 1ntroduction 3

1.1.1 PolicyResistance,theLawofUnintendedConsequences, andtheCounterintuitiveBehaviorofSocialSystems 5

1.1.2 CausesofPolicyResistance 10 l.1.3 Feedback 12

1.1.4 ProcessPoint.･TheMeaningofFeedback 14 CIlallenge:DynamicsofMultiple-LoopSystems 14

1.2 LearnlnglsaFeedbackProcess 14 1.3 BarrierstoLeamlng 19

1.3.1 DynamicComplexity 21 1.3.2 LimitedInformation 23 1.3.3 ConfoundingVariablesandAmbiguity 25

1.3.4 BoundedRationalityandtheMisperceptions ofFeedback 26

13.5 FlawedCognltiveMaps 28

1.3.6 ErymeousInferencesaboutDynamics 29 1.3.7 UnscientlficReasoning/JudgmentalErrors

andBiases 30

Challenge:HypothesisTesting 30 1.3.8 DefensiveRoutinesandInterpersonalImpediments

toLearnlng 32

1.3.9 ImplementationFailure 33

1.4 RequlrementSforSuccessfulLearnlnginComplexSystems 33 1.4.1 ImprovlngtheLearmngProcess:Virtues

ofTrl'rtualWorlds 34 1.4.2 PitfallsofⅥrtualTYorlds 35 1.4.3 WhySimulationIsEssential 37

1.5 Summary 39

xdlii

XJV Contents

2 SystemDynamicsinAetion 41 2･1 ApplicationsofSystemDynamics 41 2.2 AutomobileLeasingStrategy:GoneToday,HereTomorrow 42

2.2.1 DynamicHypothesis 44 22.2 ElaboratlngtheModel 48 2.2.3 PolicyAnalysis 51

2.2.4 ImpactandFollow-up 54

2.3 0nTimeandUnderBudget:TheDynamics ofProjectManagement 55 23.1 TheClaim 56

2.3.2 InitialModelDevelopment 57 23.3 DynamicHypothesis 58 2.3.4 TheModelingProcess 61 2.3.5 ContinuingImpact 64

2.4 PlaylngtheMaintenanceGame 66 2.4.1 DynamicHypothesis 67 2.4.2 TheImplementationChallenge 74 2.4.3 Results 76

2.4.4 TransferringtheLearning:TheLimaExperience 77 2,5 Summary:PrinciplesforSuccessfulUseofSystemDynamics 79

3 TheModelingProcess 83 3.1 ThePurposeofModeling:ManagersasOrganizationDesigners 84 3.2 TheClientandtheModeler 84

3.3 StepsoftheModelingProcess 85 3.4 Modelinglslterative 87 3.5 0verviewoftheModelingProcess 89

3.5.1 ProblemArticulationITheImportanceofPurpose 89 3.5.2 FormulatingaDynamicHypothesis 94 3.5.3 FormulatlngaSimulationModel 102 3.5.4 Testlng 103 3.5.5 PolicyDesignandEvaluation 103

3.6 Summary 104 4 StructureandBehaviorofDynamieSysもems 107

4.1 FundamentalModesofDynamicBehavior 108 4.1.1 ExponentialGrowth 108 4.i.2 GoalSeeking 111 4.1.3 0scillation 114 4.1.4 ProcessPoint 116

Challenge:IdentifyingFeedbackStructure fromSystemBehavior 117

4.2 InteractionsoftheFundamentalModes 118

4.2.1 S-ShapedGrowth 118 4.2.2 S-ShapedGT10WthwithOvershoot 121 Cha土lenge:IdentifyingtheLimitstoGrowth 121 42.3 0vershootandCollapse 123

4.3 0therModesofBehavior 127

4.3.1 Stasis,orEquilibrium 127

Contents

4.3.2 Randomness 127 4.3.3 Chaos 129

4.4 Summary 133

PARTII TOOLSFORSYSTEMSTHINKING 135

5 CallSalLoopDiagrams 137 5.1 CausalDiagramNotation 137 5.2 GuidelinesforCausalLoopDiagrams 141

5.2.1 CausationversusCorrelation 141

5.2,2 LabelingLinkPolarity 142

Challenge:AssigningLinkPolarities 143 5.2.3 DeterminingLoopPolarity 143 Challenge:IdentifyingLinkandLoopPolarity 145 CIlallenge:EmployeeMotivation 147 5.2.4 NameYourLoops 148 5.2.5 IndicateImportantDelaysinCausalLJinks 150 5.2.6 VariableNames 152

5.2.7 Tl'psforCausalLoopDiagramLayout 153 5.2.8 ChoosetheRightLevelofAggregation 154 5.2.9 Don'tPutAlltheLoopsintoOneLargeDiagram 154 52.10 MaketheGoalsofNegativeLJOOPSExplicit 155 5.2.11 DistmguishbetweenActual

andPerceivedConditions 156

5.3 ProcessPoint:DeveloplngCausalDiagrams fromInterviewData 157

Challenge:ProcessImprovement 158 5.4 ConceptualizationCaseStudy:ManaglngYourWorkload 159

5.4.1 ProblemDefinition 159 5.4.2 Ident的7ingKeyVariables 160

5･4･3 Developl:ngtheReferenceMode 160 5.4.4 DeveloplngtheCausalDiagrams 163 5.4,5 LimitationsoftheCausalDiagram 166 Challenge:PolicyAnalysiswithCausalDiagrams 168

5.5 AdamSmith'slnvisibleHandandthe FeedbackStructureofMarkets 169

Challenge:TheOilCrisesofthe1970S 172 Challenge:SpeculativeBubbles 173 Challenge:TheThoroughbredHorseMarket 174 5.5.1 MarketFailure,AdverseSelection,

andtheDeathSpiral 174 Challenge:TheMedigapDeathSpiral 176

5･6 ExplainingPolicyResistance:TrafficCongestion 177 5.6.1 MentalModelsoftheTrajficPy10blem 178 5.6.2 CompensatingFeedback:TheResponse

toDecreasedCongestion 181 5.63 TheMassTransitDeathSpiral 185 5.6.4 PolicyAnalysis:TheImpactofTechnology 188 5.6.5 CompensatingFeedback:TheSource

ofPolicyResistance 189

XVl Contents

Challenge:IdentifyingtheFeedbackStructure

ofPolicyResistance 190

5･7 Summary 190 6 StoeksandFlows 191

6.1 Stocks,Flows,andAccumulation 191

6.1.1 DiagrammingNotationforStocksandFlows 192

6.1.2 MathematicalRepresentationofStocksandFlows 193 6.1.3 TheContributionofStockstoDynamics 195

6･2 IdentifyingStocksandFlows 197 6.2.1 UnitsofMeasureinStockandFlowNetworks 198 6.2.2 TheSnapshotTest 199

Challenge:IdentifyingStocksandFlows 201 6.2.3 Conse7WationofMaterialin

StockandFlowNetworks 201

6.2.4 State-DeterminedSystems 202

6.2.5 AuxiliafTVariables 202 6.2.6 StocksChangeOnlythroughTheirRates 204 6.2.7 ContinuousTl'meandInstantaneousFlows 206

6.2.8 ContinuouslyDivisibleversusQuantizedFlows 207

6.2.9 WhichModelingApproachShouldYouUse? 208 6.2.10 Py10CeSSPoint:PortrayingStocksandFlows

inPractice 209

6.3 MappingStocksandFlows 210

6.3.1 WhenShouldCausalLoopDiagramsShow StockandFlowStructure? 210

Challenge:AddingStockandFlowStructure toCausalDiagrams 211

Cha11enge:LinkingStockandFlowStructurewithFeedback 212 6.3.2 AggregationinStockandFlowMapplng 213

Challenge:ModifyingStockandFlowMaps 213 Challenge:Disaggregation 214

6.3.3 GuidelinesforAggregation 216 6.3.4 SystemDynamicsinAction:

ModelingLarge-ScaleConstructionProjects 218 63.5 SettingtheModelBoundafT:

"ChallenglngtheClouds" 222 6.3.6 SystemDynamicsinAction.･AutomobileRecycling 225

6.4 Summary 229 7 DynamicsofStoeksandFlows 231

7.1 RelationshipbetweenStocksandFlows 232 7.1.I StaticandDynamicEquilibrium 232 7.1.2 CalculuswithoutMathematics 232

7.1.3 GraphicalIntegration 234

Challenge:GraphicalIntegration 239 7.1.4 GraphicalDIHerentiation 239

Challenge:GraphicalDifferentiation 241

7･2 SystemDynamicsinAction:GlobalWarmlng 241

Contents xvii

7･3 SystemDynamicsinAction:TheWaronDrugs 250 7.3.1 TheCocaineEpidemicafter1990 258

7･4 Summary 262 8 ClosingtheLoop:

DynamiesofSimpleStructures 263

8.1 First-OrderSystems 263

8,2 PositiveFeedbackandExponentialGrowth 264 8.2.1 Analytl'cSolutionfortheI/inearFirst-071derSystem 265 8.2.2 GraphicalSolutionoftheLinearFirst-Order

PositiveFeedbackSystem 266 8.2.3 ThePowerofPositiveFeedback:DoublingTl'mes 268 Challenge:PaperFolding 268

8.2.4 MisperceptionsofExponentialGrowth 269 8.2.5 ProcessPoint/OvercomingOverconfidence 272

8.3 NegativeFeedbackandExponentialDecay 274 8.3.1 Tl'meConstantsandHalf-Lives 279 Challenge.･Goal-SeekingBehavior 281

8.4 Multiple-LoopSystems 282 8.5 NonlinearFirst-OrderSystems:S-ShapedGrowth 285

Challenge:NonlinearBirthandDeathRates 286 8.5.1 FormalDefinitionofLoopDominance 288 8.5.2 First107derSystemsCannotOscillate 290

8.6 Sum ary 290

PARTIll THEDYNAMICSOFGROWTH 293

9 S･ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthof NewProducts 295

9.1 ModelingS-ShapedGrowth 296 9.1.1 LoglSticGrowth 296 9.1.2 AnalyticSolutionoftheLogisticEquation 297 9.1.3 0therCommonGrowthModels 299

9.1A TestingtheLogisticModel 300 9.2 DynamicsofDisease:ModelingEpidemics 300

9.2.1 ASimpleModelofInfectiousDisease 300 9.2.2 ModelingAcuteInfection:TheSIRModel 303 9.2.3 ModelBehavior:TheTl'pplngPoint 305 Challenge:ExploringtheSIRModel 308 9.2.4 ImmunizationandtheEradicationofSmallpox 309 Challenge:TheEfficacyofImm unizationPrograms 310 9.2.5 He71dlmmunity 312 9.2.6 MovingPasttheTl'pplngPoint:MadCowDisease 314 Chal1enge:ExtendingtheSIRModel 316 9.2.7 ModelingtheHW/AIDSEpidemic 319 Challenge:ModelingHIV/AIDS 321

9.3 InnovationDiffusionasInfection:

ModelingNewldeasandNewProducts 323 93.1 TheLogisticModelofInnovationDl# usion:

Examples 325

xviii Contents

9.3.2 ProcessPoint:HistoricalFitandModelValidity 328 9.3.3 TheBassDlHusionModel 332 Challenge:PhaseSpaceoftheBassDiffusionModel 333 9.3.4 BehavioroftheBassModel 334 Challenge:CritiqulngtheBassDiffusionModel 334 Challenge:ExtendingtheBassModel 335 9.3.5 FadandFashion:

ModelingtheAbandonmentofanInnovation 339 Challenge:ModelingFads 341 9.3.6 ReplacementPurchases 342 Challemge:ModelingtheLifeCycleofDurableProducts 345

9.4 Summary 346 10 PathDependenceandPositiveFeedbaek 349

10,1 PathDependence 349 Challenge:IdentifyingPathDependence 353

10.2 ASimpleModelofPathDependence:ThePolyaProcess 354 10.2.1 GeneralizingtheModel:NonlinearPolyaProcesses 357

10.3 PathDependenceintheEconomy:VHSversusBetamax 359 Challenge:FormulatingaDynamicHypothesis fortheVCRIndustry 364

10.4 PositiveFeedback:TheEngineofCorporateGrowth 364 10.4.i ProductAwareness 365

10.4.2 UnitDevelopmentCosts 367 10.4.3 PriceandProductionCost 368

10.4.4 NetworkEjfectsandComplementafTGoods 370 10.4.5 ProductDIHerentiation 371 10.4.6 NewProductDevelopment 373 10.4.7 MarketPower 374

10.4.8 MergersandAcqulSitions 375 10.4.9 WorkforceQualityandLoyalty 376 10.4.10 TheCostofCapital 378 10Al1 TheRulesoftheGame 380 10.4.12 AmbitionandAspirations 380 10.4.13 CreatingSynergyforCorporateGrowth 382

10.5 PositiveFeedback,increasingReturns,andEconomicGrowth 385 10.6 DoestheEconomyLockintoInferiorTechnologies? 387 10.7 LimitstoLockln 389

10.8 ModelingPathDependenceandStandardsFormation 391 10.8.1 ModelStructure 392 10.8.2 ModelBehavior 396

10.8.3 PolicyImplications 402 Challenge:PolicyAnalysIS 403 Challenge:ExtendingtheModel 404

10.9 Summary 406

PARTIV TOOLSFORMODELINGDYNAMICSYSTEMS 407

ll Delays 409 11.1 Delays:Anlntroduction 409

Contents XIX

Challenge:DurationandDynamicsofDelays 409 11.1.1 DefiningDelays 411

11.2 MaterialDelays:StructureandBehavior 412 11.2.1 WhatIstheAverageLengthoftheDelay? 413

11･2･2 WhatlstheDistributionoftheOutputaroundtheAverage DelayTl'me? 413

11.2.3 PipelineDelay 415

11.2.4 First107derMaterialDelay 415 11.2.5 Higher-OrderMaterialDelays 417 11.2.6 HowMuchlsintheDelay?Little'sLaw 421

Challenge:ResponseofMaterialDelaysto Steps,Ramps,andCycles 425

11.3 InformationDelays:StructureandBehavior 426

11.3.1 ModelingPerceptions:AdaptlVeExpectationsand ExponentialSmoothing 428

11.3.2 Higher-OrderInformationDelays 432 11.4 ResponsetoVariableDelayTimes 434

Challenge:ResponseofDelaystoChangingDelayTimes 435 11.4.1 NonlinearAdjustmentTl'mes:

ModelingRatchetEjfects 436

11･5 EstimatlngtheDurationandDistributionofDelays 437 11.5.1 EstimatingDelaysVVhenNumericalData

AreAvailable 437

11.5.2 EstimatlngDelaysWhenNumericalData AreNotAvailable 445

11.5.3 ProcessPoint:1砺‡lktheLine 449

11.6 SystemDynamicsinAction: ForecastlngSemiconductorDemand 449

11･7 MathematicsofDelays:KoyckLagsandErlangDistributions 462 11.7.1 GeneralFormulationforDelays 462 11.7.2 First-OTlderDelay 464

11.7.3 Higher-OrderDelays 465 11.7.4 RelationofMaterialandInformationDelays 466

11.8 Summary 466 12 CofLowsandAgingChains 469

12.1 AgingChains 470 12.1.1 GeneralStructureofAgingChains 470 12.1.2 Example:PopulationandInfrastructureinUrban

Dynamics 472 12.1.3 Example:ThePopulationPyramidandtheDemographic

Transition 474

12.1.4 AgingChainsandPopulationlnertia 480 12.1.5 SystemDynamicsinAction:

WTorldPopulationandEconomicDevelopment 481 12.1.6 CaseStudy/

Gr10WthandtheAgeStructureofOrganizations 485 12.1.7 PromotionChainsandtheLearnmgCuyve 490

XX Contents

12.1.8 MentorlngandOn-The-JobTrainlng 493

CIlallenge:TheInteractionsofTrainingDelaysandGrowth 495 12.2 Coflows:ModelingtheAttributesofaStock 497

Challenge:Coflows 503 12.2.1 CojlowswithNonconservedFlows 504

CIlallenge:TheDynamicsofExperienceandLearnlng 508 12.2.2 IntegratingCojlowsandAgingChains 509

Challenge:ModelingDesignWinsinthe Semiconductorlndustry 511

12･3 Summary 511 13 ModelingDecisionMaking 513

13.1 PrinciplesforModelingDecisionMaking 513 13.1.1 DecisionsandDecisionRules 514 13.1.2 FiveFormulationFundamentals 516

Challenge:FindingFormulationFlaws 520 13.2 FormulatingRateEquations 522

13.2.1 FractionalIncreaseRate 522 13.2.2 FractionalDecreaseRate 523

13.2.3 AdjustmenttoaGoal 523

13.2.4 TheStockManagementStructure: Rate-NormalRate+Adjustments 524

13.2.5 Flow-Resource*Productivity 524

13.2.6 Y- Yj-*EHectofXIOnY*EHectofX20nY*...*EHect ofXnonY 525

13.2.7 Y-YS+EHectofXIOnY+EjfectofX20nY+･･.+ EHectofXnonY 527

Cha互lenge:MultipleNonlinearEffects 529 13.2.8 FuzzyMINFunction 529

13.2.9 FuzzyMAXFunction 530 13.2.10 FloatingGoals 532

Challenge:FloatingGoals 533 Challenge:GoalFormationwithInternalandExternalInputs 535 13.2.ll NonlinearWeightedAverage 535

13.2.12 ModelingSearch:Hill-ClimbingOptimization 537

Chailenge:FindingtheOptimalMixofCapitalandLabor 543 13.2.13 ResourceAllocation 544

13.3 CommonPitfalls 545

13.3.1 All0utjlowsRequireFirst-OrderControl 545

Challenge:PreventingNegativeStocks 547 13.3.2 AvoidIF...THEN...ELSEFormulations 547

13.3.3 DisaggregateNetFlows 547

13･4 Summary 549 14 FormulatingNonlinearRelationships 551

14.1 TableFunctions 552

14.1.1 SpecljyingTableFunctions 552

14.I.2 Example/BuildingaNonlinearFunction 552

Contents XXl

14.I.3 ProcessPoint:TableFunctionsversus

AnalyticFunctions 562

14.2 CaseStudy:CuttingCornersversusOvertime 563 Challenge:FormulatingNonlinearFunctions 566 14.2.1 WorkingOvertime:

TheEjfectofSchedulePressureonTVorkweek 567

14.2.2 CuttingCorners:

TheEHectofSchedulePressu誓onTimeperTask 568 14.3 CaseStudy:EstimatingNonlinearFunctionsWithQualitativeand

NumericalData 569

Challenge:RefiningTableFunctionswithQualitativeData 569 14.4 CommonPitfalls 573

14.4.1 UsingtheWronglnput 573

Challenge.ACritiqulngNonlinearFunctions 575 14.4.2 ImproperNormalization 576 14.4.3 AvoidHump-ShapedFunctions 577

CIlallenge:FormulatingtheErrorRate 583 Challenge:TestingtheFullModel 585

14.5 ElicitingModelRelationshipslnteractively 585 14.5.1 CaseStudy:EstimatingPrecedenceRelationshipsin

ProductDevelopment 587 14.6 Summary 595

15 ModelingHllmanBehavior:BoundedRationalityor RationalExpectations? 597

15.1 HumanDecisionMaking:BoundedRationalityor RationalExpectations? 598

15.2 CognitiveLimitations 599 15.3 hdividualandOrganizationalResponsesto

BoundedRationality 601 153.1 Habit,Routines,andRulesofThumb 601 15.3.2 ManagingAttention 601 15.3.3 GoalFormationandSatisficing 601

153.4 ProblemDecompositionandDecentralized

DecisionMaking 602 15.4 ⅠntendedRationality 603

15.4.1 TestingforIntendedRationality:PartialModelTests 605

15.5 CaseStudy:ModelingHigh-TechGrowthFirms 605 15.5.1 ModelStructure:Ovenノiew 606

15.5.2 0rderFulfillment 607

15.5.3 CapacityAcquisition 609 Challenge:HillClimbing 615 15.5.4 TheSalesForce 615

15.5.5 TheMarket 619

15.5.6 BehavioroftheFullSystem 621

Chailenge:PolicyDesignintheMarketGrowthModel 624 15.6 Summary 629

xxji Contents

16 ForecastsandFudgeFactors:ModelingExpectationFormation 631 16.1 ModelingExpectationFormation 631

16.1.1 ModelingGrowthExpectations: TheTRENDFunction 634

16.1.2 BehavioroftheTRENDFunction 638

16.2 CaseStudy:EnergyConsumptlOn 638 16.3 CaseStudy:CommodityPrices 643 16.4 CaseStudy:Inflation 645 16.5 ImplicationsforForecastConsumers 655

Cballenge:ExtrapolationandStability 656 16.6 InitializationandSteadyStateResponseof

theTRENDFunction 658

16.7 Summary 660

PARTV INSTABILITYANDOSCILLATION 661

17 SupplyChainsandtheOriginofOscillations 663 17.1 SupplyChainsinBusinessandBeyond 664

17.1.1 0scillation,Amplification,andPhaseLJag 664 17.2 TheStockManagementProblem 666

17.2.1 ManaglngaStockIStructure 668 17.2.2 SteadyStateError 671 17.2.3 ManagingaStockIBehavior 672

Challenge:ExplorlngAmplification 674 17.3 TheStockManagementStructure 675

17.3.1 BehavioroftheStockManagementStructure 680

Challenge;ExploringtheStockManagementStructure 683 17.4 TheOriginofOscillations 684

17.4.1 MismanaglngtheSupplyLineI TheBeerDistributionGame 684

17.4.2 WhyDoIVeIgnoretheSupplyLine? 695 17.4.3 CaseStudy:BoomandBustinRealEstateMarkets 698

Challenge:ExpandingtheRealEstateModel 707 17.5 Summary 707

18 TheManufacturingSupplyChain 709 18.1 ThePolicyStructureoflnventoryandProduction 710

18.1.1 07derFulfillment 711 18.1.2 Production 713 18.1,3 ProductionStarts 714

18.1.4 DemandForecasting 716 18.1.5 ProcessPointIInitializlngaModelinEquilibrium 716

Challenge:SimultaneousInitialConditions 718 18.1.6 BehavioroftheProductionModel 720

18.1.7 EnrichingtheModel:AddingOyderBacklogs 723 18.1.8 BehavioroftheFirmwithOyderBacklogs 725

18.1.9 AddingRawMaterialslnventoYy 725 18.2 InteractionsamongSupplyChainPartners 729

18.2.I InstabilityandTrustinSupplyChains 735

Contents xxiii

18.2.2 FromFunctionalSilostoIntegratedSupplyChain Management 740

Challenge:ReenglneerlngtheSupplyChain 741 18.3 SystemDynamicsinAction:ReenglneerlngtheSupplyChainina

High-VelocityIndustry 743 18.3.1 InitialP710blemDefinition 743

18.3.2 ReferenceModeandDynamicHypothesis 746 18.3.3 ModelFormulation 749

18.3.4 TestingtheModel 749 18.3.5 PolicyAnalysIS 751

18.3.6 Implementation:SequentialDebottlenecking 753 18.3.7 Results 755

18.4 Summary 755 19 TheLaborSupplyChainandtheOriginofBusinessCycles 757

19.1 TheLaborSupplyChain 758 19.1.1 StructureofLaborandHiring 758

19.I.2 BehavioroftheLaborSupplyChain 760 19.2 InteractionsofLaborandlnventoryManagement 764

Challenge:MentalSimulationof lnventoryManagementwithLabor 766 19.2.1 Invento77-TYorkforceInteractions:Behavior 766 19.2.2 ProcessPoint:ExplainlngModelBehavior 767

Challenge:ExplainlngOscillations 767 19.2.3 UnderstandingtheSourcesofOscillation 771 Challemge:PolicyDesigntoEnhanceStability 773 19.2.4 AddingOvertime 774 19.2.5 ResponsetoFlexibleWorkweeks 776

Challenge:ReenglneerlngaManufacturingFirm forEnhancedStability 778 19.2.6 TheCostsoflnstability 779 Cballenge:TheCostsoflnstability 780

CIlallenge:AddingTrainingandExperience 780 19.3 Inventory-WorkforceInteractionsandtheBusinessCycle 782

19.3.1 IstheBusinessCycleDead? 785

19｡4 Summary 788 20 ThelnvisibleHandSometimesShakes:CommodityCycles 791

20･1 CommodityCycles:FromAircrafttoZinc 792 20.2 AGenericCommodityMarketMode1 798

20.2.1 ProductionandInventoTy 801

20.2.2 CapacityUtilization 802 20.2.3 Py10ductionCapacity 805 20.2.4 DesiredCapacity 807

Challenge:IntendedRationalityoftheInvestmentProcess 810 20.2.5 Demand 811

20.2.6 ThePrice-SettingProcess 813

20.3 Application:CyclesinthePulpandPaperlndustry 824 Cllallenge:SensitivltytOUncertaintyinParameters 828

XXrV Contents

Challenge:SensitivltytOStructuralChanges 831 Challenge:ImplementlngStructuralChangesI ModelingLivestockMarkets 836 Challenge:PolicyAnalysIS 840

20.4 Summary 84l

PARTVI MODELTESTING 843

21 7hlthandBeauty:ValidationandModelTesting 845 21.1 ValidationandVerificationAreImpossible 846 21.2 QuestionsModelUsersShouldAsk-ButUsuallyDonうー 851 21.3 PragmaticsandPoliticsofModelUse 851

21.3.1 TypesofData 853 21.3.2 Documentation 855

21.3.3 Replicability 855

21･3･4 Protectiveve.rsusRejlectiveModeling 858 21.4 ModelTestinginPractlCe 858

21.4.1 Bounda7TAdequacyTests 861 21A.2 StructureAssessmentTests 863

21.4.3 DimensionalConsistency 866 21.4.4 ParameterAssessment 866 21.4.5 ExtremeConditionTests 869

Challenge:ExtremeConditionTests 871 21.4.6 IntegrationErrorTests 872 21.4.7 BehaviorReproductionTests 874 21.4.8 BehaviorAnomalyTests 880 21.4.9 FamilyMemberTests 881 21.4.10 SurpriseBehaviorTests 882 21.4.ll SensitivityAnalysis 883 21.4.12 SystemImprovementTests 887

Challenge:ModelTesting 889 21.5 Summary 890

PARTVII COMMENCEMENT 893

22 ChallengesfortheFuture 895 22.1 Theory 895 22.2 Technology 896 22.3 Implementation 899 22.4 Education 900

22.5 Applications 901 Challenge:PuttingSystemDynamicsintoAction 901

APPENDIXA NUMERICALINTEGRATION 903

Challenge:ChoosingaTimeStep 910 APPENDIXB NOISE 913

Challenge:ExplorlngNoise 922 REFERENCES 925 INDEX 947

DynamicsofMultiple-LoopSystems 14 HypothesisTestlng 30 IdentifyingFeedbackStructurefromSystemBehavior 117 IdentifyingtheLimitstoGrowth 122 AssigningLinkPolarities 143 IdentifyingLinkandLoopPolarity 145 EmployeeMotivation 147 Processlmprovement 158 PolicyAnalysiswithCausalDiagrams 168 TheOilCrisesofthe1970s 172

SpeculativeBubbles 173 TheThoroughbredHorseMarket 174 TheMedigapDeathSpiral 176 IdentifyingtheFeedbackStructureofPolicyResistance 190 IdentifyingStocksandFlows 201 AddingStockandFlowStmcturetoCausalDiagrams 21l LinkingStockandFlowStructurewithFeedback 212 ModifyingStockandFlowMaps 213 Disaggregation 214 Graphicallntegration 239 GraphicalDifferentiation 24l PaperFolding 268 Goal-SeekingBehavior 281 NonlinearBirthandDeathRates 286

ExploringtheSIRModel 308 TheEfficacyoflmmunizationPrograms 310 ExtendingtheSIRMode1 316 ModelingHIV/AIDS 321 PhaseSpaceoftheBassDi軌lSionModel 333 CritiqulngtheBassDi軌ISionModel 334 ExtendingtheBassModel 335 ModelingFads 341

XXV

XXVl ListofChallenges

ModelingtheLifeCycleofDurableProducts 345 IdentifyingPathDependence 353 FomulatlngaDynamicHypothesisfortheVCRIndustry 364 PolicyAnalysIS 403 ExtendingtheModel 404 DurationandDynamicsofDelays 409 ResponseofMaterialDelaystoSteps,Ramps,andCycles 425 ResponseofDelaystoChangingDelayTimes 435 TheinteractionsofTrainingDelaysandGrowth 495 Coflows 503

TheDynamicsofExperienceandLearnlng 508 ModelingDesignWinsintheSemiconductorlndustry 511 FindingFormulationFlaws 520 MultipleNonlinearEffects 529 FloatingGoals 533 GoalFormationwithlntemalandExternallnputs 535 FindingtheOptimalMixofCapitalandLabor 543 PreventlngNegativeStocks 547 FormulatingNonlinearFunctions 566 RefiningTableFunctionswithQualitativeData 569 CritiquingNonlinearFunctions 575 FormulatingtheErrorRate 583 TestingtheFullModel 585 HillClimbing 615 PolicyDesignintheMarketGrowthModel 624 ExtrapolationandStability 656 ExploringAmplification 674 ExploringtheStockManagementStructure 683 ExpandingtheRealEstateModel 707 SimultaneouslnitialConditions 718

ReenglneerlngtheSupplyChain 741 MentalSimulationoHnventoryManagementwithLabor 766 ExplainingOscillations 767 PolicyDesigntoEnhanceStability 773 ReenglneerlngaManufacturlngFirmforEnhancedStability 778 TheCostsoflnstability 780 AddingTrainlngandExperience 780 IntendedRationalityofthelnvestmentProcess 810 SensitivltytOUncertaintyinParameters 828 SensitivltytOStructuralChanges 831 ImplementingStructuralChanges-ModelingLivestockMarkets 836 PolicyAnalysIS 840 ExtremeConditionTests 871

ModelTesting 889 PuttingSystemDynamicsIntoAction 901 ChooslngaTimeStep 910 ExplorlngNoise 922

● ● i_Lea-,a.fi呈ilig妄言1A読取dab和書 C⑲m 野畳ex Sys息em s

Experienceisanexpensiveschool.

Experienceissomethingyougetjustafteryouneedit.

-BenjaminFranklin

-AnollymOuS

1.1 lNTRODUCT10N

Thegreatestconstantofmoderntimesischange.AcceleratlngChangesintech- nology,population,andeconomicactivltyaretranSformlngOurworld,fromthe prosaic-theeffectofinformationtechnologyonthewayweusethetelephone- totheprofound-theeffectofgreenhousegasesontheglobalclimate.Someofthe changesarewonderful;othersdefiletheplanet,impoverishthehumansplrlt,and threatenoursuⅣival.Allchallengetraditionalinstitutions,practices,andbeliefs. Mostimportant,mostofthechangeswenowstruggletocomprehendariseas consequences,illtendedandunintended,ofhumanltyltSelf.Alltoooften,wel1- intentionedeffortstosolvepresslngProblemsleadtopolicyresistance,whereour policiesaredelayed,diluted,ordefeatedbytheunforeseenreactionsofother peopleorofnature.ManytlmeSOurbesteffortstosolveaproblemactuallymake itworse.

ThedizzylngeffectsofacceleratingChangearenotnew.HenryAdams,a perceptlVeObserverofthegreatchangeswroughtbytheindustrialrevolution,

4 PartIPerspectiveandProcess

formulatedtheLawofAccelerationtodescribetheexponentialgrowthoftech-

nology,production,andpopulationthatmadethelegacyofcolonialAmericahe inheritedirrelevant:

Since1800,Scoresofnewforceshadbeendiscovered;oldforceshadbeenraised

tohigherpowers日.･Complexityhadextendeditselfonimmensehorizons, andarithmeticalratlOSWereuselessforanyattemptataccuracy.

IfscienceweretogoondoublingorquadruplingItsCOmplexitiesevery lOyears,evenmathematicsshouldsoonsuccumb.Anaveragemindhadsuc- cumbedalreadyin1850',itcouldnolongerunderstandtheproblemin1900. (Adams1918,pp.490,496)

AdamsbelievedtheradicalchangesinsocietyinducedbytheseforcesHwould

requlreanewsocialmind."Withuncharacteristic,andperhapsironic,optlmism,

heconcluded,HThusfar,since50r10thousandyears,themindhadsuccessfully

reacted,andnothingyetprovedthatitwouldfailtoreact-butitwouldneed

toJump."

Asteadystreamofphilosophers,scientists,andmanagementgurushavesince

echoedAdams,lamentlngtheaccelerationandcallingforsimilarleapstofunda-

mentalnewwaysofthinkingandacting.Manyadvocatethedevelopmentofsys- temsthinking-theabilitytoseetheworldasacomplexsystem,inwhichwe

understandthatHyoucan'tjustdoonethingHandthat"everythinglSCOnneCtedto

everythingelse."Ifpeoplehadahollsticworldview,itisargued,theywouldthen

actinconsonancewiththelong-termbestinterestsofthesystemasawhole,iden-

tifythehighleveragepolntSinsystems,andavoidpolicyresistance･Indeed,for

some,thedevelopmentofsystemsthinkingiscrucialforthesurvivalofhumanlty･1

Thechallengefacingusallishowtomovefromgeneralizationsaboutaccel-

eratlnglearnlngandsystemsthinkingtotoolsandprocessesthathelpusunder-

standcomplexity,designbetteroperatingpolicies,andguidechangeinsystems

fromthesmallestbusinesstotheplanetasawhole.However,leam1ngaboutcom-

plexsystemswhenyoualsoliveinthemisdifficult･Weareallpassengersonan

aircraftwemustnotonlyflybutredesigninflight.

SystemdynamicsisamethodtoenhancelearnlnglnCOmplexsystems.Justas

anairlineusesflightsimulatorstohelppilotslearn,systemdynamicsis,partly,a

methodfordeveloplngmanagementflightsimulators,oftencomputersimulation

models,tohelpuslearnaboutdynamiccomplexity,understandthesourcesofpo ト

1Cyresistance,anddesignmoreeffectivepolicies.

ButlearnlngaboutcomplexdynamicsystemsrequlreSmorethantechnical

toolstocreatemathematicalmodels.Systemdynamicsisfundamentallyinterdis-

ciplinary.Becauseweareconcernedwiththebehaviorofcomplexsystems,system

1Therearemanyschoolsofsystemsthinking(forsurveys,seeRichardson1991andLane

1994).Someemphasizequalitativemethods;othersstressfo-almodeling･Assourcesofmethod andmetaphortheydrawonfieldsasdiverseasanthropology,biology,englneerlng,linguistics,psy- chology,physics,andTaoismandseekapplicationsinfieldsstillmorediverse･Allagree,however, thatasystemsviewoftheworldisstillrare･JayForresterdevelopedsystemdynamicsinthe1950s atMIT.Richardson(1991)仕acesthehistoryofthefieldandrelatessystemdynamicstoothersys- temsapproaches.

Chapter1 LearninglnandaboutComplexSystems 5

dynamicsisgroundedinthetheoryofnonlineardynamicsandfeedbackcontrol developedinmathematics,physics,andenglneerlng.Becauseweapplythesetools tothebehaviorofhumanaswellasphysicalandtechnicalsystems,system dynamicsdrawsoncognltiveandsocialpsychology,economics,andothersocial sciences.Becausewebuildsystemdynamicsmodelstosolveimportantrealworld problems,wemustlearnhowtoworkeffectivelywithgroupsofbusypolicy makersandhowtocatalyzesustainedchangeinorganizations･

Thischapterdiscussesthes女illsrequiredtodevelopyoursystemsthinkingca- pabilities,howtocreateaneffectivelearningProcessindynamicallycomplexsys-

tems,andhowtousesystem dynamicsinorganizationstoaddressimportant problems.Ifirstreviewwhatweknowabouthowpeoplelearninandaboutcom- plexdynamicsystems.Suchlearnlngisdifficultandrarebecauseavarietyof structuralimpedimentsthwartthefeedbackprocessesrequiredforlearnlngtOOCI cur.Successfulapproachestolearnlngaboutcomplexdynamicsystemsrequlre (1)toolstoelicitandrepresentthementalmodelsweholdaboutthenatureofdif- ficultproblems;(2)formalmodelsandsimulationmethodstotestandimproveour mentalmodels,designnewpolicies,andpracticenewskills;and(3)methodsto sharpenscientificreasonlngSkills,improvegroupprocesses,andovercomedefen- siveroutinesforindividualsandteams｡

1.1L下 Po!icyResistance,theLawoHJnin始tlded

eonsequemees,amem的eeoumをeF百mをu盲抽e

Behav岳oro菅Soeia日Systems

Anditwillfalloutasinacomplicationofdiseases,thatbyapplyinga remedytoonesore,youwillprovokeanother;andthatwhichremovesthe oneillsymptomproducesothers‥.

-SirThomasMore

Thebest-laidschemeso'micean'men/Gangafta-gley. -RobertBurns

Anythingthatcangowrongwillgowrong.

一日MurphyM

tVehavemettheenemyandheisus｡

-Pogo

FromThomasMorein1516toPogointhemid20thcenturyithaslongbeenac-

knowledgedthatpeopleseekingtosolveaproblemoftenmakeitworse･Ourpoli- ciesmaycreateunanticIPatedsideeffects･Ourattemptstostabilizethesystemmay destabilizeit.Ourdecisionsmayprovokereactionsbyothersseekingtorestorethe balanceweupset.Forrester(1971a)callssuchphenomenathe…counterintuitive behaviorofsocialsystems.HTheseunexpecteddynamicsoftenleadtopolicyre- sistance,thetendencyforinterventionstobedelayed,diluted,ordefeatedbythe responseofthesystemtotheinterventionitself(Meadows1982)･

FLGUREl･l

Pdicyresistance: Romanianbirth rates

Thecrudebirth rateinRomania

showlngtheeffect ofrestrictingabor- tionbeglnnlngln 1966

PartIPerspectiveandProcess

(a Jd o ado o o LJJt2¢

ĴSL u J 叩g )

a lt2t] LJlJ !g a P

nJIU

19661967196819691970197119711994 Source:1966-1971,DavldandWright(1971);1971-1994, RomanianSlat/'stI'calYearbook1995, pp.100-101. Note:1971-1994areannualaveragesl

Asanexample,considerthebirthrateinRomaniainthelate1960S｡Thecrude birthrate(birthsperyearper1000people)wasextremelylow-about15per thousand(Figure1-1).Forvariousreasons,includingnationalprideandethnic

identity,thelowbirthratewasconsideredtobeagraveproblembythegovern-

ment,includingthedictatorNicolauCeausesgu.TheCeausesguregimeresponded byimposlngpoliciesdesignedtostimulatethebirthrate.Ⅰmportationofcontr a-

ceptivedeviceswasoutlawed;propagandacampalgnSextollingthevirtuesoflarge familiesandthepatriotic(matrioticwouldbemoreaccurate)dutytohavemore

childrenwereintroduced,alongwithsomemodesttaxincentivesfわrlargerfami- lies.Perhapsmostimportant,abortion-freelyavailableondemandsince1957 throughthestatehealthcaresystem-wasbannedinOctober1966(Davidand Wright1971).

Theresultwasimmediateanddramatic.Thebirthraterosesharplytonearly

40per1000peryear,rivalingthoseofthefastestgrowlngnations･Thepolicyap- pearedtobeasensationalsuccess.However,withinmonthsthebirthratebeganto fall.Bytheendof1970,only4yearsafterthepolicywasimplemented,thebirth ratehaddroppedbelow20perthousand,closetothelowlevelsseenpriortOthe intervention.Thoughthepolicycontinuedinforce,thebirthratecontinuedtofall,

reaching16perthousandby1989-aboutthesamelowratethatledtotheimpo-

sitionofthepolicy.Whathappened?

Thesystemrespondedtotheinterventioninwaysthereglmedidnotantici- pate.ThepeopleofRomaniafoundwaysaroundthepolicy.Theypracticedalter-

nativemethodsofbirthcontrol.TheysmuggledcontraceptlVepillsanddevicesin fromothercountries.Desperatewomensoughtandfoundback-alleyabortions.

Manyofthesewereunsanitaryorbotched,leadingtoaneartriplingofdeathsdue

Chapter1 LearnlnglnandaboutComplexSystems 7

tocomplicationsofabortionfrom 1965to1967.Mosthorribly,thenumberof neonataldeathsrosebymorethan300%between1966and1967,a20%increase

intheinfantmortalityrate(DavidandWright1971)･Theresult:thepolicywas renderedcompletelyineffectivealmostimmediatelyafterimplementation.

ButtheunanticIPatedconsequencesdidn'tendwiththefailureofthepopu- lationpolicy･ThepeopleofRomania,amongthepoorestinEurope,werehaving smallfamiliesbecausetheycouldn'taffordlargerones.Childcarewasunavai1-

ableforsome.Manyotherslivedwiththeirextendedfamiliesinsmall,crowded

apartments･Jobswerescarce;incomewaslow･Manypeoplegavechildren血ey couldn'tsupporttostate-runorphanages.Thegovernment'spolicydidn'tprevent thepeopleofRomaniafromcontrollingtheirownfertility,butitdidbreedintense resentmentagalnSttheintrusivepoliciesofthereglme.In1989,whentheBerlin wallfellandthetotalitarianregimesOfEasternEuropetoppled,Romaniawasthe onlynationwherethevelvetrevolutionwasviolent.ThehatedCeauseseuandhis

equallyhatedwifeweresummarilyexecutedbyfiringsquad.Theirbloodybodies werele氏inthecourtyardof血epresidentialpalacewhilethescenewasbroadcast

onnationaltelevision.Thelawbannlngabortionwasthefirstoverturnedbythe newgovernment.Thebirthrate,alreadylow,fellfurther.Bythemid1990S,the

populationofRomaniawasactuallydecliningasbirthsdroppedbelowdeaths. ThechildrenofRomaniasufferedthemostfromthepopulationpolicy.During

theyearsofthepopulationpolicythousandsofchildrenwereplacedinthecareof stateorphanages,wheretheywerekeptlikeanimalsincribs(cages,really)with- outattentiontobasicneeds,muchlessthelove山atallofusneedanddeserve.

FoodwassoscarcethatbloodtransfusionswereroutinelyglVenaSnutritionalsup- plements･Becauseneedleswereusedrepeatedly,anepidemicofAIDSspread

rapidlyamongthechildren･Thesideeffectsofthefailedpopulationpolicycasta shadowonthehealthandhappinessOfanentirenation,ashadowstretchingover generations.

Policyresistanceisnotlimitedtodictators.Itdoesn'trespectnationalborders, politicalideology,orhistoricalepoch･ConsidertheUSgovernment'sfightagalnSt inflationintheearly1970S.Figurel12showstheConsumerPriceIndex(CPI)for

theUnitedStatesbetween1968and1976.Intheearly1970sinflationhadacceler-

atedandtheNixonadministrationfeltactionhadtobetaken.ThoughaRepubli- can,NixonchosetoimplementwageandprlCeCOntrOIs.Thepolicywasexpensive: Anewfederalbureaucracy,theCouncilonWageandPriceStability,wascreated

tooverseethecontrolsandenforcecompliance.WageandprlCecontrolswere

viewedbymanyinNixon'sownpartyasvergingOnsocialism,costlngNixon

valuablepoliticalcapital.Atfirst,thepolicyseemedtowork,althoughimperfectly. Duringso-calledPhaseIofthecontrols,therateofinflationfellbyabouthalf.The administrationdecidedthecontrolscouldberelaxed.InPhaseII,PresidentFord

(whoinheritedtheprogramfromNixon)launchedajawboningcampaign,com-

pletewithcampalgn-StylebuttonslabeledHWIN!りforHWhipInflationNow!=･

FewobserversexpectedWIN.fbuttonstohaveanyeffect,andmostfeltinflation

wouldreturntoitsratepnortothestartofcontrols.Instead,innationactuallyac-

celerateduntil,by1975,theCPIhadreturnedtothetrajectoryltWasOnPriortOthe

impositionofthepriceCOntrOIs.Lessthan4yearsaftertheinterventiontherewas

8 PartIPerspectiveandProcess

FIGUREi-2 Policyresistanceinthefightagalnstinflation

TheUSConsumerPricelndex(CPI)showingtheNixon/Fordwageandprice controls

(oo L =

e 96

)

dd 3

1968 1969 1970 1971 1972 1973 1974 1975 1976

noresidueofbene臥 Otherexamplesofpolicyresistancecanbefoundnearly

everydayinthenewspaper･Tableilllistsafew12

Machiavelli,akeenobserverofhumansystems,discussedpolicyresistanceat

length,ObservingintheDiscoursesthat

Whenaproblemariseseitherfromwithinarepublicoroutsideit,Onebrought abouteitherbyinternalorexternalreasons,Onethathasbecomesogreatthatit beginstomakeeveryoneafraid,thesafestpolicylStOdelaydealingwithitrather

thantryingtodoawaywithit,becausethosewhotrytodoawaywithitalmost alwaysincreaseitsstrengthandacceleratetheharmwhichtheyfearedmightcome fromit.(Machiavelli1979,pp.240-241).

IfindMachiavelli'sviewtoocynicalbutcansympathizewithhisfrustrationinob-

servinghisclientprinces(theCEOsofRenaissanceItaly)takeactionsthatonly

madetheirproblemsworse･AmorereflectiveviewisofferedbythelatebiologlSt

andessayistLewisThomas(1974,p.90):

Whenyouareconfrontedbyanycomplexsocialsystem,suchasanurbancenteror ahamster,withthingsaboutitthatyou'redissatisfiedwithandanxioustofix,you

cannotjuststeplnandsetaboutfixingwithmuchhopeofhelping.Thisrealization isoneofthesorediscouragementsofourcenturyI-Youcannotmeddlewithone partofacomplexsystemfromtheoutsidewithoutthealmostcertainriskofsetting offdisastrouseventsthatyouhadn'tcountedoninother,remoteparts.Ifyouwant tofixsomethingyouarefirstobligedtounderstand...thewholesystemH IntervenlnglSaWayOfcauslngtrouble.

2Furtherreading:JohnMcPhee(1989)o恥rsawonde血ldescriptionofpolicyresistanceinthe

relationshipofpeoplewithnature.McPheebrilliantlydescribestheunanticIPatedsideeffectsand policyresistancearisingfromattemptstodefeatthreeelementalforcesofnature:volcanism,flood, andfire･EdwardTenner(1996)alsoidentifiesmanyexamplesofpolicyresistance･

Chapter1 LearmnglnandaboutComplexSystems

TABLEl ll

Examplesofpollcy resistance

"UseofCheaperDrugsPushesCostsUp,NotDown,StudyFinds:Limiting whatisprescribed,asmanaged-caresystemsdo,hasunintendedeffectof

increasingcosts,resultsshow"(HeadlinejnLATl'mes,3/20/96,pl1,report- 1ngUniv,ofUtahstudyof13,000patientsinvariousHMOs).

"Washington'sbiggestconservationprogram,whichpaysfarmerstotake sojloutofcultivationforadecadetocombaterosionandhelptheenviron-

ment,isawasteofmoney,sosaysanewstudyofthelllyear-Old program..･Foreveryerodingacreafarmeridles,anotherfarmer-or sometimesthesameone-simpJyplowsupnear一yasmuchadditional erosion-prone一and..lEntheGreatPlains,forinstance,farmerssetaside 17mi"ionacres,yetthetota一cultivatedlanddroppedbyonly2m‖ionacres" (BusinessWeek,3/18/96,p.6,reportingaUniv.ofMinnesotastudy).

LowtarandnicotineclgarettesactuaHyIncreaseintakeofcarcinogens,CO, etc.assmokerscompensateforthelownicotinecontentbysmokingmore clgaretteSPerday,bytakinglonger,morefrequentdrags,andbyholdingthe smokeintheirlungslonger.

Antilockbrakesandotherautomotivesafetydevicescausesomepeopleto drivemoreaggressiveJy,Offsettingsomeoftheirbenefits,

informationtechnologyhasnotenabledthe"paperlessOffice"-papercon-

sumptionpercapitaisup.

Roadbuildingprogramsdesignedtoreducecongestionhaveincreasedtraf-

fic,delays,andpollution.

Despitewidespreaduseof一abor-savlngaPPllanCeS,Americanshave一ess leisuretodaythan50yearsago.

TheUSgovernment'swarondrugs,focuslngOninterdjctionandsupplydis- ruption(particularlycocaineproductioninSouthAmerica),withacostinthe bHions,hashadonlyasmallimpactoncocainecultivation,Production,or smuggllng.DruguseinAmericaandelsewhereremainshighr

TheUSpolfCyOffiresuppressionhasincreasedthesizeandseverityof forestfires.Ratherthanfrequent,sma"fires,firesuppressionreadstothe accumulationofdeadwoodandotherfuelsleadingtolarger,hotter,and moredangerousfires,oftenconsumngtheoldestandlargesttreeswhich previouslysurvivedsmallerfiresunharmed. Floodcontrdeffortssuchasleveeanddamconstructionhaveledtomore

severefloodsbypreventingthenaturardissipationofexcesswaterinflood plains.Thecostofflooddamagehasincreasedasthefloodplainswerede- velopedbypeoplewhobelievedtheyweresafe.

lmposlng200-mileterritoria川mitsandquotastoprotectfishstocksdid notpreventtheco‖apseoftheGeorgesBankfisheryo什thecoastofNorth America1Oncetheworld'srichest,bythemid1990smanyspecieswere commerciallyextinct,thefisherywasshutdown,thefleetswereidled, andthe-Ocaleconomieswereindepression.

DeregulationoftheUSSavingsandLoanindustry,designedtosavethe industryfronlfinancialproblems,Jedtoawaveofspecufationfo"owedby coHapse,atacosttotaxpayersinthehundredsofbjJlionsofdoHars.

AntibioticshavestimuJatedtheevolutionofdrug-resistantpathogens, includingvirulentstrainsofTB,strep,staph,andsexua"ytransmitted diseases.

Pesticidesandherbicideshavestimulatedtheevolutionofresistantpests andweeds,kiHedoffnaturalpredators,andaccumulatedupthefoodchain topoJSOnfish,birds,andpossiblyhumans.

FIGUREl l3 Event10rJlented viewoftheworld

PartI PerspectiveandProcess

Buthowcanonecometounderstandthewholesystem?Howdoespolicyresis- tancearise?Howcanwelearntoavoidit,tofindthehighleveragepoliciesthat canproducesustainablebenefit?

iI1.2 CausesofPoiitCyRest-Stance

Onecauseofpolicyresistanceisourtendencytointerpretexperienceasaseriesof events,forexample,"inventorylStoohigh,"or"salesfellthismonth."Accounts ofwhodidwhattowhomarethemostcommonmodeofdiscourse,fromthemai l -

roomtotheboardroom,fromheadlinestohistorybooks.Wearetaughtfroman earlyagethateveryeventhasacause,whichintumisaneffectofsomestillear-

liercause:"InventorylStoohighbecausesalesunexpectedlyfell.Salesfellbe-

causethecompetitorsloweredtheirprlCe.Thecompetitorsloweredtheirprice because.･･"Suchevent-levelexplanationscanbeextendedindefinitely,inanun- brokenAristotelianchainofcausesandeffects,untilwearriveatsomeFirstCause,

ormorelikely,loseinterestalongtheway. Theevent-orientedworldviewleadstoanevenLorientedapproachtoproblem

solving･Figure1-3showshowweoftentrytosolveproblems.Weassessthestate ofaffairsandcompareittoourgoals.Thegapbetweenthesituationwedesireand thesituationweperceivedefinesourproblem･Forexample,supposesalesofyour organizationwere$80millionlastquarter,butyoursalesgoalwas$100million. Theproblemisthatsalesare20%lessthanyoudesired.Youthenconsidervarious optlOnStOcorrecttheproblem.YoumightcutprlCeStOStimulatedemandandin- creasemarketshare,replacethevicepresidentofsaleswithsomeonemoreag- gressive,ortakeotheractions.YouselecttheoptlOnyoudeembestandimplement it,leading(youhope)toabetterresult.Youmightobserveyoursalesincrease: problemsolved.Orsoitseems.

Thesystemreactstoyoursolution:Asyoursalesrise,competitorscutpnces, andsalesfallagain.Yesterday'ssolutionbecomestoday'sproblem.Wearenot puppetmastersinfluencingaSystemOutthere-weareembeddedinthesystem. Thepuppetmaster'smovementsrespondtothepositionofthemarionetteonthe strlngS.Thereisfeedback:Theresultsofouractionsdefinethesituationwefacein thefuture.Thenewsituationaltersourassessmentoftheproblemandthedeci- sionswetaketomorrow(seethetopofFigure1-4).

Policyresistancearisesbecauseweoftendonotunderstandthefullrangeof feedbacksoperatinginthesystem(Figureト4).Asouractionsalterthestateofthe system,Otherpeoplereacttorestorethebalancewehaveupset･Ouractionsmay alsotrlggerSideeffects.

Goals

iiZg

.//P.I Situation

Problem 一一一一｣ト Decision → Results

Chapter1 LearninglnandaboutComplexSystems ll

Wefrequentlytalkaboutsideeffectsasiftheywereafeatureofreality.Notso. Inreality,therearenosideeffects,therearejusteHects.Whenwetakeaction,there arevariouseffects.Theeffectswethoughtofinadvance,orwerebeneficial,we

callthemain,orintendedeffects.Theeffectswedidn'tantlCIPate,theeffects whichfedbacktoundercutourpolicy,theeffectswhichharmedthesystem-these

aretheonesweclaimtobesideeffects,Sideeffectsarenotafeatureofrealitybut asignthatourunderstandingofthesystemisnarrowandflawed.

Unanticipatedsideeffectsarisebecausewetoooftenactasifcauseandeffect

werealwayscloselylinkedintimeandspace.Butincomplexsystemssuchasan urbancenterorahamster(orabusiness,society,orecosystem)causeandeffectare oftendistantintimeandspace.Narrowmodelboundariesoftenleadtobeliefsthat violatethelawsofphysics:inthemid1990sCaliforniaandtheautomobileindus- trydebatedtheintroductionofsoICalledzeroemissionvehicles(ZEVs)toreduce

airpollution.True,theZEVs-electriccars-wouldhavenotailpipe.Butthe powerplantsrequiredtomaketheelectrlCltytOrunthemdogeneratepollution.In reality,CaliforniawaspromotlngtheadoptionofDEVs-displacedemissionve- hicles-Carswhosewasteswouldblowdownwindtootherstatesoraccumulatein

nuclearwastedumpsoutsideitsborders.Electriccarsmayturnouttobeanenvi- ronmentalbooncomparedtointernalcombustion.ThetechnologylSimprovlng

rapidly,andairpollutionisamajorhealthprobleminmanycities･Butnomodeof

FIGURE1-4 Thefeedbackview

Environment

Ourdecisionsalterourenvironment,leadingtonewdecisions,

Goa･s ESdedcets

Goalsof Other Agents

butalsotriggerlngSideeffects,delayedreactions,changes ingoalsandinteⅣentionsbyothers.Thesefeedbacksmay

leadtounanticJPatedresultsandineffectivepo一icies.

12 PartI PerspectiveandProcess

transportorenergyconversionprocessisfreeofenvironmentalimpact,andno

legislaturecanrepealthesecondlawofthermodynamics･3

ToavoidpolicyresistanceandfindhighleveragepoliciesrequlreSuStOex-

pandtheboundariesofourmentalmodelssothatwebecomeawareofandunder-

standtheimplicationsofthefeedbackscreatedbythedecisionswemake･Thatis, wemustlearnaboutthestructureanddynamicsoftheincreaslnglycomplexsys- temsinwhichweareembedded.

1.1.3 Feedback

Muchoftheartofsystemdynamicsmodelingisdiscovenngandrepresentlngthe

feedbackprocesses,which,alongwithstockandflowstructures,timedelays,and nonlinearities,determinethedynamicsofasystem.Youmightimaginethatthere

isanimmenserangeofdifferentfeedbackprocessesandotherstructurestobe

masteredbeforeonecanunderstandthedynamicsofcomplexsystems.Infact,the

mostcomplexbehaviorsusuallyarisefromtheinteractions(feedbacks)amongthe

componentsofthesystem,notfromthecomplexityofthecomponentsthemselves･

Alldynamicsarisefromtheinteractionofjusttwotypesoffeedbackloops,

Positive(orself-reinforcing)andnegative(orself-correcting)loops(Figure115)･

Positiveloopstendtoreinforceoramplifywhateverishappenlnginthesystem:

ThemorenuclearweaponsNATOdeployedduringtheColdWar,themoretheSo-

vietUnionbuilt,leadingNATOtobuildstillmore.Ifafin lowersitspncetogaln

marketshare,itscompetitorsmayrespondinkind,forcingthefirmtolowerits

pncestillmore.ThelargertheinstalledbaseofMicrosoftsoftwareandlntelma-

chines,themoreattractivethe"WintelMarchitecturebecameasdeveloperssought

thelargestmarketfortheirsoftwareandcustomerssoughtsystemscompatible withthemostsoftware;themoreWintelcomputerssold,thelargertheinstalled

base.Thesepositiveloopsareallprocessesthatgeneratetheirowngrowth,lead-

1ngtOamSraces,pnCeWars,andthephenomenalgrowthofMicrosoftandlntel,

respectively.

Negativeloopscounteractandopposechange･Thelessnicotineinacigarette, themoresmokersmustconsumetogetthedosetheyneed.Themoreattractivea

neighborhoodorcity,thegreatertheinmlgrationfromsurroundingareaswillbe,

increasingunemployment,houslngPnCeS,Crowdingintheschools,andtraffic

congestionuntilitisnomoreattractivethanotherplacespeoplemightlive･The

higherthepnceofacommodity,thelowerthedemandandthegreaterthepro-

duction,leadingtoinventoryaccumulationandpressureforlowerpncestoelimi- natetheexcessstock.Thelargerthemarketshareofdominantfirms,themore

likelyisgovernmentantitrustactiontolimittheirmonopolypower･Theseloops

alldescribeprocessesthattendtobeself-1imltlng,processesthatseekbalanceand

equilibrium.

3Evenscientistssufferfromtheseproblems･Ionceheardadistinguishedphysicistarguethatthe

solutiontotheenergyproblemwastobuildhundredsofhugeoffshorenuclearpowerstations,tobe

cooledbyseawater.Thewanwastewaterwouldbepumpedbackintheoceanwhere,hesaid, "Thewasteheatwoulddisappear."Outofsight,outofmind･

Chapter1 LearninglnandaboutComplexSystems

FIGURE1-5 Positiveandnegativefeedbackloops

Positivefeedback:PositiveLoopsareself-reinforcmg. lnthiscase,morechickenslaymoreeggs,whichhatch andaddtothechickenpopuFatjon,Jeadingtostillmore eggs,andsoon･ACausalLoopDiagramorCLD(chap-

ter5)Capturesthefeedbackdependencyofchickens andeggs.Thearrowsindicatethecausalrelationships. The+stgnsatthearrowheadsindicate的at的eeffectis

positivelyrelatedtothecause:anincreaseinthe chickenpopuFatlLoncausesthenumberofeggslaideach daytoriseabovewhatitwouldhavebeen(andvice

versa:adecreaseinthechickenpopufationcausesegg layingtofaHbelowwhatitwouldhavebeen).Theloopis

self-reinforcJng,hencethelooppolarityidentifierRJf thisLoopweretheonJyoneoperating,thechickenand eggpopulationwouldbothgrowexponentiaHy.

Ofcourse,norealquantitycangrowforever.Theremust

belimlltStOgrowth.TheselrfmitSareCreatedbynegative feedback.

Negativefeedback:Negativeloopsareself-correcting. Theycounteractchange.Asthechickenpopulation grows,variousnegativeloopswi"acttobalancethe chickenpopulationwithitscarrylngCapacity.OnecFasI sicfeedbackisshownhere:Themorechickens,the

moreroadcross∫ngstheyw川attempt.Jfthereisany

traffic,moreroadcrosslngSWilHeadtofewerchickens (hencethenegative-polarityforthelinkfromroad crossingstochickens).Anincreaseinthechickenpopul latlrOnCausesmoreriskyroadcrosslngs,whichthen bringthechickenpopulationbackdown.TheBinthe centerofaloopdenotesabalanclngfeedback.lfthe road-crossingloopwastheonlyoneoperating(saybe-

causethefarmersellsa‖theヲggs),thenumberof chickenswouldgraduaHydecllneuntilnoneremained.

AHsystems,nomatterhowcomplex,consistofnet- worksofpositiveandnegativefeedbacks,anda" dynamicsarisefromtheinteractionoftheseloops withoneanother.

r ･ Eggs り chickens

ナ㌧ノ// Asystem'sfeedbackstructure

M generatesitsdynamics

Structure:

･./-~~~-ー~､､七了

chiekens 鯉croRsos?ndgS

･恵､一､ - ∫ / ■

並

Behavior:

Road

Crossings

Chickens

Time

14 PartI PerspectiveandProcess

1.i.4 ProcessPoint:TheMeaningofFeedback

Incommonparlancetheterm"feedback"hascometoserveasaeuphemismfor criticizlngOthers,asin"thebossgavemefeedbackonmypresentation･"Thisuse offeedbackisnotwhatwemeaninsystemdynamics.Further,"positivefeedback" doesnotmean"praise"and"negativefeedback"doesnotmean"criticism."Posi- tivefeedbackdenotesaself-reinforcingprocess,andnegativefeedbackdenotesa self-correctlngOne.Eithertypeofloopcanbegoodorbad,dependingonwhich wayltisoperatlngandofcourseonyourvalues･Reservethetermspositiveand negativefeedbackforself-reinforcingandself-correctingprocesses,andavoidde- scribingthecriticismyouglVeOrreceivetoothersasfTeedback.Tellingsomeone youroplniondoesnotconstitutefeedbackunlesstheyactonyoursuggestionsand thusleadyoutoreviseyourview.

Thoughthereareonlytwotypesoffeedbackloop,modelsmayeasilycontain thousandsofloops,ofbothtypes,coupledtooneanotherwithmultipletimede- lays,nonlinearities,andaccumulations.Thedynamicsofallsystemsarisefromthe interactionsofthesenetworksoffeedbacks.Intuitionmayenableustoinferthe

dynamicsofisolatedloopssuchasthoseshowninFigureト5･Butwhenmultiple loopsinteract,itisnotsoeasytodeterminewhatthedynamicswillbe.Beforecon- tinulng,trythechallengeshowninFigure1-6.Whenintuitionfails,Weusually tu仙tocomputersimulationtodeducethebehaviorofourmodels･

Dymamieso菅Mu司モ岳pBe-』⑳opSys官ems

Whatarethedynamicsofthechickenpopulationwhenbothloopsaresimultane- ouslyactive(FigureL6)?Sketchagraphshowingthebehaviorofthechicken populationovertime.Assumetheinitialchickenpopulationissmall(butincludes atleastonerooster).

r ･r ･ Eggs 鯉 chjckens り croRsosqnd｡S ･較㌧ノ// 架㌧ノ///

1.2 LEARNINGJsAFEEDBACKPROCESS

Justasdynamicsarisefromfeedback,sotooalllearningdependsonfeedback･We makedecisionsthataltertherealworld;wegatherinfomationfeedbackaboutthe realworld,andusingthenewinformationwereviseourunderstandingofthe worldandthedecisionswemaketobringourperceptlOnOfthestateofthesystem closertoourgoals(Figure1-7).

ThefeedbackloopinFigurel17appearsinmanyguisesthroughoutthesocial sciences.GeorgeRichardson(1991),inhishistoryoffeedbackconceptsinthe socialsciences,showshowbeginnlnginthe1940sleadingthinkersineconomics,

Chapterl LearninglnandaboutComplexSystems 15

Psychology,sociology,anthropology,andotherfieldsrecognizedthatthecon-

ceptoffeedbackdevelopedinphysicsandenglneerlngappliednotonlytoserv0-

mechanismsbuttohumandecisionmakingandsocialsettlngSaSWell.By1961,

Forrester,inIndustrialDynamics,assertedthatalldecisions(includinglearning)

takeplaceinthecontextoffeedbackloops･Later,thepsychologistPowers(1973,

p.351)wrote:

FeedbackissuchanalLpervasiveandfundamentalaspectofbehaviorthatitisas invisibleastheairthatwebreathe.quiteliterallyitisbehavior-Weknownothing ofourownbehaviorbutthefeedbackeffectsofourownoutputs.

ThesefeedbackthinkersfollowedinthefootstepsofJohnDewey,whorecognized

thefeedbackloopcharacteroflearnlngaroundthebeglnnlngOfthe20thcentury

whenhedescribedlearnlngaSaniterativecycleofinvention,observation,reflec-

tion,andaction(Sch6n1992).Feedbackaccountsofbehaviorandlearninghave

nowpermeatedmostofthesocialandmanagementsciences.LearnlngaSanex-

plicitfTeedbackprocesshasevenappearedinpracticalmanagementtoolssuchas

TotalQualityManagement,wheretheso-calledShewhart-DemingPDCAcycle

(Plan-Do-Check-Act)liesattheheartoftheimprovementprocessinthequality

improvementliterature(Shewhart1939;Shiba,Graham,andWalden1993).

ThesinglefeedbackloopshowninFigurel17describesthemostbasictypeof

leamlng.TheloopISaClassicalnegativefeedbackwherebydecisionmakerscom-

pareinfomationaboutthestateoftherealworldtovariousgoals,perceivedis-

crepanciesbetweendesiredandactualstates,andtakeactionsthat(theybelieve) willcausetherealworldtomovetowardsthedesiredstate.Eveniftheinitial

choicesofthedecisionmakersdonotclosethegapsbetweendesiredandactual

states,血esystemmighteventuallyreachthedesiredstateassubsequentdecisions

arerevisedinlightoftheinformationreceived(seeHogarth1981).Whendriving,

ImayturnthesteerlngWheeltoolittletobring血ecarbacktothecenterofmy lane,butasvisualfTeedbackrevealstheerror,Icontinuetotumthewheeluntilthe

carreturnstothestraightandnarrow.Ifthecurrentpriceforproductsofmyfirm

istoolowtobalanceorderswithproduction,depletedinventoriesandlongdeliv-

erydelaysmaycausemetograduallyraiseprlCeuntilldiscoveraprlCethatclears themarket.4

FIGURE1-7

LearmnglSa feedbackprocess.

Feedbackfromthe realworldtothe decisionmaker includesaFlforms

ofinformation, bothquantitative andqualitative,

了

Decisions

Rea一 Workl

ヽ hformation Feedback

L /一一/

4Dependingonthetimedelaysandotherelementsofdynamiccomplexltyinthesystem,these examplesmaynotconverge･Ittakesbutlittleice,fog,fatigue,oralcoholtocauseanaccident,and equilibriumeludesmanyindustriesthatexperiencechronicbusinesscycles.

FIGUREl ･8

Sing一e-一oop leamlng: information feedbackis

interpretedby existingmental mode一s.

TheFeamng feedbackoperates inthecontextof

existingdecision ru一es,StrategleS, culture,and institutionswhich inturnarederived fromourmenta一 models.

PartI PerspectiveandProcess

ThefeedbackloopshowninFigure1-7Obscuresanimportantaspectofthe leam1ngProcess.Informationfeedbackabouttherealworldisnottheonlyinput toourdecisions.Decisionsaretheresultofapplyingadecisionruleorpolicyto informationabouttheworldasweperceiveit(seeForrester1961,1992).Thepoli- ciesarethemselvesconditionedbyinstitutionalstructures,organizationalstrate- gleS,andculturalnorms.These,inturn,aregovernedbyourmentalmodels (Figurel18).Aslongasthementalmodelsremainunchanged,thefeedbackloop showninthefigurerepresentswhatArgyris(1985)callssingle-looplearning,a processwherebywelearntoreachourcurrentgoalsinthecontextofourexistlng mentalmodels.Single-loopleaningdoesnotresultindeepchangetoourmental models-Ourunderstandingofthecausalstructureofthesystem,theboundarywe drawaroundthesystem,thetimehorizonweconsiderrelevant-norourgoalsand values.Single-loopleamingdoesnotalterourworldview･

Mentalmodelsarewidelydiscussedinpsychologyandphilosophy.Different theoristsdescribementalmodelsascollectionsofroutinesorstandardoperatlng procedures,Scriptsforselectlngpossibleactions,cognltivemapsofadomain,ty- pologiesforcategorizlngexperience,logicalstructuresfortheinterpretationof language,OrattributiOnsaboutindividualsweencounterindailylife(Axelrod 1976;BowerandMorrow1990;ChengandNisbett1985;DoyleandFord1998; GentnerandStevens1983;Halford1993;Johnson-Laird1983;SchankandAbel-

son1977;Vennix1990).Theconceptofthementalmodelhasbeencentraltosys- temdynamicsfromthebeginningofthefield.Forrester(1961)Stressesthatall decisionsarebasedonmodels,usuallymentalmodels.Insystemdynamics,the term"mentalmodel"includesourbeliefsaboutthenetworksofcausesandeffects

thatdescribehowasystemoperates,alongwiththeboundaryofthemodel(which variablesareincludedandwhichareexcluded)andthetimehorizonweconsider

relevant10urframlngOrarticulationofaproblem･ Mostofusdonotappreciatetheubiqultyandinvisibilityofmentalmodels,

insteadbelievlngnaivelythatoursensesrevealtheworldasitis.Onthecontrary,

了

Decisions

Real Wor一d

ヽ lnformationFeedback 丸､＼ー__一一/

Strategy,Structure, MentaIModels DecisionRules ofRealWorld

iE芦璽璽■璽璽巳⊆i

Chapter1 LearnlnglnandaboutComplexSystems 17

Ourworldisactivelyconstructed(modeled)byoursensesandbrain.Figure1-9

ShowsanimagedevelopedbypsychologistGaetanoKanizsa.ThevastmaJontyof

peopleseeabrightwhitetrianglerestlngOntopOfthreecirclesandasecondtri-

anglewithblackedges.Theillusionisextremelypowerful(trytolookatthefig-

ureand"notseeHthetwotriangles!).Researchshowsthattheneuralstructures

responsiblefortheabilitytoseeillusorycontourssuchasthewhitetriangleexist

betweentheoptlCnerveandtheareasofthebrainresponsibleforprocesslngVisual information･5Activemodelingoccurswellbeforesensoryinformationreachesthe

areasofthebrainresponsibleforconsciousthought･6powerfulevolutionarypres-

suresareresponsible:Oursurvivaldependssocompletelyontheabilitytorapidly

interpretourenvironmentthatwe(andotherspecies)longagoevolvedstructures

tobuildthesemodelsautomatically.Usuallywearecompletelyunawarethese

mentalmodelsevenexist.ItisonlywhenaconstructionsuchastheKanizsatri-

anglerevealstheillusionthatwebecomeawareofourmentalmodels.

TheKanizsatriangleillustratesthenecessltyOfactiveandunconsciousmental

modelingorconstructionof"reality"atthelevelofvisualperception.Modelingof

higher-levelknowledgeislikewiseunavoidableandoftenequallyunconscious.

Figure1-10Showsamentalmodelelicitedduringameetingbetweenmycolleague

FredKofmanandateam丘.omalargeglobalcorporation.Thecompanyworked

withtheOrganizationalLearnlngCenteratMITintheearly1990storeduce

thetotalcycletimefortheirsupplychain.Atthattimethecycletimewas182days

andtheysoughttocutitinhalf.Thecompanyviewedreductionsincycletimeas

essentialforcontinuedcompetitivenessandevencorporatesurvival.Withthe

FIGURE1-9 Kanizsatriangle

Doyouseethe brightwhite trianglelylngOn topofthethree darkcirclesanda

secondtriangle?

5Seescience,256,(12June1992),pp.1520-1521.

6Evenmoreobviously,ourabilitytoseeathree-dimensionalworldistheresultofextensive modelingbythevisualprocesslngSystem,Sincetheretinaimagesaplanarprojectionofthevisual field.

FlGURE1-10 Mentalmodel

revea一edby adiagramofa company's supplychain

Thefi9urehas beensimplified comparedtothe actualchartto

protectcompany- confidential informationbutis drawntosca一e.

PartI PerspectiveandProcess

Curremtsupplychaincycletime,182days; goal,50%reduction･

Manufacturlng OrderFu折目ment LeadTime LeadTime

Customer Acceptance LeadTime

75 22 85

supportofseniormanagement,theyassembledateamtoad血esstheseissues. Atthefirstmeetingtheteam presentedbackgroundinformation,including Figure1-10.

Thefigureshowsthecurrentcycletimedividedintothreeintervalsalonga line:manufacturingleadtime,orderfulfillmentleadtime,andcustomeraccep- tanceleadtime.Orderfulfillment,whichthenrequired22days,OccupleSmore thanhalfofthetotallengthoftheline,whilethemanufactunngleadtime,thenre-

quiring75days(70daysduetosuppliers),receivesaboutone-fTourthofthelength. Customeracceptance,thenrequlrlng85days,occupleSOnlyaboutone-eighthof thetotallength.Whatthefigurerevealsistheprominenceoforderfulfillmentop- erationsinthementalmodelsofthepeopleontheteamandtheinsignificancein theirmindsofsuppliersandcustomers.Itwillcomeasnosurprisethatthemem- bersoftheteamallworkedinfunctionscontributingtoorderfulfillment.There wasnotaslnglepersonatthemeetlngrepreSentlngprocurement,noraSlnglesup- plierrepresentative,noranyonefromaccountlng,noraSlnglecustomer,UntilFred pointedoutthisdistortion,themembersofthegroupwereasunawareoftheillu- sorycharacteroftheirimageofthesupplylineaswenomallyareoftheillusory contoursourbrainsprojectOntothedatatransmittedbyouroptlCnerves.Thedis-

tortedmentalmodelofthesupplychainsignificantlyconstrainedthecompany's abilitytoreducecycletime:Eveniforderfulfillmentcouldbeaccomplishedin- stantlytheorganizationwouldfallwellshortofitsgoal.

ThetypeofreframlngStimulatedbyFred'sintervention,denoteddouble-loop learningbyArgyris(1985),isillustratedinFigurel111.Hereinformationfeed- backabouttherealworldnotonlyaltersourdecisionswithinthecontextofexisト

1ngframesanddecisionrulesbutalsofeedsbacktoalterourmentalmodels.As ourmentalmodelschangewechangethestructureofoursystems,Creatingdiffer- entdecisionrulesandnewstrategies.Thesameinformation,processedandinter- pretedbyadifferentdecisionrule,nowyieldsadifferentdecision.Alterlngthe stmctureofoursystemsthenalterstheirpattemsofbehavior･Thedevelopmentof systemsthinkingisadouble-looplearningprocessinwhichwereplaceareduc- tionist,narrow,short-run,staticviewoftheworldwithaholistic,broad,long-term, dynamicviewandthenredesignourpoliciesandinstitutionsaccordingly.

Chapter1 LearnlnglnandaboutComplexSystems

FIGURE1-ll

Double-loop

learnlng

Feedbackfromthe realworldcanalso

stimulatechanges inmentalmodels.

Suchlearnlng involvesnew

understanding orreframlngOf asituationand

leadstonewgoals andnewdecision

rules,notjust newdecisions.

了

Decisions

Rea一 World

hヽformationFeedback 丸--一一一一/i＼

LJ Strategy,Structure, MentaIModels

DecisionRules ofRealWorEd

GE璽璽寧『璽璽5i

1.3 BARRlERSTOLEARNING

ForlearnlngtOOccureachlinkinthetwofeedbackloopsshowninFigurel111

mustworkeffectivelyandwemustbeabletocyclearoundtheloopsquickly

relativetotherateatwhichchangesintherealworldrenderexistingknowledge

obsolete.Yetintherealworld,particularlytheworldofsocialaction,thesefeed-

backsoftendonotoperatewell.Morethantwoandahalfcenturieselapsedfrom

thefirstexperimentsshowingthatlemonJulCecouldpreventandcurescurvyuntil

citrususewasmandatedintheBritishmerchantmarine(Tablel12).Learningin

thiscasewaste汀iblyslow,despitetheenormousimportanceoftheproblemand

TABLEl l2

Teachingscurvy dogsnewtricks

-rotaldelay inlearnrng:

264years･

Priortothe1600S,scurvy(vitaminCdeficiency)wasthegreatestk川erof seafarers-morethanbattledeaths,storms,accidents,anda"others combI'ned.

1601:LancasterconductsacontrolledexperimentduringanEastlndia

Companyvoyage: Thecrewononeshipreceived3tsp.oflemonjulcedaily;thecrewonthree othershipsdidnot. Results:AttheCapeofGoodHopel10outof278sailorshaddied,most fromscurvy.ThecrewreceivlnglemonJulCeremainedlargelyhealthy.

1747:Dr,JamesLindconductsacontro"edexperimentinwhichscurvy

patientsweretreatedwithavarietyofelixirs.ThoserecelVlngCitruswere curedinafewdays;noneoftheothertreatmentsworked.

1795:TheBritishRoyalNavybegmsuslngCitrusonaregularbasis.Scurvy wJPedout.

1865:TheBritishBoardofTrademandatescitrususe.Scurvywipedoutin themerchantmarine.

Source:Mosteller(1981).

FlGURE1-12

Impediments tolearning

PartI PerspectiveandProcess

thedecisiveevidencesuppliedbycontrolledexperimentsthroughouttheyears.

Youmayreplythattodaywearemuchsmarterandlearnfaster･Perhaps.Yetthe

rateofcorporateandorganizationalfailureremainshigh(forexample,overone-

thirdoftheFortune500largestindustrialfin sin1970haddisappearedby1983

ldeGeus1997]).Todaytherateofchangeinoursystemsismuchfaster,andtheir

complexitylSmuchgreater.Thedelaysinlearningformanypresslngproblems

remainwoefullylong.InmostsettlngSWelacktheabilitytorunexperiments,

andthedelaysbetweeninterventionsandoutcomesaremuchlonger.Asthe

rateofchangeacceleratesthroughoutsociety,leamlngremainsslow,uneven,and

inadequate.

Figurel112showsthemainwaysinwhicheachlinkintheleamingfeedbacks

canfail.Theseincludedynamiccomplexity,Imperfectinformationaboutthestate

oftherealworld,confoundingandambiguousvariables,Poorscientificreasonlng

skills,defensiveroutines,andotherbarrierstoeffectivegroupprocesses,imple一

mentationfailure,andthemlSPerCePtlOnSOffeedbackthathinderourabilitytoun-

derstandthestructureanddynamicsofcomplexsystems.

Rea一Wor一d Unknownstructure Dynamiccomplexity Timedelays lnabilitytoconductcontrolled experlmentS

Decisions

lmplementationfailure Gameplaylng InconsIStenCy Performanceisgoal

Strategy,Structure, DecisionRu首es

'lnablMytoinferdynamics frommentalmodels

lnformationFeedback oSelectiveperceptl0n .Missingfeedback .Delay oBias,distortion,error oAmbiguity

MentalModels

Misperceptionsoffeedback Unscientlficreasonlng Judgmentalbiases Defensiveroutines

Chapter1 LeamnglnandaboutComplexSystems 21

1.3.1 DynamicComp一exity Muchoftheliteratureinpsychology,economics,andotherfieldssuggestslearnl

lngProceedsviathesimplenegativefeedbackloopsdescribedinFigureIlll･Im- plicitly,theloopsareseenasswift,linear,negativefeedbacksthatproducestable convergencetoanequilibriumoroptlmaloutcome,justaSimmediatevisualfeed-

backallowsyoutofillaglassofwaterwithoutspilling･Therealworldisnotso simple.Fromthebeginnlng,Systemdynamicsemphasizedthemultiloop,multi- state,nonlinearcharacterofthefTeedbacksystemsinwhichwelive(Forrester

1961).ThedecisionsofanyoneagentformbutoneofmanyfTeedbackloopsthat operateinanyglVenSystem.Theseloopsreacttothedecisionmaker'Sactionsin

waysbothantlClpatedandunantlClpated;theremaybepositiveaswellasnegative feedbackloops,andtheseloopswillcontainmanystocks(statevariables)and manynonlinearities.Naturalandhumansystemshavehighlevelsofdynamiccom- plexity.Table1-3Showssomeofthecharacteristicsofsystemsthatgiveriseto

dynamiccomplexlty.

MostpeoplethinkofcomplexltylntermsOfthenumberofcomponentsina systemorthenumberofcombinationsonemustconsiderinmakingadecision･ Theproblemofoptlmallyschedulinganairline'Sflightsandcrewsishighlycom-

plex,butthecomplexityliesinfindingthebestsolutionoutofanastronomical numberofpossibilities.Suchneedle-in-a-haystackproblemshavehighlevelsof combinatorialcomplexity(alsoknownasdetailcomplexity).Dynamiccomplex-

1ty,lnCOntraSt,Canariseeveninsimplesystemswithlowcombinatorialcomplex- ity.TheBeerDistributionGame(Steman1989b,chap.17･4)providesanexample:

Complexanddysfunctionalbehaviorarisesfromaverysimplesystemwhoserules canbeexplainedin15minutes.Dynamiccomplexityarisesfromtheinteractions amongtheagentsovertime.

Timedelaysbetweentakingadecisionanditseffectsonthestateofthesystem

arecommonandparticularlytroublesome.Mostobviously,delaysreducethenum- beroftimesonecancyclearoundthelearnlngloop,slowlngtheabilitytoaccu-

mulateexperience,testhypotheses,andimprove･Schneiderman(1988)estimated theimprovementhalflife-thetimerequiredtocutdefectsinhalf-inawide rangeofmanufacturingfirms.Hefoundimprovementhalflivesasshortasafew

monthsforprocesseswithshortdelays,forexamplereducingoperatorerrorina jobshop,whilecomplexprocesseswithlongtlmedelayssuchasproductdevelop一 meれthadimprovementhalflivesofseveralyearsormore･7

DynamiccomplexitynotOnlyslowsthelearnlngloop;italsoreducesthe leamlnggainedoneachcycle.Inmanycasescontrolledexperimentsareprohibi- tivelycostlyorunethical.Moreo洗en,itissimplyimpossibletocon血ctcontrolled

experiments.Complexsystemsareindisequilibriumandevolve･Manyactions yieldirreversibleconsequences.Thepastcannotbecomparedwelltocurrentcir- cumstance.Theexistenceofmultipleinteractingfeedbacksmeans itisdifficultto

holdotheraspectsofthesystem constanttoisolatetheeffectof thevariableof interest.Manyvariableschangesimultaneously,confoundingthe interpretation

7steman,Repenning,andKofman(1997)showhowthesedifferentialimprovementratesledto difficultyataleadingsemiconductormanufacturer･

TABLE1-3

Dynamic

complexity

PartI PerspectiveandProcess

Dynamiccomp一exityarisesbecausesystemsare

Dynamic:Heracritussaid,"Allischange."WhatappearstobeunchanglnglS,overa longertimehorizon,Seentovary.ChangeinsystemsoccursatmanytimescaJes, andthesedifferentscalessometimesinteract.Astarevolvesoverbilljonsofyearsas itbumsitshydrogenfuel,thencanexplodeasasupernovainseconds.Bullmarkets

cangoonforyears,thencrashinamatterofhours.

Tightlycoupled:Theactorsinthesysteminteractstronglywithoneanotherand

withthenaturalworld.EverythinglSconnectedtoeverythingelse.Asafamous

bumperstickerfromthe1960sproclaimed,"Youcan'tdojustonething."

Governedbyfeedback:BecauseofthetightcoupIHlgSamongactors,Ouractions

feedbackonthemselves.Ourdecisionsalterthestateoftheworld,CauslngChanges innatureandtriggenngotherstoact,thusglvlngusetOanewSituationwhichthen

influencesournextdecisions.Dynamicsarisefromthesefeedbacks.

Nonlinear:Effectisrarelyproportionaltocause,andwhathappenslocallylnaSys-

tem(nearthecurrentoperatingpoint)oftendoesnotapplyindistantregions(other

statesofthesystem).Nonlinearityoftenarisesfromthebasicphysicsofsystems:ln-

sufficientinventorymaycauseyoutoboostproduction,butproductioncanneverfall

belowzeronomatterhowmuchexcessinventoryyouhave.NonHnearityalsoarises

asmultjplefactorsinteractindecisionmaking:Pressurefromthebossforgreater

achievementincreasesyourmotivationandeffort-uptothepointwhereyouper-

ceivethegoaHobeimpossible.FrustrationthendominatesmotivationandyouglVe uporgetanewboss.

History-dependent:Takingoneroadoftenprecludestakingothersanddetermines whereyouendup(pathdependence).Manyactionsareirreversible:Youcan'tun-

scrambleanegg(thesecondlawofthermodynamics).Stocksandflows(accumu-

lations)andlongtimedelaysoftenmeandoingandundoinghavefundamentally differenttimeconstants:Duringthe50yearsoftheCordWararmsracethenuclear

nationsgeneratedmorethan250tonsofweapons-gradeplutonium(239pu).Thehalf lifeof239Puisabout24,000years.

Self-organdZlng:Thedynamicsofsystemsarisespontaneouslyfromtheirinternal

structure.Often,small,randomperturbationsareamplifiedandmoldedbythefeed-

backstructure,generatingpattemsinspaceandtimeandcreatingpathdependence.

Thepatternofstripesonazebra,therhythmiccontractionofyourheart,thepersis- tentcyclesintherealestatemarket,andstructuressuchasseashellsandmarkets

allemergespontaneous一yfromthefeedbacksamongtheagentsandelementsofthe system.

Adaptive:Thecapabilitiesanddecisionrulesoftheagentsincomplexsystems

changeovertime.Evolution一eadstose一ectionandproliferationofsomeagentswhile

othersbecomeextinct.Adaptationalsooccursaspeoplereamfromexperience,esI

peciaJIyastheyreamnewwaystoachievetheirgoalsinthefaceofobstacles.Learn- 1ngISnotalwaysbeneficial,however.

Counterjntuitive:lncomplexsystemscauseandeffectaredistantintimeandspace

whHewetendtolookforcausesneartheeventsweseektoexplain.OurattentionIS

drawntothesymptomsofdifficultyratherthantheunderFyngcause.Highleverage po一iciesareoftennotobvious.

Policyresistant:Thecomplexityofthesystemsinwhichweareembeddedover-

wheJmsourabilitytounderstandthem.Theresult:Manyseemlnglyobvioussolutions

toproblemsfairoractuallyworsenthesituation.

Characteri2:edbytrade･offs:Timedelaysinfeedbackchanne一smeanthelong-run responseofasystemtoaninterventionisoftendifferentfromitsshort-runresponse.

Highleveragepo一iciesoftencauseworse-before-betterbehavior,whilelowleverage policiesoftengeneratetransitoryImprovementbeforetheproblemgrowsworse.

Chapter1 LeamlnglnandaboutComplexSystems 23

ofsystembehaviorandreducingtheeffectivenessofeachcyclearoundthelearn-

1ngloop.

Delaysalsocreateinstabilityindynamicsystems.Addingtimedelaysto

negativefeedbackloopsincreasesthetendencyforthesystemtooscillate･8sys-

temsfromdrivingacar,todrinkingalcohol,toraislnghogs,toconstructionof

officebuildingsallinvolvetimedelaysbetweentheinitiationofacontrolaction

(accelerating/braking,decidingto"haveanother,Hchoosingtobreedmorehogs,

developinganewbuilding)anditseffectsonthestateofthesystem.Asaresult,

decisionmakersoftencontinuetointervenetocorrectapparentdiscrepancies

betweenthedesiredandactualstateofthesystemevenaftersufficientcorrective

actionshavebeentakentorestorethesystemtoequilibrium.Theresultisover-

shootandoscillation:stop-and-gotraffic,drunkenness,commoditycycles,andreal

estateboom-and-bustcycles(Seechapter17.4).Oscillationandinstabilityreduce

ourabilitytocontrolforconfoundingvariablesanddiscemcauseandeffect,fur-

therslowlngtherateofleamlng.

1.3.2 LILmitedlnformation

Weexperiencetherealworldthroughfilters.NooneknOwsthecurrentsalesrate

oftheircompany,thecurrentrateofproduction,orthetruevalueoftheorderback-

logatanyglVentime.insteadwereceiveestimatesofthesedatabasedonsampled,

averaged,anddelayedmeasurements.Theactofmeasurementintroducesdistor-

tions,delays,biases,errors,andotherimperfections,someknown,othersunknown andunknowable.

Aboveall,measurementisanactofselection.Oursensesandinfomationsys-

temsselectbutatinyfractionofpossibleexperience.Someoftheselectionishard-

wired(wecannotseeintheinfraredorhearultrasound).Someresultsfromour

owndecisions.Wedefinegrossdomesticproduct(GDP)sothatextractionofnon-

renewableresourcescountsasproductionratherthandepletionofnaturalcapltal

stocksandsothatmedicalcareandfuneralexpensescausedbypollution-induced

diseaseaddtotheGDPwhiletheproductionofthepollutionitselfdoesnotreduce

it.BecausetheprlCeSOfmostgoodsinoureconomicsystemdonotincludethe

costsofresourcedepletionorenvironmentaldegradation,theseexternalitiesre-

ceivelittleweightindecisionmaking(seeCobbandDaly1989fb∫thoughtfuldis- cussionofalternativemeasuresofeconomicwelfare).

Ofcourse,theinformationsystemsgovernlngthefeedbackwereceivecan

changeaswelearn.Theyarepartofthefeedbackstructureofoursystems･

ThroughourmentalmodelswedefineconstructssuchasGDPorscientificre-

search,createmetricsfortheseideas,anddesigninformationsystemstoevaluate

andreportthem.ThesethenconditiontheperceptlOnSWeform･Changesinour

mentalmodelsareconstrainedbywhatwepreviouslychosetodefine,measure,

8Technically,negativeloopswithnotimedelaysarefirst10rder;theeigenvalueofthelineariZed systemcanonlyberealandoscillationisimpossible.Addingdelays(statevariables)allowsthe elgenValuestobecomecomplexconjugates,yieldingoscillatorysolutions･Whethertheoscillations ofthelinearizedsystemaredampedorexpandingdependsontheparameters･Allelseequal,the morephaselaglnaCOntrOlloop,thelessstablethesystemwillbe.

24 PartI PerspectiveandProcess

andattendto.SeeingisbelievingandbelievinglSSeelng･Theyfeedbackonone another.

Inafamousexperiment,BrunerandPostman(1949)showedplayingcardsto

peopleuslngataChistoscopetocontrolexposuretimetothestimuli.Mostcould

identifythecardsrapidlyandaccurately.Theyalsoincludedsomeanomalous

cards,suchasablackthreeofheartsoraredtenofspades.Peopletookonaverage

fourtimesaslongtojudgetheanomalouscardsIManymisidentifiedthem

(e.g.,theysaidthreeofspadesorthreeofheartswhenshownablackthreeof

hearts).Somecouldnotidentifythecardatall,evenwithverylongexposure

times,andgrewanxiousandconfused.OnlyasmallminorityCOrreCtlyidentified

thecardsIBrunerandPostmanconcluded,"Perceptualorganizationispowerfully

determinedbyexpectationsbuiltuponpastcommercewiththeenvironment｡"

HenriBergsonputitmoresuccinctly:HTheeyeseesonlywhatthemindispre- paredtocomprehend."

Theself-reinforcingfeedbackbetweenexpectationsandperceptlOnShasbeen

repeatedlydemonstratedinawidevarietyofexperimentalstudies(seePlous1993

forexcellentdiscussion)･Sometimesthepositivefeedbackassistslearningby

sharpenlngOurabilitytoperceivefeaturesoftheenvironment,aswhenanexperi- encednaturalistidentifiesabirdinadistantbushwherethenovicebirderseesonly

atangledthicket.Often,however,themutualfeedbackofexpectationsandper-

ceptlOnlimitslearningbyblindingustotheanomaliesthatmightchallengeour

mentalmodels.ThomasKuhn(1970)citedtheBruner-Postmanstudytoarguethat

ascientificparadigmsuppressestheperceptionOfdatainconsistentwiththepara-

digm,makingithardforscientiststoperceiveanomaliesthatmightleadtoscien- tificrevolution.9

Asoneofmanyexamples,thehistoryofozonedepletionbychlorofluoro-

carbons(CFCs)Showsthemutualdependenceofexpectationandperceptionisno

laboratoryartifactbutaphenomenonwithpotentiallygraveconsequencesfor

humanlty.

ThefirstscientificpapersdescribingtheabilityofCFCstodestroyatmos-

phericozonewerepublishedin1974(MolinaandRowland1974;Stolarskiand

Cicerone1974).Yetmuchofthescientificcommunityremainedskeptical,and

despiteabanonCFCsasaerosolpropellants,globalproductionofCFCsremained

nearitsalltimehigh.Itwasnotuntil1985thatevidenceofadeepozoneholein

theAntarcticwaspublished(Farman,Gardiner,andShanklin1985).Asdescribed

byMeadows,Meadows,andRan°ers(1992,pp.151-152):

Thenewsreverberatedaroundthescientificworld.Scientistsat[NASA]‥.scram- bledtocheckreadingsonatmosphericozonemadebytheNimbus7satellite,mea- Surementsthathadbeentakenroutinelysince1978.Nimbus7hadneverindicated anozonehole.

9sterman(1985a)developedaformalmodelofKuhn'Stheory,whichshowedthatthepositive feedbackbetweenexpectationsandpercept10nSSuppressedtherecognltionofanomaliesandthe emergenceofnewparadigms.StermanandWittenberg(1999)extendedthemodeltosimulate thecompetitionamongrivaltheories.

Chapter1LearIllnglnandaboutComplexSystems 25

Checkingback,NASAscientistsfoundthattheircomputershadbeenpr0- grammedtorejectVerylowozonereadingsontheassumpt10nthatsuchlow readingsmustindicateinstrumenterror･

TheNASAscientists'beliefthatlowozonereadingsmustbeerroneousledthem

todesignameasurementsystemthatmadeitimpossibletodetectlowreadingsthat

mighthaveshowntheirbelieftobewrong.Fortunately,NASAhadsaved血eong- inal,unfiltereddataandlaterconfirmedthatozoneconcentrationshadindeedbeen

fallingsincethelaunchofNimbus7.BecauseNASAcreatedameasurementsys- temimmunetodisconfirmationthediscoveryoftheozoneholeandresulting

globalagreementstoceaseCFCproductionweredelayedbyasmuchas7years.

Those7yearscouldbesignificant:ozonelevelsinAntarcticadroppedtolessthan one-thirdofnormalin1993,andcurrentmodelsshowthatevenwithfullcompli-

ancewiththeban(thereisathrivingblackmarketinCFCs),atmosphericchlorine

willnotbegintofalluntilthefirstdecadeofthe21stcentury,andthenonlyslowly･

DatacollectednearTorontointheearly1990sshoweda5%increaseincancer-

causingUVBultravioletradiationatgroundlevel,indicatlngthatozonedepletion

alreadyaffectstheheavilypopulatedandagrlCulturallyvitalnorthemhemisphere (CulottaandKoshland1993).The血inningoftheozonelayerisaglobalphenom-

enon,notjustaProblemforpenguins.

1.3.3 ConfoundingVariablesandAmbiguity

Toleanwemustusethelimitedandimperfectinformationavailabletoustoun-

derstandtheeffectsofourowndecisions,Sowecanadjustourdecisionstoalign

thestateofthesystemwithourgoals(single-loopleaning)andsowecanrevise

ourmentalmodelsandredesignthesystemitself(double-loopleaming).Yetmuch

oftheinformationwereceiveisambiguous.Ambiguityarisesbecausechangesin

thestateofthesystemresultingfromourowndecisionsareconfoundedwithsi一

multaneouschangesinahostofothervariables･Thenumberofvariablesthat

mightaffectthesystemvastlyoverwhelmsthedataavailabletoruleoutaltemative

theoriesandcompetlnglnterPretations･Thisidentificationproblemplaguesboth

qualitativeandquantitativeapproaches.Inthequalitativerealm,ambiguityarises

fromtheabilityoflanguagetosupportmultiplemeanlngS･IntheopenlngSOlilo-

quyofRichaydIll,thehump-backedRichardlamentshisdefomlty:

Andtherefore,sinceIcannotprovealover Toentertainthesefairwe111SPOkendays, Iamdeterminとdtoproveavillain Andhatetheidlepleasuresofthesedays･

(i,i,28-31)

DoesRichardcelebratehisfreechoicetobeevilorresignhimselftoapredestined

fate?DidShakespeareintendthedoublemeaning?Rich,ambiguoustexts,With

multiplelayersofmeanlngOftenmakeforbeautifulandprofoundart,alongwith

employmentfわrliterarycritics,butalsomakeithardtoknowthemindsofothers,

ruleoutcompetinghypotheses,andevaluatetheimpactofourpastactionssowe candecidehowtoactinthefuture.

26 PartIPerspectiveandProcess

Inthequantitativerealm,englneerSandeconometricianshavelongstruggled

withtheproblemofuniquelyidentifyingthestructureandparametersofasystem

fromitsobservedbehavior.Elegantandsophisticatedtheoryexiststodelimitthe

conditionsinwhichonecanidentifyasystemfromitsbehavioralone･Inpractice

thedataaretooscarceandtheplausiblealtemativespecificationsaretoonumer-

ousforstatisticalmethodstodiscriminateamongcompetlngtheories.Thesame

dataoftensupportwildlydivergentmodelsequallywell,andconclusionsbasedon

suchmodelsarenotrobust.AsLeaner(1983)putitinanarticleentitledHLet's TakethèCon'OutofEconometricsM:

Inordertodrawinferencesfromdataasdescribedbyeconometrictexts,1tisneces-

SarytomakewhimsicalassumptlOnS.‥Thehaphazardwayweindividuallyand collectivelystudythefragilityofinferencesleavesmostofusunconvincedthatany inferenceisbelievable.10

1･3L4 BoundedRatiolla!嘩 andthe脚isperc甲tions ofFeedback

Dynamiccomplexityandlimitedinfomationreducethepotentialforleamlngand

performancebylimitingOurknowledgeoftherealworld･Buthowwiselydowe

usetheknowledgewedohave?Doweprocesstheinfo-ationwedogetinthe

bestwayandmakethebestdecisionswecan?Unfortunately,theanswerisno.

Humansarenotonlyrationalbeings,Coollyweighingthepossibilitiesand

judgingtheprobabilities.Emotions,reflex,unconsciousmotivations,andother

nonrationalorirrationalfactorsallplayalargeroleinourjudgmentsandbehavior. Butevenwhenwefindthetimetoreflectanddeliberatewecannotbehaveina

fullyrationalmanner(thatis,makethebestdecisionspossiblegiventheinforma-

tionavailabletous).Asmarvelousasthehumanmindis,thecomplexityofthereal

worlddwarfsourcognltlVeCapabilities.HerbertSimonhasbestarticulatedthe

limitsonhumandecision-makingabilityinhisfamous"principleofboundedra-

tionality,"forwhichhewontheNobelMemorialPrizeineconomicsin1979:

ThecapacltyOfthehumanmindforformulatingandsolvingcomplexproblemsis verysmallcomparedwiththesizeoftheproblemwhosesolutionisrequiredforob- jeCtivelyrationalbehaviorintherealworldorevenfわrareasonableapproximation tosuchobjectiverationality.(Simon1957,p.198)

Facedwiththeoverwhelmingcomplexityoftherealworld,timepressure,andlim-

itedcognltlVeCapabilities,Weareforcedtofallbackonroteprocedures,habits,

rulesofthumb,andsimplementalmodelstomakedecisions.Thoughwesome-

timesstrivetomakethebestdecisionswecan,boundedrationalitymeansweof-

tensystematicallyfallshort,limitingourabilitytolearnfromexperience.

Wh ileboundedrationalityaffectsalldecisioncontexts,itisparticularlyacute

indynamicsystems･indeed,experimentalstudiesshowthatpeopledoqultepoorly

mIamnotarguingthateconometricsshouldbeabandoned,despiteitsdifficulties･Onthecon-

trary,Wiseuseofnumericaldataandstatisticalestimationiscentraltogoodsystemdynamicsprac- tice,andmoreeffortshouldbedevotedtotheuseofthesetoolsinsimulationmodeldevelopment andtesting,Seechap.21.

Chapter1LearninglnandaboutComplexSystems 27

insystemswithevenmodestlevelsofdynamiccomplexity(Table1-4).These

studiesledmetosuggestthattheobserveddysfunctionindynamicallycomplex

settingsarisesfrommisperceptionsoffeedback･Thementalmodelspeopleuse toguidetheirdecisionsaredynamicallydeficient･Asdiscussedabove,people generallyadoptanevent-based,open-loopviewofcausality,Ignorefeedback processes,failtoappreciatetimedelaysbetweenactionandresponseandinthe reportingOfinformation,donotunderstandstocksandflowsandareinsensitiveto

nonlinearitiesthatmayalterthestrengthsofdifferentfeedbackloopsasasystem evolves.

SubsequentexperimentsshowthatthegreaterthedynamiccomplexltyOfthe environmenttheworsepeopledorelativetopotential.Further,theexperiments showthemlSPerCePtlOnSOffeedbackarerobusttoexperience,financialincentives,

experience,andthepresenceofmarketinstitutions(see,e.g.,DiehlandSterman 1993;PaichandSterman1993;KampmannandSterman1998).

TherobustnessofthemlSPerCePtlOnSOffeedbackandthepoorperformance theycauseareduetotwobasicandrelateddeficienciesinourmentalmodel.First, ourcognltlVemapsOfthecausalStructureofsystemsarevastlysimplifiedcom-

paredtothecomplexityofthesystemsthemselves.Second,Weareunabletoinfer

correctlythedynamicsofallbutthesimplestcausalmaps.Botharedirectconse- quencesofboundedrationality,thatis,themanylimitationsofattention,memory, recall,infomationprocesslngCapability,andtimethatconstrainhumandecision making.

TABLEl･4

Misperceptions offeedback havebeen documented

inmany experimentaf studies.

lnasimpleproduction-distributionsystem(theBeerDistributionGame), people,fromhighschoolstudentstoCEOs,generatecostlyfluctuations (businesscycles).Averagecostsweremorethan10timesgreaterthan optimal(Sterman1989b).

SubjectsresponsibleforcapitalinvestmentinasimplemultipIIer-accelerator modeloftheeconomygeneratelargeamplitudecycleseventhoughcon-

sumerdemandisconstant.Averagecostsweremorethan30timesgreater thanoptimal(Sterman1989a)l

Subjectsmanaglngafirminasimulatedconsumerproductmarketgenerate theboomandbust,prlCeWar,andshake-outcharacteristicofindustriesfrom videogamestochainsaws(PaichandSterman1993).

ParticipantsinexperimentalassetmarketsrepeatedlybidprlCeSWe"above fundamentalvalue,onlytoseethemplummetwhena"greaterfool"canno longerbefoundtobuy.Thesespeculativebubb一esdonotdisappearwhen theparticipantsareinvestmentprofessionals,whenmonetarylnCentivesare provided,orwhenshort-seHingisaEIowed(Smith,Suchanek,andWi"iams 1988).

Fnaforestfiresimulation,manypeopfeaIIowtheirheadquarterstoburn downdespitetheirbeste什ortstoputoutthefire(Brehmer1989).

lnamedicalsetting,Subjectsplaylngthero一eofdoctorsordermoretests whilethe(simulated)patientssickenanddie(KIeinmuntzandThomas 1987).

28 PartI PerspectiveandProcess

1.3.5 F長awedCognitiveMaps

Causalattributionsareacentralfeatureofmentalmodels.Weallcreateandupdate cognltlVemapsOfcausalconnectionsamongentitiesandactors,fromtheproI saic-ifItouchaflameIwillbeburned-tothegrand-thelargerthegovernment deficit,thehigherinterestrateswillbe.StudiesofcognltlVemapsShowthatfew incorporateanyfeedbackloops.Axelrod(1976)foundvirtuallynofeedback processesinstudiesofthecognltlVemapsOfpoliticalleaders;rather,peopletended toformulateintuitivedecisiontreesrelatingpossibleactionstoprobableconse- quences-anevenトlevelrepresentation･Hall(1976)reportssimilaropenlloop mentalmapsinastudyofthepublishingindustry.D6rner(1980,1996)foundthat peopletendtothinkinslnglestrandcausalseriesandhaddifficultyinsystemswith sideeffectsandmultiplecausalpathways(muchlessfeedbackloops).Similarly, experimentsincausalattributionshowpeopletendtoassumeeacheffecthasasin-

glecauseandoftenceasetheirsearchforexplanationswhenthefirstsufficient causeisfound(seethediscussioninPious1993).

TheheuristicsweusetojudgecausalrelationsleadsystematicallytocognltlVe mapsthatignorefeedbacks,multipleinterconnections,nonlinearities,timedelays, andtheotherelementsofdynamiccomplexity.Thecausalfieldormentalmodelof thestageonwhichtheactionoccursiscrucialinframlngPeOPle'sjudgmentsof causation(EinhornandHogarth1986).Withinacausalfield,peopleusevarious cuestocausalityincludingtemporalandspatialproximltyOfcauseandeffect,tem- poralprecedenceofcauses,covariation,andsimilarityofcauseandeffect.These heuristicsleadtodifficultylncomplexsystemswherecauseandeffectareoften distantintimeandspace,whereactionshavemultipleeffects,andwherethede- layedanddistantconsequencesaredifferentfromandlesssalientthanproximate effects(orsimplyunknown).Themultiplefeedbacksincomplexsystemscause manyvariablestobecorrelatedwithoneanother,confoundingthetaskofjudging cause･However,peoplearepoorjudgesofcorrelation･Experimentsshowpeople cangenerallydetectlinear,positivecorrelationsamongvariablesiftheyareglVen enoughtrialsandiftheoutcomefeedbackisaccurateenough.However,Wehave greatdifficultyinthepresenceofrandomerror,nonlinearlty,andnegativecorrela- tions,oftenneverdiscoveringthetruerelationship(Brehmer1980).

AfundamentalprlnCipleofsystemdynamicsstatesthatthestructureofthe systemglVeSrisetoitsbehavior.However,peoplehaveastrongtendencytoat- tributethebehaviorofotherstodispositionalratherthansituationalfactors,thatis, tocharacterandespeciallycharacterflawsratherthanthesysteminwhichthese peopleareactlng.Thetendencytoblamethepersonratherthanthesystemisso strongpsychologistscallitthe"fundamentalattributionerror"(Ross1977).In complexsystemsdifferentpeopleplacedinthesamestructuretendtobehavein similarways.Whenweattributebehaviortopersonalitywelosesightofhowthe structureofthesystemshapedourchoices.Theattributionofbehaviortoindivid- ualsandspecialcircumstancesratherthansystemstructuredivertsourattention fromthehighleveragepointsWhereredesignlngthesystemorgovernlngPOlicy canhavesignificant,sustained,beneficialeffectsonperformance(Forrester1969, chap.6;Meadows1982).Whenweattributebehaviortopeopleratherthansystem structurethefわcusofmanagementbecomesscapegoatlngandblameratherthan

Chapter1 LeamlnglnandaboutComplexSystems 29

thedesignoforganizationsinwhichordinarypeoplecanachieveextraordinary results.ll

1.3.6 ErroneoushferencesaboutDynamics

EvenifourcognltlVemapsOfcausalstructurewereperfect,learnlng,especially

double-looplearnlng,wouldstillbedifficult･Touseamentalmodeltodesigna

newstrategyororganizationwemustmakeinferencesabouttheconsequencesof decisionrulesthathaveneverbeentriedandforwhichwehavenodata.Tbdoso

requiresintuitivesolutionofhigh-ordernonlineardifferentialequations,ataskfar

exceedinghumancognitivecapabilitiesinallbutthesimplestsystems(Forrester

1971a;Simon1982).Inmanyexperimentalstudies,includingDiehlandSteman

(1995)andSterman(1989a),theparticipantsweregivencompleteknowledgeof allstructuralrelationshipsandparameters,alongwithperfect,comprehensive,and

immediateknowledgeofallvariables･Further,thesystemsweresimpleenough

thatthenumberofvariablestoconsiderwassmall.Yetperfbmancewaspoorand

learnlngWasSlowIPoorperformanceinthesetasksisduetoourinabilitytomake

reasonableinferencesaboutthedynamicsofthesystemdespltePerfectandcom- pleteknowledgeofthesystemstructure.

Peoplecannotsimulatementallyeventhesimplestpossiblefeedbacksystem,

thefirst-orderlinearpositivefeedbackloop･12suchpositivefeedbackprocessesare

commonplace,fromthecompoundingofinteresttothegrowthofpopulations. WagenaarandSagaria(1975)andWagenaarandTimmers(1978,1979)showed

thatpeoplesignificantlyunderestimateexponentialgrowth,tendingtoextrapolate

linearlyratherthanexponentially.UsingmoredatapolntSOrgraphingthedatadid

nothelp,andmathematicaltrainlngdidnotimproveperformance.

BoundedrationalitysimultaneouslyconstrainsthecomplexltyOfourcognltlVe mapsandourabilitytousethemtoantlClpatethesystemdynamics.Mentalmod-

elsinwhichtheworldisseenasasequenceofeventsandinwhichfeedback,non-

linearlty,timedelays,andmultipleconsequencesarelackingleadtopoor

performancewhentheseelementsofdynamiccomplexityarepresent.Dysfunction

incomplexsystemscanarisefromthemlSPerCePtlOnOfthefeedbackstructureof

theenvironment･Butrichmentalmodelsthatcapturethesesourcesofcomplexity

cannotbeusedreliablytounderstandthedynamicsIDysfunctionincomplexsys-

temscanarisefrom faultymentalsimulation-themlSPerCePt10nOffeedback dynamics.Thesetwodifferentboundsonrationalitymustbothbeovercomefor

effTectivelearningtOOCCur･Perfectmentalmodelswithoutasimulationcapability

yieldlittleinsight;acalculusforreliableinferencesaboutdynamicsyieldssys-

tematicallyerroneousresultswherI_appliedtosimplisticmodels.

llRepenningandSterman(1999)showhowthefundamentalattribution?rroraroseina majormanufacturingOrganization,thwartingtheireffortstoimproveoperationsandproduct development･

12Thefirst10rderlinearpositiveloopISrepresentedbythedifferentialequationdx/dt-gxand yieldspureexponentialgrowth,x-x｡exp(gt);seechap.8.

30 PartIPerspectiveandProcess

1.3,7 UnscientificReasonhg:

Judgmenta=≡rrorsandBiases

Tolearneffectivelylnaworldofdynam iccomplexltyandimperfectinformation

peoplemustdevelopwhatDavisandHogarth(1992)callHinsightskills"-the

skillsthathelppeopleleanwhenfeedbackisambiguous:

lT]heinterpretationoffeedback...needstobeanactiveanddisciplinedtaskgov- ernedbytherigorousrulesofscientificinference.Beliefsmustbeactivelychal- lengedbyseekingpossibledisconfirmlngevidenceandaskingwhetheralternative beliefscouldnotaccountforthefacts(emphasisinoriginal).

Unfortunately,peoplearepoorintuitivescientists,generallyfailingtoreasoninac-

cordancewiththeprlnCiplesofscientificmethod.Forexample,peopledonotgen-

eratesufficientalternativeexplanationsorconsiderenoughrivalhypotheses.

Peoplegenerallydonotadequatelycontrolforconfoundingvariableswhenthey

exploreanovelenvironment.People'sjudgmentsarestronglyaffectedbythe

frameinwhichtheinformationispresented,evenwhentheobjectiveinformation

isunchanged.Peoplesufferfrom overconfidenceintheirjudgments(under-

estimatinguncertainty),wishfulthinking(assessingdesiredoutcomesasmore

likelythanundesiredoutcomes),andtheillusionofcontrol(believingonecanpre-

dictorinfluencetheoutcomeofrandomevents).Peopleviolatebasicrulesof

probability,donotunderstandbasicstatisticalconceptssuchasregressiontothe

mean,anddonotupdatebeliefsaccordingtoBayes'rule.Memoryisdistortedby

hindsight,theavailabilityandsalienceofexamples,andthedesirabilityofout-

comes.Andsoon.Hogarth(1987)discusses30differentbiasesanderrorsdocu-

mentedindecision一makingresearchandprovidesagoodguidetotheliterature

(seealsoKahneman,Slovic,andTversky1982).Theresearchconvincinglyshows

thatscientistsandprofessionals,notonly"ordinary"people,sufferfrommanyof

thesejudgmentalbiases.

Amongthefailuresofscientificreasoningmostinimicaltolearningistheten-

dencytoseekevidenceconsistentwithcurrentbeliefsratherthanpotentialdiscon-

firmation(EinhomandHogarth1978･,KlaymanandHa1987).Inafamousseries

ofexperiments,Wasonandcolleaguespresentedpeopletasksofthesortshownin

Figure1113･13Beforecontinulng,trythechallengeshowninthefigure･

HypothesisTesting Youareshownthesefourcards.Eachcardhasaletterononesideandanumberon

theother.Whatisthesmallestnumberofcardsyoushouldturnovertotesttherule thatcardswithvowelsononesidehaveevennumbersonthereverse?Whichare

they?

E]㊦E]E] 13ThesummaryoftheWasontestisdrawnfromPlous(1993,chap.20).

Chapter1 LearnlnglnandaboutComplexSystems 31

Inoneversionyouareshownonesideoffourcards,eachwithaletteronone

sideandanumberon血eother,sayE,K,4,and7.Youaretoldthatiracardhasa

vowelonit,thenithasanevennumberontheotherside.Youmustthenidentify

thesmallestsetofcardstoturnovertoseeiftheproposedruleiscorrect.

WasonandJohnson-Laird(1972)foundthatthevastmajorityofsubjectsse-

lectedEorEand4as仙eanswers.Lessthan4%gavethecorrectanswer:Eand7.

Therulehasthelogicalform lfp,thenq.Falsificationrequiresobservationof

pandnot-q.TheonlycardshowingpistheEcard,soitmustbeexamined(the

backof山eEcardmustbeanevennumberfortheruletohold).Theonlycard

showingnot-qisthe7,soittoomustbeexamined.TheKand4cardsareirrele-

vant.Yetpeopleconsistentlychoosethecardshowlngq,aChoicethatcanonly

providedataconsistentwiththetheory,butcannottestit;ifthebackofthe4isa

consonant,youhaveleanednothing,sincetheruleissilentaboutthenumbersas-

sociatedwithconsonants.Experimentsshowthetendencytoseekconfirmationis

robustinthefaceoftrainlnginloglC,mathematics,andstatistics.SearchstrategleS

thatfocusonlyonconfirmationofcurrentbeliefsslowthegenerationandrecogn1-

tionofanomaliesthatmightleadtolearnlng,Particularlydoublelloopleam lng.

SomearguethatwhilepeopleerrinapplyingtheprlnCiplesofloglC,atleast

peoplearerationalinthesensethattheyappreciatethedesirabilityofscientificexI

planation.Unfortunately,thesituationisfarworse.Therational,scientificworld-

viewisarecentdevelopmentinhumanhistoryandremainsrare.Manypeople

placetheirfaithinwhatDostoyevsky'sGrandlnqulSitorcalled"Ⅰ血-acle,mystery,

andauthority,=forexample,astrology,ESP,UFOs,creationism,consplraCytheo-

riesofhistory,channelingofpastlives,cultleaderspromisingArmageddon,and

Elvュssightings.Thepersistenceofsuchsuperstitiousbeliefsdependspartlyon血e

biastowardsconfirmingevidence.WadeBoggs,formerBostonRedSoxbatting

champion,ateChickeneverydayforyearsbecauseheoncehadaparticularlygood

dayattheplateafteradinneroflemonchicken(Shaughnessy1987).During血is

timeBoggswonfivebattingchampionships,provlngthewisdomofthe"chicken

theory.HConsiderthecontinuedpopularityofastrology,psychics,andeconomic

forecasters,whopublicizetheirsuccessesandsuppresstheir(morenumerous)

failures.Rememberthatthe40thpresidentoftheUnitedStatesandfirstladyman-

agedaffairsofstateonthebasisofastrology(Robinson1988)･Anditworked:He wasreelectedinalandslide.

Suchlunacyaside,therearedeeperandmoredisturbingreasonsforthepreva-

lenceoftheselearnlngfailuresandthesuperstitionstheyengender･Humanbeings

aremorethancognltlVeinformationprocessors.Wehaveadeepneedforemo-

tionalandsplrltualsustenance.ButfromCopernicanheliocentrismthroughevolu-

tion,relativlty,quantummechanics,andG6delianuncertainty,sciencehasstripped

awayancientandcomfortingbeliefsplacinghumanltyatthecenterofarational

universedesignedforusbyasupremeauthority.Formanypeoplescientific

thoughtleadsnottoenlightenmentandempowermentbuttoexistentialangstand

theabsurdityofhumaninslgnificanceinanincomprehensiblyvastuniverse･

Othersbelievescienceandtechnologyweretheshocktroopsforthetriumphof

materialismandinstrumentalismoverthesacredandspiritual.Theseantiscientific

reactionsarepowerfulforces.Inmanywaystheyareimportanttruths･Theyhave

ledtomanyofthemostprofoundworksofartandliterature･Buttheycanalsolead

tomindlessnew-agepsychobabble.

32 PartiPerspectiveandProcess

ThereadershouldnotconcludefromthisdiscussionthatIamanaivedefender

ofscienceasitispracticednoranapologistfortherealandcontinulngdamage donetotheenvironmentandtoourcultural,moral,andspirituallivesinthename

ofrationalityandprogress.Onthecontrary,Ihavestressedtheresearchshowing

thatscientistsareoftenaspronetothejudgmentale汀OrSandbiasesdiscussed

aboveaslaypeople.Itispreciselybecausescientistsaresubjecttothesamecog- nitivelimitationsandmoralfailuresasothersthatweexperienceabominations

suchastheUSgovemmentfundedresearchinwhichplutoniumwaslnjeCtedinto

seriouslyillpatients,andinwhichradioactivecalciumwasfedtoretardedchil-

dren,allwithouttheirknowledgeorconsent(Mann1994)･Acentralprincipleof

systemdynamicsistoexamineissues血.ommultipleperspectives;toexpandthe boundariesofourmentalmodelstoconsiderthelong-termconsequencesand"side

effects"ofouractions,includingtheirenvironmental,cultural,andmoralimplica- tions(Meadows,Richardson,andBruckmann1982).

1.3.8 DefensiveRoutinesandhterpersonai

Empediments†oLearning

Leaningbygroups,whethersystemdynamicsisusedornot,canbethwartedeven

ifpartlCIPantSreceiveexcellentinfomationfeedbackandreasonwellasindividu-

als.Werelyonourmentalmodelstointerpretthelanguageandactsofothers,con-

structmeaning,andinfermotives.However,asForrester(1971)argues,

Thementalmodelisfuzzy.Itisincomplete.Itisimpreciselystated･Furthermore, withinoneindividual,amentalmodelchangeswithtimeandevenduringtheflow ofaslngleconversation.Thehumanmindassemblesafewrelationshipstofitthe contextofadiscussion.As thesubjectshiftssodoesthemodel･･･lE]achpartici- pantinaconversationemploysadifferentmentalmodeltointerpretthesubject･ Fundamentalassumptionsdifferbutareneverbroughtintotheopen.

Argyris(1985),ArgyrisandSch6n(1978),Janis(1982),Schein(1969,1985, 1987),andothersdocumentthedefensiveroutinesandculturalassumptionspeo-

plerelyon,oftenunknowlngly,tointeractwithandinterprettheirexperienceof others.Weusedefensiveroutinestosaveface,assertdominanceoverothers,make

untestedinferencesseemlikefacts,andadvocateourpositionswhileappearlngtO

beneutral.Wemakeconflictlng,unStatedattributionsaboutthedatawereceive･

Wefailtodistinguishbetweenthesense-dataofexperienceandtheattributionsand

generalizationswereadilyformfromthem･WeavoidpubliclytestlngOurhy-

pothesesandbeliefsandavoidthreatenlnglSSueS･Aboveall,defensivebehavior

involvescoverlnguPthedefensivenessandmaklngtheseissuesundiscussable,

evenwhenallpartiesareawaretheyexist.

Defensiveroutinesaresubtle.Theyoftenarrivecloakedinapparentconcern

andrespectforothers.ConsiderthestrategycalledHeaslng-1n:H

Ifyouareabouttocriticizesomeonewhomightbecomedefensiveandyouwant himtoseethepolntWithoutundueresistance,donotstatethecriticismopenly;ln- stead,askquestionssuchthatifheanswersthemcorrectly,hewillfigureoutwhat youarenotsaying(Argyris,Putnam,andSmith1985,p･83)･

Chapter1 LearlllnglnandaboutComplexSystems 33

Buteaslng-inoften

Createstheverydefensivenessthatitisintendedtoavoid,becausetherecIPlent typlCallyunderstandsthattheactoriseaslng-inJndeed,easlng-1nCanbesuccessful onlyifthereclplentunderstandsthatheissupposedtoanswer仇equestionsina particularway,andthisentailstheunderstandingthattheactorisnegativelyevalu- atingtherecipientandactingasifthiswerenotthecase(Argyris,Putnam,and Smith1985,p.85).

Defensivebehavior,inwhichtheespousedtheoriesweoffertoothersdifferfrom

ourtheoriesinuse,preventsleamingbyhidingimportantinformationfromothers,

avoidingpublictestlngOfimportanthypotheses,andtacitlycommunicatlngthat

wearenotopentohavingourmentalmodelschallenged,Defensiveroutinesoften

yieldgroupthink(Janis1982),wheremembersofagroupmutuallyreinforcetheir

currentbeliefs,suppressdissent,andsealthemselvesofffromthosewithdifferent

viewsorpossibledisconfirmlngeVidence･Defensiveroutinesensurethatthemen-

talmodelsofteammembersremainillfomed,ambiguous,andhidden.Thus

learningbygroupscansufferevenbeyondtheimpedimentstoindividualleam lng.

1.3.9 hplementationFailure

lntherealworlddecisionsareoftenimplementedimperfectly,furtherhindering

leamlng.Evenifateamagreedonthepropercourseofaction,theimplementation

ofthesedecisionscanbedelayedanddistortedastheactualorganizationresponds.

Localincentives,asymmetricin丘)rmation,andprivateagendascanleadtogame

playlngbyagentsthroughoutasystem.Obviouslyimplementationfailurescan

hurttheorganization.ImperfectimplementationcandefeattheleamlngProcessaS

well,becausethemanagementteamevaluatingtheoutcomesoftheirdecisions

maynotknowthewaysinwhichthedecisionstheythoughttheywereimplement-

1ngWeredistorted.

Finally,intherealworldofirreversibleactionsandhighstakestheneedto

maintainperformanceoftenoverridestheneedtolearnbysuppressingnewStrate-

giesforfeartheywouldcausepresentharm eventhoughtheymightyieldgreatin-

sightandpreventfutureham.

lh4 REQUJREMENTSFORSuccESSFULLEARNMG弓N

CoMPLEXSYsTEMS

Wefacegraveimpedimentstoleam lnglnCOmPlexsystemslikeanation,firm,or

family･Everylinkinthefeedbackloopsbywhichwemightteamcanbeweakened

orcutbyavarietyofstructures.Someofthesearephysicalorinstitutionalfeatures

oftheenvironment一也eelementsofdynamiccomplexity仙atreduceopportuni-

tiesforcontrolledexperimentation,preventusfromlearningtheconsequencesof ouractions,anddistorttheoutcomefeedbackwedoreceive.Someareconse-

quencesofourculture,groupprocess,andinqulryS女ills.Stillothersarefunda一

mentalboundsonhumancognltlOn,particularly血epoorqualityofourmental

mapsandourinabilitytomakecorrectinferencesaboutthedynamicsofcomplex

nonlinearsystems.

FIGURE1-14

1dealizedleamlng PrOCeSS

EffectivelearnEng involves continuous

experimentation inboththevirtuaf worldandrea一 world.Feedback frombothinforms

thedeve一opment ofmental

models,formal mode一s,and

thedesignof experimentsfor thenextiteration.

PartI PerspectiveandProcess

1.4.1 hprovingtheLearningPTOCer'S: VirtuesofVirtua一Wor一ds

WhatthenaretherequlrementSforsuccessfullearnlnglnCOmplexsystems?Ifwe

aretocreateusefulprotocolsandtoolsforlearnlngeffectivelyinaworldofdy-

namiccomplexltyWemustattendtoalloftheimpedimentstolearnlng･Figure

1-14Showshowthelearningfeedbackswouldoperatewhenalltheimpediments

toleamlngareaddressed.Thediagramfeaturesanewfeedbackloopcreatedbythe useofvirtualworlds.Virtualworlds(theterm isSch6n'S[1983])arefomalmod-

els,simulations,or"microworldsM(Papert1980),inwhichdecisionmakerscanre-

freshdecision-makingskillS,conductexperiments,andplay.Theycanbephysical

models,roleplays,orcomputersimulations.Insystemswithsignificantdynamic

complexity,Computersimulationwilltypicallybeneeded(仇Ollghtherearenotable

exceptions,suchastheBeerDistributionGame(Ste-an1989b)andtheMainte一

れanceGamedescribedinsection2.4,alongwithrole-play/computerhybridssuch

Rea一Wor一d Unknownstructure Dynamiccomplexity Timedelays lnabllitytoconductcontrolled experiments

VirtualWor一d

Knownstructure Variablelevelofcomplexity Contro‖edexperiments

Decisions RealWorld:

lmplementation failure Gameplaylng Inconsistency PerformancelS 90al

Virtua日World: Perfectimplementation Consistentincentives Consistentapp一ication ofdecisionrules LearnlngCanbegoal

Sirategy,Structure, DecisionRules

Simulat10nusedtoinfer dynamlCSOfmental mode一scorrectly

InformationFeedback VirtuadWorld: Complete, accurate, immediate feedback

RealWor一d: Selectiveperception Missingfeedback De一ay Bias,dlStOrtIOn,error Ambiguity

MentalModels MappingOHeedbackstructure DisciplinedappllCationof scientlflCreasoning Discussabilityofgroup process,defensivebehavior

Chapter1 LearnlnglnandaboutComplexSystems 35

asFishBanks,Ltd･(Meadows,Fiddaman,andShannon1993)･Manyofthetools ofsystemdynamicsaredesignedtohelpyoudevelopuseful,reliable,andeffective modelstoserveasvirtualworldstoaidlearnlngandpolicydesign.

Ⅵr山alworldshaveseveralvirtues.First,theyprovidelow-costlaboratories forlearnlng.Thevirtualworldallowstimeandspacetobecompressedordilated. Actionscanberepeatedunderthesameordifferentconditions.Onecanstopthe actiontoreflect.Decisionsthataredangerous,infeasible,Orunethicalinthereal systemcanbetakeninthevirtualworld.Thuscontrolledexperimentationbecomes possible,andthetimedelaysinthelearnlngloopthroughtherealworldaredra- maticallyreduced.Intherealworldtheirreversibilityofmanyactionsandtheneed tomaintainhighperformanceoftenoverridethegoalofleamingbypreventlngex-

perimentswithuntriedpossibilities("Ifitain'tbroke,don'tfixit" ).Inthevirtu a l

worldyoucantrystrategiesthatyoususpectwillleadtopoorperformanceoreven (simulated)catastrophe･Oftenpushingasystemintoextremeconditionsreveals moreaboutitsstructureanddynamicsthanincrementaladjustmentstosuccessful strategleS.Virtualworldsaretheonlypracticalwaytoexperiencecatastrophe inadvanceoftherealthing.Thusagreatdealofthetimepilotsspendinflight simulatorsisdevotedtoextremeconditionssuchasenginefailureorexplosive decompression.

Virtualworldsprovidehigh-qualityoutcomefeedback.InthePeopleExp71eSS ManagementFlightSimulator(Sterman1988a),forexample,andsimilarsystem dynamicssimulations,playersreceiveperfect,immediate,undistorted,andcom- pleteoutcomefeedback.InanaftemoononecangainyearsOfsimulatedexperi-

ence.Thedegreeofrandomvariationinthevirtualworldcanbecontrolled.Virtual worldsofferthelean ergreatercontroloverstrategy,leadtomoreconsistentdeci- sionmaking,anddeterimplementationfailureandgameplaylng.Incontrasttothe realworld,which,likeablackbox,hasapoorlyresolvedstructure,virtualworlds canbeopenboxeswhoseassumptlOnSarefullyknownandcanevenbemodified by血elearIler.

ⅥrtualworldsforleamlngandtrainlngareCOmmOnplaceinthemilitary,ln pilottrainlng,1npowerplantoperations,andinmanyotherrealtimetaskswhere humanoperatorsinteractwithcomplextechnicalsystems.Virtualworldsarealso commoninprofessionssuchasarchitectureandenglneenngthatlendthemselves totheuseofphysicalmodels(Sch6n1983).Theuseofvirtualworldsinman- agerialtasks,wherethesimulationcompressesintominutesorhoursdynamicsex- tendingoveryearsordecades,ismorerecentandlesswidelyadopted･Yetthese arepreciselythesettlngSWheredynamiccomplexltylSmostproblematic,where theleamingfeedbacksdescribedaboveareleasteffective,andwherethestakesare highest.

1.4.2 PittallsofVirtualWorlds

VirtualworldsareeffectivewhentheyengagepeopleinwhatDeweycalled"re- nectivethought"andwhatSch6n(1992)calls"reflectiveconversationwiththe situation."Thoughsimulationmodelsandvirtualworldsmaybenecessaryfor effectiveleamlngindynamicallycomplexsystems,theyarenotsufficienttoover- cometheflawsinourmentalmodels,scientificreasonlngSkills,andgroup prOCeSSeS･

36 PartI PerspectiveandProcess

Obviously,whilethevir山alworldenablescontrolledexperimentation,itdoes notrequlrethelearnertoapplytheprlnCiplesofscientificmethod.Manypartici- pantsinsystemdynamicsprojectslacktrainlnglnscientificmethodandawareness ofthepitfallsinthedesignandinterpretationofexperiments.Acommonlyob- servedbehavioramongmodelersandinworkshopsusingmanagementflightsim- ulatorsisthevideogamesyndromeinwhichpeopleplaytoomuchandthinktoo little.Peopleoftendonottaketimetoreflectontheoutcomeofasimulation,iden-

tifydiscrepanciesbetweentheoutcomesandtheirexpectations,formulatehy- pothesestoexplainthediscrepancies,andthendeviseexperimentstodiscriminate amongthecompetlngaltematives.Effectiveleam1ngusingSystemdynamicswill oftenrequlretrainingforpartlCIPantSinscientificmethod.Protocolsfortheuseof simulationsshouldbestructuredtoencourageproperprocedure,suchaskeeping laboratorynotebooks,explicitlyformulatinghypothesesandpresentlngthemtothe group,andsoon.

DefensiveroutinesandgroupthinkcanoperateintheleamlnglaboratoryJust asintherealorganization.Indeed,protocolsforeffectivelearnlnglnVirtualworlds suchaspublictestingOfhypotheses,accountability,andcomparisonofdifferent strategleSCanbehighlythreatenlng,inducingdefensivereactionsthatprevent leaming(IsaacsandSenge1992).Theuseofsystemdynamicstostimulatelearn- 1nglnOrganizationsoftenrequlreSmembersoftheclientteamtospendtimead- dresslngtheirowndefensivebehavior.Managersunaccustomedtodisciplined scientificreasoningandanopen,trustingenvironmentwithlearningaSitsgoalWill havetobuildthesebasicskillsbeforeasystemdynamicsmodel10rindeed,any model-canproveuseful.Developlngtheseskillstakeseffortandpractice.

Still,settlngSWithhighdynamiccomplexltyCangarblethereflectiveconver- sationbetweenthelearnerandthesituation.Longtlmedelays,Causesandeffects thataredistantintimeandspace,andtheconfoundingeffectsofmultiplenonlin- earfeedbackscanslowleamlngevenforpeoplewithgoodinsightandgroup processskills.LearnlnglnVirtualworldscanbeacceleratedwhenthemodeling processalsohelpspeopleleanhowtorepresentcomplexfeedbackstructuresand understandtheirimplicationsratherthansimplypresentlngtheresultsofananaly- sis.ToleanindynamicallycomplexsystemspartlCIPantSmusthaveconfidence thatthemodelisanappropnaterepresentationoftheproblemtheycareabout｡ Theymustbelieveitmimicstherelevantpartsoftherealworldwellenoughthat thelessonsemergingfromthevirtualworldapplytotherealone.Todevelopsuch confidencethevirtualworldmustbeanopenboxwhoseassumptionsCanbein- spected,Criticized,andchanged.Tblean,p∬tlClpantSmustbecomemodelers,not merelyplayersinasimulationgame.

Inpractice,effectivelearningfrommodelsoccursbest,andperhapsonly, whenthedecisionmakerspartlClpateactivelyinthedevelopmentofthemodel. ModelinghereincludestheelicitationoftheparticlpantS'existlngmentalmodels, includingarticulatingtheissues(problemstructuring),selectingthemodelbound- aryandtimehorizon,andmapplngthecausalstructureoftherelevantsystem. Alongwithtechniquesdevelopedinsystemdynamics,manytoolsandprotocols forgroupmodel-buildingarenowavailable,includingcausalloopdiagrams, policystructurediagrams,interactivecomputermapplng,andvariousproblem structuringandso氏systemsmethods(see,e.g.,Checkland1981;Eden,Jonesand

Chapter1 LeamlnglnandaboutComplexSystems 37

Sims1983;Lane1994;Morecroft1982;MorecroftandSterman1994;Reagan-

Cirincioneetal･1991;Richmond1987,1993;Rosenhead1989;Sengeand Sterman1992;andWolstenholme1990).

1,4,3 WhySjmuZationtsEssentはI

ElicitingandmappingtheparticIPantS'mentalmodels,whilenecessary,isfarfrom sufficient.Asdiscussedabove,thetemporalandspatialboundariesofourmental modelstendtobetoonarrow.Theyaredynamicallydeficient,omittingfeedbacks, timedelays,accumulations,andnonlinearities.Thegreatvirtueofmanyprotocols andtoolsforelicitationistheirabilitytoimproveourmodelsbyencouraglngPeo- pletoidentifytheelementsofdynamiccomplexltynormallyabsentfrommental models.However,mostproblem structurlngmethodsyieldqualitativemodels showingcausalrelationshipsbutomittlngtheparameters,functionalforms,exter-

nalinputs,andinitialconditionsneededtofullyspecifyandtestthemodel.Re- gardlessoftheformofthemodelortechniqueused,theresultoftheelicitationand

mappingprocessisnevermorethanasetofcausalattributions,initialhypotheses aboutthestructureofasystem,whichmustthenbetested.

Simulationistheonlypracticalwaytotestthesemodels･ThecomplexltyOf ourmentalmodelsvastlyexceedsourcapacitytOunderstandtheirimplications. TypicalconceptualmodelssuchasthetypeofcausaldiagramshowninFigurel16 aretoolargeandcomplextosimulatementally.Withoutsimulation,eventhebest conceptualmodelscanonlybetestedandimprovedbyrelyingonthelearnlng fTeedbackthroughtherealworld.Aswehaveseen,thisfeedbackisveryslowand oftenrenderedineffectivebydynamiccomplexlty,timedelays,inadequateand ambiguousfeedback,poorreasoningSkills,defensivereactions,andthecostsof experimentation.Inthesecircumstancessimulationbecomestheonlyreliableway totesthypothesesandevaluatethelikelyeffectsofpolicies.

Somescholarsarguethatformalmodelingcanatbestprovidequantitative precisionwithinpreexistlngProblemdefinitionsbutcannotleadtofundamentally newconceptions(forvariousviewsseeDreyfusandDreyfus1986andthediscusI sic-ninLane1994).Onthecontrary,formalizingqualitativemodelsandtesting themviasimulationoftenleadstoradicalchangesinthewayweunderstandreaレ 1ty.Simulationspeedsandstrengthensthelearningfeedbacks.Discrepancies betweenformalandmentalmodelsstimulateimprovementsinboth,including changesinbasicassumptlOnSSuchasmodelboundary,timehorizon,anddynamic hypotheses(seeForrester1985andHomer1996forphilosophyandexamples)･ WithoutthedisciplineandconstraintimposedbytherlgOrOuSteStlngenabledby simulation,itbecomesalltooeasyfわrmentalmodelstobedrivenbyideologyor unconsciousbias.

Somearguethatformalizationforcesthemodelertoomitimportantaspectsof theproblemtopreservetractabilityandenabletheoremstobeprovedortoomit softvariablesfTorwhichnonumericaldataexist.Theseareindeeddangers.Thelit- eratureofthesocialsciencesisrepletewithmodelsinwhicheleganttheoremsare derivedfromquestionableaxioms,wheresimplicitydominatesutility,andwhere variablesknowntobeimportantareIgnoredbecausedatatoestimateparameters areunavailable.Systemdynamicswasdesignedspecificallytoovercomethese

38 PartIPerspectiveandProcess

limitationsandfromthebeginnlngStressedthedevelopmentofusefulmodels;

modelsunconstrainedbythedemandsofanalytictractability,basedonrealisticas-

sumptionsabouthumanbehavior,groundedinfieldstudyofdecisionmaking,and

utilizlngthefullrangeofavailabledata,notonlynumericaldata,tospecifyandes-

timaterelationships(seeForrester1961,1987)･

Somepeopledon'tbelievethatmodelsofhumanbehaviorcanbedeveloped.

Simulationsofnaturalandtechnicalsystemssuchastheclimateoranoilrefinery

arebasedonwell-understoodlawsofphysics,but,itisargued,therearenocom-

parablyreliablelawsofhumanbehavior.Thisviewoverestimatesourunderstand-

1ngOfnatureandunderestimatestheregularitiesinhumandecisionmaking.As

KennethBouldingpolntSOut,HAnythingthatexistsispossible･MYouwillseemany

examplesofmodelsofhumansystemsthroughoutthisbook(seealsothemodels

inLevineandFitzgerald1992;Roberts1978;Langleyetal･1987;Steman1985a;

Homer1985;andmanyofthemodelscitedinSastryandSteman1993).

IsitpossibletolearneffectivelyincomplexsettingsWithoutsimulation?Can

theuseofproblemstructurlngmethods,elicitationtechniques,andotherqualita-

tivesystemsmethodsovercometheimpedimentstolearning?Ifintuitionisdevel-

opedhighlyenough,ifsystemsthinkinglSincorporatedinprecollegeeducation

earlyenough,orifwearetaughthowtorecognlZeaSetOfHsystemarchetypesH

(Senge1990),willwebeabletoimproveourintuitionaboutcomplexdynamics

enoughtorendersimulationunnecessary?

Theanswerisclearlyno.Itistruethatsystemsthinkingtechniques,including

systemdynamicsandqualitativemethodssuchassoftsystemsanalysis,Canen-

hanceourintuitionaboutcomplexsituations,Justasstudyingphysicscanimprove

ourintuitionaboutthenaturalworld.14AsWolstenholme(1990)argues,qualitative

systemstoolsshouldbemadewidelyavailablesothatthosewithlimitedmathe一

maticalbackgroundcanbenefitfromthem.Iamastrongadvocatefortheintro-

ductionofsystemdynamicsandrelatedmethodsatalllevelsoftheeducational

system.Yetevenifweallbeganseriousstudyofphysicsinkindergartenandcon-

tinueditthroughaPh.D.,itisludicroustosuggestthatwecouldpredictthetrack

ofahurricaneorunderstandbyintuitionalonewhathappenswhentwogalaxies

collide.Manyhumansystemsareatleastascomplex･Evenifchildrenlearnto

thinkinsystemsterms-agoallbelieveisvitallyImportant-itwillstillbenec-

essarytodevelopformalmodels,solvedbysimulation,tolearnaboutsuchsys- tems.

Mostimportant,whenexperimentationinrealsystemsisinfeasible,simulation

becomesthemain,andperhapstheonly,wayyoucandiscoverforyourselfhow

complexsystemswork.Thealternativeisrotelearnlngbasedontheauthorityof

theteacherandtextbook,amethodthatdullscreativltyandstuntsthedevelopment

ofthescientificreasonlngSkillsneededtolearnaboutcomplexity.

14suchknowledgeofbasicphysicsisdesperatelyneeded.WhenaskedthequestionHIfapenis droppedonthemoon,willit(a)noataway;(b)floatwhereitis;(C)falltothesurfaceofthe moon?H48outof168StudentsinphysicscoursesatiowaStateUniversltygaveincorrectanswers･ Typicalstudentexplanationswere"ThegravltyOfthemooncanbesaidtobenegligible"and"The moon'savacuum,thereisnoexternalforceonthepen･Thereforeitwillfloatwhereitis."(Partee, personalcommunication,1992).

Chapter1LearninglnandaboutComplexSystems 39

Theimplicationsforthisbookareclear.Systemdynamicsisnotaspectator

sport:ThroughoutthebookIhavetriedtoencouragetheactiveparticlpationof

you,thereader･YouwillfindChallengesineachchapter-examplesforyouto

considerandworkthroughyourself,suchasthechickenandeggcausalloopdia-

graminFigure1-6andtheWasoncardpuzzleinFigureト13.Someoftheseare

followedbyasuggestedresponse.Othersarenot.Asyouworkthroughthebook,

extendtheexamples.Buildthemodels･Experimentwiththem.Applyyourskills

tonewproblemsandnewissues･And,mostofall,havefun･15

1.5 SuMMARY

Complexdynamicsystemspresentmultiplebarrierstolearnlng.Thechallengeof

betterlngthewayweleanaboutthesesystemsisitselfaclassicsystemsproblem.

Systemdynamicsisapowerfulmethodtogalnusefulinsightintosituationsof

dynamiccomplexltyandpolicyresistance.Itisincreaslnglyusedtodesignmore

successfulpoliciesincompaniesandpublicpolicysettlngS.However,noone

methodisapanacea.OvercomlngthebarrierstolearnlngrequlreSaSynthesisof manymethodsanddisciplines,from mathematicsandcomputerscienceto

psychologyandorganizationaltheory.Theoreticalstudiesmustbeintegratedwi仙

fieldwork･Interventionsinrealorganizationsmustbesubjectedtorigorous follow-upresearch.

Thefieldofsystemdynamicsisitselfdynamic.Recentadvancesininteractive

modeling,toolsforrepresentationoffeedbackstructure,andsimulationsoftware

makeitpossibleforanyonetoengageinthemodelingprocess.Corporations,unit

versities,andschoolsareexperimentlngVlgOrOuSly･Thelibraryofsuccessfulln-

terventionsandinsightfulresearchisgrowlng.Muchfurtherworkisneededtotest

theutilityofthetoolsandprotocols,evaluatetheirimpactonindividualandorga-

nizationallearning,anddevelopeffectivewaystotrainotherstousethem.Never

befbrehavethechallengesofourincreasinglydynamicworldbeenmoredauntlng.

Neverbeforehavetheopportunitiesbeengreater.It'sanexcltlngtimetObelearn-

1nglnandaboutcomplexsystems.

15TheaccompanyingCD-ROMandwebslte(http://www.mhhe.coI〟sterman)includethemodels developedinthetextandsimulationsoftwareyoucanusetorunandextendthem.

Sぎ§書e-三?_-呈互きき一語員i3_ti主だ§言訳Ae喜iLl呈呈

lSystem dynamics]isanapproachthatshouldhelpinimportanttop- managementproblems...Thesolutionstosmallproblemsyieldsmall rewayds.VefToftenthemostimportantp710blemsarebutlittlemoredlMicultto handlethantheunimportant.Manylpeople]predeterminemediocreresultsby settinginitialgoalstoolow.Theattitudemustbeoneofenterprisedesign.The

expectationshouldbeformajorimprovement...Theattitudethatthegoalis toexplainbehavio73Whichisfairlycommoninacademiccircles,isnot sujficient.Thegoalshouldbetoft'ndmanagementpoliciesandorganizational structuresthatleadtogreatersuccess.

-JayW.Forrester(IndustrialDynamics,1961,p.449).

Thischapterpresentsthreecasestudiesofthesuccessfulapplicationofsystemdy-

namicstosolveimportantrealworldproblems.Thecasesspanarangeofindus- triesandissues.Theyillustratedifferentcontextsfortheuseofsystemdynamics

anddifferentmodelingprocesses,fromlarge,dataintensivemodelstosmallmod- els,1nteraCtivemanagementflightsimulators,androle-playlnggames.Thecases illustratehowsystemdynamicscanbeusedtohelpsolvehigh-stakesproblemsin

realtime.Thecasesillustrate血eprlnCiplesdiscussedinchapter1andpreview manyofthetoolsandmethodsdiscussedinsubsequentchapters.

2.1 AppLICAT!ONSOFSysTEMDYNAMICS

Systemdynamicshasbeenappliedtoissuesrangingfromcorporatestrategytothe dynamicsofdiabetes,fromthecoldwararmsracebetweentheUSandUSSRto

thecombatbetweenHIVandthehumanimmunesystem.Systemdynamicscanbe

42 PartI PerspectiveandProcess

appliedtoanydynamicsystem,withanytimeandspatialscale.Intheworldof

businessandpublicpolicy,systemdynamicshasbeenappliedtoindustriesfrom aircrafttozincandissuesfromAIDStowelfarereform.l

Developlnganinsightfulmodelisdifficultenough;uslngmodelingtohelp

changeorganizationsandimplementnewpoliciesisevenharder.Thegreatestpo-

tentialforimprovementcomeswhenthemodelingprocesschangesdeeplyheld

mentalmodels.Yetthemorefundamentalthementalmodelyouchallenge,the

moredefensivetheclientmaybe.Toresolvethedilemmatheclientsmustdiscover

theinsightsforthemselvesbyactiveparticlpationinthemodelingprocess.

Thischapterpresentsthreecasestudiesillustratlngtheprocess.Eachad-

dressedanimportantrealworldissue.Eachinvolvedadifferentcontextandthere-

foreusedadifferentapproach･Yeteachalsosucceededininvolvingtheclientsas

partnersinthemodelingprocess,inchanglnglong-establishedmentalmodels,and

ingeneratlngSignificantbenefit.

2.2 AuTOMOBILELEASINGSTRATEGY:

GoNEToDAY,ilEREToMORROW2

Inthe1990sanewwaytobuycarsemergedintheUnitedStates-theusedcar

superstore.NationalchainslikeCarMaxandAutoNationofferedalargeselection

ofclean,lowmileagelatemodelcarswithwarranties,roadsideassistanceplans,

andotheramenitiestraditionallyavailableonlytonewcarbuyers.Superstoresales

grewfromnothingin1992tomorethan$13billionin1998.Internetcarvendors

begantosprlngupaSWell.Manyanalystsbelievedthecombinationofsuperstores andinternetsalesheraldedarevolutionintheretailautomarket.

In1995SomeseniormanagersatGeneralMotorswereconcernedaboutthe

impactofthesuperstoresonnewcarsales･WouldtheycutintoGM'scoremarket?

WouldtheyforceprlCeSdown?HowcouldGM respond?RonZarella,thenvice

presidentandgroupexecutiveforNorthAmericanvehiclesales,service,andmar-

keting(VSSM)andlaterpromotedtopresidentofGM'sNorthAmericanregion,

neededawaytoexaminetheseissues.

Therewaslittleresearchontheusedcarmarketavailabletohelp.Formany

decadesthenewandusedcarmarketswereonlylooselycoupledbecausepeople

tendedtokeeptheircarsalongtlme.Marketresearchintheearly1990sshowed

newcarbuyerswerekeeplngtheircarsanaverageofmorethan6years･Thebulk

ofusedcarsofferedforsalewere40rmoreyearsoldandwerepoorsubstitutesfor

newcars.Theprevailingmentalmodelintheautoindustry,IncludingGM,was

lRichardson(1996),Roberts(1978),andMorecroftandSterman(1994),amongothers,provide examplesoftheapplicationofsystemdynamicstoimportantproblemsinawiderangeofindustries

andpublicpolicyissTes･Mosekilde(1996)describesapplicationsinphysicsandbiology･Ford (1999)describesenvlrOnmentalapplications.

2ThiscaseisbasedontheworkoftheGeneralMotorsStrategySupportCenter,ledbyNICk Pudar.Ⅰ'mgratefultoNickandGMforpermissiontopresentthecaseandtoNickandMarkPaich forhelplnitspreparation.

Chapter2 SystemDynamicsinAction 43

thatautocompanieswereinthebusinessofsellingnewcars;thevehiclespeople

tradedinwereoldandeffectivelydisappearedintoaseparatesystem,theusedcar

market.HTherearereallytwomarkets一mewandused,"theexecutivedirectorof

salesoperationsatFordtoldTheWallSt71eetJournalin1994(3June,p.Bl).

ZarellacontactedVinceBarabba,thengeneralmanagerofcorporatestrategy

andknowledgedevelopmentintheVSSM organization,anddescribedhiscon-

cems.Barabba,formerheadoftheUSCensusBureau,alsoheadeduptheDecision

SupportCenter(DSC)andaskedNickPudar,thenaseniorbusinessanalystinthe

DSC,toworkonthesuperstoreissue.TheDSCisaninternalgroupGMformedto

helpbusinessunitsandprojectteamsthroughoutthecompanydevelopandimple-

mentstrategy.TheDSCusesavarietyofanalyticaltools,includingsystemdy-

namics.Morethansimplyagroupofanalyticalmodelers,theDSCdevelopeda

sophisticatedapproach,thedialoguedecisionprocess,designedtobuildconsensus

thatleadstoaction,notmerelyanalysisandreports･BarabbaandPudar(1996)de-

scribethedialoguedecisionprocessas

adisciplineddecisionmakingprocesswhichinvolvesaseriesofstructureddial loguesbetweentwogroupsresponsiblelbrreachingadecisionandimplementlng theresultingactionplan･Thefirstgroup(DecisionReviewBoard)consistsofthe decision-makers,whogenerallyrepresentdifferentfunctions.Wh attheyhavein commonistheauthoritytoallocateresources:people,capltal,materials,tlme,and equipment...Thesecondgroup(CoreTeam),consistsofH.thosewithastakein theimplementation.

Thedialoguebetween血etwogroups,whichinvolvessharingandlearnlngfor both,takesplaceinfoursequentialstages:1)framingtheproblem;2)developing alternatives;3)conductingtheanalysis;and4)establishingconnection･Eachof thesefourstepsiscompletedbytheCoreTeamandsupportedbyfacilitators equlppedwithdecisionanalytictools･Attheendofeachphase,theyhaveadia- loguesessionwiththeDecisionReviewBoardwheretheyJOlntlyreviewthe progress･Inanatmosphereofinquiry･-Seniorleadershipconverseswithacross- functionalteamofmanagersonatopicOfmutualstrateglCimportance･

PudartoldZarellahewouldneedtocommittoaseveralhourmeetingeachweek

foramon血Htobesureweareworkingontherightproblem."WhileZarella's

schedulewasextremelytightheofferedtomeetwithBarabbaandPudarthe

nextday.

Pudar,workingwithMarkPaich,anexternalsystemdynamicsconsultantand

professorofeconomicsatColoradoCollege,DarrenPostoftheDSC,andTomPa-

terson(anotherconsultanttotheDSC)scrambledtodevelopaninitialmodelofthe

issue.Thatafternoontheydevelopedasimplediagramrepresentingthestocksand

flowsofcarsthroughthenewandusedmarketsandsomeofthefeedbacksthat

mightcouplethem.Theydeliberatelykeptitverysimple,bothtobesurethey

couldcompleteitintimeandsotheycouldexplainitclearly･

ThatnightPudardevelopedasimple,workingsimulationmodeloftheinter- actionsbetweenthenew andusedmarkets.Themodelincludedsectorsfor

newandusedcars(dividedintoGM andnon-GM vehicles)andtrackedvehicles

fromproductionthroughinitialsaleorlease,trade-in,theusedcarmarket,and,

44 PartI PerspectiveandProcess

ultimately,Scrapplng.ItalsotrackedtheflowsofcustomersmovlngIntoandout ofthemarketandincludedasimpleconsumerchoicemodelforthenew/usedpur- chasedecision.Pudaruseddataathandandhisjudgmenttoestimateparameters.

Figure21lshowsasimplifieddiagramoftheinitialmodel.Thestructurein blackcapturestheprevailingmentalmodelfocusedonthenewcarmarket.Theleft sidetracksthestocksandflowsofvehicles.Startingatthetop,theinventoryof unsoldnewcarsisincreasedbyproductionanddrainedbynewcarsales.Newcar salesaddtothestockoflatemodelcarsontheroad･Peoplesellortradeintheircar andbuyanewonewithafrequencydefinedbytheaveragetrade-intime･

Figure2-1alsoshowsthemainfeedbacksoperatinginthenewcarmarket. ManufacturersanddealerspaycloseattentiontothestockofnewcarsJnventory coverageofabout45daysprovidesagoodbalancebetweentheselectionavailable ondealerlotsandcarryingcosts.Lowcoveragehurtssalesbecausecarsaren't available;highinventoriesslashdealerandautomakerprofitsascarryingcostsball loon.Ifinventorycoveragerisesabovenormal,carmakerscutproduction,which helpsreduceinventoriesbacktonormal.Theresponseofproductiontoinventories formsthenegative(balancing)ProductionControlfeedbackloop,B1.However, automakersarereluctanttocutproductionandinanycase,ittakestime.Thedelay inadjustingProductionmeansinventoriestendtofluctuatearounddesiredlevels asdemandvaries.

ThesecondmainresponsetoexcessinventoriesislowerprlCeS.Wheninven-

torycoverageishigh,dealersaremorewillingtocuttheirmarginsandmanu- facturersofferincentivessuchascash-backandlowannualpercentagerates (APRs)Onloansfinancedthroughtheircreditdivisions.Lowerpricesmakenew carsmoreattractiverelativetothecarspeoplealreadyown.Peopletradeintheir oldcarssooner,boostingnewcarsalesuntilinventoriesfallbacktonormal(the negativePricingloop,B2).

2.2月 DynamicHypo帥es妄s

Challengingtheconventionalwisdom,theteamexpandedthestockandflowstruc- turetoincludelatemodelusedcars.Ⅰnsteadofdisappearlng,trade-insaddtoin- ventoriesoflatemodelusedcarsOndealerlotsoravailableforauction.When

thesecarsarepurchased,theyreenterthestockoflatemodelcarsontheroad.The sumofthecarsontheroadandcarsondealerlotsisthetotalstockoflatemodel

vehicles(shownbythelargerectangleinFigure2-1);thesecarsgraduallyageinto thepopulationofoldercarsandareeventuallyscrapped.Themodelusedan"aging chain"tokeeptrackofthecarsontheroadandinusedcarinventoriesbyトyear cohorts.Theagingchain(chapter12)allowedtheteam toexaminehowthe numberof1-,2-,and3-year-oldcarsontheroadandforsalechangedinresponse tosales.

Thestockandnowperspectivemotivatedthemodelingteamtoaskwherethe superstoresgotthelargeinventoriesofattractivelatemodelcarstheyrequired. Partoftheanswerwasthegrowlngqualityofnewcars･Stimulatedbythehigh qualityofforeigncars,particularlytheJapaneseimports,allmanufacturershad

Chapter2 SystemDynamicsinAction

FdGURE2･l AsimpFemodeloHheautomobilemarket

Rectanglesrepresentstocksofcars;pIPeSandvalvesrepresentflowsbetween

categories(chapter6).Arrowsandpolarities(+or-)indicatecausalinfluences:

AnincreaseinNewCarhventoryleadstoanincreaseinInventoryCoverage(anda

decrease一eadstoadecrease);anincrease(decrease)inInventoryCoveragecauses

PewCarPricestodecrease(increase);Seechapter5･Graystructurewasnotcaptured Fntheprevalllngindustrymentalmodelinwhichnewandusedcarmarketsdonot interact.

46 PartiPerspectiveandProcess

investedinmajorqualityprograms.Thoughtherewasstillroomforimprovement, bythe1990Sthequalityanddurabilityofnewcarswassignificantlyhigherthanin the1980S.

ButqualitylmprOVementalonecouldnotexplaintheriseofthesuperstores. BythetimemostcarsaretradedintheyaretoooldtocompeteagalnStnewCars

andareunsuitableforthesuperstores.Qualityimprovementsmightevenlengthen thetrade-incycletime,reducingthesupplyoflatemodelusedcars.

Theanswerwasleaslng.Intheearly1990sleaslngWasthehotnewmarketing

toolintheautomobileindustry.LeasingOfferedwhatseemedtobeasure-fireway toboostsales,Risingqualitymeantthemarketvalueof2-,3-,and4-year01dcars wasmuchhigherrelativetonewcarsthaninthepast.Thehighertheresidualvalue

attheendofalease,thelowertheleasepayments.LeasesalsoglVeCustomersthe optiontObuythecarwhentheleaseexplreSatthespecifiedresidualvalue,trans-

ferringtheriskoffluctuationsinthemarketvalueofusedvehiclesfromthecus- tomertothecarmaker.Mostimportanttothemanufacturers,typicalleasetermsare

2to4years,Stimulatingsalesbycuttlngthetrade-incycletime･LeasingIncreased from4.1%ofallnewcarsalesin1990tomorethan22%in1997.

Fromtheperspectiveoftheprevailingmentalmodel,leasingWasaboon.First, itstimulatedsales.Wheneverinventoriesrisecarmakerscouldincreaseincentives

forleasingthroughleasesubvention.SubventionlowersleasepaymentsbyasI suminghigherresiduals,lowerinterestrates,Orlowerinitialcapltalization;typi-

callycarmakerswouldraiseresidualvaluesaboveguidebookvaluesforusedcars･ Lowerleasepaymentsboosttheattractivenessofnewcarsandinducesomepeople totradetheircurrentcarforanewleasedvehicle(formingthebalancingLease

lncentiveloopB3inFigure2-1).Second,theshortertheaverageleaseterm,the shorterthetrade-intimeandthegreaterthesales(thebalancingLeaseTermloop B4).Ifallnewcarbuyersswitchedtoleaseswithanaveragetermof3years,the

trade-incycletimewouldbecutinhalfandnewcarsaleswoulddouble-allelse equal.

ThemodelingteamquicklychallengedtheassumptlOnthatallelsewasequal･ Whilea6-yearoldcarュsapoorsubstituteforanewcar,a1-to3-year-oldcarwith lowmileagemightbeattractivetomanypeople.AsthegrowlngVOlumeofleases

expiredtheusedcarmarketcouldbefloodedwithhigh-qualitynearlynewcars･ UsedcarprlCeSmightplummet.Somepeoplewhomighthavetradedtheircurrent carsfornewonesoptinsteadforofflleasevehicles,raisingtheaveragetrade-in

timeandreturningmorelatemodelusedcarstothestockofcarsontheroad(the balancingUsedCarMarketloop,B5).Leasingalsoshortenstheaveragetrade-in cycletime,raislngtheaveragequalityofusedcarsforsale･Morepeopleoptfor offlleasevehiclesinsteadofbuyingnew.Theaveragetrade-intimeforthepopuh

tionasawholerises,formingthebalancingUsedCarQualityloop,B6･Evenmore interestlng,theusedmarketcouldfeedbacktoaffectthefractionofcustomerswho

choosetobuytheircarwhentheirleaseexplreS･If,atleaseend,usedcarprlCeSare higherthantheresidualvaluewrittenintothelease,thecustomercanpurchasethe carbelowmarketvalue.Thecustomerretentionfractionwouldrise.If,however,

usedcarpricesdroppedbelowresidualvalues,theretentionfractionwouldfallas morecustomersturnedtheircarsbacktothelessor.Theinventoryoflatemodel

Chapter2 SystemDynamicsinAction 47

CarswouldriseandusedcarprlCeSWOulddropstillmore,inaviciouscycle,the

positive(self-reinforcing)PurchaseOptionloop,Rl.3 However,thefTeedbacksshowningrayoperatewithalongdelay(roughly

equaltotheaverageleaseterm)andwerepoorlyunderstoodintheindustry.Leas-

1ngStimulatessalesintheshor t-run.Unawareofthestructureshowningrayln

Figure2-1,theexperienceoftheearly1990Staughtcarmakersthatleasing

works-andtheydivertedstillmoremarketingdollarstosubventionandshorter terms.

Initialresultssuggested,however,thatleaslngWOuldeventuallycreateaglut

ofhigh-qualitynearlynewcars,depresslnglatemodelusedcarprlCeS.Newcar

saleswouldsufferasmoreconsumersoptedforcheapoff-leasevehicles.Thecar-

makers'creditcompanies(GeneralMotorsAcceptanceCorporation[GMAC],

FordCreditCorporation,andChryslerCreditCorporation)wouldfacelossesas

marketvaluesfellshortoftheresidualvaluetheyhadbookedandasfewercon-

sumersexercisedtheiroptlOntObuy,turnlngthecarbacktothelessorsinstead.

ThefollowlngdayPudarandhisteampresentedtheseresultstoZarella,in-

cludingthestructureoftheinitialmodelandsimulationsshowlngtheproblemsag一

gressiveleaslngCOuldcause.Byshortenlngtrade-incycletimesthroughleaslng

andneetsales,Carmakerswerecreatingaglutofhigh-qualityusedcarsatattrac-

tiveprlCeS.Superstoresweresimplythemarketresponsetotheopportunltythe manufacturersthemselveshadcreated.

Usedcarsuperstoreswereonlythesymptomofadeeperproblem-theleasing

policiesofthecamakers.LeaslngIncreasedsalesintheshortrunbutsetinmotion

feedbacksthatcausedsalestoslumpwhentheleasedvehiclesreenteredthemar-

ket･Intheolddays,peoplekepttheircarslongenoughthattrade-inseffectively

disappearedfromconcern.Butinaworldofshort-termleases,newcarsaregone

today,heretomorrow.

Therealizationthatsuperstoreswereanendogenousconsequenceofthecar-

makers'Ownactionsdramaticallyredefinedthefocusofthework.Initialmodel

analysissuggestedGM shouldde-emphasizeleaslng,exactlycountertoindustry trends.

Theseeffectsmayseemobvious(especiallynowthatyouhavereadthede-

scriptionofthemodelabove),andautoindustryexecutivesdidknowthatsome

offlleasecarswouldreenterthemarket.However,mostdiscountedthepossibility

ofanyproblems.In1994,USATodayquotedaGeneralMotorsleasingexecutive

whosaid,HThedemandforcarscomingOffleasesistriplethesupply.Lease-end

carshaveǹotcreatedabottleneckintheindustry'H(2November).ADetroit-area

3ThePurchaseOptionlooplSpartiallyoffsetbecausecustomersturnlngtheircarsbackto lessorspurchaseanothervehicle.IfleasecustomersusedtheirpurchaseoptlOntOmakeapurearbi- trageplaywhenusedcarprlCeSfellbelowresidualvaluesbyturnlngtheircarsinandimmediately buyingidenticalonesatthelowermarketprlCe,thentheneteffectofchangesintheretentionfrac- tionwouldbezero.However,somecustomersturnlngtheircarsbacktolessorswillbuyanewcar ordifferentusedcar,possiblyfromacompetitor･OnnetalowerretentionfractionforaglVenmake andmodelwilltendtopushpricesforthatcardownstillmore,trlggerlngevenlowerretention･ TheseeffectswerecapturedinthefullmodelbutforclarltyarenotShowninFigure211A

48 PartI PerspectiveandProcess

Cadillacdealerdismissedanylinkagebetweenthenewandusedmarketsforhigh- endcars,scoffing,"You'llnevergetaluxurybuyertotakeacarwith30,000miles onit"(TheWallStyleetJournal,3June1994).Inthesamearticle,TheJournalwent

ontonotethatFord'Sexecutivedirectorofsalesoperations

arguesthattheindustryhashadachronicshortageofgoodtwo-year-oldcarsto sell‥.HThis[short-termleasing]bringsthecarsbackatjusttherighttime,when demandishighest,Hhesays･Moreover,theused-carmarketisatleasttwiceasbig asthenewICarmarketandcaneasilyabsorbtheprojectedvolumes.

Theunderlyingstrengthinused-Cardemandwillsafelyabsorbthevolumeof usedvehiclescomlngOfflease,withoutcannibalizlngnew-CarSales,Hpredicts... [an]autosecuritiesanalystatSalomonBros.

Thereappearedtobeampleevidencetosupporttheseviews･Usedcarsalesgrew from37.5millionin1990tonearly42millionin1995while1995newcarsales

wereabout15million,ariseofonlyaboutamillionvehicles/yearsince1990.

UsedcarprlCeSrosemorethan6%/yearbetween1990and1995,muchfasterthan

inflation.WithrislngusedcarprlCeS,moreandmorepeopleoptedtokeeptheirve-

hiclewhentheirleaseexpired･Manyintheindustry,lnCludingGM,arguedthat

strongdemandandrisingusedcarvaluesJustifiedevenhigherresidualvalues,a1-

lowlnglowerleasepaymentsandboostlngnewCarSalesstillmore.

Whiletheinitialresultswereintrlgulng,moreworkwasneededbeforecredi- blepolicyrecommendationscouldbemade,muchlessanyactiontaken.Evenif

leasingWasadevil'sbargaln,everyCarmakerfeltstrongpressuretomatchthe

termsandpricesofitscompetitors.Onceallmajormanufacturerswereoffering

shortleasetermswithaggressivesubvention,unilaterallybackingawayfromleasl

lngmightrisktoomuchmarketshare.Zarellaaskedtheteamtocontinuethemod-

elingtoaddressthesequestions.TheDSCformedadecisionreviewboard,chaired

byZarellaandBarabba,tooverseetheprojectandthemodelingteamthenbegan

torefinethemodelandgatherthedataneededtocalibrateit･Theyhad20days.

2.2,2 E】'-lbora軸 gthenilodLng

ThemodelingteaminterviewedpeopletllrOughouttheorganizationtounderstand

theissuesandgatherdata･ThroughthemeetlngSOfthecoreandmodelingteams theyopenedupthemodeltocriticalreviewandpresentedinterim resultsfor discussion.

Oneareaforimprovementwasthetreatmentofthecompetitionandsegmen-

tationofthemarketintodifferentvehicletypes.Somearguedforexplicittreatment

ofeverymajormanufacturerandmarketsegment･BrandloyaltylSimportant: PeoplewhoboughtGMcarslasttimearemorelikelytobuyanotherGMcarthan

non-GMowners.TheyalsoarguedthatGMcustomersweredifferentfromFordor

Hondacustomersandthatmarketsforluxurycars,familysedans,sportutilityve- hicles,andsoonwerealldifferent.Theteamcounteredthatthedatarequirements

forsuchadetailedmodelwouldbeenormousandwoulddelaydevelopmentofa

usefulmodel.Theypreferredaniterativeapproach,withmorelimiteddisaggrega- tion;ifsensitivltyanalysisshowedthatfurthersegmentationwasneededthey

couldthenrevisethemodeltoincludemoredetail.Theteamagreedtoseparatethe

Chapter2 SystemDynamicsinAction 49

marketintoGM andnon-GM vehiclesbuttorepresentonlyasingleaggregate

vehicletype.

Anotherimportantareaofdiscussionwasdisaggregationofthecustomerbase. Paralleltotheflowofcarsbetweenthe"ontheroad"and"forsale"stocksare

stocksandflowsofdrivers.Everycartradedinmovesacustomerfrom"onthe

roadHtoHinthemarket;"everyneworusedcarsoldputsadriverontheroad

again.Changesintherelativeattractivenessofnewandusedcarsshiftthepropor-

tionofdriversinthemarketoptlngforanewcar.Thechoicebetweennewand

usedvehiclesalsodependsontheirpastbehavior.Thechanceacustomerwill

lease,buynew,orbuyuseddependsonwhetherheorsheleased,boughtnew,or

boughtusedlasttime.Somemembersoftheorganizationpolntedoutthatthecom-

pany,throughextensivemarketresearch,alreadyknewalotaboutconsumerbe-

haviorinthenewcarmarket.Theyinsistedthatthedynamicmodelincorporate

thesedatasotheDSCcouldspeakwithonevoiceandavoidtheneedtoreconcile

conflictingmodels.

Toaddressthebrandloyaltyandconsumerbehaviorissuesthemodelingteam

disaggregatedthecustomerbaseintoseveralcategories:thosewholeasedanew

car,purchasedanewcar,Orpurchasedusedcarsofvariousages.Figure2-2Shows

asimplifiedrepresentationoftheresultingtransitionmatrix･Eachentryinthema-

trixistheprobabilitythatbuyerscomingfromaparticularcategoryshowninarow

will,whentheynexttradein,movetothecategoriesshowninthecolumns.The

actualmatrixhadtwiceasmanycategoriesasitincludedprobabilitiesforeach

purchaseoptlOnfわrbothGM andnon-GM vehicles.

Thetransitionprobabilitiesinthematrixwerenotconstantbutchangedas

theprlCeSOfnewandusedcarschanged.LowerpaymentsonGMleasesincrease

FIGURE2-2 Thematrixshows

theprobability

p(=)thatcus- tomersineach

categoryshown inrowiwHl,on

trade-in,move

tothecategory

incolumnJ. Thetransition

probabilitiesin thefulHmode一

arevariableand

dependonrelative

prlCeS.Thefull

matrixdisaggre-

gatesGMand non-GMvehicles.

NewCar

New

1-Yr一〇】d

2-Yr一〇ld

3-Yr一〇ld

4-YトOFd

oM= TO= 武芸DG誓言gt70.焉,a:oy挙 :tJSbt:

PurchaseCa｢LeaseUsedCarUsedCar∪sedCarUsedCar

p(i,j)

Source:AdaptedfromGMDecIS10nSupportCenterdiagram･Usedwith permlSSion.

50 PartI PerspectiveandProcess

theproportionoptlngforaGM lease,whilelowerusedcarprlCeSincreasethe shareofpeoplebuyingusedcarsattheexpenseofnewpurchasesandleases.The responsetosuchchangesdifferedforeachcategoryofcustomer.

Thedisaggregationofthemodelwasnotaccomplishedinonestepbutinsev- eraliterations･Ateachstagemodelingteammembersmadesuretheyunderstood thestructureandbehaviorofthemodelandpresentedittoZarellaandhisteamfor commentandreview.Eachiterationtheyincorporatedthecriticismsandsugges- tionstheyreceived.Evenwiththelimiteddisaggregationofthemodelthedata challengeswereformidable･Giventhe20-daydeadline,theteamhadtousedata alreadyavailableinvariouspartsoftheorganization.Themarketresearchdatafor newcarswereexcellent.Dataonleaslng,arelativelynewphenomenon,were

sketchy･Andconsistentwiththeprevailingmentalmodelthatdownplayedthe usedcarmarket,therewasalmostnoresearchdescribinghowpeopletradedoff newandlatemodelusedvehicles.Theydrewonthebestdatasourcesavailable andusedjudgmentandqualitativedatawherenumericaldatawerenotavailable.

Attheendofthe20daystheteammetagalnWithZarellaandhisteamJnstead ofpresentlngthemodelandresults,theyconfiguredthemodelasaninteractive managementflightsimulator･A"dashboard"containeddialsandgaugesreportlng standardaccountinginformationsuchasinventorylevels,salesvolumes,prices, marketshare,andprofitability.Playerssetproductiontargets,incentives,lease tems,andsoon.Byclickingabuttononthescreenplayerscouldgetadditionalin- formationincludingthestructureandassumptlOnSOfthemodel.

ByplayingthegameinsteadoflistenlngtOapresentation,Zarellaandhisteam exploredthedynamicsofleasingforthemselves.Theycouldtryvariousstrategies, fromaggressivesubventionofleasestopullingoutoftheleasemarketaltogether, andseetheimpactonsalesandprofitsintheshortrunandthelongrun.TheydisI coveredthatthefullimpactofleaslngdecisionstookupt05yearstoplayout. Whileleaslngdidprovidealifttosalesintheshortrun,itoftencausedproblems whentheoff-leasecarsreturnedtothemarket.

After20daysthemodelingprocessrevealedthechallengesleasingPOSedfTor thecompanyandindicatedpreliminarypolicyrecommendations.However,before anyconsensusfわractioncouldbedeveloped,theprocesshadtobebroadenedto includeotherkeydecisionmakersthroughoutNorthAmericanOperations(NAO).

ThemodelingteambegantoworkwiththeLeasingStrategylmplementation Team,ataskforceincludingpeoplefrommarketing,finance,andotherfunctions. Theirmandatewastoboostmarketshareandprofitability･Theydidn'tthinka modelwasnecessary,didn'ttrustthemodelingapproach,andopposedtheinitial recommendations.Viewedthroughthelensoftheirmentalmodel,thisposi- tionwasentirelyrational･Thesuccessofleaslngandstrengthoftheusedcar marketprovidedampleevidencethatcompetitiveleaslngWasessentialtoGM's Strategy･

Workingwithyourcriticsisoftenthebestwaytoimproveyourunderstanding ofcomplexissues.Overthenextfewmonthsthemodelingteamrefinedthemodel structure,improvedthedataandcalibration,andtestedthemodeloverawide rangeofconditions.Theymetwiththeleaslngteamaboutonceamonthtopresent interimresultsandlistentocrltlqueS.

Chapter2 SystemDynamicsinAction 51

2.2.3 PolicyAnalysis Astheirconfidenceintheformulationsandcalibrationofthemodelgrew,theteam

turnedtopolicyanalysis.Policyleversincludeleasetermsandsubventionlevels,

alongwithpurchaseincentives,fleetsales,andvariousdecisionrulesforproduc-

tion.Theimpactofeachpolicycombinationdependedonthepoliciesofthecom-

petitorsandahostofmarketuncertainties,from changesintheeconomy,

demographics,gasolineprices,andinterestratestochangesintheunitcostsof

eachcarmaker,Carquality,andbrandloyalty.

Thecombinationofpoliciesandmarketscenariosdefineapolicymatrix.The

teamusedthemodeltofindtheoptimalleasepoliciesforeachcellinthematrix.

Figure213ShowsasampleillustratingthenetpresentvalueofGM profitsasa

functionofleasingpolicy(noleasingvs12-,3-,or4-yearterms)foreachcombi-

nationofcompetitorleasetermsandeconomicgrowthscenario(stable,boom,or recession).

ThepolicyanalysisShowedthattherewasnogolngback:Profitswithoutleasl

lngWereconsistentlynegative,reflectingtheattractivenessofleasingtOconsumers

andtheprlSOner'sdilemmathatunilaterallystopplngleasingWhilecompetitors

continuedtoofferitdramaticallyreducedGM sales･

TheanalysisalsoshowedthatGM'sprofitswereconsistentlyhigherwith4-

yearleaseterms.Four-yeartermsweresuperioroverawiderangeofcompetitor

strategleSanduncertainties.LongertermshavetwomainbeneficialeffectsIFirst,

thoughshortertermsdoshortenthetrade-incycle,theresultingglutofnearlynew

carsdepressesusedpricessomuchthatthesubstitutionofusedfornewpurchases

offsetstheirbenefit.IntermsofFigure2-1,theUsedCarMarket,UsedCarQual-

1ty,andPurchaseOptionloopsoverwhelmthebenefitoftheLeaseTermandLease

FIGURE2-3 PolicyanalysIS

ThepollCymatrix showsthe

simulatednet

presentvalue

(NPV)ofGM

profitsasa functionofGM's

leaslngPOllCy

(noleasingor21tO

4-yearterms)for eachcombination

ofeconomic

scenarioand

competitor

strategy･

!Jle u a 3S

3 !∈ O u O 3 山

a lq C tS

u o

!ss a 3 O tj

CompetitorLeaseTerm

2year 3year 4year

Source'AdaptedfromGMDSCdiagram.Usedwithpermission･

FIGURE2-4 Bathtub

diagramto iHustrate

theimpact

oHeaslng

PartI PerspectiveandProcess

Incentiveloops.Four-yeartermsmeanthecarscomlngOffleasearelessattractive

substitutesfornewcars,whilestillspeedingthetrade-incyclesomewhat.

Thesecondbenefitoflongertermsisamoresubtle,disequilibriumeffect.By increaslngthesubstitutabilitybetweennewandnearlynewusedcars,short-term

leasesincreasedthevulnerabilityofearnlngStOindustrydownturns.Ratherthan

showlngCOmplexdiagramssuchasFigure2-1toexplainwhy,Pudardeveloped Figure2-4,showingthestockoflatemodelvehiclesasabathtub.Thebathtubdi-

agramusesasimplemetaphortoillustratethedynamicsofleaslng.Thestockof

newandnew-CarsubstitutesisincreasedbyproductionandtheflOwoflatemodel

usedcarscomingofflease(andoutofrentalcarfleets).Salesdrainthetub.

Duringrecessions,autosalesdrop.Thewaterlevelinthetubrises.Camakers

comeunderpressuretocutprlCeSandsubsidizeleasestodraincarsoutofthetub

fasterandalsocutproductiontostoptheinflow.However,theflowofnewcarsub-

stitutesintothemarketfromexplrlngleasescannotbeturnedoff.Whenarecession

hits,leasessoldduringtheprecedingboomcontinuetoexplre,boostingthelevel

inthetub･LowerusedcarprlCeSandconcernsoverfutureincomeleadmorepeo-

pletoturntheirofトleasecarsbacktothelessorratherthanexercISlngtheiroptlOn

tobuy･Thelargertheshareofnewcarssoldthroughleaslng,thelargertheun-

stoppableflowofreturningVehicles.Pricesareforceddownevenfarther,andpr o -

ductioncutsmustbeevendeeper,slgnificantlyerodingprofits.

Theteam usedthebathtubdiagram inpresentationstoseniormanagers

throughoutthefirm,includingallbrandmanagers.Ofcoursetheformalanalysis,

modelstructure,andotherdetailswerepresented,butthebathtubprovidedapow-

erfulmetaphortocommunicateanimportantdynamicinsightandhelpedinthe difficultprocessofchangingmentalmodels.

Whydoshort･term leasesmakeusmorevulnerable duringaneconomicdownturn?

Production NewCarSubstitutes

.WhenindustrydemandfaHs,theflowofreturningleasecarscannotbestopped -Pricesofusedcarsw川bedrivendown; -NewcartransactionpnceswiHbeforceddown; -SomereturningJesseeswilloptforcheapusedcars.

●Pricedoesnotalterthesupplyofnewcarsubstitutes SourcerrGMDecisIOnSupportCenter.UsedwlthpermlSSion.

Chapter2 SystemDynamicsinAction 53

PudarandhisteammadetwomainrecommendationstoZarellaandother

seniormanagersinNAO･First,GMshouldshiftincentivestofavorlongerleases andmovethemixoftheleaslngportfoliotowardahigheraverageterm.Second, theyrecommendedthatallproposalsfornewprlClngandmarketingprogram sfor一 mallyincludeanalysisoftheirimpactontheusedcarmarketanditsfeedbackto thenewcarmarket.Theyrecommendedthemarketresearchorganizationcreate newclinicstoassessnew/used/leaseconsumerchoicebehaviorsothatup-to-date datawouldbeavailableonanongolngbasis.Theyalsosupportedchanglngthe incentivesandmetricsformanagersofthecargroupstoincludetheprofitorloss GMACrealizedasaresultofleaslng,

Manybrandmanagersandbrandanalystswereinitiallyopposedtotheserec- ommendations･Theyarguedthatconsumershadbeenconditionedtoprefershort- termleases･CompetitionwasintenseandGM'smarketsharehadbeenslipplng. Ford,inparticular,wasaggressivelypushing2-yearleaseswithsignificantsub- vention;unlessGM respondedinkind,theyargued,marketsharewouldsuffer more･Giventhetremendouspressuretheyfacedtostaycompetitive,theywerenot willingtosacrificemarketshareandprofitstodaytoavoidthepossibilitythatleasl lngmightleadtoproblemsinafewyears.Brandmanagersandthesalesorganiza- tionputstrongpressureontheseniormanagementofNAOtoincreaseresidual levels･TheypointedtostrongusedcardemandandrisingusedcarpricestOJuStify increasedresiduals.Theyalsoarguedthatsubventionlevelsshouldbeincreased

evenfurtherabovethehigherresidualstheywererecommending･Finally,theyar一 guedforadecreaseinthefractionofoff-leasevehiclesGM predicteditwould havetotakebackatleaseend.Thecostsofsubventionaredeferredbecausethey areonlyrealizedwhencarscomeofflease.AccountlngrulesrequlreCarmakersto setasidereservestocovertheexpectedcostofsubvention;thesereservesreduce currentperiodearnlngS･Theamountsetasideinreservesdependsonthefraction ofcarstheyexpecttobereturned.IfcustomersexercisetheiroptlOntObuywhen theirleaseexplreSthenGMACneverhastopaythedifferencebetweenthesub- ventedresidualandmarketvalue.Manybrandmanagersbelievedthatthestrong usedcarmarketmeantreservesweretoohighandcouldsafelybecut,allowingthe cardivisionstoshowhighercurrentperiodprofitswhileincreasingmarketshare. Theysupportedtheircasewithspreadsheetsinwhichrecenttrendstowardhigher usedcarprlCeSandhighercustomerretentionofoff-leasevehicleswereassumed tocontinue,thatis,inwhichallfeedbacksbetweenthenewandusedmarkets werecut.

Thedynamicmodel,incontrast,suggestedthatusedcarprlCeSWOuldsoonde- clineasthelargevolumeofleasedandfleetvehiclessoldinthelastfewyears reenteredthemarket.Theteamヲsanalysissuggestedsomeofthesurgeinusedcar prlCeSWasatemporaryblipgeneratedbytheusedcarsuperstoresastheybought heavilytostocktheirlots.Whenthatperiodofinventorybuildingended,usedcar saleswouldslumpwhiletheflOwofcarscomingOffleasecontinued.Asused prlCeSfellbelowthecontractedresiduals,morecustomerswouldterminatetheir leasesearlyandfewerwouldexercisetheiroptiontObuy,decreaslngtheretention fractionandboostingthesupplyoflatemodelusedcarsstillmore.GMwouldhave totakeasignificantchargeagalnStearnlngSforresidualreconciliation,andnewcar saleswouldsufferascustomersoptedforlatemodelofflleasevehicles.

FIGURE2-5

UsedcarprlCeS, 1989-1999

Jndexshowsthe

usedcarandtruck

componentofthe USConsumer

PriceIndex,

seasonaHy adjusted.

PartI PerspectiveandProcess

SeniormanagersatNAOdecidedtofocuson36-to48-monthtermsandelim-

inated2-yearleases.Theyalsochosenottoincreaseresidualvaluesandmovedto fullaccrualofresidualriskincalculatingreserves.Thesedecisionsmadesubven- tionmuchmoreexpensivetobrandmanagersandraisedleasepayments.

2.2.4 ぎmpactandFoHow･up In1997afloodofoff-leasevehiclesinundatedthemarket･UsedcarprlCeSfellsig- nificantly(Figure215).Thedatashowtheaggregateforallusedcars;thedropfor latemodelvehicleswasmuchsteeperandwasmostsevereinthesegmentsin

whichleasinghadgrownmostrapidly. AsprlCeSfell,fewercustomersoptedtokeeptheircars.TheConsumerBankl

lngAssociationreportedthatthefractionofvehiclesfromexplrlngfull-termleases returnedtolessorsJumpedfrom29%in1997to39%in1998･Aboutthree-quarters ofalloff-leasevehiclesretumedtolessorsincurredlosses;theaveragelossin1998

was$1878pervehicle,220%morethantheaveragefor1993. GM'searlyactionhelpeditavoidtheselosses,whileothercarmakersfound

themselvesfacinghugereconciliationcharges.ProfitsatFordCreditCorporation fell$410millionin1997Comparedt01996,a28%drop,largelyduetolosseson

offlleasevehicles.AtGMAC,netincomefromautomotivefinanclngoperations fellonly$36million,lessthan4%,andoverallGMACprofitsrosemorethan6%.

In1997severalcarmakers,includingFordandNissanUSA,attemptedtoprop

upwholesalepricesfortheircarsbypayingdealerstokeepofトleasecarsinstead ofreturningthemtothemanufacturerforsaleatauction.Fordpaiddealers$700to

$6000(dependingonthemodel)foreach21yearOldofflleasevehiclethedealer agreedtokeep,dippingIntoitsresidualreservesforthefirsttimetodoso.This policyreducedthenumberof2-year-oldcarssoldatauction,butofcourse,since retentionofthesecarsaddedtodealerinventories,thenumberofthesecarsdealers

boughtatauctionfellbythesameamount,Sowholesalepricescontinuedtoslide.

In1998GECapitaldroppeditspartnershipwithChryslertofinanceleasesbe- cause,asAutomotiveNews(24August,p.1)reported,

0 0

L = 寸?

N96

トi

■】l

llll

lll

1988 1990 1992 1994 1996 1998 2000

Source:USBureauofLaborStatistics,seriesCUSROOOSETAO2.

Chapter2 SystemDynamicsinAction 55

GECapitalAutoFinancialServicesgotburnedonresidual-valuelossesin1997. Muchofthatwasduetooff-leaseproductsfromChrysler...GECapitalcited residuallossesasonereasonforthedeclineinoperatingProfitsforConsumer Services,theGEunitthatincludesAutoFinancialServices.Profitsfellfrom $1.3billionin1996to$563million[in1997].

In1998netincomeatFordCreditrose$53millionoverthedepressedlevelof

1997butremained25%belowthenetfor1996･4GMAC'snetonautofinanclng

rose$74millionover1997,ariseof4%over1996,andtotalGMACprofitfor

1998rose$181millionover1996,againof15%.In1998Fordandothercar-

makersbelatedlyfollowedGM'Sleadandbegantomoveawayfromshort-term

leaslng.

Since1996theleaslngmodelhasbeenupdatedseveraltimes,disaggregated

furthertoseparatethecarandlighttrucksegments,andusedtoexamineissues

suchassalesoffleetvehicles.Themodelisnowusedonanongolngbasisby

NAO'sPortfolioPriclngTeam,thegroupresponsibleforreviewandapprovalof

allprlClngandiIICentiveprogramsinNorthAmerica･

Pudar,nowDirectoroftheDSC(renamedtheStrategySupportCenter[SSC]),

reportsthattheSSCcontinuestoapplysystemdynamics,incombinationwith

otheranalyticmethods,toawiderangeofissues,fromnegotiatingJOlntVentures

wlthforeigngovernmentstodesigningbusinessplansfornewproducts,services, andbusinessunits.

2.3 0NTlMEAN【)uNDEF3BL旧GET:

THEDYNAMICSOFPROJECTMANAGEMENT5

In1970,Ingal1sShipbuildingofPascagoula,MississIPPl,wonamajorCOntraCttO

buildafleetof30newdestroyersfortheUSNavy･Combinedwithits1969con-

tractfor9LHAs(anamphibiousassault/aircraftcarrier),Ingallsfounditselfinthe

happypositionoflandingtwoofthelargestshipbuildingprogramsintheworld

andlookedforwardtohealthysalesandprofitsforyearstocome.Bythemid1

1970S,however,Ingallswasindeeptrouble,facingcostoverrunsprojectedtoexI ceed$500million.Withannualsalesinthemid-1970sof$500-800million,the

overrunthreatenedtosinklngalls,anditsparentLittonlndustries,altoge血er.Ad-

justedforinflationtheoverrunwouldexceed$1.5billionin1999dollars.

BothcontractswereawardedastotalpackageprocurementprojectsWithafirm

fixed-pricecontractstructureinwhichIngalls"wasprovidedonlywiththeperfor-

mancespecifications,andwasthereaftersolelyresponsibleforallsystemdesign,

detaileddesign,materialsprocurement,plannlng,teStlng,andconstructionH

(Cooper1980,p.22)｡

Bothprogramsinvolvedinnovativeandtechnicallysophisticatednewdesigns･

TheDDclassmultimissiondestroyersweretwiceaslargeasearlier"tincans."The

4Excludingone-timeincomefromassetsales･

5ThissectionisbasedonCooper(1980)andpersonalcommunicationwithKenCooper (president,Pugh-RobertsAssociates),RichGoldbach(formerlywithIngallsn-ittonIndustriesand currentlypresident,MetroMachineCorporation),andmanyothersatPugh-RobertsAssociates. Ⅰ'mgratefulfortheirhelp.

56 Part∫PerspectiveandProcess

LHAwasalsoanentirelynewdesign.Morethan20Storieshighandthreefootball fieldslong,eachLHAcarriesacomplementof2000battle-readyMarinesand200 Combatvehiclesthatcanbedeployedbylandingcraftandseveraldozenheli- copters.TheDDandLHAcontractsrequiredamassivemobilizationoflngalls're- sources.Alreadyoneofthelargestshipyardsintheworld,Ingallsdoubledits workforcetomorethan20,000.Duringthistimetherewereshortagesofsome skilledtradesandcriticalmaterials.Ingallsalsohadtocreateneworganizational structurestomanagethetwoprograms.

Large-scaleprqJectsareamongthemostimportantandconsistentlymisman-

agedendeavorsinmodernsociety.Large-scaleprojectsincludethedesignandcon- structionofcivilworksandinfrastructure(e.g.,bridges,tunnels,powerplants,and telecommunicationsnetworks),militarysystems(e.g"aircraft,ships,andweapons systems),andnewproductsineveryindustry(e.g"software,automobiles,semi- conductorchipdesign,andwaferfabconstruction).

Projectsofalltypesroutinelyexperiencecostoverruns,delays,andquality problems.CooperandMullen(1993)examinedasampleoflargecivilianandmil- itaryprojects(averaging130,000person-hoursofplannedworkoveraboutayear forthecivilianprojectsand170,000person-hoursofplannedworkovermorethan 2yearsforthemilitaryprojects).Theyfoundcommercialprojectscost140%and took190%aslongasoriginallyscheduled,whiledefenseprojectscost310%ofthe orlglnalestimatesandtook460%aslongtocomplete.

Delays,costoverruns,andqualityproblemsincommercialnewproductde- velopmentcankillacompany,particularlyinhigh-velocltyindustriessuchassoft- wareandhightechnology.Overrunsanddelaysincivilworksandmilitaryprojects canaffecttheeconomicvitalityofaregionandtheabilityofanationtodefend itself'.

2.3.1 TheClaim

TheNavyandIngallsdisagreedsharplyoverthecausesofthedelaysandcost ove汀un.IngallsbelievedthemajorityOfthecostoverrunwascausedbytheac- tionsoftheNavy.Asiscommoninlarge,lengthyprqJects,thetechnologleSand systemstobeusedintheDDandLHAshipswerenotmatureatthetimethecon- tractswereawarded.Technologiesfornavigation,intelligence,communications, andweaponssystems,forexample,wereadvancingrapidly,andtheNavynat u -

rallysoughttoincorporatethemostup-to-datesystemsintheships･RichGold- bach,thenaseniormanageratlngallsandoneofthekeyparticlpantSintheclaim,

commentedthat"Ingallswasconvincedthatthegovernmentinterferedwiththe deslgnfortheLHAfromthestartbymicro-managlngthedesignprocess."As high-leveldesign,detaileddesign,andevenconstructionproceeded,Ingallsre- ceivedmanythousandsofdesignchanges血･omtheNavy.Ingallsbelievedthat muchoftheoverrunwascausedbytheimpositionofthesedesignchanges.After theNavyrepeatedlyrefusedtocompensatelngallsforthesecosts,Ingallsbrought aclaimagainsttheNavytorecoverthe$500millioninlossesitexpected.

Suingyourcustomersisalwaystricky.hthecaseoflngallsitwasparticularly delicate.Ingallsbroughttheclaimearly,whilethetwoprogramsstillhadmany yearstorunJngallshadtocontinuetomanagethetwoprogramsandmaintaina

Chapter2 SystemDynamicsinAction 57

goodworkingrelationshipwiththeNavywhilesimultaneouslypursuingtheclaim･

Further,sincecommercialshipbuildingwasindeclineintheUS,theNavywas

Ingalls'mostimportantcustomerandwouldbefortheindefinitefuture･6

TheNavyconcededthatithadgeneratedthedesignchangesbutarguedthat

theirimpactwaslimitedtothedirectcostofreissulngthespecificationsandre-

workingtheaffectedengineeringdrawlngS･Thetotalcostofthesedirectimpacts

wasasmallfractionofthetotalclaimJngallscounteredthatadesignchangecould

createmuchlargercosts,forexample,byalterlngthesequenceoftasksandre-

qulrlngovertimeandunscheduledhiringthatinterferedwithotherphasesofthe

work,dilutedexperience,andreducedproductivityeveninworkphasesnotdi-

rectlyaffectedbychangeorders.Ingallsbelievedsuchrippleeffectscouldmulti-

plythedirectimpactofachangenoticemanytimes,leadingtoslgnificantoverall

HdelayanddisruptlOn."

TheNavycounteredthatthesupposeddelayanddisnlptlOnWereactuallythe

resultofcontractormismanagementordeliberateunderbiddingtowinthecontract.

DisputesoverthedelayanddisruptlOnCOmpOnentOfpriorclaimsthroughoutthe

defenseindustryoftendraggedoutovermanyyears･TheNavyhadneverpaida

significantdelayanddisruptionClaim.

2.3.2 書nitiaEModelDeveJopmenモ

Ingallsspentseveralyearspursulngtheclaim,buttraditionalprojectmanagement

toolsdidnotprovideameanstoquantifytherlPPleeffects.Ingallsturnedto

system dynamicstoquantifythedelayanddisruPtlOnCreatedbyNavydesign

changes･Themodel,developedbyPugh-RobertsAssociatesofCambridge,

Massachusetts,simulatedallphasesoftheDDandLHAprojects,fromtheaward

ofthecontracttothedeliveryofthelastship,then5yearsinthefuture.

Themodelultimatelycontainedmanythousandsofequations,averylarge

modelindeed(especiallyconsideringthestateofcomputertechnologyatthetime).

Itbegan,however,asamuchsmallermodeldesignedtoilluminatethebasicfeed-

backsthatmightberesponsibleforrippleeffects.Themodelingteam worked

closelywithlngalls'claimmanagementorganization,includingmanagers丘･omall

majorPhasesofeachprogramandkeyattomeys.LeadmodelerKenCooperde-

scribedtheprocessthisway(1980,pp.26-27):

TheIngallsprojectteamguidedandreviewedthedecisionofwhatelements toincludeinthemodel,andwithwhatmeasuresandinwhatdetailtoinclude

them...lD]ozensofindividualsinallstagesofshipbuilding,fromworkers throughvicepresidents,wereinterviewed.Theyofferedqualitativeandquantitative observationsonshipdesignandconstrlユCtion.Asthedesignofthemodelbeganto gel,thenumericaldatarequlrementSWereClarified;amassivedatacollectionef- fort,lnCOnCertWithotherelementsoftheclaim,wasundertaken.Thesedataand

infわrmationprovidedenoughmaterialtoassembleapreliminarymathematical modelofaslngleworkphase.Theequations,parameters,anddetailedoutput werereviewedbytheprojectteam,andseveralmodelmodificationsmade.

6Dueinparttotheproblemsencounteredintheprogram,thenumberofLHAsutlimately builtwascutto5･LHA5,theUSSPeleliu,wascompletedinmid1980,aswasthelastDDclass destroyer,USSFletcher.

FIGURE2-6 Stockandf一ow

structureofa

projectPhase

Rectang一es

representthe stockoftasks,

Straightlinesand

valvesrepresent flowsoftasks

between

categories

(chapter6).

Qualityisthe fractionoftasks

donecorrectly.

Thediagramis

nlgniysimplifieci andomitsseveral

taskcategories andflowsincluded

inthefu川model.

PartI PerspectiveandProcess

2.3.3 DynamicHypothesis

AfulldescrlPt10nOfthefeedbackstructureofthemodelisbeyondthescopeofthis

discussion;thissectionprovidesonlyafewillustrationsofthetypeofrippleef- fectsthemodeladdressed.

Figure216showsahighlysimplifiedstockandflowstructurefortheflowof

workwithinaslngleprq】ectphase.Thetaskscouldbehigh-levelsystemsdesign

tasks,preparationofdetailedenglneerlngdrawlngS,OrCOnStruCtionofavessel.

Therectanglesandvalvesrepresentthestockandflowstructureofthesystem17

Thestocksrepresenttheaccumulationsofworkindifferentcategories;thevalves

representtheflowoftasksthroughthesystem.Initiallyalltasksareinthestockof

WorktobeDone.CompletingataskrequlreSresourcesSuchasaproductivelabor

forcewithapproprlateSkills;thenumberandproductivityOfthelaborforcevary

overtimeasprojectconditionschange.Taskscanbedonecorrectlyorincorrectly,

dependingonthequalityofthework.Tasksdonecorrectlyaddtothestockof

WorkReallyDonewhiletaskscontainlngerrorsOfvarioustypesaddtothestock

ofUndiscoveredRework.Workqualityisoftenqultelow,asnewIPrOductdevel-

opmentandlarge-scaleprojectsusuallyInvolvenewtechnologies,materials,and

systemsandofteninvolveuniquenewcircumstances.CooperandMullen(1993)

PeopleProductivityQuality

ObsoJescence Rate

cSstomer

Cha∩ges

Source:AdaptedfromadlagramdevelopedbyPugh-RobertsAssociates,Cambridge,MA.Usedwith pe｢mlSSion.

7Mathematically,eachstockistheintegraloftheflowsinlesstheflowsout.Stocksandflows arediscussedinchapters6and7.

Chapter2 SystemDynamicsinAction 59

foundtheaveragefractionofworkdonecorrectlythefirsttimeintheirsampleto

be689uorcommercialprojectsandjust34%fordefenseprojects.

Uncoverlngerrorstakestimeandresources.Often,errorsareonlydetectedby

adownstreamphase,aswhenadesignflawisdiscoveredduringtheconstruction

phase.Tasksinthestockofundiscoveredreworkarethereforeperceivedtobe

completeandaretreatedasdonebytheorganization･Discoveryoferrorsbyqual-

1tyassurance,teStlng,Oradownstreamphasemovestheimperfectlydonetasksto

thestockofKnownRework.CooperandMullen(1993)foundaveragereworkdisI

coverydelaysofabout9monthsforbothcivilandmilitaryprojects,aSignificant

fractionofscheduledprojectduration･

Changesincustomerspecificationshaveeffectssimilartothediscoveryof

errors.Specificationchangesmakesomeworkpreviouslydonecorrectlyobsolete,

movingthosetasksfromthestockofWorkReallyDonetothestockofKnown

Rework.Theaffectedphasemustrecallworkitpreviouslyreleasedtootherphases

anduponwhichthosedownstreamphaseshavebasedtheirownwork.Theor一

ganizationmustthenincreasetheresourcesandattentiondevotedtorework,slow-

1ngCOmpletionofremainlngbaseworktasksandpotentiallydisruptlngtheentire

projeCt18

0bviouslycustomerchangesthatmakecompleteddesignworkobsoleteare

costlybecausetheaffectedtasksmustbereworked;thesearethedirectimpactsof

changestheNavywaswillingtopayfor.Buttheindirecteffectscanbemanytimes

larger.Figure217Showsafewofthefeedbacksthatexplainhowtheindirectef-

fectsofcustomerchangescouldbeamplified.

Asaprojectfallsbehindcontractorshaveonlyafewchoices･Theycanputthe

existingWOrkforceonovertime,thusincreaslngtheeffectivenumberofpeople

workingontheproject.Thisnegativeorbalancingfeedbackistheintendedeffect

ofovertimeandisshowninthediagrambysolidlines.However,excessiveorex-

tendedovertimecausesfatigueandburnout.Productivityandqualityfall,reducing

progressandincreaslngthestockofundiscoveredrework.Burnoutalsoleadsto

absenteeismandattritionasemployeesrequesttransfersorquit,reducingthenum-

berofpeopleontheproJeCt･Theseunintendedeffects,shownasdashedlines,form

positive(self-reinforcing)feedbacksthatactasviciouscyclestoundercutthe

progress-en h anclngeffectofovertime.Toavoidthesideeffectsofovertimemore

peoplecanb ehired(anotherbalancingloop).Butrapidhiringdilutestheexperi-

encebaseoftheemployeesIIfthepoolofqualifiedworkersinthereglOnissmall

relativetoh iringneeds,acceleratedhiringlowerstheaveragequalityofavailable

candidates.RecruitlngStandardsoftenerodesovacanciescanbefilledquickly･A ll

theseeffectslowerproductivltyand qualityandslowprogressevenasmanage一

mentseekstoboostheadcountandspeedprogress.

8Mostlargemilitaryandcivilianprojectsspecifydeadlinesfordelivery･Failuretomeetthe

deadlineleadstopenalties,knownasliquidateddamages(LDs),foreverydaytheprojectislate., LDscanrapidlymounttomanymillions･IndisputessuchasdiscussedheretheLDsformthe prlmarybasisforthecustomer'scounterclaimagalnStthecontractor･Inseveralcasesforwhich systemdynamicsmodelshavebeenusedthedifferencebetweenthecontractordelayanddisrupt10n claimandthecustomer'scounterclaimwasseveralbilliondollars.EvenwhenLDsdonotapply,as forin-housecommercialproductdevelopmentprojects,everydaytheprojectislateerodesthe competitivenessoftheproductandthesalesandprofitsitcangenerate･

60 PartIPerspectiveandProcess

FIGURE2-7 Sideeffectsofcorrectivemeasuresleadtoviciouscycles

AscustomerchangescauseaprojecttOfa"behind,managementcanacceleratethe schedule,useovertime,andhiremorepeople,formlngnegativefeedbacksdesigned togettheprojectbackontrack(Solidlines).However,eachofthesenegativeloopstrig-

gerssideeffectsthatundercuttheintendedeffects,formingviciouscycles(positivefeed- backs,shownbythedashedlines).

Source:AdaptedfromadlagramdevelopedbyPugh-RobertsAssociates,Cambndge,MA.UsedwEthpermISSion.

Asaprojectfallsbehindschedulemanagementoftenpressuresemployeesto

workharderandcompressestheschedulebyoverlapplngactivitiesthatshouldbe

doneinsequence.ApparentproductivltyrlSeS,buttherearealsounantlClpatedside

effects.Schedulecompressionforcespeopletodoworkoutofsequence,meanlng

importantinformationormaterialsfrom upstream phasesarenotavailable･ Detaileddesignmaystartbeforesystemdesignismatureandstable.Prototype

buildsmaybeginbeforecomponentspecificationsarecomplete19schedulecom-

pressionalsoleadstoworksitecongestion,beitoverloadedCAD/CAMfacilities

inenglneenngOraCrowdedconstructionsite.Managersandsupervisorsfindtheir

9Manyorganizationstodayhaveadoptedconcu汀entenglneerlngpracticesdesignedtoshorten developmentcycletimes.Successfuldeploymentofconcurrentenglneerlngisdifficultandevenin highlyconcurrentprogramsthedegreeofoverlapbetweendifferentphasescanbetooaggressive, leadingtoexcessiverework.SeeFordandSterTan(1998a)and(1998b)forsystemdynami.Cs modelsofconcurrentenglneerlng,WithapplicationstOSemiconductordesign.SeealsosectlOn14.5.

Chapter2 SystemDynamicsinAction 61

timeisincreaslnglyconsumedbymeetlngStOWOrkoutconflictsarislngfromthe acceleratedscheduleandadhoc,last-minutecoordinationofout-of-Sequenceac-

tivities･Stressfromworkpressure,increasedfirefighting,andconstantchangesin schedulescanleadtomoraleproblemsthatcutproductivltyandqualityandin- creaseabsenteeismandattrition･Theseeffectsarefurthermultipliedbytherework cycle･Lowerqualitymeansmoretaskscontainerrors.Becausemanyerrorsarenot discoveredimmediately,subsequentworkbeginsuslngdesigns,materials,andin- formationthatappeartobecorrectatthetimebutarelaterrecalledforrework.

Thuscustomerchangescandisruptanddelayupstreamactivitiessuchassys- temdesign･Thesephasesmustthenrecallsomepreviouslyreleasedwork,sode- laysandqualityproblemscascadetodownstreamphasessuchasdetaileddesign, materialsprocurement,andconstruction.Thedownstreamphasesmustthenredo muchoftheirjob,oftenatgreatexpense(particularlywhenconstructionhasal- readybegun)･TotheextentdifferentprojectssuchastheDDandLHAprograms shareresourcessuchasworksites,workers,supportinfrastructure,andmanage- ment,problemsinonecanspillovertoanother,

Thediagramsabovearehighlysimplified,andmanyotherimportantfeed- backscapturedinthefullmodelareomitted(howmanyothersucheffectscanyou identifyfromyourownexperience?).Buttheyillustratehowapparentlysmall changesincustomerspecificationscansnowballintomuchlargerdelayanddis- ruptlOndespltemanagement'sbesteffortstogettheprojectbackontrack.The modelaugmentedtraditionalprojectanalysisthroughtheexplicitrecognltlOnOf thereworkcycle,variablestaffproductivltyandquality,andthebaneofmostde- velopmentprojects-undiscoveredrework･Conventionally,anyindirecteffects wereviewedasasmalladditionalpercentageoverthedirectcosts･Explicitrecog- nitionofthefeedbackstructuredescribedherehelpedexplainhowtheindirectef- fectsofcustomerchangescouldbemanytimeslargerthanthedirecteffects.

213･4 TheModel岳ngProcess

Themodelingteamassembledthefullmodelbyreplicatingthegenericproject phasemoduletorepresenteachphasefわreachshiplneachprogram.Themajorac- tivities(systemdesign,detaileddesign,procurement,construction,etc.)weredis- aggregatedfurtherwherenecessary;forexample,constructionwasdividedinto severalmajoractivities(e.g.,hull,piping,electrical,etc.)andtheconstruction workforcewasdisaggregatedbymajorcrafts(e.g.,steelworkers,electricians,etc.). Constructionprogressforeachshipwasrepresentedseparately.Eachinstanceof thegenericphasemodulewascalibratedtotheparticularactivltyltrepresented. Theindividualactivities,phases,andprogramswerelinkedbyadditionalstructure representlngOVerallprogrammanagement,progressmonitorlng,SCheduling,hir- 1ng,resourceallocation,andsoon.

Amodelofthisscopecouldneverbebuilt,Calibrated,maintained,orunder- stoodifsuchamodulararchitecturewerenotused.Torepresentsuchadiversear- rayofactivitiesthegenericmodulehadtobeextremelyrobust.Considerableeffort wentintoextremeconditionsteststoensurethatthemodelbehavedapproprlately underanyconceivablecombinationofinputsorconditions(Seechapter21).The teamworkedtoensurethemodelwasconsistentwithallavailableinfわrmation,

62 PartIPerspectiveandProcess

includingthequalitativeassessmentsgleaned血.ominterviewsandobservationsin

thefield,notonlythenumericaldata.

Earlyontheteamcomparedtheoutputofthemodeltothehistoryofthepro-

jectstOdate･Thepurposeofthecomparisontohistoricalbehaviorwasnottoprove

toIngallsthatthemodelwasright,butrathertoidentifyareaswherethemodel

requiredimprovement.Thesecomparisonssometimesidentifiedomissionsand

problems,leadingtorevisionsinmodelstructureandparameters.Othertimes,

discrepanciesbetweenmodelanddatasuggestedthedatawereinconsistentor

incomplete,leadingtoadditionaldatacollection,interviews,andrefinementofthe

valuesandjustificationforparameters･Thisprocessledtothreemajorandmany minoriterationsinthemodel.

Themodelultimatelyreplicatedthehistoricalperformanceoftheprojects

quiteWell.But,asdiscussedinchapter21,itisqulteeasytOfitamodeltoasetof

data.Itisalsonecessarythatthemodelreplicatethedatafortherightreasons,rea-

sonsthemodelersandlngalls'managementunderstandandcanexplaininplain

language.WhileparticularlyimportantintheadversarialsettlngOfalargelawsuit,

theseareimportantinanymodelingprojeCt･Ultimatelytheclientsforanymodel-

1ngProjectWilltakeactiononlytotheextenttheirmentalmodelshavechanged.In

tum,theclients'mentalmodelsareunlikelytochangeunlesstheyhaveconfidence

intheintegrltyandappropriatenessOftheformalmodel.Developingthatconfi-

dencerequiresamodelingprocessthatglVeStheclientstheopportunltytOdelveas

deeplyintothedetailsastheywant,toquestionanyassumptlOn,andtochallenge anyresult.Openlngthemodeltoreviewbytheclientsisalsoessentialforthemod-

elerstoensureitaddressestheissuestheclientcaresmostdeeplyaboutandtogen-

eratethebestmodelforthatpurpose.

TouncovermodelflawsandcreateopportunitiesfortheIngallsteamtochal1

1engethemodelthemodelingteamusedseveralotherprocedures｡Cooper(1980,

p.27)explains:

First,Weestablishedattheoutsetexplicitlimitsofreasonablenessforeachnumeri- calparameterinthemodel;thesewouldnotbeviolatedinordertoachieveamore

"accurate"simulation.Further,thenumericalparametersindifferentsectionsofthe modelwererequiredtobeconsistentwithoneanotherintermsofrelativemagnl -

tude.Theseguidelines.Hwereneverviolated.Themodelwasalsosubjectedtoa seriesof"Shocktests"toassessrobustnessinrespondingasthecompanywouldto radicallydifferentcircumstances.Finally,severaldifferentplausiblecombinations ofequationsandparametersweretestedtoexploreHalternativemodelsHthatmight accuratelyrepresentIngausoperations.

Astimepassedthemodel-generatedProjectionsforscheduleandcoststurnedout

tobequiteClosetowhatactuallyhappened,furtherboostingCOnfidenceintheabil1

1tyOfthemodeltocapturetheunderlyingstructureoftheprojects.

Themodelingteam assessedthesystemwideeffectsoftheNavy'sdesign

changesbycomparlngtwoSimulations.The"as-builtHcasewasthehistoricalsim-

ulationincludingalltheNavydesignchanges;thiswascomparedtotheHwould

have"Caseinwhichthedesignchangeswereremoved.Thedifferenceintotalcosts

andcompletiontimesrepresentedthecumulativeimpactofthedesignchanges.

Sensitivityanalysisthenplacedconfidenceboundsaroundtheestimatedcostofthe

delayanddisruptlOn.

Chapter2 SystemDynamicsinAction 63

Themodelalsoallowedlngallstoestimatetheroleofitsownmanagementde-

cisionsintheovermn.Simulationsofalternativepoliciesshowedhowmuchlower

projectcostsanddurationmighthavebeenifIngallshadmanagedtheprojectmore

effectivelyLTheabilitytoquantifythecontributionofcustomerinterferenceand

contractormismanagementtothedelaysandcostoverrunwasacriticalpartof山e

process･Goldbach(personalcommunication,1999)describedthedisputeresolu-

tionprocessprlOrtOthedevelopmentofthesystemdynamicsmodelas

Justabunchoffinger-polntlng.Acontractorwouldsay"Here'swhatthegovern- mentdidwrong"andblamealltheirproblemsonthat.Thenthegovernmentwould sendtheGAOlGeneralAccountingOffice]intofindallthethingsthecontractor didwrong.Itwentnowhere.

Theproblemwasthatwiththe[prqjectmanagement]technologiesavailable atthetimetherewasnowaytoseparatetheimpactofgovernmentandcontractor problemsorexaminethesynergybetweenthem.Intheendwehadtohavethe abilitytosayHherearethethingsthecontractordidn'tdowellandherearethe thingsthegovernmentdidn'tdowell,andhere'showmucheachcontributedto costsandtime."

TheadversarialsettlngOfalargedisputeaccentuatestheneedforarobust,well-

understoodmodelwhoseparametersandassumpt10nSCanbejustifiedwithinde-

pendentdata.Aspartofthediscoveryprocessinthelawsuitlngallshadtotu仙the

model,documentation,analysts,andsupportingdataovertotheNavy,whichhired

itsownexpertstotrytodebunkit.Acommoncriticismofsuchmodels,andone

usedbytheNavy,isthattheparametersandassumptlOnSare"COOkedHtoachieve

apreselectedoutcome."Garbagein,garbageo叫日仏eywouldsay,andargued血at

themodelwasmerelyacomplicatedrusedesignedtoimpressthecourt.

TheNavy'Soutsideexpertsexaminedandcriticizedthemodel.Aftertheyde-

liveredtheirreports,themodelingteam,alongwithlngallsmanagementandtheir

attorneys,Navyofficials,thegovernment'sattorneys,andtheNavy'SoutsideexI

pertsmetforseveraldaysinalargeconferenceroomtodiscussthecrltlque.Each

issuewasdiscussedindetail,fromhighlevelissuesofmodelingmethodologyand

modelarchitecturetospecificequationsandparameters･Ingallsandthemodeling

teamthenhadachancetorespond.Theyrevisedthemodeltoaddressthecriti-

cismsleveledbytheNavy'sexperts.Inthenextroundofmeetings,theyshowed

theNavyteamhowtheyhadmodifiedthemodeltoincorporatethechangesthe

Navy'sexpertswanted.Repeatlngthecomparisonoftheas-builttowouldhave

cases,themodelingteamfoundthatthefractionoftheoverrunanddelaycaused

bytheNavy'sdesignchangeshadactuallylnCreaSed･10

TheNavyclearlyexpectedthatincorporatingthecritiquesa_ndparameteresti一

matesofitsexpertsintothemodelwouldshowmoreoftheoverrunwasdue

tocontractormismanagement.Thecounterintuitiveresultthattheclaim value

mGiventhetechnologyofth etime(mainframecomputersoperatingwithtime-sharing,teletype

printers7and100baudacousticcouplermodems)itwasnotfeasibletor望themodelliveinthe meetlngS･Themodeldeveloperspainfullyrecallovemightsessionsrunnlngthemodelonthe largestcomputerthenavailable.TodayitispossibletobringthemodeltosuchmeetlngSOnalaptop andmakemanychangesinassumpt10nSOnthespot,Slashingthecycletimeforexperimentation andgreatlylnCreaSlngClientinvolvement.

64 PartIPerspectiveandProcess

increaseddemonstratedtoallthatitisactuallyquitedifficulttoenglneeramodel

togenerateapreselectedresult.Goldbachcommented,"Forthe丘rsttimetheNavy

sawthatlngallshadacrediblecase."Intensivenegotiationsthenbeganatthehigh- estlevelsofLittonandtheNavy.InJune1978thepartiessettledoutofcourt.In-

gallsreceived$447million. ThustheclientsforthemodelingworkwerenotonlyIngalls'managementand

attorneysbutalsothecourtandtheNavy.Itmayseemcounterintuitivetoinclude theopposlngSideamongtheclientgroupforamodelusedinalawsuit.Andindeed

theNavyattemptedtodiscreditthemodelandhaveitexcludedfromtheproceed- lngS.However,totheextentthemodelbecamethefocus,eventhroughthecrltlque oftheNavyexperts,thestructuresinthemodelandthedynamicstheygenerated

startedtobecomethecommonframeworkfordiscussionoftheclaimbyallpar- ties.Theprocessofchanglngmentalmodelswaswellunderway.Thisprocesshas sincebeenobservedinmanyotherconflicts(see,e.g.,WeilandEtherton1990,Re-

icheltandSteman1990).Experienceshowsthatthebettertheoppositions'under- standingofthemodel,themorelikelyltWillbeinfluentialintheresolutionofthe dispute.

Thoughthesettlngherewasalawsuit,theprocessappliestoanymodeling project.Evenwhentheclientsfortheworkareallfromthesamemanagement team,therewillalwaysbedifferentsidesandfactions,proponentsandopponents

ofeachpolicy.Onlytheintensiveinvolvementoftheclientsinthemodeling processcancreatetheunderstandingoftheissuesneededtochangeentrenched mentalmodelsandleadtoconsensusforaction.

2.3.5 Continuing】mpact

Thesystemdynamicsmodelwasthesoletechnicalbasisforthedelayanddisrup-

tioncomponentofIngalls'claimagalnSttheNavy･Estimatesfromtheattorneys andlngallsmanagementHplacethemodel'sdollarcontributiontothesettlement between$170-350millionH(Cooper1980,pp.28).Butthesesums,largeasthey are,underestimatethebenefitsofthemodelingprocess.Thelawsuititselfcanbe

viewedasalargeprojectthatgenerateditsownrippleeffects.Byachievingaset- tlementalittleover2yearsafterbeginningthemodelingprocess(averyshortin-

tervalinsuchlargedisputes),

Thedirectdollarcostsofcontinuingtheclaime恥rtwereavoided[legalfeesand courtcosts].Evenmoresignificant,however,wasthevastamountofmanagerial andprofessionaltimeandtalent(anentire"claimorganization"ofover100Ingalls personnel)thatwouldhavecontinuedtobespentonsomethingotherthanship designandconstruction‥.Aboveall,theeliminationoftheadversaryrelationship betweenlngallsanditsbestcustomerwasamilestoneachievement(Cooper1980, p.28).

SincethisgroundbreakingworkPugh-Robertsandotherfirmshavegoneontoap- plysystemdynamicstodisputestotalingmanybillionsofdollars.Theserange

from othermilitaryandcommercialshipbuildingprojectstoaerospaceand weaponssystems,powerplants,civilworkssuchasthecross-channeltunnel,and softwareprojects.Inmostcasescontractorsusethemodelsinactionsagainsttheir customers.Ineachcasethedefendantshavesoughttodebunkthemodelsand

Chapter2 SystemDynamicsinAction 65

excludethemfromtheallowableexperttestimonybuteachtimethemodelshave beenallowedandhavecontributedtofavorablesettlements.

Whilethedollarvalueoftheseactionsisimpressiveandofundoubtedbenefit

totheplaintiffs,thedamage(thecostovemn)hasalreadybeendone,andthedis-

puteisonlyoverwhopays.Therealleverageliesinuslngthesemodelsproac-

tivelysooverrunsanddelaysareavoidedinthefirstplace.SincethefirstIngalls

model,manyorganizationshavegoneontoapplysimilarmodelstothemanage-

mentoflarge-scaleprojectsinawiderangeofindustries(forexamplesseesec-

tions6.3.4and14.5).llIngallsitselfhasuseddescendantsofthatfirstmodelto

helpmanagevirtuallyeveryprogramsincetheLHAandDD.Thebenefitsofsuch

proactivemodelingarehardertoquantifybutlikelyoutweighthevalueofdispute

settlementsmanytlmeS.

Asoneillustration,RichGoldbachleftlngallsinthelate1970stoheadup

MetroMachine,ashipyardinNorfolk,Vlrglnia.Thensmallandstruggling,Metro

todaylSahighlysuccessfulyardspecializinglnrePalrandrefittingworkforthe

Navywithabout700employeesandsalesofabout$90mlllioIVyear.Goldbachin-

troducedawiderangeofinnovativemanagementpracticesincludingemployeein-

volvement･ThefirmislOO%employeeowned,withuniversalparticipationinthe

employeestockownershipplan.MetrohaswonseveralawardsforthehighquaL

1tyOftheirwork,includingNationalSmallBusinessPrimeContractoroftheYear

andtheUSNavyAEGISExcellenceAward"forsuperiorperformanceinquality,

reliability,deliveryandcost"-thefirsteverglVentOarePalryard･

Modelscontinuetoplayanimportantrole.Goldbachcommissionedthede-

velopmentofasimulationmodeltoprojectthefinancialconsequencesofvarious

decisionsforupto10years.Metrousesthemodeltoassessacquisitions,capital

investmentdecisions,newventures,andallaspectsofbiddingforjobs.

Webuiltthemodeltoaspeclification]IprovidedbasedonwhatIlearnedfromthe lngallsmodel.Themodelhelpsthegovernmentunderstandourbidsbetter.Itlets theDCAAlDefenseContractAuditAgency,aDepartmentofDefenseagencythat auditsdefensecontractorbidsandassessestheirabilitytodothework日ookataト

ternativescenarios.Weusethemodelinteractivelywiththem.Thereisanon-Site DCAAauditorwhoknowsthemodel.ShecanaskustorunanysetofassumptlOnS, andweusuallygettheanswerbackinanhour(Goldbach,personalcommunication, 1999).

Thefinancialsimulationhasbeenveryeffective,butfarmoreimportant,Goldbach

says,arethelessonshelearnedaboutthechallengesofmanaglngCOmplex

Systems:

Forthe[shipbuilding]industryithoughtiwasaprettysophisticatedmanager,butit changedmywholeperspective.IneverhadtheabilityIthinkIgotfromworking w ithsystemdynamicstoask"howwillthisdecisionrlppleout?MIgottothepolnt thatIhadthementalself-disciplinetofightmyImpulsesandnotJustdothemacho th ingwhenthere'saproblem･Theplaylngfieldchangeswhileyou'replayingthe

llseealsoAbdel-HamidandMadnick(1989a-C,1990,1991);Cooper(1993a-C,1994);Cooper andMullen(1993);FordandSterman(1998a-b);Homeretal.(1993);WeilandEtherton(1990); andYourdon(1993).

66 PartIPerspectiveandProcess

game.NowIaskhowcustomers,employees,Suppliersandsoonwillreacttowhat wemightdo.SometimeslgetitrightandsometimesIdon't.

Itpermeateseveryaspectofmythinking.I'madifferentpersonthanIwas before.

2.4 PLAYlNGTHEMNNTENANCEGAME12

In1991,WinstonLedet,thenamanagerinGulfCoastRegionalManufacturlng

ServicesatDuPont,reflectedontheresultsofanin-housebenchmarkingstudy

documentlngalargegapbetweenDuPont'smaintenancerecordandthoseofthe

best-practicecompaniesintheglobalchemicalsindustry.

Thebenchmarkingstudyrevealedanapparentparadox:DuPontspentmore

onmaintenancethanindustryleadersbutgotlessforit.DuPonthadthehighest

numberofmaintenanceemployeesperdollarofplantvalueyetitsmechanics

workedmoreovertime.Sparepartsinventorieswereexcessiveyettheplantsre-

1iedheavilyoncostlyexpeditedprocurementofcriticalcomponents.Most

disturbing,DuPontspent10-30%moreonmaintenanceperdollarofplantvalue

thantheindustryleaders,whileatthesametimeoverallplantuptlmeWasSOme 10-15%lower.

Manypeoplefoundtheresultsofthebenchmarkingstudytobecounterintu-

itive.Theirmentalmodelssuggestedthatequipmentqualityshouldsufferandup-

timeshouldbelowinacompanythatspendslittleonmaintenance,whilespending

moreonmaintenanceshouldyieldhigh-qualityequipmentandhighuptlme.How

couldDuPontbespendingmoreandgettlngless?

Manypeopleblamedtheproblemonthedifficultcompetitiveenvironment.

ThechemicalsindustrylSmatureandintenselycompetitive･Becausethereislittle

productdifferentiationforbulk(Commodity)feedstocks,Chemicalmanufacturers

competeonotherdimensions,mostlycostanddeliveryreliability･Sincetheearly

1970Stheindustrywashitbyonecrisisafteranother:Twosevereenergycrises

wreakedhavocwithinputandoperatlngcosts.Alwayscyclical,thethreeworstre-

cessionssincetheGreatDepressioncausedwidespreadexcesscapacity.Newcom-

petitorsfromthePacificrimandtheoil-richnationsoftheMiddleEastenteredthe

market,Environmentalconcernsandregulationsweregrowlng.

Ledetknewallthis;hehadlivedthroughitduringhis25yearswithDuPont.

ButblamingOutsideforcesfortheproblems,whilepsychologicallysafe,didn't

provideanyleveragetoimprove.Ledetfeltthattheexplanationoftheparadoxlay

notintheoutsidepressuresthecompanyhadfacedduringtwoturbulentdecades

butinitsresponsetothosepressures.

Ledetandhisteamneededawaytoexplorethewaysinwhichdifferentparts

ofthemaintenancesysteminteracted,explainwhypastattemptstoimprovehad

failed,andassistinthedesignofnewpolicies.Andtheyneededtoexplainthese

complexdynamicstotheexperiencedplantoperationsandmaintenancepeople w hohadtotakeaction.

12Ⅰ'mindebtedtoWinstonP.LedetandWinston∫.Ledet(principals,TheManufacturingGame),

PaulMonus(BPChemicals),andMarkPalCh(ColoradoCollege)forpermissiontopresenttheir workandtheirassistanceinthepreparationofthematerial･ThanksalsotoTonyCardella,Mark Downlng,VinceFlynn,andtherestoftheDuPontteam.

Chapter2 SystemDynamicsinAction 67

Ledetandhisteambeganthedevelopmentofasimulationmodeltocapture thesystemwide,dynamicbenefitsandcostsofdifferentmaintenanceinitiatives. Theydevelopedthemodelwiththeassistanceofanexperiencedmodeler,Mark Paich.Themodelwasdevelopedinteractively,withtheparticlpationofLedetand otherkeyteammembers･Theroleoftheexpertmodelerwasmoreofacoachand facilitator,andthemodelingprocessinvolvedextensivehands-onworkshopsin whichthemodelwasdiscussed,tested,andchangedinrealtimeasmembersofthe modelingteamidentifiedproblemsorareasneedinglmPrOVement.

DuPont,likemostlargefirms,alreadyusedanumberofmaintenanceplan- nlngtools.ThesetoolstendtofocusonthedetailcomplexltyOfthemaintenance challenge,forexample,databasestotrackthemaintenancehistoryofeachindi- vidualpieceofequipment,Statisticalmodelstooptlmizemaintenanceschedules, schedulingsystemstoasslgnmechanicstoplannedandreactivework,andsoon. Thesetoolsareimportantfor仙eday-to-daymanagementoflargeplantsbutthey don'tcapturethedynamiccomplexltyOfthemaintenancesystem.Wherethede- tailedplannlngandschedulingmodelstrackedeachpumpandmotorintheplant separately,thedynamicmodeldividedallequlpmentintoJustthreecategories:op- erable,brokendown,ortakendownforplannedmaintenance.Butwheretheex- istlngmodelsassumedfailureratesandrepalrcostsanddurationswereexogenous, thedynamicmodeltreatedthesefactorsendogenously.Itencompassedtechnical issuessuchasequlpmentCharacteristics;loglSticalissuessuchassparepartsavai 一

ability,maintenancescheduling,andmechanicasslgnmentS;humanresourcesis- suessuchasmechanicskill,training,andmotivation;andfinancialissues includingmaintenancebudgets,resourceallocation,andoverallplantperformance. Thesystemdynamicsmodelwasacomplementto,andnotareplacementfor,ex- istlngplannlngandschedulingtools.

2.4.1 DynamicHypothes套s

Usingthemodelasalaboratorytodesignandtestdifferentpolicies,theteamgrad- uallydevelopedanappreciationforthedynamiccomplexltyOfthemaintenance system.ThedynamichypothesistheydevelopedexplainedtheparadoxthatDu Pontspentmoreonmaintenanceandgotlessforltlntermsofuptlmeandequlp- mentreliability.

Themodelingprocessledtoseveralimportantconceptualshiftsintheway theyviewedmalntenance･Priortothemodelingworkmaintenancewaslargely seenasaprocessofdefectcorrection(repairoffailedequipment)andthemainte- nancefunctionwasviewedasacosttobeminimized･Thefirstconceptualshift wastochangethefocusfromdefectcorrectiontodefectpreventionanddefect elimination.Themodelthereforecenteredonthephysicsofbreakdownsrather

thanthecostminimizationmentalitythatprevailedthroughouttheorganization. Equipmentfailswhenasufficientnumberoflatentdefectsaccumulateinit.Latent defectsareanyproblemthatmightultimatelycauseafailure.TheyIncludeleaky oilsealsinpumps,dirtyequlpmentthatcausesbearingwear,pumpandmotor shaftsthatareoutoftrueandcausevibration,poorlycalibratedinstrumentation, andsoon.ApumpwithaleakyoilsealordirtybearlngSCanStillrunbutwilleven-

tuallyfailunlesstheselatentdefectsareeliminated.

68 PartI PerspectiveandProcess

Thetotalnumberoflatentdefectsinaplant'sequipmentisastock(Figure

218)･Defectsarecreatedbyoperations(normalwearandtear)andbycollateral

damagearisingfrombreakdowns(whentheoilleaksoutofthepumpbearingand

thebearlngSeizes,theshaftmaybebent,themotormayoverheat,andthevibra-

tionmaybreakcouplingsandpipes,introducingnewproblems)IMoresubtly, maintenanceactivltyCanCreatenewdefects,throughmechanicerrorsortheuseof

poorqualityreplacementparts･Thelowertheintrinsicdesignqualityoftheequl P -

ment,themoredefectstheseactivitiescreate.

Thestockofdefectsisdrainedbytwoflows:reactivemaintenance(repairof

failedequipment)andplannedmaintenance(proactiverepairofoperableequip-

ment).13Eachoftheseactivitiesformsabalancingfeedbackloop.AsdefectsacI cumulate,thechanceofabreakdownincreases.Breakdownsleadtomorereactive

FIGURE2-8 Defectcreationandelimination

Thediagramissimplified.lnthefullmodelequlPmentWasdividedintooperable,broken down,andtakendownforplannedmaintenance,withanassociatedstockoflatent defectsforeachcategory.

13plannedmaintenanceincludespreventive(time-based)work,e.g.,replacewornpartson pumpseverynmonths,andpredictive(condition-based)work,e.g,,replacewornpartsonapump ifvibrationexceedsacertaintolerance.

Chapter2 SystemDynamicsinAction 69

maintenance,and,afterrepalr,theequlPmentisreturnedtoserviceandthestock

ofdefectsisreduced(theReactiveMaintenanceloopBl).Similarly,scheduled

maintenanceorequipmentmonitoringmayrevealthepresenceoflatentdefects(a

vibratingpump,anoilleak).Theequipmentisthentakenoutofserviceandthede-

fectsarecorrectedbeforeabreakdownoccurs(thePlannedMaintenanceloopB2).

Obviouslybreakdownsreduceplantuptlme.Inaddition,mostplannedmain-

tenanceactivityalsoreducesuptlmeSinceplannedmaintenancefrequentlyre-

qulreSOperableequlpmentbetakenoutofservicesotheneededworkcanbedone･

Figure2-8Showsonlythemostbasicphysicsofdefectaccumulation.Thetwo

negativefeedbacksregulatingthestockofdefectsappeartobesymmetrical:De-

fectscanbeeliminatedeitherbyplannedmaintenanceorrepairOffailedequlp-

ment.Thefullsystem ismorecomplex,however,andincludesanumberof

positive,self-reinforcingfeedbacks(Figure219).

FrGURE2-9 Positivefeedbacksundercuttingplannedmaintenance

70 PartI PerspectiveandProcess

Considertheimpactofthefirstoilcrisisinlate1973.Inputandoperatlngcosts skyrocketed.Butthesevererecessionthatbeganin1974meantchemicalproduc- erscouldnotpasstheentirecostincreaseontoconsumers.Underintensefinancial

pressure,allplantsandfunctionshadtocutcosts･Ifmaintenancedepartmentsare askedtocutexpensesnearlyallofthecuthastocomefromactivitiessuchasplan一

mlngandpreventivemaintenance:Whencriticalequlpmentbreaksdown,itmust befixed.Atthesam etime,financialpressureleadstootheractions(e.g.,postpon1

1ngreplacementofolder,lessreliableequlpmentOrrunnlngequlpmentlongerand moreaggressivelythanoriginaldesignspecificationsindicate),whichincreasethe maintenanceworkload.Withresourcesforplannedmaintenancediminishingand maintenanceneedsincreasing,thestockofdefectsgrows.Breakdownsincrease.

Breakdownscausecollateraldamage,directlyincreasingthestockofdefectsfur- therandleadingtostillmorebreakdownsinaviciouscycle(thepositiveloopRl).

Becausethetotalnumberofmechanicsislimited,morebreakdownsnecessarily pullmechanicsoffplannedworkasmanagementreasslgnSmechanicstorepalr work.ButmanymechanicsalsopreferrepalrWOrk.Aplannedmaintenanceman-

agerinoneplantcommented,HWe'Vehadseveralpeoplewhosaytheywanttoget involvedinpreventiveworkbutwhenanoutagecomesand[they]haveachance towork14-16hoursperweekovertimetheysayt̀ohellwiththisvibration[mon-

itoring]stufF,Ⅰ'mgoingtotheoutagearea."'Withlessplannedwork,breakdowns increasestillmore,formlngthereinforcingGototheOutageloopR2.

TherisingbreakdownratemeansmorecriticalequlPmentWillbeoutofser- viceawaitlngrepair.Plantuptlmefalls.Plantoperatorsfindithardertomeetde- mand.WhenamechanicormaintenancesupervisorrequeststhatacertainpleCeOf

equipmentbetakenofflinetocorrectlatentdefects,theharriedlinemanageris likelytoshoutsomethinglikeHIcanbarelymeetdemandasitisandyouwantme

totakethislinedown?NowayJfyoumaintenancepeopleweredoingyourjob,I wouldn'thavesomanydownpumpsinthefirstplace.Nowgetoutofhere,I've gotaplanttorun."ThebalancingTooBusyforPMloop(B3)meansoperatorsare

lesswillingtotakeworkingequlpmentdownforplannedmaintenancewhenup- timeislow.Thesideeffectofthatpolicy,however,isafurtherincreaseindefects

andbreakdownsandstillloweruptlme･Theplantslowlyslidesdowntheslippery slope(reinforcingloopR3)intoatrapofhighbreakdownsandlowuptime,With nearlyallmaintenanceresourcesdevotedtocrisismanagement,firefighting,and

repairwork.

ThepositivefeedbacksRltoR3Operatefairlyquicklybutarenottheonly viciouscyclesthatcandragaplantintothetrapoflowreliabilityandhighcosts. TheoperationalfeedbacksinFigure2-9areembeddedinalargersystemshownin Figure2-10.

Ahigherbreakdownrateincreasescosts(duetoovertime,thenonroutineand

oftenhazardousnatureofoutages,theneedtoexpeditepartsprocurement,col- lateraldamage,etc.).Theresultingpressuretocutcostsleadstoareductionin

thequalityofparts,increaslngthestockofequipmentdefectsandleadingto stillmorebreakdownsandstillhighercosts(thePartQualityloopR4).Costpres- surealsoreducesinvestmentinequlpmentupgradesandotherdesignimprove-

ments,sobreakdownsincreasefurther(theDesignImprovementloopR5).As costsrisetrainlngformaintenanceworkersiscut,particularlytraininglnPlanned

Chapter2 SystemDynamicsinAction

FJGURE2-10 Additionalpositivefeedbacksreadingtoareactivemaintenanceculture

ThecontentsoftheroundedrectanglerepresentthestructureinFigure2- 9.

maintenancetechniques(theTrainingloopR6).Costpressurealsoforcesthemain-

tenancedepartmenttodownsize.Thefirsttogoaretheplannersandsched-

ulers-unlikemechanics,theydon'tactuallyfixanything,andwithlessandless

plannedmaintenancegc･lngOnthereislessforthemtodo･Withoutadvanceplan- nlng,partkits,equlpmenthistories,andenglneerlngdrawlngSfわrmaintenance

workarelessavailable,lowering血equalityofworkstillmore(thePlanning

CapabilityloopR7).

Aparallelsetofself-reinforcingfeedbacksoperatetoreducethemaintenance

budgetevenascostsrise.Loweruptlmedirectlyconstrainsproductionand

thereforerevenue,forclngbudgetcutsthroughouttheorganization.Worse,high

72 PartI PerspectiveandProcess

breakdownratesandlowuptlmemeantheplantislessabletomeetitsdelivery commitments･AsitdevelopsareputationforpoordeliveryreliabilitytheprlCeit canchargeandvolumeofbusinessitattractsdecline,furthererodingrevenueand profitandforcingstillmorebudgetcuts.Costpressurerisesstillfurther,accelerat-

1ngthepartquality,trainlng,designimprovement,andplannlngCapabilityloops･ TheseloopsaresummarizedastheRevenueErosionandReputationErosionloops (R8andR9).

Afteryearsofcostpressure,DuPonthaddevelopedacultureofreactivemain- tenance･Unreliableequlpmentandfrequentbreakdownshadbecomeanaccepted occurrence.Organizationalnormsandroutinesforwrltlngupworkorders,sched- ulingmaintenanceeffort,andorderingpartshadcometoreflectaworldoffrequent breakdowns.Mechanicsspentmostoftheirtimefightingfires.Mechanicswho werescheduledforplannedmaintenancewereroutinelypulledofftodoreactive work･Mechanicsknewtheycouldworkovertimeonaregularbasisandconsid- eredovertimepayapartoftheirregularincome･Theknowledgethatequlpment wasunreliablehadevenledtoinstallationofbackuppumpsinmanysites,embed- dingthelow-reliabilitycultureinthephysicallayoutandcapltalcostsoftheplants. Astheyearspassedtheworkforceincreasinglyconsistedofpeoplewhohadnever experiencedanythingotherthanthereactiveregime.Forthem,theequipmentWas intrinsicallyunreliable,lowuptlmeWasnormal,andreactivemaintenancewas businessasusual(theReactiveCultureloopRIO).

Asthemodeldevelopedtheycalibratedittorepresentatypicalplant･Ⅰnthe early1990satypicalDuPontchemicalplantwasvaluedat$400millionandspent about3-3.5%ofitsvalueannuallyonmaintenance,or$12to$14million/year. Thesparepartsstorestockedmorethan60,000parts.Itemployedabout90main- tenancemechanicswhomightcompleteasmanyas25,000workordersperyear. AverageuptlmeWas83.5%.Maintenanceexpensesaccountedfor15140% of directproductioncosts,dependingontheprocessandproduct.Theamountof moneyDuPontspentcompanywideonmaintenanceinthelate1980swasabout $1billion/year,asignificantfractionofnetincome.

Oncethemodelwasadequatelycalibratedtothehistoricaldata,thenextstep wastodesignhighleveragepoliciestoescape丘.omthereactivereglme.Theteam simulatedtheimpactofdifferentpolicies,includingthosethathadbeentriedinthe pastandfailed.Table211showstheresultsofselectedsimulations.

OptimlZlngtheuseofschedulingalone,withinthetraditionalcost-minimiza- tionmindset,hadonlyamodestimpact･Throughbetterschedulingtheplantcould stillmeetitstraditionaluptlmeOf83.5%withlO%fewermechanics,generating savingsof$350,000/year.Implementingafullsuiteofproactivemaintenancepoli- cies,includingbetterplannlngSystems,parts,reliabilityenglneerlng,andsoon,al- lowedtheplanttoachievethetraditionaluptlmeWithonly61mechanics,savlng $1.2million/year.

However,deploylngthesamesuiteofproactivepolicieswithoutdownsizlng alloweduptimetoriseabove93%andgenerated$9million/yearinadditional profit･Whythedifference?Thecost-minimizationapproachmeansanylmPrOVe- mentinproductivltygeneratedbytheadoptionofimprovedmaintenancetech- nlqueSisimmediatelyharvestedasheadcountreduction･Resourcesforplanned maintenanceremainconstrained･Theorganizationcontinuestofightfiresand

Chapter2 SystemDynamicsinActioll

TABLE211

ResuJtsfrom

se一ectedpo一icy simufations

Cases1and2:

Minimize

maintenance

costssubjectto

uptime≧initial

uptime. Case3:Maximize

pfantprofitsubject tomechanic

headcount≦

initialheadcount.

PorlCyMix

Changein Head Profit

CountUptime (Sminion/year)

0･TypicafplantunderexlrStingpolicies 91 83.5 0.00

llUseschedulingtominimize maintenancecosts

2.Minimizecostsviafullsuiteof

proactivemaintenancepolicies

3.MaximizeplantprofitviafuHsuiteof proactivemaintenancepolicies

82 83.5 0.35

61 83.5 1.20

91 93.3 9.00

Source･'WinstonLedet,MarkPaich,TonyCardella,andMarkDown'lng(1991),"TheValueof lntegratjngtheCMLTKeyPursuits,"DuPontInternalreport.

focusonreactivemaintenancebutdoessomoreefficiently.Incontrast,imple-

mentlngthenewpolicieswithoutdownsizingfreesupresourcesthatcanberein-

Vestedinstillmoreplannedmaintenance.Asbreakdownsfall,Stillmoremechanics

arereleasedfromfirefightingandoutagestodoevenmoreplannedwork.Main-

tenanceexpensesdrop,releaslngresourcesthatcanbeinvestedintrainlng,parts

quality,reliabilityenglneerlng,Planningandschedulingsystems,andotheractivi-

tiesthatcutdefectsandbreakdownsstillmore.Higheruptlmeyieldsmorerevenue

andprovidesadditionalresourcesfわrstillmoreimprovement.Forexample,UPI

gradingtoamoredurabletypeofpumpsealimprovesreliability,allowlngmain-

tenanceintervalstobelengthenedandinventoriesofreplacementsealstobecut.

Allthepositiveloops血atonceactedasviciouscyclestodragreliabilitydown

becomevirtuouscycles,progressivelyandcumulativelyreducingbreakdownsand

improvinguPtlme.Theresultisatremendoussynergy,withthecombinedeffectof

theindividualpoliciesgreatlyexceedingthesumoftheirimpactswhenimple-

mentedindividually.

Themodelalsorevealedanimportantinsightaboutthetransitionpathfollow-

1nglmplementationofthenewpolicies.ThesimulationresultsinTable2-1show

thatproactivemaintenancepolicieswithreinvestmentoftheresultsultimately

lowersmaintenancecostsandboostsuptlme.Immediatelyafterimplementation,

however,maintenancecostsincreaseanduptlmefalls･Why?Ittakestimeforthe

plannedworktocutthebreakdownrate;intheshortruntheplantmustbearthe

costofboththerepairworkandtheadditionalplannedmaintenanceeffort.Uptime

fallsbecauseadditionaloperableequlPmentmustbetakenoffllinesoplanned

maintenancecanbeperformed･Onlylater,asthestockoflatentdefectsstartsto

fall,doesthebreakdownratedrop.Asitdoes,expensesfallanduptlmerises.This

worse-before-betterbehaviorisqulteCOmmOnincomplexsystems.However,if

managersdonotunderstandwhyitoccursorhowlongltmightlast,theymayIn-

terprettheshor t-rundeteriorationinperfわrmanceasevidencethat血epolicies don'tworkandthenabandonthem.

74 PartI PerspectiveandProcess

2.4.2 The芸mp始mentationCh;州enge

Ledetandhiscolleaguesfeltthatthenewperspectivestheydevelopedonthe

maintenanceproblemcouldimprovethecontributionofDuPont'smaintenance

program tocorporateprofitability.Nowtheirchallengewastoimplementthe

neededchanges.Theteamwroteawhitepaperdetailingtheresultsofthemodel-

1ngStudyandgavepresentationsthroughouttheorganizationTheresult?Nothing

happened.Peoplewouldsay,HWealreadyknowthatplannedmaintenanceisa

goodidea,""Wetriedthosepoliciesandtheydidn'twork,"or"Yourmodeldoesn't accountforx,"

Ledetrealizedthattheclientgroupfortheproject-thegroupofpeoplewhose

behaviorhadtochangeforanyresultstoberealized-wasfarbroaderthanthe

managementteamresponsibleformaintenance･Nothingcouldhappenwithoutthe

cooperationandwillingpartlClpationofhugenumbersoflinemanagers,equlp-

mentoperators,andmaintenancemechanics･Theclientgroupnumberedinthe thousands.ReflectingOntheirownlearnlngProcess,modelingteammembers

realizedthattheirviewshadchangedradicallybecausetheyhadparticipatedinan

iterativeprocessofmodeling.Theyhadseenthemodelevolve,hadchallengedand

questionedit,hadseentheirconcemsaddressed,andhadgonethroughtheprocess

ofworkingoutthefeedbackstructuresthatexplainedthedynamicsofthesystem.

SomehowtheyhadtorecreatethatlearningProcessthroughouttheplants,fromtop

managementtothelowest-grademechanics.

Itwasobviouslyimpossibleforthethousandsofpeopletheyhadtoreachto

particlpateinmodelingworkshopsoreventoglVethemthemodelsotheycould workwithitthemselves.NonehadtrainlnglnSystemdynamicsorcomputermod-

eling.Linesupervisorsandmaintenancemechanicsareactionorientedandhave

littlepatienceforpresentationswithlotsofchartsandgraphs･

LedetwasfamiliarwiththeBeerDistributionGame,arole-playlngmanage一

mentflightsimulatorofamanufacturlngSupplychaindevelopedbytheMITSys-

temDynamicsGroupasanintroductiontosystemsthinking･14workingwithhis son,Ledetconvertedthemaintenancemodelintoaninteractiverole-playsimula-

tionthattheycalledtheManufacturingGame(seeLedet1999).Thegamewas

embeddedina2-dayworkshoporlearnlnglaboratorydesignedtobehighlyinter-

active,toputpeopleatease,andtocreateanenvironmentforlearnlngthatad-

dressedemotionalaswellascognltiveissues･

Thegamesimulatesaty p lCalplant.Therearethreeroles:operationsmanager,

maintenancemanager,an d sp arepartsstoresmanager.Theoperationsmanageris

chargedwithmeetlngdem an d andhasequlpment,representedbychips,todoso･

AsproductionproceecLS, red m arkersrepresentinglatentdefectsareplacedonthe

equlpmentChips･Whenenoughredmarkersaccumulate,theequlpmentbreaks

downandcapacityfalls.Themaintenancemanagermustthenallocatemechanics

torepairtheequlpmentandmustgotothesparepartsstoretoseeiftheneeded

14TheBeerDistributionGameisanenjoyableandeffectiveintroductionnotonlytosupply chainmanagementbutalsototheprinciplesofsystemsthinkingingeneral(Seechapter17;also Sterman1989b,1992andSenge1990fordescnptlOnS,butnotuntilafteryouhaveplayedthe

game).

Chapter2 SystemDynamicsinActlOn 75

parts(determinedbyarollofthedice)areavailable･Ifthepartsareinstock,the

equlpmentisrepairedJfnot,themechanicsmustwaituntiltheyareavailableor

paytohavedeliveryexpedited.Altematively,themaintenancemanagercansched-

uleplannedwork,orderingtheneededpartsandallocatlngmechanicsinadvance.

Plannedmaintenancecanonlybedone,however,iftheoperationsmanageragrees

totakeoperatlngequlpmentOutOfservice.Eachroundtheparticipantsmakedeci-

sionssuchashowmuchequipmenttOtakedownforplannedmaintenance,howto

allocatemechanicsandmaintenanceresources,andhowmanysparepartstoorder･

Revenueandcostarerecorded,alongwithproduction,uptlme,inventories,andso

on.Whilethegameishighlysimplifiedcomparedtorealplants,andevencom-

paredtotheorlglnalsimulationmodel,itrealisticallycapturesthetimedelays,

costs,andotherparameterscharacterizingaPlant.

Desplteitsmanysimplificationsthegamerapidlybecomesinmanywaysa

realplant,withrealemotionsandconflictsamongplayers.Initializedwithhigh

breakdownsandlowuptlme,themaintenancemanager'sattemptstoincrease

plannedmaintenanceareoftenrebuffedbytheoperationsmanager,whofacesin-

tensepressuretomeetdemand,justasintherealworld･

Teamswhostickwiththeprevailingcost-minimization,reactivemaintenance

policiesareabletokeepcostslowforawhile･Butasdefectsbuilduptheyfind

theiruptlmeSlowlysinkingandcostsgraduallyrlSlng.Teamswhodofollow

throughwithaplannedmaintenancestrategyImmediatelyfindcostsrisingandup-

timefallingasequipmentistakenofflineforplannedmaintenance.Soon,how-

ever,costsbegintofallanduptlmerises.Bycompresslngtlmethegameallows

peopletoexperiencetheworse-before-betterdynamicinafewhoursinsteadofa fewmonths.

TwomembersoftheimplementationteamatDuPont'SWashingtonWorks

complexinParkersburg,WestⅥrginia,describedhowtheyusedthegametocaト

alyzeabroad-basedimprovementprogram:

Theteamwasinitiatedwithatwo-daylearnlnglab.I･1earnlngtheconceptsofde- fecteliminationandexperienclngtheManufacturlngGame...Thebasicconcepts arepresentedindifferentmannerssothatalllearnlngmodesareutilized-visual, auditoryandkinesthetic.Thematerialispresentedinthefわrmoflectures,Skitsand particIPativeexercisesinanoff-siteenvironment.Postersandmusicareused･The atmosphereismuchdifferentthanroutineplantmeetingsOrtrainlng,tOOPenuP theirthinking-.Throughinteractiveexercises,theteamdevelopstheirpersonal aspirationsforimprovingtheareawheretheyhavechosentowork･･･lThen] they･-developanactionplantoimmediatelystartworking･15

Thegameandlear王11nglaboratoryprovedpopularthroughoutthecompany･But

playlngltOnceWithasmallgroupofmanagerswasn'tenough･Theteamfound

thattheyhadtorunseveralworkshopsforaglVenplantbeforeacriticalmassof

peopleemergedtoleadactionteamsthatputproactivemaintenancepoliciesinto

practice･OftentheplantneededtodevelopItsOWnCapabilitytorunthegameand

workshopsoitcouldbe doneondemandbylocalpeople,withtheirsite-specific

15Tewksbury,R.,andR.Steward(1997)ImprovedProductionCapabilityProgramat DuPont'sWashingtonWorks,Proceedingsofthe1997SocietyforMaintenanceandReliability annualconference.

FIGURE2-ll Worse-before- betterbehaviorof maintenancecosts

atatypICalplant

Graphshows directcost

savlngSafter implementation oHheleamlng laboratoryand newmaintenance

po一iciesata particularplant･ Verticalaxis

disguisedL

PartIPerspectiveandProcess

experienceandauthority.Ledet'Steamthushadtodevelopagroupoftrainedfa-

CilitatorsandatrainlngprocessSOthatthequalityoftheworkshopcouldbemain- tainedasitspreadintotheplants.Thedemandfortheworkshopgrewslowlyat first,butasfavorablewordofmouthabouttheexperienceandresultsspread,more andmoreplantsaskedLedet'sgrouptoruntheprogramforthem.Thesurgeinde一 mandstressedthenumberofskilledfacilitators,whichlaggedbehind.Bytheend of1992some1200peoplehadpartlCIPatedintheworkshopandmorethan50fa-

cilitatorshadbeencertified.

2.4.3 Results

By1994anumberofplantsthroughouttheGulfCoastreglOnhadadoptedthe learninglabandassociatedpolicies.Figure2-11showsthedirectmaintenancecost savlngSforaparticularplantafterimplementationoftheprogram.Justasseenin themodelandthegame,thefirsteffectofthenewpoliciesisanincreaseincosts. OnlyafterseveralmonthsdidthecostsavlngSbegintoaccumulate.

Amongplantsthatimplementedtheprogrambytheendof1993,themean

timebetweenfailure(MTBF)forptlmPS(thefocusoftheprogram)rosebyanav- erageof12%eachtimecumulativeoperatlngexperiencedoubled,whiledirect maintenancecostshadfallenanaverageof20%･In23comparableplantsnotim- plementlngtheprogramthelearnlngrateaveragedjust5%perdoublingofcumu- lativeexperienceandcostswereupanaverageof7% (Carroll,Sterman,and Marcus1998).TheprogramatWashingtonWorksboostednetproductioncapabil- ity20%,improvedcustomerservice90%,andcutdeliveryleadtimeby50%,all withminimalcapitalinvestmentandareductioninmaintenancecosts.Itisdiffi- culttoestimatethetotalbenefitoftheprogramforthecompanyasawhole,but conservativeestimatesexceed$350millioIJyearinavoidedmaintenancecosts.

Thestorydoesnotendhere,however｡Successcreatesitsownchallenges. WhathappenstoaplantafteritsucceedsinimprovlngMTBFsandcuttlngmain- tenanceexpendltures?Oneissuerelatedtothepersistenceofthecost-savlng

(p a s!n B s !p a 一L, 3 S )

s B u !̂ E2S I S O 3

a ^ !l t2 1n ∈

Source:A"en(1993).

ll/9212/921/93 2/93 3/93

Chapter2 SystemDynamicsinAction 77

mentality.Amemberofthemodelingteamcommented,"Assoonasyougetthe problemsdown,peoplewillbetakenawayfromtheeffortandtheproblemswill gobackup}'Infact,cost-cuttlngProgramsmandatedbycorporateheadquarters didcausesignificantdownsizlngthroughouttheentirecompanyandlimitedtheir abilitytoexpandtheprogram.

AnotherproblemforDuFontwasrewardingthemodelingteam.Ledetbe- lievedthegameandlearnlnglaboratoryhadgreatpotentialtostimulateimprove一 meれtinawiderangeofcompaniesandindustries･HebegantoreceivelnqulrleS fromotherfirmsinterestedinusingthegame.Ledetacquiredtherightstothegame fromDuPont,tookearlyretirement,andbecameanentrepreneur,workingwith othercompaniestoimplementtheapproach,These丘rmsincludeotherchemicals manufacturersalongwithfirmsintheenergy,automotive,andhigh-techsectors･

2,4.4 Transferr妻ng帥eLeaning:

TheLimaExper岳ence

Oneoftheorganizationsthatadoptedthemaintenancegameandothersystemdy- namicstoolswasBritishPetroleum(BP).16BP'sLima,Ohio,refinerywasbuiltin

1886byJohnD.RockefellertosupplyfuelandpetrochemicalstotheMidwest1 Oncethe"QueenoftheFleet,"costcuttingduringthe1980Shadledtothesame

splralofincreasingbreakdowns,declinlngperfわrmance,andstillmorecostcuttlng thathadplaguedDuPont.Bytheearly1990sitwasapoorperformerandlagged wellbehindotherUSrefineries.Anumberofimprovementprogramsweretried, withlittlesuccess,andBPbegantothinkaboutsellingorclosingthefacilitywhile trylngtOCutCOStS･

In1994theLimafacilityIntroducedthemaintenancelearnlnglabandgame alongwithsomeothertoolsofsystemdynamicssuchastheBeerDistribution Game.Thiswasnotatopmanagementintervention:Thegamewasinitiallycham- plOnedbyanequlpmentSpecialist,amaintenancetrainlngSupervisor,andaneng1- neer,PaulMonus,thenworkinglnCOntinuousimprovement.Successfulpilot projectsledrefinerymanagementtorun80%ofallemployeesthroughthepro- gram.Soondozensofimprovementteamswereinplace.Duringthefirst6months maintenancecostsballoonedby30%.Managementwaspreparedforthisworse- before-betterdynamic,however,andfocusedontheimprovementsgeneratedby theactionteams.Momentumbegantobuild.

InJanuary1996BPannouncedthatitintendedtoselltheLimarefineryand steppedupitscostCuttinganddownsizlng.AfewmonthslaterBPstunnedtheem- ployeesbyannouncingthatitcouldnotfindabuyeratasatisfactorypriceand wouldthereforeclosetherefinery.

Theannouncementwasadeepblowtotheworkersandthecity･TheLima facilitywasoneofthemostimportantemployersinthecommunlty,OCCupylng 650acresofprlmerealestateandgeneratlng400jobswithpayroll,utility, andotherpaymentspumpingmorethan$60million/yearintoLima'sdepressed eCOnOmy･

16BPmergedwithAmocoin1998,aftertheworkdescribedherewasdone･

TABLE2-2

Improvementat

theLimarefinery

PartI PerspectiveandProcess

Someemployeesbecamediscouragedandquestionedthevalueofcontinuing

theprogramofdefecteliminationandproactivemaintenance.Afewtransferredto

otherBPfacilitiesorleftaltogether.WinstonLedetdescribedwhathappenednext:

Forthosewhodecidedtostaywiththeship,anewsplritemerged.Theyrealized thattheyneededafutureinLimaandshouldtakeresponsibilityforcreatlngthat future.Thefirststepwastoensurethattheexitofmanyexperiencedpeopledidnot throwthembackinthereactivemode.Thisheightenedthesenseofurgencytodo

defectelimination.Itactuallycreatedaclearerfocusforthepeoplewhoremained. Theywerealltherebecausetheyhadchosentobethere･17

Soonthecumulativeimpactofthenewmaintenancepoliciesandattitudeswas

clearlyvisibleintheperformanceoftheplant.Table212highlightssomeofthe results.

Thedramaticimprovementsintherefinerydidnotgounnoticed.OnJuly2,

1998,thebammerheadlineoftheLimaNewsannounced"OilRefineryRescued."

ClarkUSA,aprivatelyheldFortune500Companywithrefininganddistribution

interests,agreedtobuytheLimarefineryfromBPfor$215millionandkeepitop-

eratlngaSarefinery.Manypeopleandorganizationscontributedtotherescueof

therefinery.Yetwithoutthedramaticimprovementsinrefineryoperationsstimu-

latedbythesystemsthinkingInterventionitisunlikelyClark,oranybuyer,Would

haveofferedenoughforthefacilitytokeepltrunnlng.

1.LimaRefinerypumpMTBFupfrom12to58months(pumpfa‖ures downfrommorethan640in1991to131jn1998).Directsavings: $1.8million/year.

2.Totalflare10ffofhydrocarbondownfroml.5%to0.35%.Directsavlngs: $0.27/barrel.lmprovedenvironmentalquality.

3.On｣ineanaJyzeruptimeimprovementfrom75%andnottrustedto97% andtrusted,permittingreaHimeoptimizationofproductflow.Savings: $0.i010.12/barrel

4.Thirty-fourproductionrecordsset.

5.SafetylncidentsandIosthourscutbyfactorof41

6.Cashmarginimprovedby$0.77perbarrelofoilprocessed.

7.Totalnewva山ecreated:$43million/year.Totalcost:$320,000/year. Ratio:143:1.

8.BPwidelearnlnglnitiativeunderwayforallotherrefineriesandplants. Over2000peoplefromsitesintheUS,UK,Australia,NorthSea,Alaska, andEuropehadparticIPatedin的eworkshopandgameby1998.

Source:PaulMonus,personalcommunication;Monus,P.(1997)"ProactlveManufacturlngatBP's LimaOilRefinery,"presentedatNationalPetroleumRefEnerSAssoclatl0nMalntenanCeConference, 20-23May1997,NewOrleans,andGrlfflth,｣.,D.Kuenzll,andPMonus(1998)"Proact】veManufac- tunng.AcceleratingStepChangeBreakthroughslnPerformance,"NPRAMaintenanceConference, MC-98-92.

17TMGNews,15September1998･

Chapter2 SystemDynamicsinAction 79

Thesuccessofthelearnlnglaboratoryandmaintenancegameillustratesthe realpurposeofthemodelingprocess.Themodel,game,andworkshopdon'tteach anyonehowtomaintainapumpbetterorhowtodovibrationmonitonng.DuPont, BP,andotherorganizationsalreadyhaveplentyoftechnicaltoolsandknowledge. Instead,thegameandlearnlnglaboratoryenablepeopletoexperiencethelong- termorganizationwideconsequencesoftheiractions,toenactafutureinwhichold waysofbehavingarechanged,andtoexperienceemotionallyaswellascognl- tivelywhatitmightbeliketomakethetransitiontoahigh-performlngPlant･

TheLimaexperienceillustratesthepowerofashiftinmentalmodels.TheBP teamreducedbutaneflare-Offtozero,generatingannualsavingsof$1.5million/ yearandreducingpollutionaswell.Theefforttook2weeksandcost$5000,a returnoninvestmentof30,0009も/year.Whathadstoppedthemfromimplementlng thisimprovementlongago?Membersoftheteamknewabouttheproblemand howtosolveitfor8years.Theyalreadyhadalltheenglneerlngknow-howthey neededtosolvetheproblem andmostoftheequipmentandmaterialswere alreadyonsite.Theonlybarrierswerethementalmodelsthroughwhichemploy- eescametobelievethattheywerepowerless,thattheproblemwasimposedby externalforcesbeyondtheircontrol,andthatafewpeoplecouldnevermakea difference.

Theseentrenchedmentalmodelschangedinfouressentialways.Thebelief thattheproblemwasouttherehadtochangefrom"ourequipmentislousyand there'snothingwecandoaboutit"to"OurequipmentPerfomspoorlyasaresult ofourownpastpolicies-1fwechangeourbehavior,theequlpmentWillrespond.H Thefocusondefectcorrectionthroughrepairshadtoshifttoafocusondefectpre-

ventionandelimination.Thefocusonminimizingmaintenancecostshadtoshift tomaximlZlngOVerallorganizationalperformance.Andtheyhadtorealizethates- Caplngthetrapofreactivemaintenancenecessarilyinvolvedaworse-before-better tradeoff.

Theformalmodelwasessential,asitledtotheinitialinsightsintothedynam- icsofprocessimprovementandthesynerglSticeffectsofhighleveragepolicies. Themodelalsoallowedthemodelingteamtodevelopthegameandhelpedmake itrealistic.Ultimatelyimplementationsuccessrequiredthemodelingteamtoem- bedtheirinsightsintoalearnlngenvironmentthatinvolvedtheactiveparticipation ofthepeopleonthefrontlines,thatenabledpeopletodiscoverthoseinsightsfor themselves,andthatspokenotonlytotheirheadsbutalsototheirhearts･

2.5 SuMMARY:PR;NC!PLESFORSljCCESSFJuLUSEOF

SYsTEMDyNAM;CS

Thoughtheprojectsdescribedabovedifferedinmanyways,theyallillustratea numberofprinciplesforeffectivedevelopmentandimplementationofsystemdy- namicsmodels(Seechapter3;seealsoForrester1961;Roberts1977/1978;and MorecroftandSterman1994):

1.Developamodeltosolveaparticularproblem,nottomodelthesystem. Amodelmusthaveaclearpurposeandthatpurposemustbetosolvethe problemofconcerntotheclient.Modelersmustexcludeallfactorsnot

80 PartI PerspectiveandProcess

relevanttotheproblemtoensuretheprojectscopeisfeasibleandtheresults timely.Thegoalistoimprovetheperformanceofthesystemasdefinedby theclient.Focusonresults.

2.ModelingshouldbeintegratedintoaprojeeWromthebeginnmg. Thevalueofthemodelingprocessbeginsearlyon,intheproblem definitionphase.Themodelingprocesshelpsfocusdiagnosisonthe structureofthesystemratherthanblamlngproblemsonthepeoplemaking decisionsinthatstructure.

3.BeskepticalabolltthevalueofmodelingandforcetheHwhydowe needit"discussionatthestartoftheproject.

Therearemanyproblemsforwhichsystemdynamicsisnotuseful･ Carefu11yconsiderwhethersystemdynamicsistherighttechniqueforthe problem.Modelersshouldwelcomedifficultquestionsfromtheclients abouthowtheprocessworksandhowitmighthelpthemwiththeir problem.Theearliertheseissuesarediscussed,thebetter.

4.Systemdynamicsdoesnotstandalone.Useothertoolsandmethodsas appropriate. MostmodelingprojectsarePartOfalargereffortinvolvingtraditional strateglCandoperationalanalysis,includingbenchmarking,statisticalwork, marketresearch,etc.Effectivemodelingrestsonastrongbaseofdataand understandingoftheissues,Modelingworksbestasacomplementtoother tools,notasasubstitute.

5.FoellSOnimplementationfromthestartoftheproject. ImplementationmuststartonthefirstdayoftheproJeCLConstantlyask, Howwillthemodelhelptheclientmakedecisions?Usethemodeltoset prlOritiesanddeterminethesequenceofpolicylmplementation･Usethe modeltoanswerthequestion,Howdowegettherefromhere?Carefully considertherealworldissuesinvolvedinpullingvariouspolicylevers. Quantifythefullrangeofcostsandbenefitsofpolicies,notonlythose alreadyreportedbyexistingaCCOuntlngSyStemS･

6.Modelingworksbestasaniterativeprocessofjointinquirybetween dientandConsultant.

ModelinglSaprocessOfdiscovery･Thegoalistoreachnewunderstanding ofhowtheproblemarisesand血enusethatunderstandingtodesignhigh leveragepoliciesforimprovement･Modelingshouldnotbeusedasatool fcLradvocacy.Don'tbuildaclienfjspriorOPlnionaboutwhatshouldbe doneintoamodel.Useworkshopswheretheclientscantestthemodel themselves,inrealtime.

7.Avoidblackboxmodeling. Modelsbuiltoutofthesightoftheclientwillneverleadtochangein deeplyheldmentalmodelsandthereforewillnotchangeclientbehavior. Involvetheclientsasearlyandasdeeplyaspossible.Showthemthemodel･ Encouragethemtosuggestandruntheirowntestsandtocriticizethe model.Wわrkwiththemtoresolvetheircriticismstotheirsatisfaction.

Chapter2 SystemDynamicsinAction 81

8.Validationisacontinuousprocessoftestingandbuildingconfidencein themodel.

Modelsarenotvalidatedaftertheyarecompletednorbyanyonetestsuch astheirabilitytofithistoricaldata.Clients(andmodelers)buildconfidence

intheutilityofamodelgradually,byconstantlyconfrontingthemodelwith dataandexpertopinion-theirownandothers'.Throughthisprocessboth modelandexpertopinionswillchangeanddeepen.Seekoutopportunities tochallengethemodel'sabilitytoreplicateadiverserangeofhistorical eXljerlenCeS.⊥

9.Getapreliminarymodelworkingassoonaspossible｡Adddetailonly aSneeeSSary･ Developaworkingsimulationmodelassoonaspossible.Don'ttryto developacomprehensiveconceptualmodelprlOrtOthedevelopmentofa simulationmodel,Conceptualmodelsareonlyhypothesesandmustbe tested.Formalizationandsimulationoftenuncoverflawsinconceptual mapsandleadtoimprovedunderstanding･Theresultsofsimulation experimentsinformconceptualunderstandingandhelpbuildconfidencein theresults.Earlyresultsprovideimmediatevaluetoclientsandjustify continuedinvestmentoftheirtime.

10.AbroadmodelboundarylSmoreimportantthanagreatdealofdetail.

Modelsmuststrikeabalancebetweenauseful,operationalrepresentation ofthestructuresandpolicyleversavailabletotheclientswhilecapturlng thefeedbacksgenerallyunaccountedforintheirmentalmodels.Ingeneral, thedynamicsofasystememergefromtheinteractionsofthecomponents inthesystem-Capturingthosefeedbacksismoreimportantthanalotof detailinrepresentingthecomponentsthemselves.

ll.Useexpertmodelers,notnovices. WhilethesoftwareavailableformodelinglSeasilymasteredbyahigh schoolstudentorCEO,modelinglSnotCOmputerprOgrammlng.Youcannot developaqualitativediagramandthenhanditofftoaprogrammerfor codingIntoaSimulationmodel.Modelingrequiresadisciplinedapproach andanunderstandingofbusiness,skillsdevelopedthroughstudyand experience.Gettheexpertassistanceyouneed.UsetheprojectaSan opportunltytOdeveloptheskillsofothersontheteamandintheclient organization,

12｡Implementationdoesnotendwithasingleproject. Inal1threecasesthemodelingworkcontinuedtohaveimpactlongafter theinitialprojectWasover.Modelsandmanagementflightsimulatorswere appliedtosimilarissuesinothersettlngS.Themodelersdevelopedexpertise theyappliedtorelatedproblemsandclientsmovedintonewpositionsand neworganizations,takingtheinsightstheygainedand,sometimes,anew wayofthinking,withthem.Ⅰmplementationisalong-termprocessof personal,organizational,andsocialchange.

甘言はき呈t,畠曽呈主嘩苧it串∈e軍§

Perhapsthefaultlforthepoorimplementationrecofldformodels]liesinthe

originsofmanagerialmodel-making-thetranslationofmethodsandprin- Ciplesofthephysicalsciencesintowartimeoperationsresearch. .If hypothesis,data,andanalysisleadtoproofandnewknowledgeinscience, shouldn'tsimilarprocessesleadtochangeinorganizations?Theansweris obviousINO!Organizationalchanges(ordecisionsorpolicies)donot instantlyjlowfromevidence,deductivelogic,andmathematicaloptimization.

IEdwardB.Robertsl

lnchapter1theconceptofavirtualworldwasintroducedasawaytospeedthe

learnlngprocess,andchapter2showedhowmodelsbecamevirtualworldstohelp

solveproblemsinthreedifferentsituations.Howcanvirtualworlds(models)be

usedmosteffectively?Howcanusefulvirtualworldsbecreated?Modelingtakes

placeinthecontextofrealworldproblemsolving,withallitsmessiness,ambi-

guity,timepressure,politics,andinterpersonalconflict.Thepurposeistosolvea

problem,notonlytogaininsight(thoughinsightintotheproblemisrequiredto

designeffect_ivepolicies),Modeling,asapartofthelearningprocess,isiterative,

acontinualprocessofformulatinghypotheses,testlng,andrevision,ofbothformal

andmentalmodels.Experimentsconductedinthevirtualworldinformthedesign

andexecutionofexperimentsintherealworld;experienceintherealworldthen

leadstochangesandimprovementsinthevirtualworldandinparticlpantS'mental

1Roberts,E.(1977),"Strategiesforeffectiveimplementationofcomplexcorporatemodels," Interfaces7(5);alsochapter4inRoberts(1978).Thepaperremainsasuccinctandstillrelevant statementoftheneedforanimplementationfocus丘.omtheverystartofanymodelingproject.

84 PartI PerspectiveandProcess

models.Thischapterdiscussesthepurposeofmodeling,describestheprocessof systemdynamicsmodeling,theroleoftheclient,andthemodeler'Sprofessional andethicalresponsibilities･

3.1 THEPuRPOSEOFMoDELING:

MANAGERSASORGANIZAT10NDESIGNERS

JayForresteroftenasks,Whoarethemostimportantpeopleinthesafeoperation ofanaircraft?Mostpeoplerespond,Thepilots.Infact,themostimportantpeople arethedesigners.Skilled,well-trainedpilotsarecritical,butfarmoreimportantis designlnganaircraftthatisstable,robustunderextremeconditions,andthatordi- narypilotscanflysafelyevenwhenstressed,tired,orinunfamiliarconditions.In thecontextofsocialandbusinesssystems,managersplaybothroles.Theyarep1- lots,makingdecisions(whotohire,whatpricestoset,whentolaunchthenew product)andtheyaredesigners,shapingtheorganizationalstructures,Strategies, anddecisionrulesthatinfluencehowdecisionsaremade.Thedesignroleisthe mostimportantbutusuallygetstheleastattention.Tわomanymanagers,especially seniormanagers,spendfartoomuchtimeactingaSPilots-makingdecisions,tak1 1ngcontrolfromsubordinates-ratherthancreatlnganOrganizationalstructure consistentwiththeirvisionandvaluesandwhichcanbemanagedwellbyordinary people(seeForrester1965).

Tbdaydesignlnganewaircra氏isimpossiblewithoutmodelingandsimulation･ Managersseekingtoenhancetheirorganizationaldesigns女ills,however,continue todesignbytrialanderror,byanecdote,andbyimitationofothers,thoughthe complexltyOftheirorganizationsrivalsthatofanaircra氏･Ⅵrtualworldsprovide animportanttoolformanagersinboththeoperationandespeciallythedesignof theirorganizations｡

Thereisclearlyaroleformodelsthathelpmanagerspilottheirorganizations better,andsystemdynamicsisoftenusefulforthesepurposes.Buttherealvalue oftheprocesscomeswhenmodelsareusedtosupportorganizationalredesignJn IndustrialDynamics,Forrestercallsforcourageintheselectionofproblems,sayl lng,HThesolutionstosmallproblemsyieldsmallrewards-･Thegoalshouldbe to丘ndmanagementpoliciesandorganizationalstructuresthatleadtogreatersuc- cess,"Focusyourmodelingworkontheimportantissues,Ontheproblemswhere yourworkcanhavelastingbenefit,Ontheproblemsyoucaremostdeeplyabout･

3.2 THECuENT.ANDTHERIloDELEF篭

ModeiingdoesnottakepllaCeillSPierldidisolation.ItisembeddedillanOrgani- zationandsocialcontext.Evenbefわrethemodelingprocesspersebegins,血e modelermustgalnaccesstOtheorganizationandidentifytheclient.Theclientis notthepersonwhobringsyouintoanorganizationorchamplOnSyourWork,nor eventhepersonwhopaysforthemodelingstudy,thoughitishelpfultohave contacts,champions,andcash.Yourclientsarethepeopleyoumustinfluencefor yourworktohaveimpact･Theyarethosepeoplewhosebehaviormustchangeto solvetheproblem.YourclientcanbeaCEOoramachineoperatoronthefactory floor.Clientscanbeindividuals,groups,orentirecommunities･Theclientfora

Chapter3 TheModelingProcess 85

modelingstudycanbeyouracademiccolleagues,thepublicatlarge,orevenyou r -

self･Inthediscussionthatfollows,Iwillfocusonmodelingprojectsconductedfor organizations.Theprocess,however,issimilarfortheseothercontextsaswell.

Tobeeffectivethemodelingprocessmustbefocusedontheclients'needs.

Theclientsforamodelingprojectarebusy.Theyareembroiledinorganizational

politics.Theyarelookingoutfortheirowncareers.Theirconcernissolvinga problemandtakingactionintherealworld.Theycarelittlefortheeleganceof

yourtheoryorclevernessofyourmodel･Modelingisdonetohelptheclient,not forthebenefitofthemodeler.Theclientcontextandrealworldproblemdetermine

thenatureofthemodel,andthemodelingprocessmustbeconsistentwiththe clients'skills,capabilities,andgoals.Thepurposeistohelptheclientssolvetheir

problem.Iftheclientsperceiveyourmodeldoesnotaddresstheirconcernsorlose confidenceinit,youwillhavelittleimpact.Focusyourmodelingworkonthe

problemsthatkeeptheclientsupatnight. Thepoliticalcontextofmodelingandtheneedtofocusontheclients'problem

doesnotmeanmodelersshouldbehiredguns,willingtodowhatevertheclients

want･Modelersshouldnotautomaticallyaccedetoclients'requeststoinclude moredetailortofocusononesetofissueswhilelgnOrlngOthers,JusttOkeepthe

clientsonboard･Agoodmodelingprocesschallengestheclients'conceptlOnOfthe problem.ModelershavearesponsibilitytorequlretheirclientstoJustifytheir

oplnions,groundtheirviewsindata,andconsidernewviewpolntS.Whenthe clientsaskyoutodosomethingyouthinkisunnecessaryormlSguided,youmust workwiththemtoresolvetheissue.

Unfortunately,fartoomanyclientsarenotinterestedinlearningbutinuslng modelstosupportconclusionsthey'Vealreadyreachedorasinstrumentstogaln powerintheirorganizations.Sadly,fartoomanyconsultantsandmodelersare

onlytooeagertooblige.Asamodeleryouhaveanethicalresponsibilitytocarry outyourworkwithrigorandintegrlty.Youmustbewillingtoletthemodeling

processchangeyourmind･YoumustHspeaktruthtopower,Htellingtheclientsthat theirmostcherishedbeliefsarewrong,ifthatiswhatthemodelingprocessreveals, evenifitmeansyouwillbefired.Ifyourclientspushyoutogeneratearesult

they'veselectedinadvanceorthatisnotsupportedbytheanalysis,pushback.If yourclients'mindsareclosed,ifyoucan'tconvincethemtousemodelinghon-

estly,youmustquit･Getyourselfabetterclient･2

3,3 STEPSOFTHEMoDEuNGPROCESS

Inpractice,asamodeleryouarefirstbroughtintoanorganizationbyacontact whothinksyouoryourmodelingtoolsmightbehelpful.Yourfirsts+LePiStOfind outwhattherealproblemisandwhotherealclientis.Yourinitialcontactmaynot

betheclient,butonlyserveasagatekeeperwhocanintroduceyoutotheclient. AsthemodelingprojectProceeds,youmayfindtheclientgroupexpandsor changes.Assumethatyou'vesuccessfullynegotiatedentrytotheorganizationand

2wallace(1994)providesagoodcollectionofarticlesaddressingtheethicalissuesfacing modelers.

TABLE31l

StepsoHhe

modelingprocess

PartI PerspectiveandProcess

1.ProblemArticulation(BoundarySelection)

oThemese]ection:Whatistheproblem?Whyisitaproblem?

oKeyvariables:Whatarethekeyvariablesandconceptswemust consider?

｡Timehorizon:Howfarinthefutureshouldweconsider?Howfarbackin

thepastlietherootsoftheproblem?

oDynamicproblemdefinition(referencemodes):Whatisthehistorical

behavjorofthekeyconceptsandvariab-es?Whatmighttheirbehavior bejnthefuture?

2.FormulationofDynamicHypothesis

｡hitialhypothesisgeneration:WhatarecurrenHheoriesoftheproblem- aticbehavior?

.Endogenousfocus:Formulateadynamichypothesisthatexplainsthe dynamicsasendogenousconsequencesofthefeedbackstructure.

oMappng:Developmapsofcausalstructurebasedoninitialhypotheses, keyvariables,referencemodes,andotheravailabledata,uslngtools suchas

oModelboundarydiagrams,

oSubsystemdiagrams,

.CausaHoopdiagrams,

oStockandflowmaps,

｡Policystructurediagrams, ･Otherfacilitationtools.

3.FormulationofaSimulationModel

oSpeeifieationofstructure,decisJrOnrules.

｡Estimaiionofparameters,behavioralrelationships,andinitialconditions.

｡Testsforconsistencywiththepurposeandboundary.

4･Testing

oComparisontoreferencemodes:Doesthemodelreproducetheprob-

1embehavioradequatelyforyourpurpose?

｡Robustnessunderextremeeonditjons:Doesthemodelbehaverealis-

ticaHywhenstressedbyextremeconditions?

｡Sensitivity:HowdoesthemodelbehavegFVenuncertaintyJnParame- ters,initia一conditions,modelboundary,andaggregation?

. 日 . Manyothertests(Seechapter21).

5.Po一icyDesignandEvaluation

oScenariospecification:Whatenvironmenta一conditionsmightarise?

oPolicydesign:Whatnewdecisionru一es,StrategleS,andstructuresmight betriedintherealworld?Howcantheyberepresentedinthemodel?

. "Whatjf" }'anarysis:Whataretheeffectsofthepolicies?

oSensitivityanalysis:HowrobustarethepollCyrecommendationsunder differentscenariosandgivenuncertainties?

ohteractionsofp0日icies:Dothepoliciesinteract?AretheresynergleSOr compensatoryresponses?

Chapter3 TheModelingProcess 87

identifiedthe(initial)clients.Howdoyouproceedtodevelopamodelwhichcan

behelpfultothem?3

Thereisnocookbookrecipeforsuccessfulmodeling,noprocedureyoucan

followtoguaranteeausefulmodel.ModelinglSinherentlycreativeJndividual

modelershavedifferentstylesandapproaches.Yetallsuccessfulmodelersfollow

adisciplinedprocessthatinvolvesthefollowingactivities:(1)articulatingthe

problemtobeaddressed,(2)formulatingadynamichypothesisortheoryaboutthe

causesoftheproblem,(3)formulatingasimulationmodeltotestthedynamichy-

pothesis,(4)testingthemodeluntilyouaresatisfieditissuitableforyourpurpose,

and(5)designingandevaluatingpoliciesforimprovement.Table3-1liststhese stepsalongwithsomeofthequestionseachstepaddressesandtheprlnClpaltools usedineach(seealsoRan°ers1980).

3.4 MoDELINGIsITERATIVE

Beforediscusslngeachofthesestepsinmoredetail,itisimportanttoplacethe

modelingprocessincontextwiththeongolngactivitiesofthepeopleinthesystem.

ModelinglSafeedbackprocess,notalinearsequenceofsteps･Modelsgothrough

constantiteration,continualquestionlng,testing,andrefinement.Figure311re-

CaststhemodelingprocessshowninTable3-1moreaccuratelyasaniterative

cycle･Theinitialpurposedictatestheboundaryandscopeofthemodelingeffort,

butwhatislearnedfromtheprocessofmodelingmayfeedbacktoalterourbasic

understandingoftheproblemandthepurposeofoureffort.Iterationcanoccur

fromanysteptoanyotherstep(indicatedbytheinterconnectionsinthecenterof

thediagram)･Inanymodelingprqjectonewilliteratethroughthesestepsmany times.4

FIGURE3- 1

Themode‖ng processis iterative.

Resultsofany stepcanyield insightsthatlead torevisionsin

anyea仙erstep (indicatedbythe linksinthecenter

ofthediagram)･

3ThereisahugeliteratureonmethodsforplannedorganizationalchangeandgrouplnterVen-

tions･SeeparticularlyArgyrisandSch6n(1996),BeckhardandHarris(1987),Dyer(1995), Michael(1997),andSchein(1987,1988).

4Homer(1996)providesanexcellentdiscussio.nofthevalueofiterationandrigorinsystem dynamics,notonlylnacademicresearchbutalsolnCOnSultingwork,withavarietyofexamples･

FIGURE3-2

Mode一inglS embeddedin

thedynamics ofthesystem.

Effectivemode=ng invo一vesconstant iterationbetween

experimentsand learn-ngJnthe virtualworldand

experiments andleamlngln therealworld.

PartI PerspectiveandProcess

Mostimportantly,modelinglSembeddedinthelargercycleoflearnlngandac-

tionconstantlytakingplaceinorganizations(anddescribedinchapter1)･Pilots

stepIntoanaircraftflightsimulatorandlearnmorequickly,effectively,andsafely howtooperatetherealaircraft,thenputtheseskillstouseintherealthing.They

feedbackwhattheylearnflyingtherealthingtothesimulatordesignerssothe simulatorscanbecontinuallylmprOVed.Whatpilotsanddesignerslearninthe simulatorisusedintherealworld.Andwhattheylearnintherealworldisusedto

changeandimprovethevirtualworldofthesimulator･Soitiswithmanagement flightsimulatorsandsystemdynamicsmodels.Figure3-2Showsthemodeling

processembeddedintheslngle-anddouble-loopleamingfeedbacksdiscussedin chapterI.Simulationmodelsareinformedbyourmentalmodelsandbyinforma-

tiongleanedfromtherealworld.Strategies,Structures,anddecisionrulesusedin therealworldcanberepresentedandtestedinthevirtualworldofthemodel.The

experimentsandtestsconductedinthemodelfeedbacktoalterourmentalmodels andleadtothedesignofnewstrategleS,newStructures,andnewdecisionrules･ Thesenewpoliciesarethenimplementedintherealworld,andfeedbackabout theireffectsleadstonewinsightsandfurtherimprovementsinbothourformaland

Chapter3 TheModelingProcess 89

mentalmodels.ModelinglSnotaOne-ShotactivitythatyieldsTheAnswer,butan

ongolngprocessOfcontinualcyclingbetweenthevirtualworldofthemodeland therealworldofaction.

3.5 0vERV日EW OFTHEMoDELENGPROCESS

3.5.1 ProblemArticulation:

The!mPOi､tanceofPurpose

ThemostimportantsteplnmodelinglSproblemarticulation･Whatistheissuethe

clientsaremostconcernedwith?WhatproblemaretheytrylngtOaddress?Whatis therealproblem,notjustthesymptomofdifficulty?Whatisthepurposeofthe model?

AclearpurposeisthesinglemostimportantIngredientforasuccessfulmod- elingstudy.Ofcourse,amodelwithaclearpurposecanstillbemisleading,un- wieldy,anddifficulttounderstand.Butaclearpurposeallowsyourclientstoask

questionsthatrevealwhetheramodelisusefulinaddressingtheproblemtheycare about.

Bewaretheanalystwhoproposestomodelanentirebusinessorsocialsystem

ratherthanaproblem.Everymodelisarepresentationofasystem-agroupof functionallyinterrelatedelementsformingaCOmPlexwhole.Butforamodeltobe

useful,itmustaddressaspecificproblemandmustsimplifyratherthanattemptto mirroranentiresystemindetail.

Whatisthedifference?Amodeldesignedtounderstandhowthebusinesscy-

Clecanbestabilizedisamodelofaproblem･Itdealswithaspecificpolicyissue. Amodeldesignedtoexplorepoliciestoslowfossilfueluseandmitlgateglobal warmlnglSalsoamodelofaproblem;ittooaddressesonlyalimitedsetofissues.

AmodelthatclaimstobearepresentationoftheentireeconomylSamodelofa wholesystem.Whydoesitmatter?Theusefulnessofmodelsliesinthefactthat theysimplifyreality,Creatlngarepresentationofitwecancomprehend.Atruly comprehensivemodelwouldbejustascomplexasthesystemitselfandjustasin- Scrutable.YonClausewitzfamouslycautionedthatthemaplSnottheterritory.It's

agoodthingitisn't:Amapasdetailedastheterritorywouldbeofnouse(aswell asbeinghardtofold).

Theartofmodelbuildingisknowingwhattocutout,andthepurposeofthe modelactsasthelogicalknife.Itprovidesthecriteriatodecidewhatcanbeig- noredsothatonlytheessentialfeaturesnecessarytofulfillthepurposeareleft.In

theexampleabove,sincethepurposeofthecomprehensivemodelwouldbetorep- resenttheentireeconomicsystem,nothingcouldbeexcluded.Tbanswerallcon一

ccivablequestionsabouttheeconomy,themodelwouldhavetoincludean overwhelmlngarrayOfvariables.Becauseitsscopeandboundaryaresobroad,the modelcouldneverbecompleted.Ifitwere,thedatarequiredtouseitcouldnever

becompiled.Iftheywere,themodel'sunderlyingassumptlOnSCOuldneverbe examinedortestedJftheywere,themodelbuilderscouldneverunderstandits behaviorandtheclients'confidenceinitwoulddependontheauthorityofthe modelerandothernonscientificgrounds.MihailoMesarovic,adeveloperofearly

90 PartIPerspectiveandProcess

globalsimulations,capturedtheimpossibilityofbuildingmodelsofsystemswhen

hesaid,HNomatterhowmanyresourcesonehas,onecanenvisionacomplex enoughmodeltorenderresourcesinsufficienttothetask."(Meadows,Richardson,

andBruckmann1982,p.197).

Amodeldesignedforaparticularpurposesuchasunderstandingthebusiness

cycleorglobalclimatechangewouldbemuchsmaller,sinceitwouldbelimitedto

thosefactorsbelievedtoberelevanttothequestionathand.Forexample,thebusi-

nesscyclemodelneednotincludelong-ten trendsinpopulationgrowth,resource

depletion,orclimatechange.Theglobalwarmlngmodelcouldexcludeshorトーerm

dynamicsrelatedtointerestrates,employment,andinventories.Theresulting

modelscouldbesimpleenoughsothattheirassumptlOnSCOuldbeexamined.The

relationoftheseassumptlOnStOthemostimportanttheoriesregardingthebusiness cycleandclimatechangecouldthenbeassessedtodeterminehowusefulthemod-

elswerefortheirintendedpurposes.Ofcourseevenmodelswithwell-definedpu r -

posescanbetoolarge.Butwithoutaclearpurpose,thereisnobasistosay"we

don'tneedtoincludethat"whenamemberoftheclientteammakesasuggestion.

Insum:Alwaysmodelaproblem.Nevermodelasystem･

Usuallythemodelerdevelopstheinitialcharacterizationoftheproblem

throughdiscussionwiththeclientteam,supplementedbyarchivalresearch,data

collection,interviews,anddirectobservationorparticipation.Therearemany

methodsavailabletoworkwithagrouptoelicittheinformationneededtodefine

theproblemdynamicallywhilestillkeeplngtheconversationfocusedfirmlyonthe

clientsandtheirproblem.5Twoofthemostusefulprocessesareestablishingrefer- encemodesandexplicitlysettingthetimehorizon.

ReferenceModes

Systemdynamicsmodelersseektocharacterizetheproblemdynamically,thatis,

asapatternofbehavior,unfoldingovertime,whichshowshowtheproblemarose

andhowitmightevolveinthefuture.Youshoulddevelopareferencemode,liter-

allyasetofgraphsandotherdescrlptlVedatashowingthedevelopmentofthe problemovertime.Referencemodes(so-Calledbecauseyoureferbacktothem

throughoutthemodelingprocess)helpyouandyourclientsbreakoutoftheshort-

termevent-orientedworldviewsomanypeoplehave･Tbdosoyouandtheclients

mustidentifythetimehorizonanddefinethosevariablesandconceptsyou

considertobeimportantforunderstandingtheproblemanddesigningPOliciesto solveit.

TimeHon'zon

Thetimehorizonshouldextendfarenoughbackinhistorytoshowhowtheprob-

lememergedanddescribeitssymptoms.Itshouldextendfarenoughintothe

futuretocapturethedelayedandindirecteffectsofpotentialpolicies.Mostpeople

dramaticallyunderestimatethelengthoftimedelaysandselecttimehorizonsthat

5seethereferencesinnote9formodelingtoolsthatareeffectiveforrea一timemodelingwith organizationsandteamsincludingelicitingandstructurlngthementalmodelsofagrouptodefine theproblem.

Chapter3 TheModelingProcess 91

arefartooshort･AprlnCIPaldeficiencylnOurmentalmodelsisourtendencyto

thinkofcauseandeffectaslocalandimmediate.Butindynamicallycomplexsys-

tems,Causeandeffectaredistantintimeandspace.Mostoftheunintendedeffects

ofdecisionsleadingtopolicyresistanceinvolvefeedbackswithlongdelays,farre-

movedfromthepolntOfdecisionortheproblemsymptom･Workwithyourclients

tothinkaboutthepossiblereactionstopoliciesandhowlongtheymighttaketo

playoutandthenincreasethetimehorizonevenfurther.Alongtlmehorizonisa

criticalantidotetotheevenLorientedworldviewsocrlpplingtoourabilitytoiden-

tifypatternsofbehaviorandthefeedbackstructuresgeneratlngthem.

ThechoiceoftimehorizondramaticallyinfluencesyourperceptionOfthe

problem.Figure3-3showsproduction,consumptlOn,andimportsofpetroleumin

theUnitedStatesfrom1986to1996.Thehistoricaltimehorizonis10years,al-

readyalongtimerelativetomostdiscussionofenergypolicy(theoilshocksof

the1970sareconsideredancienthistoryinmostpolicydebatetoday).Thegraphs

showproductionslowlytrendingdown,consumptlOntrendingslowlyup,and

thereforeimportsgrowlngmodestly.Pricesfluctuateinanarrowbandbetween

$14and$23perban℃1,lowerthananytimesincethe丘rstoilcrisisin1973(though

pricesdidspiketo$40/barrelaftertheIraqiinvasionofKuwait,theysoonfell

back)･Theenergysystemappearstoberelativelystable;thereislittleevidenceof

along-termproblem.

FIGURE3-3

USoilproduction, consumption, imports,andpr]ce overa10-year timehorizon

1986 1988 1990 1992 1994 1996

MqJ$066L

Source:EIA(USEnergylnformatl0nAgency)AnnualEnergyF7eviewr

FIGURE3-4 USoilproduction, consumption, imports,andprlCe overa130-year timehorizon

PartI PerspectiveandProcess

NowconsiderFigure3-4,showingthesamevariablesfromnearthebeginning oftheoilera(thepetroleum industrybeganinearnestin1859withColonel

Drake'sfamouswellinTitusville,Pennsylvania)･Theimpressioniscompletely different.ThehistoryoftheoilindustrylntheUnitedStatesisdividedintotwo

reglmeS･From1920through1973,consumptlOngreweXpOnentiallyatanaverage

rateof4･3%/year･Productionnearlykeptpace,asexplorationandbetterdrilling

techniquesmorethanoffsetdepletion.Startinglnthe1950S,importsgrewslightly,

StimulatedbytheavailabilityofcheapforeignOil.Pricesfluctuated,oftendramat-

ically,butalongaslowlydeclinlngtrendastechnologylmprOVed.Allthischanged

in1970･In1970,domesticproductionofoilpeaked.It'sbeenfallingeversince,

despitetheintenseexplorationstimulatedbythemuchhigherprlCeSOfthe1970s

andearly1980S･USproductionfromthelower48statesandadjacentoffshorearea

in1996stoodatonly54%ofitspeaklevel.EventheadditionofPrudhoeBayand

thetrams-Alaskaplpelinedidnothalttheslide,andAlaskanproductionpeakedin

1988･HigherprlCeSfollowlngthe1970Soilshocks,alongwiththedeepestreces-

sionssincetheGreatDepression,cutthegrowthofconsumptlOn,butimportsnev-

erthelessreached61%oftotaloilconsumptionby1996.

Changlngthetimehorizoncompletelychangestheassessmentoftheproblem. Viewedwithatimescaleconsistentwiththelifeoftheresource,itisclearthatthe

petroleumproblemwasn'tsolvedinthe1980sbuthasbeensteadilygettlngworse.

¶m

,■l

^ e

clJS ]a JJt2g

u O ≡ !yU

1870 1890 1910 1930 1950 1970 1990

Source:Production&consumption:1870-1949,Davidsen(1988),1950-1966,EIAAnnua/Energy

F7eview･Price:1880-1968,Davldsen(1988);1968-1996,EIAAnnualEnergyReview,Refiners AcqulSit10nCost.

Chap te r 3 T h eM odelingPro cess 93

Petroleumisafinitenonrenewableresource.IntheUS,depletionbegantodomi-

natefindingratesinthe1960S,leadingtoaninevitabledeclineinproduction,ade-

clinethatbeganin1970.TheUnitedStatesisthemostheavilyexploredand

denselydrilledregionOftheworld.Theverysuccessofearlywildcattersinfind-

1ngOilmeansthereislesslefttofindnow.WhilenotallthepetroleumintheUS

hasbeenfoundorrecovered,consumptlOnCOntinuestoexceedtherateatwhich

whatremainsisfound.Consequently,1mpOrtSCOntinuetogrow,leadingtostill

greaterdependencyontheunstablePersianGulfreglOn,Stillmorepoliticaland

economicpowerfortheoilexportlngCOuntriesandlessfortheUS,and,eventu-

ally,higheroilprices,eitheratthepumporinthedefensebudget･6

Theoilindustryillustratesthedangersofselectingatimehorizontooshortto

capturetheimportantdynamicsandfeedbackscreatlngthem.Ofcourse,onecan

errtoofarintheotherdirection.Figure3-5Showsagraphdevelopedbythelate

petroleumgeologistM･K血gHubbert.Hubbertinventedthemostsuccessfultech-

niqueforforecastlngfossilfuelproductionevercreated.In1956heestimatedthe

ultimaterecoverablepetroleumresourcesoftheUStobebetween150and200bil-

lionbarrelsandforecastthatHthepeakinproductionshouldprobablyoccurwithin

theinterval1966-1971"(Hubbert1975,p.371)･Hispredictionofdeclinecameat

atimewhentheUSGeologicalSurveyprojectedultimaterecoverableresources

nearlythreetimesaslargeandclaimedHthesizeoftheresourcebasewouldnot

limitdomesticproductioncapacltyGinthenext10to20yearsatleast,andproba-

blylnot]foramuchlongertime" (Gillette1974).Theactualpeakoccurredin

1970atalmosttheprecisevalueHubberthadpredicted,oneofthemostaccurate

long-termforecastsonrecord.Hubbert'ssuccesslaylnexplicitlymodelingoilas

anonrenewableresource.Productioncouldgrowexponentiallyintheearlyphases

FIGURE3-5 Thefossilfuel

erashownwitha

timehorizonof

15,000years

uo !ton po l

d ^ 6Jau u

l]S S

O m

110,000 -5000

Source:AdaptedfromHubbert(1962)

irogne o.ndus.Z もS.｡i. 5000 Year Revolutl0nShock

6ThereisalargeliteratureofenergymodelinglnSystemdynamics70rlglnatlngWithworkin Meadowsetal･(1974)･See,e.g.,Backus(1996),BunnandLarsen(1997),Fiddaman(1997), Ford(1990,1997,1999),FordandBull(1989),Naill(1977,1992),andNailletal.(1992)for workonnationalandglobalenergymarkets,electricutilities,globalclimatechange,andother energypolicylSSueS･

94 PartI PerspectiveandProcess

ofitslifecyclebuthadtofalltozeroasitwasdepleted,forcingatransitiontore-

newableenergysources･7Tbemphasizethetransitorynatureoffossilfuelciviliza-

tion,Hubbertshowedtheproductionoffossilfuelsonatimescalefrom the

beginnlngOftheagrlCulturalrevolution10,000yearsagoto5000yearsinthefu-

ture.Againstthisbackdrop,thefossilfueleraisseenasatransitoryspike-a

unlqueperiodduringwhichhumanltylivesextravagantlyoffarichinheritanceof

irreplaceablenaturalcapital.Thepictureissobering.ButHubbert'splmPle,asit

wascalledbycritics,takesatimehorizontoolongtobeusefultopolicymakers

whoinfluencepublicpolicyorcorporatestrategyaffectingenergyprices,regula-

tions,capitalinvestment,andR&D.

Thechoiceoftimehorizoncandramaticallyinfluencetheevaluationof

policies.Intheearly1970saUSgovernmentagencyconcernedwithforeignaid

sponsoredamodelfocusedontheSahelreglOnOfsub-SaharanAfrica.TheSahel

wasthenexperienclngrapidpopulationgrowthatthesametimethedesertwas

expandingsouthward,reducinggrazlnglandforthenomadicherders'cattle.The

purposeofthemodelwastoidentifyhighleveragepoliciestospureconomic

developmentintheregion.Themodelwasusedtoassesstheeffectsofmanyof

thepoliciestheninuse,suchasdrillingboreholestoincreasethewatersupplyfor

cattlebytappingdeepaquifersorsubsidizingcropssuchassorghumandground

nuts.Runnlngthemodeltotheyear2000,aroundnumberseveraldecadesinthe

futureatthetime,Showedthatthepoliciesledtoimprovement.Subsidiesin-

creasedagrlCulturaloutput.Boreholespermittedcattlestockstogrow,increaslng

thesupplyofmilkandmeatandthewealthoftheherders.However,runnlngthe

modelintothefirstdecadesofthe21stcenturyshowedadifferentoutcome:larger

stocksofcattlebegantooutstripthecarrylngCapaCltyOfthereglOn.Asthecattle

overbrowsedandtrampledthegrasslands,erosionanddesertificationincreased.

Thecattlepopulationdroppedsharply,creatingafooddeficitinthereglOn.Selectl

lngatimehorizontooshorttocapturethesefeedbacksfavoredadoptionOfpoli-

ciescountertothelong-terminterestsofthereglOn'speopleandthemissionofthe

clientorganization･8

ModelersmustguardagalnStaCCeptlngtheclient'sinitialassessmentoftheap-

propriatetimeframe.Oftenthesearebasedonmilestonesandroundnumbershavl

lnglittletodowiththedynamicsoftheproblem,suchastheendofthefiscalyear,

Orthenext5-yearplannlngCycle.Agoodruleofthumbistosetthetimehorizon

severaltimesaslongasthelongesttimedelaysinthesystem,andthensome.

3息2 Formu月a抽gaDynamicHypo竜的es岳s

Oncetheproblemhasbeenidentifiedandcharacterizedoveranappropriatetime

horizon,modelersmustbegintodevelopatheory,calledadynamichypothesis,to

7stermanandRichardson(1985),Stermanetal.(1988),andSterman,Richardson,andDavidsen

(1990)modeltheworldandUSpetroleumlifecyclesandstudythee.Volutionofestimatesofthe resourcebase,ShowingwhyHubbertwassoaccuratewhileotherestlmationmethodsprovedso wildlyoveroptlmistic.

8picardiandSeifert(1976)describeoneofseveralmodelsoftheSahelregion(themodel describedabovewasnotpublished).

Chapter3 TheModelingProcess 95

accountfortheproblematicbehavior.Yourhypothesisisdynamicbecauseitmust

provideanexplanationofthedynamicscharacterlZlngtheproblemintermsofthe

underlyingfeedbackandstockandflowstructureofthesystem.Itisahypothesis

becauseitisalwaysprovisional,subjecttorevisionorabandonmentasyoulearn

fromthemodelingprocessandfromtherealworld.

Adynamichypothesisisaworkingtheoryofhowtheproblemarose.Itguides

modelingeffortsbyfocuslngyouandyourclientsoncertainstructures.Muchof

theremainderofthemodelingprocesshelpsyoutotestthedynamichypothesis,

bothwiththesimulationmodelandbyexperimentsanddata_collectioninthereal world.

hpractice,discussionoftheproblemandtheoriesaboutthecausesofthe

problemareJumbledtogetherinconversationwithclientteams.Eachmemberof

ateamlikelyhasadifferenttheoryaboutthesourceoftheproblem;youneedto

acknowledgeandcapturethemall.ManytlmeSthepurposeofthemodelistosolve

acriticallyImportantproblemthathaspersistedforyearsandgeneratedgreat

conflictandnotalittleanimosltyamongmembersoftheclientteam.Allwill

tenaciouslyadvocatetheirpositionswhilederidingtheviewsofothersinthe

group･Earlylnthemodelingprocess,themodelerneedstoactasafacilitator,cap-

turlngthesementalmodelswithoutcriticizlngOrfilteringthem.Clarifyingand

probingquestionsareoftenuseful,butthemodeler'sroleduringthisearlyphaseis

tobeathoughtfullistener,notacontentexpert･Avarietyofelicitationtechniques

anddiagrammlngtoolshavebeendevelopedtoassistyouinfacilitatlngaProduc-

tiveconversationtoelicitpeople'Stheoriesaboutthecausesoftheproblem･9Your

goalistohelptheclientdevelopanendogenousexplanationfortheproblematic

dynamics.

EndogenousExplanatlron

Systemdynamicsseeksendogenousexplanationsforphenomena.Theword"en-

dogenous"means"arisingfromwithin･''Anendogenoustheorygeneratesthedy-

namicsofasystemthroughtheinteractionofthevariablesandagentsrepresented

inthemodel･Byspecifyinghowthesystemisstructuredandtherulesofinterac-

tion(thedecisionrulesinthesystem),youcanexplorethepatternsofbehaviorcre-

atedbythoserulesandthatstructureandexplorehowthebehaviormightchange

ifyoualterthestructureandrules.Ⅰncontrast,atheoryrelyingonexogenousvari-

ables(those"arisingfromwithout,"thatis,from outsidetheboundaryofthe

model)explainsthedynamicsc･fvariablesyoucareaboutintermsofothervari-

ableswhosebehavioryou'veassumed.Exogenousexplanationsarereallynoex-

planationatall;theysimplybegthequestion,Whatcausedtheexogenous

variablestochangeastheydid?Thefocusinsystemdynamicsonendogenousex-

planationsdoesnotmeanyoushouldneverincludeanyexogenousvariablesin

yourmodels.ButthenumberofexogenousInputsShouldbesmall,andeachcan-

didateforanexogenousInputmustbecarefullyscrutinizedtoconsiderwhether

9Theliteratureongroupmodelbuildingisgrowingrapidly.Reagan-Cirincioneetal.(1991), MorecroftandSterman(1994),Vennix(1996),andVennixetal.(1997)providegoodoverviewsof toolsandtechniquestoelicitandcapturethementalmodelsofteamsandclientgroups.

96 PartI PerspectiveandProcess

thereareinfactanyImportantfeedbacksfromtheendogenouselementstothecan-

didate.Ifso,theboundaryofthemodelmustbeexpandedandthevariablemustbe modeledendogenously.

Theconsequencesofnarrowmodelboundariesandrelianceonexogenous variablesareoftenserious.AtypicalexampleisprovidedbytheProjectIndepen- denceEvaluationSystem(PIES)model,ahybridmodelbasedonlinearprogram- mlng,eCOnOmetrics,andinput/outputanalysisusedinthe1970sbytheUSFederal EnergyAdministration(FEA)andlaterbytheUSDepartmentofEnergy.Asde- scribedbythePEA,thepurposeofthemodelwa-stoevaluatediffererl-tenergyPOli- ciesaccordingtothefollowlngCriteria:theirimpactonthedevelopmentof alternativeenergysources;theirimpactoneconomicgrowth,inflation,andunem- ployment;theirreglOnalandsocialimpacts;theirvulnerabilitytoimportdisrup- tions;andtheirenvironmentaleffects.

SurprlSlngly,consideringthestatedpurpose,thePIESmodeltreatedtheecon- omyasexogenous.Themodeleconomy(includingeconomicgrowth,interest rates,inflation,worldoilprices,andthecostsofunconventionalfuels)wascom- pletelyunaffectedbytheenergysituation(includingprices,policies,andproduc- tion).Inthemodel,evenafullembargoofimportedoiloradoublingofoilprices wouldhavenoimpactontheeconomy.

TreatlngtheeconomyexogenouslymadethePIESmodelinherentlycontra- dictory.Becauseitassumedhighratesofeconomicgrowthandlowpriceelastici- ties,ltprq】eCtedhugeincreasesinenergydemand,requlrlngevengreaterincreases inthecapitalrequlrementSOftheenergysectorascheapdomesticoilwascon- sumed.Inthemodel,thesehugeinvestmentsinenergyproductionweresatisfied withoutreducinglnVeStmentOrCOnSumptlOnintherestoftheeconomyandwith noimpactoninterestratesorinflation.Ineffect,themodellettheeconomyhave itsplcandeatittoo.

InpartbecauseitIgnoredthefeedbacksbetweentheenergysectorandtherest oftheeconomy,thePIESmodelconsistentlyprovedtobeoveroptlmisticJn1974 themodelprqectedthatby1985theUSwouldbewellonthewaytoenergy independence:energyImportsWOuldbeonly3.3millionban℃lsperdayand productionofshaleoilwouldbe250,000barrelsperday.Furthermore,these developmentswouldbeaccompaniedbyoilpricesofabout$22perbarrel(1984 dollars)andbyvigorouseconomicgrowth.Itdidn'thappen.Ⅰmportsinthelate 1980Swereabout5.5millionbarrelsperdayandgrewtomorethanhalfofoilcon- sumptlOnbythemid1990S.Shaleoilandotherexoticsynfuelsnevermaterialized･ ThissituationprevaileddespitehugereductionsinoildemandcausedbyoilprlCeS intheearly1980sgreaterthan$30/bblandthemostseriousrecessionsincethe GreatDepression.

Abroadmodelboundarythatcapturesimportantfeedbacksismoreimpor- tantthanalotofdetailinthespecificationofindividualcomponents.Itisworth notlngthatthePIESmodelprovidedabreakdownofsupply,demand,andpricefor dozensoffuelsineachreglOnOfthecountryyetitsaggregateprojections weren'tevenclose.Whatpurposewasservedbytheeffortdevotedtoforecastlng thedemandforJetfuelornaphthainthePacificNorthwestwhenthebasicasI sumptlOnSWereSOpalpablyInadequateandthemainresultsweresowoefully erroneous?

Chapter3 TheModelingProcess 97

MapplngSystemStructure Systemdynamicsincludesavarietyoftoolstohelpyoucommunicatethebound一

打yofyourmodelandrepresentitscausalstructure･Theseincludemodelbound- arydiagrams,subsystemdiagrams,causalloopdiagrams,andstockandflow

mapS･

Modelboundarychart. Amodelboundarychartsummarizesthescopeofthe modelbylistlngWhichkeyvariablesareincludedendogenously,whichareexoge- nous,andwhichareexcludedfromthemodel.

Toillustrate,Table312showsamodelboundarydiagramforamodeldesigned

tostudythefeedbacksbetweentheenergysystem andtheeconomy(Sterman

1983).PartlyinreactiontothelimitationsofexistingmodelssuchasPIES,theDe- partmentofEnergylnthelate1970ssoughttodevelopdynamicmodelswitha broaderboundary(Naill1977,1992).Thepurposeofthemodelwastoexplorethe

impactofhigherenergypricesOneconomicgrowth,unemployment,inflation,and interestratesandhowthesemacroeconomicconsiderationsmightconstrainthede-

velopmentofnewenergysources.Thetimehorizonofthemodelwasquitelong (195012050)tocapturethefulltransitionfromfossilfuelstorenewableorother energysourcesandconsistentwiththelongtlmedelaysinthedevelopment,con- struction,andusefullifeofenergy-producingandenergy-consumingCapital stocks.

Incontrasttonearlyallmodelsusedtoaddresstheseissuesatthetime,the modelhadabroadboundary,withallmajormaCrOeCOnOmicvariablesgenerated endogenously.UnlikethePIESmodel,thecapltal,labor,andenergyrequlrementS

TABLE312 Modelboundary chartforarong- termmode一of

energy-economy interactions

Endogenous Exogenous Excluded

GNP Population Inventories

Consumption TechnologlCalchange Internationaltrade investment Taxrates

Savings

Prices(realandnominal)

Wages(realandnominal) lnflationrate

Laborforceparticlpation

Emp一oyment

Unemployment lnterestrates

Moneysupply Debt

Energyproduction

Energydemand

EnergyImports

Energypolicies

(exceptwithOPEC) Environmenta一constraints

Nonenergyresources lnterfuelsubstitution

Distributionalequity

Source:Sterman(1983).

98 PartI PerspectiveandProcess

oftheenergyindustrieswereendogenousandtheenergyindustryhadtocompete agalnStOthersectorsfortheseresources.Themodelstillcontainedseveralexoge- nousvariables.Theseincludepopulation,therateofoveralltechnologlCal

progress,andtheprlCeOfimportedoil･Werethesee呆ogenousvariablesaccept- able?Populationgrowthandtheoverallrateoftechnicalprogressmightbeaf- fectedbychangesinenergyprlCeSandconsequentchangesintherateofeconomic

growth.However,thesefeedbacksseemedlikelytobesmall･Thedecisionto modeltheprlCeOfimportedoilexogenouslyismoreproblematic･ClearlytheprlCe ofoilaffectsboththedemandforandsupplyofenergylntheUnitedStates,deter-

miningthequantityImported.Asamajorimporter,changesinUSoilimportscan dramaticallyalterthesupply/demandbalanceoftheoilexportlngnations,feeding backtothepriceOfoilintheworldmarketTreatlngImportPrlCeSeXOgenOuSly cutsanimportantfeedbackloop.IndiscussingtheboundaryofthemodelIargued thattherewereinfactimportantfeedbacksbetweentheUSenergysystemandthe worldoilmarket.ButlalsoarguedthatthedynamicsoftheworldprlCeWereSO complexthatincorporatlngthemendogenouslywasbeyondthescopeandpurpose oftheprq】ect.Ihadpreviouslyhelpedbuildamodeloftheworldoilmarketforthe USDepartmentofEnergyandhopedthatultimatelythetwomodelscouldbe JOined.ThemodelboundarychartalertedtheclientstoaquestionableassumptlOn sotheycouldevaluatewhattheeffectofthemisslngfeedbackmightbe.

ThelistofexcludedconceptsalsoprovidesimportantwarnlngStOthemodel user.Themodelomittedinventoriesofgoodsandmaterials(andhenceshort-ten businesscycles)-noprobleminsuchalong-termmodeHnternationaltradewas excluded,exceptfortheflowsofoil,goods,capital,andmoneybetweentheUS andtheoilexportlngnations.ThepetrodollarsflowlngtOOPECandtheirrecy- clingasexportsorfbrelgninvestmenthadtobeincluded,buttoincludenonenergy tradewouldhaveexpandedthemodelintoaglobalmacroeconomicsystem,andI wouldprobablystillbeworkingonit,Environmentalconstraintsandnonenergy resourcessuchaswaterthatmightlimitnewenergysourceslikesynfuelswereexI cluded,meanlngCOnClusionsabouttherateofdevelopmentoftheseexoticenergy sourceswouldbeoveroptlmistic.Themodelalsotreatedtheenergysystemina fairlyaggregatefashion,sointerfuelsubstitution(oilvs･gas,forexample),wasnot considered,anotheroptlmisticassumption.Finally,themodeldidnotconsider incomedistribution,eventhoughsomeenergypoliciessuchasgasolinetaxesare

regressiveunlessoffsetbychangesintheincometaxcode･Thepurposeoflisting alltheseomissionsfromthemodelwastohelpmodelusersdecideforthemselves

whetherthemodelwasapproprlatefortheirpurpose･ Modelboundarydiagramsaresurprisinglyusefulandshockinglyrare･Often,

modelsareusednotastoolsofinqulrybutasweaponsinawarofadvocacy, Insuchcasesmodelersseektohidetheassumpt10nSOftheirmodelsfrompotential critics.Butevenwhenthemodelers'motivesarebenign,manyfeeluncomfortable

listlngWhatthey'veleftout,seetheomissionsasflawsandprefertostressthe strengthsoftheirmodel.WhilethistendencylSnatural,itundercutstheutilityof yourmodelandweakenstheabilityofpeopletolearn丘.omandimproveyour work.Byexplicitlylistlngtheconceptsyouhavechosennottoinclude,atleast fornow,youprovideavisiblereminderofthecaveatstotheresultsandlimitations ofthemodel,WithoutaclearunderstandingoftheboundaryandassumptlOnS,

Chapter3 TheModelingProcess 99

modelsconstructedforonepurposearefrequentlyusedforanotherforwhichthey

areill-suited,Sometimesproducingabsurdresults.Alltoooftenmodelswithcom -

pletelyInappropriateandevenbizarreassumptlOnSaboutexogenousandexcluded

variablesareusedinpolicymakingbecausethemodelusersareunabletoexam-

inetheboundaryofthemodelsthemselvesandthemodelershavenotprovided

thatinformationforthem(chapter21providesexamples;seealsoMeadowsand

Robinson1985).

Subsystemdiagram.Asubsystemdiagramshowstheoverallarchitectureof

amodel.EachmajorSubsystemisshownalongwiththeflowsofmaterial,money,

goods,information,andsooncouplingthesubsystemstooneanother.Subsystems

canbeorganizationssuchasthefirmandthecustomerororganizationalsubunits

suchasoperations,marketing,andproductdevelopment･Subsystem diagrams

conveyinformationontheboundaryandlevelofaggregationinthemodelby

showingthenumberandtypeofdifferentorganizationsoragentsrepresented.

Theyalsocommunicatesomeinformationabouttheendogenousandexogenous variables.

Inthe1960SJayForresterservedontheboardsofseveralsuccessfulhigh-tech

companiesandbecameinterestedinthedynamicsofcorporategrowth.Tbhelp

him thinkaboutthestrategicissuesfacingthesefirms,Forrester(1964,p.32)

createdamodeldesigned"toshowhowthedifferingkindsofcorporategrowth

patternscanbecreatedbydifferentcorporatepoliciesandmanagementattitudes

andbytheinteractionsbetweenacompanyanditsmarket.HFigure3-6showsthe

referencemode.Forrester(pp.32133)explained:

Theveryrarecompanygrowssmoothly,asincurveA,andeventuallyreaches ahealthysustainedplateauofmaturelife.Morefrequently,thecompanyfollowsa pattern,asincurveB,whereitappearstosucceedatfirstandthenencountersa severecrisisthatleadstobankruptcyormerger.Often,thepatternisgrowthstag- nation,asincurveC,markedbyneithersuccessnorfailure.Ofthosecompanies whichdoshowalong-termgrowthtrend,themostcommonpatternisthatin curveD,wheregrowthisaccompaniedbyrepeatedcrisis.

FIGURE3-6 Patternsof

corporategrowth

Time

Sou/℃e.'AdaptedfromForrester(1964).

100

FIGURE3-7 Subsy stem diagra mfor Forrester's corpo rategrowth

mode一

PartiPerspectiveandProcess

Forresterarguedthat"contrarytofirstimpressions,onecannotexplainthese

differencesonthebasisoftheparticularindustryorthetypeanddesignofprod-

ucts...Onemustthereforelookdeeperintothestructureofinformationflowsand

thepolicieswhichguideoperatingdecisions"(p･33)･Todosothemodelconsisted

oftwosubsystems,thecompanyandthemarket(Figure3-7)･

Thetwosubsystemsarecoupledbytheobviousflowsoforders,product,and

money:Thefirmreceivesordersfromthemarket,shipsproduct,andreceivespay-

ment.Butinaddition,thefirmsendssignalstothemarketincludingthepriceOf

theproduct,itsavailability(measuredbythedeliverydelay),itsfunctionality,

quality,suitabilitytocustomerneeds,andotherintangibleattributesofthecom-

pany'sreputation.Themarketrespondstotheseslgnalsthroughtheorderrateand

throughcustomerfeedbackaboutprlCe,quality,service,productfeatures,andso

on.Thediagramelegantlypresentstheessentialfeedbackprocessescouplinga

firmtoitsmarket,StressesthatordersdependonmuchmorethanprlCe,andbegins

tosuggestthestructurewhichmustbecapturedwithineachsubsystem･Forrester

reflectedontheimportanceofthisconceptualframeworkinhisthinking:

Definingthesystemboundaryandthedegreeofaggregationaretwoofthemost difficultstepsinsuccessfulmodeling.Inthisparticularstudy,parLtimeeffortfor abouttwoyearswasdevotedtofalsestartsbeforearrivlngatthepointshownin [Figure3-7].Thereafter,onlyeightweekswererequiredtocreatetheentiresystem ofsome200equations.

Chapter15presentsasimpleversionofthismodel,Forrester'S"marketgrowth

model,"andshowshowdifferentmanagementpoliciescancreatethepatternsof

growthdescribedinFigure3-6.

Amoredetailedsubsystem diagram isshowninFigure3-8･Thediagram showsthearchitectureforamodelofasemiconductormanufacturer(Sterman,

Repenning,andKofman1997).Thepurposeofthemodelwastoexplorethe

dynamicsofprocessimprovementprograms.Thefirmhadimplementedavery

Source:AdaptedfromForrester(1964).

Chapter3 TheModelingProcess 101

successfulqualityImprovementprogram.However,despitedramaticimprove-

mentsinquality,productivity,andcustomerresponsiveness,operatlngProfit

andthestockprlCefell,leadingtolayoffS･Exploringthisparadoxrequireda modelwithabroadboundarybothwithintherepresentationofthefirmandin

interactionsofthefirmwithitsenvironment.Besidestheusualsubsystemsfor

manufacturlng,Productdevelopment,andaccountlng,themodelincludesa

processimprovementsectorandasectorlabeled"FinancialStress."TheFinancial

Stresssubsystemisnotanorganizationalsubunitbutrepresentstopmanage一

mentdecisionsregardinglayoffs,investment,andtheattentionglVentOProcess

FIGURE3･8 Subsystemdiagramformodelofasemiconductorfirmanditsquality improvement∑program

Source:AdaptedfromSterman,Repenning,andKofman(1997).

102 PartI PerspectiveandProcess

improvement.Thesedecisionswereaffectedbythefirm'sfinancialhealthandthe threatoftakeover(asinfluencedbythemarketvalueofthefirmrelativetobook valueandcashflow).Thediagramalsoshowsthatthefirm'ssalesandmarket shareareendogenous,asiscompetitorbehavior(notethatcompetitorsrespondnot onlytothefirm'spricebutalsotoitsqualityimprovementefforts).Thestockprice andmarketvaluationofthefirmarealsoendogenous.

Subsystemdiagramsareoverviewsandshouldnotcontaintoomuchdetail. ThediagraminFigure3-8isqulteCOmplex;subsystemdiagramsshouldgenerally besimpler.Multiplesubsystemdiagramscanbeusedtoconveythehierarchical structureoflargemodels.

CausaHoopdiagrams,Modelboundarychartsandsubsystem diagrams showtheboundaryandarchitectureofthemodelbutdon'tshowhowthevariables arerelated.Causalloopdiagrams(CLDs)areflexibleandusefultoolsfordia- grammlngthefeedbackstructureofsystemsinanydomain･Causaldiagramsare simplymapsshowingthecausallinksamongvariableswitharrowsfromacause toaneffect.Chapter2providesexamples;chapter5coverstherulesfortheircon-

structionandinterpretationindepth.

Stockandflowmaps.Causalloopdiagramsemphasizethefeedbackstruc- tureofasystem.StockandflOwdiagramsemphasizetheirunderlyingphysical structure.Stocksandflowstrackaccumulationsofmaterial,money,andinforma-

tionastheymovethroughasystem.Stocksincludeinventoriesofproduct,popul lations,andfinancialaccountssuchasdebt,bookvalue,andcash.Flowsarethe

ratesofincreaseordecreaseinstocks,suchasproductionandshipments,births anddeaths,borrowingandrepayment,investmentanddepreciation,andreceipts andexpenditures.Stockscharacterizethestateofthesystemandgeneratethein- formationuponwhichdecisionsarebased.Thedecisionsthenaltertheratesof flow,alteringthestocksandclosingthefeedbackloopsinthesystem.Chapter2 showsexamples;chapters6and7discussthemapplngandbehaviorofstocksand flows.

Policystructurediagrams.Thesearecausaldiagramsshowingtheinforma- tionlnPutStOaParticulardecisionrule.Policystructurediagramsfocusattention ontheinformationcuesthemodelerassumesdecisionmakersusetogovernthe ratesofflowinthesystem.Theyshowthecausalstructureandtimedelaysin- volvedinparticulardecisionsratherthanthefeedbackstructureoftheoverallsys- tem.Chapter15providesexamples;seeMorecroft(1982)fordetails.

3.5.3 FormulatingaS…muttltionModeE Onceyou'Vedevelopedaninitialdynamichypothesis,modelboundary,andcon- ceptualmodel,youmusttestthem.Sometimesyoucantestthedynamichypothe- sisdirectlythroughdatacollectionorexperimentsintherealsystem.Mostofthe time,however,theconceptualmodelissocomplexthatitsdynamicimplications areunclear.Asdiscussedinchapter1,Ourabilitytoinfercorrectlythedynamicsof acomplexmodelisextremelypoor.Further,inmanysituations,especiallyhuman systems,itisdifficult,dangerous,unethical,OrsimplylmPOSSibletoconductthe

Chapter3 TheModelingProcess 103

realworldexperimentsthatmightrevealtheflawsinadynamichypothesis.Inthe maJOrltyofcases,youmustconducttheseexperimentsinavirtualworld.Todoso, youmustmovefromtheconceptualrealmofdiagram stoafullyspecifiedformal

model,completewithequations,parameters,andinitialconditions. Actually,formalizlngaCOnCePtualmodeloftengeneratesimportantinsight

evenbeforeitisreadytobesimulated.FormalizationhelpsyoutorecognlZeVague conceptsandresolvecontradictionsthatwentunnoticedorundiscussedduringthe conceptualphase.Formalizationiswheretherealtestofyourunderstandingoc-

curs:Computersacceptnohandwavingarguments.Indeed,themostexperienced modelersroutinelywritesomeequationsandestimateparametersthroughoutthe

modelingprocess,evenintheearliestphasesofproblemarticulationandconcep-

tualization10ftenwiththeclients-asawaytoresolveambigultyandtestinitial hypotheses.Systemdynamicspracticeincludesalargevarietyoftestsonecan applyduringthefomulationstagetoidentifyflawsinproposedformulationsand

improveyourunderstandingofthesystem.

3.5.4 1Tesling

Testingbeginsassoonasyouwritethefirstequation.Partoftesting,Ofcourse,is

comparlngthesimulatedbehaviorofthemodeltotheactualbehaviorofthesys- tem.ButtestlngInvolvesfarmorethanthereplicationofhistoricalbehavior.Every variablemustcorrespondtoameaningfulconceptintherealworld.Everyequa-

tionmustbecheckedfordimensionalconsistency(soyouaren'taddingapplesand oranges).Thesensitivityofmodelbehaviorandpolicyrecommendationsmustbe assessedinlightoftheuncertaintylnaSSumptlOnS,bothparametricandstructural.

Modelsmustbetestedunderextremeconditions,conditionsthatmaynever havebeenobservedintherealworld.WhathappenstotheGDPofasimulated

economyifyousuddenlyreduceenergysuppliestozero?Whathappensinamodel ofanautomakerifyouraisetheprlCeOfitscarsbyafactorofonebillion?What happensifyousuddenlyIncreasedealerinventoriesbylOOO%?Eventhoughthese conditionshaveneverandcouldneverbeobserved,thereisnodoubtaboutwhat

thebehaviorofthesystemmustbe:Withoutenergy,theGDPofamodernecon- omymustfallnearlytozero;withaprlCeOnebilliontimeshigher,thedemandfor

thefirm'scarsmustfalltozero;Withahugesurplusofcarsondealerlots,produc- tionshouldsoonfalltozerobutcannotbecomenegative.Youmightimaginethat modelswouldneverfailtopasssuchobvioustests,thatproductionwithoutenergy,

demandforgoodsthatcostmorethanthetotalwealthofmanynations,andnega- tiveproductionwouldneverarise.Butyou'dbewrong.Manywidelyusedmodels ineconomics,Psychology,management,andotherdisciplinesviolatebasiclawsof

physics,eventhoughtheymayreplicatehistoricalbehaviorquitewell(Seesection 9.3.2andchapter21).Extremeconditionstests,alongwithothertestsofmodelbe- havior,arecriticaltoolstodiscovertheflawsinyourmodelandsetthestagefor

improvedunderstanding.

3.5.5 Po‖CyDesignandEva一uation

Onceyouandtheclienthavedevelopedconfidenceinthestructureandbehavior ofthemodel,youcanuseittodesignandevaluatepoliciesforimprovement.

104 PartIPerspectiveandProcess

Policydesignismuchmorethanchanglngthevaluesofparameterssuchasatax rateormarkupratio.PolicydesignincludesthecreationofentirelynewstrategleS, Structures,anddecisionrules.Sincethefeedbackstructureofasystemdetermines itsdynamics,mostofthetimehighleveragepolicieswillinvolvechanglngthe

dominantfeedbackloopsbyredesignlngthestockandnowstructure,eliminating timedelays,changlngtheflowandqualityofinformationavailableatkeydecision polntS,Orfundamentallyreinventlngthedecisionprocessesoftheactorsinthesys-

tem.

Therobustnessofpoliciesandtheirsensitivltytouncertaintiesinmodelpara- metersandstructuremustbeassessed,includingtheirperformanceunderawide rangeofalternativescenarios.Theinteractionsofdifferentpoliciesmustalsobe considered:Becauserealsystemsarehighlynonlinear,theimpactofcombination policiesisusuallynotthesumoftheirimpactsalone.Oftenpoliciesinterfere withoneanother;sometimestheyreinforceoneanotherandgeneratesubstantial SynergleS･

3】6 SuMMARY

Thischapterdescribedthemodelingprocess.Whiletherearecertainstepsallmod- elersgothrough,modelinglSnotaCOOkbookprocedure.Ⅰtisfundamentallycre- ative.Atthesametime,modelinglSadisciplined,scientific,andrigorousprocess, challenglngthemodelerandclientateverysteptosurfaceandtestassumptlOnS, gatherdata,andrevisetheirmodels-bothformalandmental.

ModelinglSiterative.NooneeverbuiltamodelbystartlngWithstep1and progresslnglnSequencethroughalistofactivities･ModelinglSaCOntinualprocess ofiterationamongproblemarticulation,hypothesisgeneration,datacollection, modelformulation,testing,andanalysis.Therearerevisionsandchanges,blindall 1eysandbacktracking.Effectivemodelingcontinuallycyclesbetweenexperiments inthevirtualworldofthemodelandexperimentsanddatacollectioninthereal world.

Modelsmustbeclearlyfocusedonapurpose･Neverbuildamodelofasys- tem.Modelsaresimplifications;withoutaclearpurpose,youhavenobasisforex- Cludinganythingfromyourmodelandyoureffortisdoomedtofailure.Therefore themostimportantstepinthemodelingprocessisworkingwithyourclienttoar- ticulatetheproblem-therealproblem,notthesymptomsoftheproblem,thelaト estcrisis,orthemostrecentfad.Ofcourse,asthemodelingprocessleadsyouto deeperinsight,yourdefinitionandstatementoftheproblemmaychange.Indeed, suchradicalreframlngSareOftenthemostimportantoutcomeofmodeling.

ThepurposeofmodelinglStOhelptheclientssolvetheirproblem.Thoughthe modelingprocessoftenchallengestheclients'concept10nOftheproblem,ulti- mately,iftheclientperceivesthatyourmodeldoesnotaddresstheirconcern,you canhavelittleimpact.Themodelermustnotgrowattachedtoamodel,nomatter howelegantorhowmuchtimehasbeeninvestedinit.Ifitdoesn'thelptheclients solvetheirproblem,itneedstobereviseduntilitdoes.

Modelingtakesplaceinanorganizationalandsocialcontext･Thesettingmay beabusinessbutcanalsobeagovernmentagency,ascientificcommunity,aPubl licpolicydebate,oranyotherorganization.Modelersareinevitablycaughtupln

Chapter3 TheModelingProcess 105

thepoliticsofthecommunltyandpersonalitiesofitsmembers.Modelersrequlre bothfirst-rateanalyticalskillsandexcellentinterpersonalandpoliticalskills.

Finally,modelershaveanethicalresponsibilitytopursuethemodelingprocess withrigorandintegrity.ThefactthatmodelinglSembeddedinanorganizational contextandsubjecttopoliticalpressuresdoesnotrelieveyouofyourresponsibil- ltytOCarryOutyourworkwiththehigheststandardsofscientificinqulryandpro- fessionalconduct.Ifyourclientisnotwillingtopursuethemodelingprocess honestly,quitandfindyourselfabetterclient.

Strut,hireandBehaviorof

Dy弧盈m量eSys患ems

L,ikeallsystems,thecomplexsystemisaninterlockingstructureoffeedback

loops. .Thisloopstructuresurroundsalldecisionspublicorprivate, consciousorunconscious.Theprocessesofmanandnature,ofpsychologyand physics,ofmedicineandengineeringallfallwithinthisstructure.

lJayW.Forrester,UrbanDynamics(1969),p.107,

Thebehaviorofasystemarisesfromitsstructure.Thatstructureconsistsofthe feedbackloops,stocksandmows,andnonlinearitiescreatedbytheinteractionof thephysicalandinstitutionalstructureofthesystemwiththedecision一making processesoftheagentsactlngWithinit･Thischapterprovidesanoverviewofdy- namicsfocuslngOntherelationshipbetweenstructureandbehavior.Thebasic modesofbehaviorindynamicsystemsareidentifiedalongwiththefeedback structuresgeneratingthem.Thesemodesincludegrowth,createdbypositivefeed- back;goalseeking,createdbynegativefeedback;andosciillations(including dampedoscillations,limitcycles,andchaos),Createdbynegativefeedbackwith timedelays.MorecomplexmodessuchasS-Shapedgrowthandovershootandcol- lapsearisefromthenonlinearinteractionofthesebasicstructures.Thechapteralso illustratestheconceptofreferencemodestocapturedynamicbehaviorandcausal

loopdiagramsasamethodtorepresentfeedbackstructure.

107

108 PartIPerspectiveandProcess

4.1 FuNDAMENTALMoDESOFDYNAMICBEHAV10R

Changetakesmanyforms,andthevarietyofdynamicsaroundusisastounding. Youmightimaglnethattheremustbeacorrespondinglyhugevarietyofdifferent feedbackstructurestoaccountforsucharicharrayofdynamics.Infact,mostdy- namicsareinstancesofafairlysmallnumberofdistinctpatternsofbehavior,such asexponentialgrowthoroscillation.Figure4-1showsthemostcommonmodesof behavior.

Themostfundamentalmodesofbehaviorareexponentialgrowth,goalseek- 1ng,andoscillation.EachoftheseisgeneratedbyasimplefTeedbackstructure: growtharisesfrompositivefeedback,goalseekingarisesfromnegativefeedback, andoscillationarisesfromnegativefeedbackwithtimedelaysintheloop.Other commonmodesofbehavior,includingS-shapedgrowth,S-Shapedgrowthwith overshootandoscillation,andovershootandcollapse,arisefromnonlinearinter- actionsofthefundamentalfeedbackstructures.

4tlEI Exponentia;Growth

Exponentialgrowtharisesfrompositive(self-reinforcing)feedback･Thelargerthe quantlty,thegreateritsnetincrease,furtheraugmentlngthequantltyandleadingto ever-fastergrowth(Figure412).Theparadigmcasesarecompoundinterestandthe growthofpopulations.Themoremoneyyouhaveinvested,themoreinterestyou earn,sothegreateryourbalanceandthegreaterstillthenextinterestpaymentwill be.Thelargerthepopulation,thebiggerthenetbirthrate,addingtothepopulation andeventuallyleadingtostillmorebirths,inanever-acceleratingSpiral.Pureex- Ponentialgrowthhastheremarkablepropertythatthedoublingtimeisconstant: thestateofthesystemdoublesinafixedperiodoftime,nomatterhowlarge.

FJGURE4-1 Commonmodesofbehaviorindynamicsystems

ExponentialGrowth

OvershootandCoHapse

ノ ′ ＼ Time-

Chapter4 StructureandBehaviorofDynamicSystems 109

Ittakesthesamelengthoftimetogrowfromoneunittotwoasitdoestogrow fromonemilliontotwomillion.ThispropertylSadirectconsequenceofpositive

feedback:thenetincreaseratedependsonthesizeofthestateofthesystem(See chapter8).Positivefeedbackneednotalwaysgenerategrowth.Itcanalsocreate self-reinforclngdecline,aswhenadroplnStockprlCeSerodesinvestorconfidence

whichleadstomoreselling,lowerprlCeS,andstilllowerconfidence. Whataboutlineargrowth?Lineargrowthisactuallyqulterare.Lineargrowth

requiresthattherebenofeedbackfromthestateofthesystemtothenetincrease rate,becausethenetincreaseremainsconstantevenasthestateofthesystem

changes.Whatappearstobelineargrowthisoftenactuallyexponential,but viewedoveratimehorizontooshorttoobservetheacceleration.

Figure4-3showssomeexamplesofexponentialgrowth.Growthisneverper- fectlysmooth(duetovariationsinthefractionalgrowthrates,cycles,andpertu r -

bations),butineachcaseexponentialgrowthisthedominantmodeofbehavior. Thoughthedoublingtimesvarywidely(fromabout40yearsforworldpopulation toabout2yearsforsemiconductorperfomance),thesesystemsallexhibitthe

sameenormousaccelerationcausedbypositivefeedback.

ProcessPoint:WhenaRatelsNotaRate

Indynamicmodeling,theterm "rate"generallyreferstotheabsoluterateof

changeinaquantlty･Thepopulationgrowthexampleabovestates,Hthelargerthe

FIGURE4-2

Exponentialgrowth:Structureandbehavior

Thecausalloopdiagraminthebottomhalf ofthefigureshowsthefeedbackstructure thatgeneratesexponentialgrowth.Arrows indicatethedirectionofcausalinfluences.

Here,StateoftheSystemdeterminesNet lncreaseRate(the一owerarrow),andNet lncreaseRateaddstoStateoftheSystem (theupperarrow).Signsatarrowheads (+or-)indicatethepolarityofthe relationship,Apositivepolarity,indicated by+,meansanincreaseinthe independentvariablecausesthe dependentvariabletoriseabovewhatit wouldhavebeen(andadecreasecauses adecrease).Negativesigns(seeFigure 4-4)meananincrease(decrease)in theindependentvariablecausesthe dependentvariabletodecrease(increase) beyondwhatitwouldhavebeen.Loop identifiersshowthepolarityoftheloop, eitherpositive(self-reinforcing,denoted byR)ornegative(balancing,denoted byB;seeFigure4-4).Chapter5 discussescausaHoopdiagramsindepth.

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Chapter4 StmctureandBehaviorofDynamicSystems ill

population,thegreaterthebirthrate."Theterm"birthrate"herereferstothenum-

berofpeoplebompertimeperiod.Forexample,thebirthrateinacltyOfonemiL

lionpeoplemightbe20,000peopleperyear.Often,however,theterm"rate"is

usedasshorthandforthefractionalrateofchangeofavariable.Forexample,the

birthrateisofteninterpretedasthenumberofbirthsperyearperthousandpeople

(alsoknownasthecrudebirthrate).Thecrudebirthrateinthecityofonemillion

wouldbe20birthsperyearperthousandpeople,or29uyear.Similarly,wecom-

monlyspeakoftheinterestrateortheunemploymentrate.ThewordHrate"in

thesecasesactuallymeans｡ratio":theinterestrateistheratiooftheinterestpay一

mentsyoumustmakeeachperiodtotheprlnClpaloutstanding;theunemployment

rateistheratioofthenumberofunemployedworkerstothelaborforce.

Youmustcarefullydistinguishbetweenabsoluteandfractionalratesofchange andbetweenratesofchangeandratios.Selectvariablenamesthatminimizethe

chanceforconfusion.Besuretochecktheunitsofmeasureforyourrates.The

unitsofmeasureforratesofflOwareunits/timeperiod;theunitsofmeasurefor

fractionalratesofflowareunitsperunltPertimeperiod-1/timeperiods.Forex-

ample,theinterestrateonyourcreditcardisnot,say,12%,but12%peryear;or,

equivalently,1%permonth(0･12/yearorO･Ol/month)ITheeconomydoesn'tgrow at,say,3.5%,butatafractionalrateof3.5%/year｡

4.1x2 GoaESeeking

Positivefeedbackloopsgenerategrowth,amplifydeviations,andreinforce

change.Negativeloopsseekbalance,equilibrium,andstasis.Negativefeedback

loopsacttobringthestateofthesysteminlinewithagoalordesiredstate.They

counteractanydisturbancesthatmovethestateofthesystemawayfromthegoal.

AllnegativefeedbackloopshavethestructureshowninFigure4-4.Thestateof

FIGURE4-4

Goalseeking: structureand

behavior

+ Stateofthe System

Goal

(Desired StateofSystem)

Discrepancy Corrective Action

112 PartI PerspectiveandProcess

thesystemiscomparedtothegoal.Ifthereisadiscrepancybetweenthedesired andactualstate,co汀eCtiveactionisinitiatedtobringthestateofthesystemback

inlinewiththegoal.Whenyouarehungry,youeat,satisfyingyourhunger;when tired,yousleep,restorlngyourenergyandalertness･Whenafirm'sinventory

dropsbelowthestockrequiredtoprovidegoodserviceandselection,production increasesuntilinventorylSOnceagalnSufficient.

EverynegativelooplnCludesaprocesstocomparethedesiredandactualcon-

ditionsandtakecorrectiveaction.Sometimesthedesiredstateofthesystemand

correctiveactionareexplicitandunderthecontrolofadecisionmaker(e.g.,the desiredlevelofinventory).Sometimesthegoalisimplicitandnotunderconscious control,Orunderthecontrolofhumanagencyatall.Theamountofsleepyouneed

tofeelwellrestedisaphysiologicalfactornotunderyourconsciouscontrol･The equilibriumsurfacetemperatureoftheearthdependsonthefluxofsolarenergy andtheconcentrationofgreenhousegasesintheatmosphere,amongotherphysi- calparameters.Andacupofcoffeecoolsvianegativefeedbackuntilitreaches roomtemperature･

Inmostcases,therateatwhichthestateofthesystemapproachesitsgoaldi-

minishesasthediscrepancyfalls.Wedonotoftenobserveaconstantrateofap- proachthatsuddenlystopsJustaSthegoallsreached･Thegradualapproacharises becauselargegapsbetweendesiredandactualstatestendtogeneratelargere- sponses,whilesmallgapstendtoelicitsmallresponses･Theflowofheatfrom yourcoffeecuptotheairintheroomislargerwhenthetemperaturegapbetween themislargeanddiminishesasthegapfalls.Whencoffeeandroomtemperatures areequal,thereisnonetheatflowbetweenthem.

Whentherelationshipbetweenthesizeofthegapandthecorrectiveactionis linear,therateofadjustmentisexactlyproportionaltothesizeofthegapandthe resultinggoal-Seekingbehaviorisexponentialdecay･Asthegapfalls,sotoodoes theadjustmentrate.Andjustasexponentialgrowthischaracterizedbyitsdoubling

time,pureexp?nentialdecayischaracterizedbyitshalfllfe-thetimeittakesfor halftheremalnlnggaptObeeliminated(Seechapter8)･

Figure4-5showsexamplesofgoal-seekingbehavior.Thetopleftpanelshows therateofdefectgenerationinthewaferfabricationprocessofamajorSemi- conductormanufacturer.In1987,thecompanybeganaprocessimprovement

programusingprinciplesofTotalQualityManagement･Thegoaloftheprogram waszerodefects.In4yearsthedefectratedeclinedfrom1500ppmtoabout150 ppm.Notethatasthedefectratefell,therateofimprovementdeclined.Thetop rightpanelshowstheaverageloadfactor(uptime)fortwoFinnishnuclearpower plantsstartedupin1978.Thefractionoftheyeartheplantsoperatedincreased

rapidlyatfirst,thenmoreslowly,untilamaximumofabout94%wasreached.The bottomleftpanelshowstheshareofalladvertisingdollarsspentontelevisionin theUS.Growthwasrapidinthe1950S,butreachedafairlysteadylevelofabout 20-25%by1980.Thebottomrightpanelshowstheroughlyexponentialdeclinein automobile-relatedfatalitiesintheUSper100millionvehiclemilesdriven.De-

spitethesubstantialdeclineindeathriskpermile,thenumberofmilesdrivenhas grownexponentially,Sothetotalnumberkilledontheroadseachyearhasfluctu- atedbetweenabout30and50thousandsincethe1930S.

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FIGURE4-6 0sciHation: structureand behavior

Delayscanexist inanyoHhe causaHJ-nksina

negativefeedback loop.OsciHation canoccurifthere

aredelaysinat Jeastoneof the一inksina

negativeloop.

PartI PerspectiveandProcess

4.1.3 0sc‖ation

Oscillationisthethirdfundamentalmodeofbehaviorobservedindynamicsys-

tems.Likegoal-seekingbehavior,oscillationsarecausedbynegativefeedback loops.Thestateofthesystemiscomparedtoitsgoal,andcorrectiveactionsare takentoeliminateanydiscrepancies.Inanoscillatorysystem,thestateofthesys-

temconstantlyovershootsitsgoalorequilibriumstate,reverses,thenundershoots, andsoon･Theovershootlngarisesfromthepresenceofsignificanttimedelaysin thenegativeloop.Thetimedelayscausecorrectiveactionstocontinueevenafter thestateofthesystemreachesitsgoal,forcingthesystemtoadjusttoomuch,and triggeringanewcorrectionintheoppositedirection(Figure4-6)･

Oscillationsareamongthemostcommonmodesofbehaviorindynamicsys- tems.Therearemanytypesofoscillation,includingdampedoscillations,limitcy- cles,andchaos(Seesection4.3.3).Eachvariantiscausedbyaparticularfeedback structureandsetofparametersdeterminlngthestrengthsoftheloopsandthe lengthsofthedelays.Buteverytypeofoscillationhas,atitscore,anegativefeed- backloopwithdelays.

OscillationscanariseifthereisasignificantdelaylnanyPartOfthenegative loop.AsshowninFigure4-6,theremaybedelaysinanyoftheinfo-ationlinks makinguptheloop.Theremaybedelaysinperceivlngthestateofthesystem causedbythemeasurementandreportlngSystem.Theremaybedelaysininitiat- 1ngcorrectiveactionsafterthediscrepancylSPerceivedduetothetimerequired

+ Stateotthe

Action

Delays＼

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Measurement, Reporting,and Perception Delays

/ G.a日 (Desired

StateotSystem)

Discrepancy Corrective Actjon ＼孟edcTf;isnt_rAti'zfnagnd

Delays

Chapter4 StructureandBehaviorofDynamicSystems 115

toreachadecision.Andtheremaybedelaysbetweentheinitiationofacorrective

actionanditseffectonthestateofthesystem.Ittakestimeforacompanytomea-

sureandreportinventorylevels,timeformanagementtomeetanddecidehow

muchtoproduce,andmoretimewhilerawmaterialsprocurement,thelaborforce,

andotherneededresourcesrespondtothenewproductionschedule.Sufficiently

longdelaysatanyoneofthesepolntSCOuldcauseinventorytooscillate.

Figure4-3showedrealGDPintheUS.Thedominantmodeofbehaviorinthe

dataisexponentialgrowth.ButthegrowthisnotsmoothOutputfluctuatesaround

thegrowthtrend.ⅠnthetoppanelofFigure4-7theseoscillationsarerevealedby

detrendingtheGDPdata(removingthebestfitexponentialfunction).Aftertheex-

ponentialgrowthisremoved,thebusinesscycleisclearlyvisibleasafluctuation

averaglngabout5%inamplitudeandwithanaverageperiodofabout4years.A

longerandlargerfluctuationinrealproductionisalsoapparent,Withpeaksrelative

totrendaround1910and1970-theso-calledeconomiclongwave･lThebottom

panelsofFigure4-7showtwocriticalbusinesscycleindicators-capacityutiliza-

tionintheUSmanufacturingSectorandthecivilianunemploymentrate.Theam-

plitudeofthebusinesscycleintheseimportantvariablesisquitelarge.Utilization

typicallyfluctuates15pointsfrom peaktotrough(nearly20% ofitsaverage

value),whileunemploymentduringthepostwarperiodintheUShasrangedfrom

under3%tonearlyIl啄ofthelaborforce,withmuchhighervaluesinEurope.

Notethatthebusinesscycle(andmostrealworldoscillations)isnotperfectly

regular.Youshouldnotexpectittobe.Manypeoplethinkacyclemustbeaspre-

dictableasthedawn,asregularastheorbitsoftheplanets,assmoothandsym一

metricastheswlngOfapendulumclock.Buttheseparadigmsofperiodicityare

specialsystems.Theplanetsinteractmainlywiththesunandonlyweaklywithone

another･2Apendulumclockhasbeencarefullydesignedtogeneratearegularmo-

tionbyisolatingItsCOmPOnentSfromtheenvironment･Biological,social,andeco-

nomicsystems,incontrast,involvehugenumbersofinteractionsamongtightly

coupledelements.Theyarecontinuouslybombardedbyperturbationsthatcause

theirmotiontobesomewhatirregular,a(usuallynonlinear)combinationoftheir

endogenousdynamicsandtheseexogenousshocks(Seesection4･3･2)･

lThelongwave,orKondratievcycle,hasanaverageperiodofabout60yearsand,asseeninthe data,anamplitudemuchlargerthantheshorトtermbusinesscycle･Sterman(1986)andForrester (1977,1983)presenttheoryandevidencefortheexistenceandfeedbackstructuregeneratingthe

long†ave･Steman(1985b)presentsasimplemodelofthelongwave;Sterman1989areportsan expe.rlmentaltestofthemodel,andSterman(1989C)showsthatm.anyofthedecisionrulescharac- terlZlnghumansubjectsintheexperimentgeneratechaoticdynamlCSl

2Actua11y,theapparentregularltyOfthesolarsystemisilltlSOry･Thelengthofthedayisincreas- 1ngaStidalandfrlCtionalforcesdissipatetheearth'srotationalenergy･Recentresearchshowsthat theorbitsofmostoftheplanetsarechaoticandthatchaoticresonancesamongtheplanetscanhurl meteoritesandasteroidsfromdistantorbitsintotrajectoriesthatcrosstheearth'sorbit,perhapsac-

countingfortheimpactsnowbelievedtohavecausedthemajorextinctions･Itisonlyourshort(by heavenlystandards)recordofobservationsthatcausesustoperceive也esolarsystemtobestable andpredictable.Peterson(1993)providesanexcellentnontechnicaltreatmentofchaoticdynamics

inthesolarsystem;DiacuandHolmes(1996)covertheorやnsofchaosintheoriesofcelestialme- chanics.JackWisdomofMITpioneeredcomputersimulatlOnSthatrevealedthechaoticcharacter ofthesolarsystem(seeWisdom1987forareview).Seesection4.3.3formoreonchaos.

116

FIGURE4-7 0scHation:

examples

Thebusiness

cyclellnthe UnitedStates.

Top:Deviation ofrea一GDP

fromLong-term exponentia=rend.

MI'ddle:Capacity utilization.

Bottom:Civilian

unemployment.

PartI PerspectiveandProcess

uSRealGOPDeviationfrom Trend 4

(uo 葛

t=J I )

P u aJ

1 u 10 と

u O葛 d.̂

凸 1850 1900 1950 2000

CapacityUtilization.USManufacturing 95

70 1945

㌔ 6

1955 1965 1975 1985 1995

USUnemploymentRate

1945 1955 1965 1975 1985 1995

Source:HistoricalStatlSticsoftheUnltedStates,USBureauofEconomicAnalysIS.

4.1.4 ProcessPoint

Theconnectionbetweenstructureandbehaviorprovidesausefulheuristicforthe

conceptualizationprocess･AnytlmeyouObserveexponentialgrowthinavariable, youknowthereisatleastonepositivefeedbackinwhichthevariablesofinterest

participate(andpossiblymore).Therewill,ofcourse,bemanynegativeloops

presentaswell･However,ifthesystemisexhibitingexponentialgrowth,thenyou

knowthatpositiveloopsaredominant(atleastduringtheregimeinwhichgrowth

Chapter4 StructureandBehaviorofDynamicSystems 117

occurs).Youcanthenguidethediscussionamongtheclientgrouptowardtheiden-

tificationofself-reinforcingprocessesITypically,thegroupwillbeabletoidentify manypositiveloopsinvolvingthevariablesofinterest.Ofcourse,itisnotpossi- bletotellwhichofthesecandidateloopsareactiveandcontributingtothebehav-

ior,northeirrelativestrengths,withoutrecoursetodataand/ormodelsimulations. ButfocuslngOntheconnectionbetweenstructureandbehaviorhelpsgenerate fruitfulhypothesesaboutthekeyloops.

Similarly,anytlmeyouObservetheothercoremodesofbehavior,youimme- diatelyknowwhattypesofloopmustbedominant,guidingyourinitialsearchfor

thestructuresresponsible･Oscillation,forexample,mustmeanthereisanimpor-

tantnegativefeedbackwithsignificanttimedelays.Youcanthenaskaboutthede- cisionprocessesbywhichthevariableisregulatedandthetimedelaysinthe perceptionofthestateofthesystem,inthedecisionprocess,andintheresponse ofthesystemtothecorrectiveactionsofthedecisionmakers.

Acaveat:Thisheuristichelpsintheidentificationofthefeedbackstructures responsiblefortheobservedbehavior.Inaddition,itisessentialtoconsiderwhat

structuresexistbuthavenotyetplayedasignificantroleinthehistoryofthesys- temorleftatraceintheavailabledata.Asthesystemevolvestheselatentfeed-

backsmaybecomedominant,dramaticallychangingthedynamics,shiftingtrends andpattems,andalteringthesystem'sresponsetopolicies･Identifyingpotential shiftsinloopdominancearisingfromlatentstructuresisavaluablefunctionof modeling.

Tbillustrate,returntothecaseofexponentialgrowth･NorealquantltyCan growforever.Eventually,Oneormorenegativeloopswillbecomedominantas variouslimitstogrowthareapproached.Immediatelyafteridentifyingsomeposi- tiveloopspotentiallyresponsibleforobservedgrowth,youshouldask,Whatneg- ativeloopsmightstopthegrowth?Mostpeoplecaneasilygenerateawiderange ofpotentiallimitsandconstraintstothegrowthofthesystem･Identifyingthepo- tentialconstraintstogrowthisapowerfulwaytoidentifypossiblefuturebottle-

necksandlimits,evenifthereisnoevidenceofaslowdowninthedata.Aswith

theidentificationofpositiveloops,emplricalinvestigationandmodelingarere- quiredtodeterminewhichnegativeloopsarestrongest,whatlimitstogrowththey reflect,andwhetherthoselimitscanberelaxedortightenedbyotherfeedbacksor throughpolicyinterventions(Seesection4.2.1).

Edent≡晋yELngFeedbackStruc官urefi'omSysモemBehav励

l･Identifythepositiveloopsresponsibleforthegrowthintheexamples showninFigure4-3.Sketchacausalloopdiagramtocapturetheloopsyou identify.Identifyasmanynegativefeedbacksthatmighthaltgrowthin thesesystemsasyoucan.

2･Identifythenegativeloopsthatmightberesponsibleforthegoal-seeking behaviorsshowninFigure415.Identifythestateofthesystem,thegoal, andthecorrectiveaction(S)foreachcase.Whatcounterforcesmight preventthestateofthesystemfromreachingltSgoal?

118 PartI PerspectiveandProcess

3.Identifythenegativeloopsandtimedelaysthatmightberesponsibleforthe oscillationsineconomicaffairsillustratedbyFigure4-7.Identifythestate ofthesystem,thegoal,thecorrectiveaction,anddelays.Estimatethe lengthofthetimedelaysyouidentify.

4.2 lNTERACTrONSOFTHEFUNDAMENTALMoDES

Thethreebasicmodesofbehavior-exponentia_Igrowth,goalseeking,andoscill lation-arecausedbythreebasicfeedbackstructures:positivefeedback,negative feedback,andnegativefTeedbackwithdelays.Other,morecomplexpatternsofbe- haviorarisethroughthenonlinearinteractionofthesestructureswithoneanother.

4E2.1 S-ShapedGrowth

Asdiscussedabove,norealquantitycangrow(ordecline)forever:eventuallyone ormoreconstraintshaltthegrowth.Acommonlyobservedmodeofbehaviorin dynamicsystemsisS-shapedgrowth-growthisexponentialatfirst,butthengrad- uallyslowsuntilthestateofthesystemreachesanequilibriumlevel.Theshapeof thecurveresemblesastretched-out"S"(Figure4-8)･Tbunderstandthestructure underlyingS-ShapedgrowthitishelpfultousetheecologicalconceptofcarTylng capacity･ThecarrylngCaPaCltyOfanyhabitatisthenumberoforganismsofa particulartypeitcansupportandisdeterminedbytheresourcesavailableinthe

FIG URE 4-8 S-shapedgrowth: structureand be hav ior

//一､1私†Stateofthe

Resource

Net

C.iona百吋 Rp_W‖r,Fractiona一

Nethcrease AdequacyRate Carrying Capacity

普 -＼一一一/ .7u

Chapter4 StmctureandBehaviorofDynamicSystems 119

environmentandtheresourcerequirementsOfthepopulation･Asapopulation

approachesitscarrylngCapaClty,resourcesperCapitadiminishtherebyreducing

thefractionalnetincreaserateuntilthereareJustenoughresourcespercapltatO

balancebirthsanddeaths,atwhichpointthenetincreaserateiszeroandthepop-

ulationreachesequilibrium.Anyrealquantltyundergolngexponentialgrowthcan

beinterpretedasapopulationdrawlngOntheresourcesinitsenvironment･Asthe

capacltyOftheenvironmentisapproached,theadequacyoftherequiredresources

diminishes,andthefractionalnetincreaseratemustdecline.Thestateofthesys-

temcontinuestogrow,butataslowerrate,untilresourcesareJustSCarCeenough

tohaltgrowth.Ingeneral,apopulationmaydependonmanyresources,eachcre-

atlnganegativeloopwhichmightlimltgrOWth･Theconstraintthatismostbind-

ingdetermineswhichofthenegativeloopswillbemostinfluentialasthestateof

thesystemgrows.

Thecarryingcapacityconceptissubtleandcomplex.Whileitisappropriateto

considerthecarrylngCapaCltyOfanenvironmenttobeconstantinsomesituations,

ingeneralthecarrylngCapaCltyOfanenvironmentisintimatelyintertwinedwith

theevolutionanddynamicsofthespeciesitsupports.Wehumansalterthecarry-

1ngCapaCltyOftheplanetinwaysbothintendedandunintended,throughthede-

velopmentoftechnologyenablinggreaterutilizationofresources,throughchanges

inculturalpracticesandnormsforconsumptlOnOfresourcespercaplta,and

throughconsumptlOn,depletion,anderosionofthevariousresourcesuponwhich

wedepend.Evenso-Calledlowerspeciesinteractwiththeirenvironmenttoalter

thecarryingCapacity.Theco-evolutionofflOwersandpollinatingInsectsPermit-

tedgreaterpopulationdensitiesforboth.Similarly,allbusinessesandorganiza-

tionsgrowinthecontextofamarket,society,andphysicalenvironmentthat

imposeslimitstotheirgrowth.Aswithnaturalpopulations,theselimitscanin-

creaseordecrease,bothexogenouslyand,moreimportantly,endogenously,asthe

organizationinteractswithitscustomers,competitors,Suppliers,regulators,and

otherentitiesinthesystem.Ingeneral,Onemustmodelthevariousresourcesthat

togetherdeterminethecarrylngCaPaClty-foraspeciesoranorganization-asan

endogenouselementofthesystem.

DespitethedynamiccharacterofthecarrylngCapaClty,thereis,atanymo-

ment,alimittothesizeofthepopulation(thecurrentcarryingcapacity),which,if

exceeded,causesthepopulationtofall.Further,thecarrylngCaPaCltyItselfcannot

growforever.Thelawsofthermodynamicsdictateanabsolutelimittothecarrying

capacltyOftheearth,thoughthereisnoagreementamongscholarsastowhatthat

levelis,howitischanging,WhetherpopulationshouldgrowtothecarrylngCa-

pacltyOrbevoluntarilystabilizedbelowit,Orwhetherapopulationaslargeasthe

carrylngCaPaCltywouldenableareasonablequalityoflifeorprovideonlythebare minimumforsubsistence.3

AsystemgeneratesSIShapedgrowthonlyiftwocriticalconditionsaremet.

First,thenegativeloopsmustnotincludeanysignificanttimedelays(iftheydid,

thesystemwouldovershootandoscillatearoundthecarrylngCapaClty;SeeSection

3Forgooddiscussionoftheuncertaintyindefinitionsandestimatesoftheearth'scarrylng capacity,seeCohen(1995)･Forsystemdynamicsmodelsinwhichthecarryingcapacityofthe earthistreatedendogenouslyanddynamically,SeeM eadows,Meadows,andRan°ers(1992)･

120

FIGURE4･9

S-shapedgrowth: examples

PartiPerspectiveandProcess

100

Gr-owthofSunflowers

0 14 28 42

Days

56 70 84

USCableTelevisionSubscribers

1950

100

LL)

s ut2 ! U ZS ^ LJd P %

1960 1970 1980 1990 2000

AdoptionofCardiacPacemakerbyPhysicians

1960 1962 1964 1966 1968 1970 1972

Source:Sunflowers:Lotka(1956,p.74);CableTV:Kurian(1994),StatlStlCalAbstractoftheUS; Pacemakeradoption:Homer(1983,1987).

4･212)ISecond,thecalTyingcapacitymustbefixed.Itcannotbeconsumedbythe

growthofthepopulation,lestthepopulationexhaustitsresourcesandforceitself

intoextinction,asapopulationofyeastconsumesthesugarinacaskofwine,ul-

timatelycausingfermentationtostop(Seesection4.23).

Chapter4 StructureandBehaviorofDynamicSystems 121

AkeyaspectofthestructuregeneratingS-Shapedgrowthisthattheinteraction

ofthepositiveandnegativeloopsmustbenonlinear.Atfirst,whenthestateofthe systemissmallrelativetotheresourcebase,theliI血tstogrowtharedistantandthe

positiveloopsdominate.Anadditionalunitaddedtothestateofthesystemcon-

tributesmoretothenetincreaseratethanitdecreasesthefractionalnetincrease

ratebyreducingresourceadequacy.Thestateofthesystemgrowsexponentially.

However,asadirectconsequenceofthatgrowth,theadequacyoftheresource basefalls.Asthelimitstogrowthareapproached,thenegativeloopsgrowstronger

andstronger,untiltheybegintodominatethedynamicsITheinflectionpointinthe curveisthepolntWherethesystem,thoughstillgrowing,Shiftsfromacceleration todeceleration.TheinflectionmarksthepolntatWhichthereisashiftinloop

dominance.ItisthepolntatWhichanadditionalunitaddedtothestateofthesys- temreducesthefractionalnetincreaseratemorethanitaddstothetotalpopulation

drivingthegrowth.

Figure4-9showssomeexamplesofSIShapedgrowth･Whetherthegrowthof aplant,thediffusionofanewproductorservicesuchascabletelevision,orthe

adoptionofanewideaortechnologylikethecardiacpacemaker,growthalways confrontslimits.

4.2.2 S-Sh叩edGrow帥withOvershoot SIShapedgrowthrequlreSthenegativefeedbacksthatconstraingrowthtoact

swiftlyasthecarrylngCaPaCltylSaPPrOaChed･Often,however,therearesignifi- canttimedelaysinthesenegativeloops.Ⅵmedelaysinthenegativeloopsleadto thepossibilitythatthestateofthesystemwillovershootandoscillatearoundthe

carryingcapacity(Figure4-10).Figure411lshowssomeexamplesofSIShaped growthwithovershootandoscillation.

FIGURE4-10

S-Shapedgrowth withovershoot andoscillation: structureand behavior

Net l + hcrease stateofthe Rate 阜RI system

･FR･a控 -ラ主ヲ･

Fractiona一 Netlncrease ＼二ノ Resource Carrylng

Rate.,-d dequa.L capacity

122

FIGURE4111 S-Shapedgrowth withovershoot

andoscillation:

examples

PartI PerspectiveandProcess

( s u o ≡

!M )

u O !t t2 r n do d

PopulationofLondon

1850 1900 1950 2000

USAluminum Production

1900 1920 1940 1960 1980 2000

Source.'LondonPopulation:1800-1960,MltChe"(1975,p.77);1970-1995,1997AnnualAbstractof Statistics,UKOfflCeforNationalStatistics.AlumFnumProduction:USGS;http'//minerals.er.usgs.gov/ minerals/pubs/Commodlty/

lden輔yingtheLimitstoGrowth

Whatarethelimitstogrowthforthepopulationofacityandtheriseinproduction

ofcommoditiessuchasaluminum?Identifythenegativefeedbacksthathaltthe

growthineachcase.Identifythetimedelaysresponsiblefortheovershootand fluctuation.4

4InUrbanDynamics,Forrester(1969)presentsamodelofurbangrowthandstagnation,show- inghowmanyurbanrenewalpoliciesactuallyacceleratethedecayoftheinnercity･Mass(1975) andSchroeder,Sweeney,andAlfeld(1975)extendandapplytheresultsofUrbanDynamics,and AlfeldandGraham(1976)buildupasimplifiedversionoftheUrbanDynamicsmodelsuitablefor teaching.

Chapter4 StructureandBehaviorofDynamicSystems 123

4.2.3 0VershootandCoHapse Thesecondcriticalassumpt10nunderlyingSIShapedgrowthisthatthecarrylng capacltyisfixed･Often,however,theabilityoftheenvironmenttosupporta growlngpopulationiserodedorconsumedbythepopulationitself･Forexample, thepopulationofdeerinaforestcangrowsolargethattheyoverbrowsethe vegetation,leadingtostarvationandapreclpltOuSdeclineinthepopulation.Figure 4-12ShowsthefeedbackstructureandtypicalbehaviorfTortheovershootandcol- lapsebehaviormode.

ConsumptlOnOrerosionofthecarryingCapacitybythepopulationcreatesa secondnegativefeedbacklimltlnggrowth.Populationgrowthnowcutsresource adequacytwoways:byreducingtheresourcesavailablepercapltaandbyreduc- 1ngtotalresources.AsintheS-shapedgrowthcase,whenresourcesareinitially amplethepositivegrowthloopdominatesandthestateofthesystemgrowsexpo- nentially.Asitgrows,resourceadequacydrops･Thenegativeloopsgraduallygala instrength.Atsomepolnt,thenetincreaseratefallstozero,andthepopulation reachesitsmaximum･ButunliketheS-shapedgrowthcase,thesystemdoesnot reachequilibrium･Whenthepopulationreachesitspeak,therateofdeclineofthe carryingcapacityisatitsmaximum.Thecarryingcapacitycontinuestodrop,re- sourcespercapitafallfurther,andthenetincreaserateofthepopulationbecomes negative.Thestateofthesystemdeclines.Evenasitdeclines,theremainlngpop- ulationcontinuestoconsumethecarrylngCapaClty,SOresourcesperCapltaremain

FIGURE4-12 Overshootand

co‖apse:structure andbehavior

Net / 一一 → 像 † I- +c onsumption/ State ofthe

Er10Sionof

CarryingCapacity

･F cRra･etau 'teh LCti.nal 吋 ReLq｡U,CeFractional

Neth cr'ease Rate

＼J

Resource Carry-ng Adequacy Capacity

1サ＼_メ- / トー/ /

･o s e q e t ]2 P

Lut2 a J I S e te

C] Ea CI!Jd LJS C

3 ‥S a

D !Jd La ^

ニS .(C6 6

L) uP LuJ a lS P u t2 L P

!]2 d

‖!j t2 1V

. (N 6 6 L)

u]2 ピ

P u t2 'u !N 2 1j

'u き

0品

‥̂ l10g d tZ U L t2 O P n

N .a D !N

S S a 盲

L IS 一j e ) u !JC V W

? u O !tC N Ll u a S a J

d -0 9 6 L 川s

e lt=1 S

P a l!u⊃

aL l〓

S D uS !tt 21S 一t?｡ !J O

IS 一〓 L os 6 7 ト 8 9 L ‖q C )OP P t2 H

･. a DJn O S

9 9 6

C B 6

L I

L. ¢ 6

6 ト 6

トト 6

Sト 6

9 e 6

寸 9 6

N 9

6 L1

0 9 6

O ト 6 L

9 ト

6 L.

⊂〉 ⊂l ⊂l てり eq ー

'zo^oJl/令

0 0

0 N

O 6 6 L.

S a O !J d

J a ^

l!S

O 9 6 L

O ト 6 L

0 9 6 L

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O e e L

124

ゝ 1 .3 t? d t2 U

J a ≧ O d

J t2 a 一U n N

P 一) 0 き

u ! a 6 u t= LJU

la N

0 0 0 0 寸 M N ▼-

Jt2∂ /̂仙M Put2SnOLl⊥

ド

LJ3 1C 3

上 U O P P e H

P u e I6 u u

き a N

s a ld Lu t=X a

‥aS d p " o D P u e 10 0 LJS L O ^ O

C L ･寸

u u n

I』 lt和人/SuO⊥〇!JllaM uO日日M

Chapter4 StructureandBehaviorofDynamicSystems 125

insufficientandthepopulationkeepsfalling.Ifthereisnoregenerationofthecar-

ryingcapacity(ifitisstrictlynonrenewable),theequilibriumofthesystemisex-

tinction:anynonzeropopulationcontinuestoconsumetheresourcebase,forcing ittozero,andwithit,thepopulation.ifthecarrylngCapaCltyCanberegeneratedor

supplementedwithrenewableresources,anonzeroequilibriumcanbesustained･ Figure4-13showssomeexamplesofovershootandcollapse･TheNewEng-

landHaddockfisherycollapsedduetooverfishingofGeorgesBank,onceoneof theworld'Srichestfishingareas.OverfishinghasalsoshutdowntheCanadianand

UScodfishery,andsimilaroverexploitationiscommoninfisheriesaroundthe world･5Nuclearpowerconstructiongroundtoahaltinthe1980sashigh-level

waste-andpublicconcernoversafety-accumulatedandasthecostsofnuclear powersteadilyescalated.TheAtariCorporationwastheleaderofthefirstwaveof homeandarcadevideogamesinthelate1970S.Salesdoubledroughlyeveryyear

from1976through1982.Abruptsaturationofthemarket-depletionofthestock ofpotentialcustomers-ledtoaprecipitousdropinsalesfrom$2billionperyear

in1982to$100millionperyearin1984,Thecompanylostabout$600million duringthecollapse.Silverexperiencedaclassicspeculativebubbleinthelate 1970S,WithpricesrlSlngtenfoldinayear,thencollapsingevenmorePreCIPltOuSly.

TheinterplaybetweenpopulationandcarryingCapacityleadingtoovershoot andcollapseisillustratedinFigure4-14,whichshowsthepopulationofEaster lsland(RapaNuiinthelocallanguage)andameasureofthecarryingcapacityde-

rived丘.ompollencoresindicatlngtheextentoftreecover･ EasterIsland,oneofthemostremotespotsonearth,isasmallislandofabout

160km2locatedintheeasternPacific･EasterIslandismostfamousforthegiant

stonestatues,knownasmoai,thatdottheisland･Radiocarbondatingputsthear- rivalofthefirstsettlers,intrepidsailorsofPolynesianorlgln,atabouttheyear400

andnotlaterthan690.Populationisestimatedtohavegrownslowlyuntilabout 1100,whengrowthaccelerateddramatically,perhapsdoublingabouteverycen- tury,untilabouttheyear1400.Pollencountsfromsoilcoresandotherrecords showthatpriortOthealTivalofthefirsthumans,EasterIslandwaslushlyforested

andsupportedadiversesetoffauna,particularlybirds(BahnandFlenley1992; Steadman1995).However,asthehumanpopulationgrew,theforestswerepro-

gressivelycuttoprovidewoodandfiberforboats,Structures,ropes,andtools,as wellastoprovidefirewood.ThePolynesianrat,whicharrivedwiththeorlglnal settlers,hastenedthedeclinebykillingbirdsandeatingtheseedsandnutsofthe

nativepalm. Byabouttheyear1400,deforestationwasnearlycomplete.Thelossoftree

coverdramaticallyreducedtheisland'sca汀ylngCapaClty･Thereisclearstrati一

graphicevidencethatsoilerosionincreasedwithdeforestationasrainwashed

awaytheunprotectedsoil.Withouttreecover,windspeedsatgroundlevelin- creased,CarrylngStillmorevaluablesoilintothesea･Theerosionwassosevere

5TheHFishbanks"simulation(Meadows,Fidda聖an,andShannon1993)isawonderfulrole-play managementflightsimulatorillustratlngthedynamlCSOfrenewableresourcessuchasfisheries.

126

FIGURE4-14

Estimated

populationand treecoverof Easterlsland

Top:Population estimatesfor Easterlslandare

highlyuncenain. Thegraphshows thelikelyrangeof populationbased ondatainBahn

andFlen】ey(1992, pp.80,178ff).

Bottom:PoHen recordsfromsoil

coreatRan°Kau, Easterlsland,

showlngdecline inthefractionof

poHenfromtrees andshrubs, indicatingthe deforestatio∩ oftheisland

(remainderof poHenfrom grasses,sedges, herbs,andferns). Deforestation

wasessentialEy completeby about1400.

PartI PerspectiveandProcess

⊂ 0 :冒;(8 ち 5000 (1 0 EL

( l t

2) 0〓

0 % )

aニO dq

n ･J L J

S Pu E!

aaJト

PopulationofEasterlsland

400 800 1200 1600 2000

TreeCover

0 590 910950 1400 Year ±50 ±60±70 ±60

Note:Timeaxesfortopandbottomgraphsdiffer.

Source:BahnandFfenley(1992,p.174).

Depth (meters)

thatsedimentwashed血.omthehigherelevationseventuallycoveredmanyofthe

moai,SothatEuropeanvisitorsthoughtthegiantstatueswereJustheads,whenin

facttheywerecompletetorsosaveraglng20feetinheight.Deforestationalsoin-

creasedevaporationfromthesoilandmayhavereducedrainfall.ThefTewstreams

ontheislanddriedup,furtherreducingfoodproductionandthefreshwatersupply.

Eventually,fishing,theothermainsourceoffood,alsofell,asboats,lines,and

hooks,allmadefromwood,couldnolongerbereplaced.WhenthefirstEuropeans

arrived,theislandersprizedwoodaboveallotheritemsofferedintrade.Mostof

thebirdspecieslivlngOnEasterIslandbecameatleastlocallyextinct.Only1of

about25indigenousspeciesstillnestsontheislandtoday(Steadman1995).

Chapter4 StructureandBehaviorofDynamicSystems 127

AsthecarrylngCapacitydeclined,populationgrowthslowed,reachingapeak

generallyestimatedtobebetween6000and10,000peoplearoundtheyear1600.

ApreclpltOuSdeclineinpopulationhadsetinbyabout1680,accompaniedby

maJOrChangesinsocial,political,andreligiousstructures.Spearpointsandother

toolsofwarappearedforthefirsttime,andthereisevidenceoflargebattles

amongcompetlnggrOupS･Somescholarsbelievethereisevidenceofcannibalism

duringthisperiod.ThefirstEuropeansknowntovisitEasterIslandarrivedin1722

andfoundasmallandpoorpopulation･Scholarsgenerallyacceptanestimateof

2000peoplein1786･AfterPeruvianslaveraidsandasubsequentsmallpoxepl-

demicthepopulationfelltoIllin1877.Thepopulationrecoveredtoabout2100

bytheearly1990S,largelytheresultofimmigrationandsettlementfromChile,

whichhasgovernedtheislandsince1888.

TheovershootandcollapseofEasterlslandisbutoneofmanysimilar

episodesdocumentedinthehistoryofislandbiogeography(seeKirch1997).In

eachcase,populationgrowthledtodeforestation,theextinctionofnativespecies,

andunfavorablechangesinlocalclimate,rainfall,andagriculturalproductivity,

followedbystarvation,conflict,and,often,populationcollapse･6

4.3 0THERMoDESOFBEHAV;OR

Growth,goalseeking,oscillation,andtheircombinations:arethesetheonlypaレ

ーemsofbehaviorsystemscanexhibit?No,buttheycoverthevastmaJOrltyOfdy-

namics･Thereareotherpatterns,fTorexample:(1)stasis,orequilibrium,inwhich

thestateofthesystemremainsconstantovertime;and(2)randomvariation.

4.3.1 Stasis,crEqL毒川briL汀n

Constancyariseseitherbecausedynamicsaffectingthestateofthesystemareso

slowthatchangeisimperceptibleorbecausetherearepowerfulnegativefeedback

processeskeepingthestateofthesystemnearlyconstanteveninthefaceofenvi-

ronmentaldisturbances.Inthefomercase,changeistooslowrelativetoyourtime

horizontobemeaningful.Inthelattercase,constancylSanexampleofhighlyef-

fectivegoal-seekingbehavior.Thefirmnessandreliabilitywithwhichyouremain

incontactwiththegroundwhenstandingreflectstheequilibriumcausedbya

powerfulnegativefeedbackloop:asgravltyCausesyoutOSinkintotheearth,the

electronsintheatomsofthegroundexertgreaterandgreaterupwardfわrceon

theelectronsintheatomsofyourfeetuntilthe氏)rceoftheirmutualelectrostatic

repulsionjustoffsetstheforceofgravlty,atWhichpointyoucometorest.

4.3.2 Randomness

Manyvariablesappeartovaryrandomly.Inmostsituations,randomnessisamea-

sureofourignorance,notintrinsictothesystem.(Exceptinquantummechanics,

6TheEasterIslanddataabovearedrawnprimarilyfromBahnandFlenley(1992),Kirch(1984), andVanTilburg(1994).Theseworks,alongwithKirch(1997)andSteadman(1995),providea goodsurveyofrecentresearchonthebiologlCalandhumanhistoryofRapaNuiandotherisland eCOSyStemS･

128 PartI PerspectiveandProcess

whereEinstein'sfamouslamentHGoddoesnotplaydicewiththeuniverse!" appearstobewrong･However,therandombehaviorofelementaryparticlesnear thePlanckscalehaslittleifanybearlngOnthedynamicsofmacroscoplCSystems suchasacompany)･Whenwesaythereare"randomMvariationsin,say,thede- mandforafirm'sproduct,whatweactuallymeanisthatwedon'tknowtherea-

sonsforthesevariations･Wearerevealingthelimitationsofourunderstanding,not characterizlngafeatureofreality･Thedemandforafirm'sproductmaybegrow-

1ngandmayalsoexperienceaseasonalcycle.Thefirmmayunderstandandcan perhapsevenforecastthetrendandseasonalcyclewithsomeaccuracy.Butafter accountingforthesesourcesofchange,peopletendtocalltheresidualvariation

randomasifthecustomersweresomehowrollingdicetodecidewhethertobuy theproduct.Peoplegenerallyhavereasonsforbehavingastheydo,buttheman- agersofthefirmarenotawareofeithertheirdecisionru1esortheinformationthey usetomaketheirdecisions.Themanagers'modelofcustomerbehaviorisim- perfect.Ifthefirmcould,throughadditionalmodelingandfieldwork,discover thoserulesandtheirInputs,theycouldexplainmoreofthetotalvariationinde-

mand,andsomeofwhatwasformerlydeemedrandomwouldnowberesolved intotheirtheoryofthesystemstructure.

Asapracticalmatter,noonecanneverknowallthelocalconditionsandidio- syncrasiescauslngaCustomertOplaceanordertodayorwaituntiltomorrowor causeamachinetobreakdownnowinsteadof3hoursfromnow.Theaggregate impactoftheindividualdeviationsfromaveragebehaviormeanssystemsare bathedinacontinuousrainofrandomshocks｡EnglneerStermtheserandomper- turbations"noise,"afterthedistortionheardontelephonelinescausedbythermal fluctuationsoftheatomsinthewires.Ofcourse,therainofrandomshocksin-

cludestheoccasionaldownpour,orevenflood(forexample,notetheimpactof WWIIoneconomicoutputintheUS,Figure4-3).

Therainofrandomnoisefallingonoursystemsdoesplayanimportantrolein dynamics,however.Byconstantlyknockingsystemsawayfromtheircurrenttra- jectory,noisecanexcitemodesofbehaviorthatotherwisewouldliedormant.A

pendulumswlnglnglntheairwilltendtowardsequilibriumasfrictiondissipates itsenergy;eventuallythebobofthependulumcomestorest,straightdown.How- ever,perturbthebobwithsmall,randomjolts,andsoonitwillbeginswlnglng, somewhatirregularly,Witharhythmclosetoitsnaturalfrequency.Thestructureof thesystemhasthepotentialtooscillate,butenergy丘.omsomeextemalsourcesuch ashigh-frequencyrandomnoiseisrequiredtoexciteitslatentdynamics(chapters 18120provideexamples).Randomnoisecanalsounfreezesystemsthatarestuck onlocaloptima,sendingthemintoanewneighborhoodwherethedynamicsare quitedifferent,andcandeterminewhichofmanyequallyattractivepathsasystem takes,contributingtopathdependence(seechapter10).Thesedisturbancescanbe modeledasrandomvariationsaroundtheaveragebehaviorglVenbytheequations capturingthefeedbackstructureofthesystem･Othertimesitismoreappropriate tomodeltheindividualelementsandactorsinthesystem,inwhichcasenonaver- agebehaviorarisesfromtheheterogeneltyOfthepopulationofagents.Theseroles forrandomperturbationswillbeexploredinlaterchapters.

Chapter4 StructllreandBehaviorofDynamicSystems 129

4.3.3 Chaos

lnrecentyearschaoshasbecomeaubiqultOuSbuzzwordinthepopularpressand

managementliterature･Booksandarticlesbyahostofnewagemanagementgu-

ruswarncompaniestoHmanageattheedgeofchaosHorbeovertakenbymore

nimblecompetitors.Extravagantclaimshavebeenmadethatchaosisanewand

radicallydifferentscience,Onewhichisfundamentallynonlinearandcomplex,One

thatcan'tbeexplainedwithoutsomemysteriousnewtheory.Actually,theterm

"chaos"hasanarrowandprecisetechnicalmeanlngindynamicaltheory.Unfortu-

nately,thehungerforthelatestfadinthebusinessworld,reinforcedbymarketing

hypeattendingthedevelopmentofchaosandcomplexltytheory,hasledtothe

misappropriationanddilutionoftheterm.ToexplainchaosIfirstdescribesome

morecom ontypesofoscillations.

DampedOscillatlrOnS:LocalStability

Oneimportantcharacteristicofoscillationsisdamplng:ifanoscillatorysystemis

perturbedonceandthenleftundisturbed,willthefluctuationsdieout?Ifso,thecy-

cleisdamped･Manysystemsaredampedoscillators･Theclassicexampleisapen-

dulumlikeachild'sswlng:Givenaslnglepush,thearctraversedbytheswlng

steadilydiminishesasfrictiondissipatesitsenergy,untiliteventuallycomesto

rest.Ifyoucouldreducethefrictionalenergylossesofthependulum,damplng

wouldbeweakeranditwouldtakelongerandlongerforequilibriumtobereestabl

lishedafterashock.Inthe(unattainable)limitofzerofriction,asingleshock

wouldcauseaperpetualoscillationataconstantamplitude.

TheequilibriumofthedampedpendulumissaidtobelocallystableIPertur- bationswillcausethesystemtooscillate,butitwilleventuallyreturntothesame

equilibrium.Thequalifier"locally"isimportant.Realsystemsarenonlinear,

meanlngthatthefeedbackloopsandparametersgovern1ngthedynamicsvaryde-

pendingonthestateofthesystem(wherethesystemisoperatinginstatespace-

thespacecreatedbythestatevariablesofthesystem).7Localstabilitymeansthe

perturbationshavetobesmallrelativetononlinearitiesthatmightcauseotherdy一

manicstoemerge,aswhenthependulumisswungsoharditbreaks.

Manyrealworldoscillatorsaredamped,buttheoscillationsneverdieaway

becausethesystemsarecontinuallybombardedwithnoise.Manymodelssuggest

thattheshort-ten businesscycle(Figure4-7)isadamped,locallystableoscilla-

tion(chapter19)･Theoscillatorystructureisasetofnegativefeedbackloops

throughwhichfirmsadjustproductiontocontroltheirinventoriesofproductsand

rawmaterials.Theseloopsareoscillatorybecauseofthelagsintheadjustmentof

productiontochangesindemandandinventory,particularlydelaysinhiringand

7Inasimplependulum,therearetwostatevariables:thepositionofthependulumanditsmo-

mentum.Thesetwostatesdefineatwo-dimensionalspace,andthestateofthesystemisdefinedat anytimebythepointinthatspacecorrespondingtothepositionandmomentumofthependulum. Asthependulumswmgsthroughitsarc,itstrajectorytracesOutaCurveinstatespace.Morecom- plexsystemshavehigh-dimensionalstatespaces,buttheconceptofatrajectorylnStateSpacere- mainsthesame.

130

FIGURE4-15 Damped osciHationina mode一oftheBeer DistributionGame

Notethe

nonlinearity: betweenweeks 30and45there

isalargesurplus ofinventorybut ordersare constrainedtobe

nonnegative.

PartiPerspectiveandProcess

materialsacquisition(Forrester1961;Mass1975).Inthesemodels,boththeper- sistenceandirregularltyOfthebusinesscyclearecausedbytheexcitationofthe economybyrandomshocks,justasthesimplependulumdiscussedabovefluctu- atessomewhatirregularlywhenperturbedbynoise.

Figure4-15Showsanexampleofdampedoscillationinasimplemodelofa firmbasedontheBeerDistributionGame(Sterman1989b,chap.17).Thegame representsthesupplychaininatypicalmanufacturlngindustry･Thesupplychain hasfoursectors:aretailer,wholesaler,distributor,andfactory.Eachstageisiden- ticalandmanagedbyadifferentperson.Themanagersstrivetominimizetheir costsbycontrollingInventoriesastheyseektomeetincomingdemand･Thesimu- lationshowstheresponseofthefactoryorderratetoaone-timechangeincus- tomerorders.Thedecisionruleusedbyeachagentinthesimulationwasestimated fromthebehaviorofactualplayers.Inresponsetotheshockindemand,factoryor- dersexhibitadampedoscillationwhichreturnsthesystemtoequilibriumafter about70weeks.Herethenegativeloopistheprocessbywhicheachstageinthe supplychainmanagesitsinventory:orderingmorewheninventoriesareinade- quateandlesswhentheyarehigh.Thedelaysarise丘.omthetimerequiredto processordersandproduceanddeliverthebeer･

ExpandingOscil/atl'onsandLim/'tCycles

Whilemanyoscillatorysystemsaredamped,theequilibriaofothersystemsare locallyunstable,meaningthatsmalldisturbancestendtomovethesystemfarther away血.omtheequilibriumpolnt.Imaglneaballbalancedontopofahill･Aslong astheballlsexactlybalancedonthehilltop,itremainsinequilibrium･Butthe slightestbreezepushestheballdownthehilleversoslightly,leadingtoastill greaterforcedownhill,inapositivefeedback.Theequilibriumisunstable･While anequilibriummaybelocallyunstable,anyrealsystemmustbegloballystable･ Globalstabilitymeansthetrajectoriesofthesystemdonotdivergetoinfinity: thetrajectoriesareboundedbecausethepositivefeedbacksleadingtotheaccel- eratlngflightfromthebalancepointmustultimatelybelimitedbyvariousnega- tiveloops.Theballcannotaccelerateindefinitely,butwillcometorestatthe bottomofthehill.

( 竜

¢ き＼S l!u n )

s La P LO ^ )0 83 t=j

Chapter4 StructureandBehaviorofDynamicSystems 131

IfanoscillatorysystemwithalocallyunstableequilibriumisglVenaSlight nudgeoffitsequilibriumpoint,itsswlngSgrowlargerandlargeruntiltheyarecon-

strainedbyvariousnonlinearities･Suchoscillationsareknownaslimitcycles,to denotethenonlinearlimitsrestrictlngtheiramplitude.Inlimitcycles,thestatesof

thesystemremainwithincertainranges(theyarelimitedtoacertainregionofstate

space).Inthesteadystate,aftertheeffectsofanyinitialperturbationshavedied out,alimitcyclefollowsaparticularorbit(closedcurve)instatespace･Thesteady stateorbitisknownasanattractor,sincetrajectoriesnearenoughtoitwillmove

towardit,justasthebobofthedampedpendulumisattractedtoitsstableequilib- riumpolnt.

Figure4-16ShowsanexampleofalimitcyclefromtheBeerDistribution

Game.Thesituationinthefigureisthesameasdescribedaboveforthedamped oscillationexceptthattheparametersoftheorderingdecisionruleareslightlydif- ferent.Asinthecaseofthedampedoscillation,theparameterscharacterizethebe-

haviorofanactualplayer.Again,thereisaone-timechangeincustomerdemand･ Insteadofdyingout,thecyclepersistsindefinitely,eventhoughtheenvironment

iscompletelyunchanglng.Thefigureshowsthecyclebothasatimeseriesandas asoICalledphaseplotwithordersontheverticalaxisandinventoryonthehori- zontalaxis,showlngtheclosedorbitperpetuallytracedbythesystem･

Ofcourse,limitcyclesarenotperpetualmotionmachines･Theenergyre- quiredtomaintainthecyclemustbeprovidedfromasourceoutsidetheoscillator･

Limitcyclesarequitecommon.Yourlifedependsonthem-yourheartbeatand respirationarelimitcycles.Thecircadianrhythms(dailyfluctuationsinalertness, hormoneproduction,andahostofotherphysiologicalparameters)observedina1-

mostallorganisms,frombacteriatopeople,arelimitcycles･Manycyclesinthebil ologicalworldalsoappeartobelimitcycles,includingcyclesinpredator-prey

populations,CyclesinthemassfruitlngOfcertainplantspeciessuchasPi畠onplneS andsomebamboos,andtheperiodicpopulationexplosionsofcertaininsectssuch

asthe17-yearcicada(seeMurray1993).Manymodelssuggestthatverylong-term

FIGURE4-16 AlimitcyclegeneratedintheBeerDistributionGame

Left:Timeseriesoffactoryorders.Thecyclerepeatsindefinitelywithoutanyexternalvariation. R/'ght:Theorbitofthesystemisaclosedcurve,ShownherewithfactoryordersplottedagalnStnet factoryinventory(inventorylessbacklog).

1(よ O aJ VLJ Sl Eu n )

sJapjo )̂0 13t2j

600 700 800 900 1000

Weeks -30 ･20 -10 0 10 20

FactoryNetlnventory

132 PartIPerspectiveandProcess

fluctuationsintheworldeconomyknownas"longwaves"areself-perpetuatlng limitcycles(Sterman1985;Forrester1983).Sterman(1989a)reportsanexperi- mentinwhichpeoplemanagedasimpleeconomicmodel;thevastmaJOrltygener-

atedlongwavesmuchlikethebehaviorofthemodel･Steman(1989C)Showsthat manyofthedecisionrulescharacterizlngthehumansubjectsgeneratechaosand variousformsoflimitcycle.

Chaotl'cOscillalions

Chaos,likedampedfluctuationsandlimitcycles,isaformofoscillation･How- ever,unlikelimitcycles,achaoticsystemfluctuatesirregularly,neverexactlyre- peatlng,eventhoughitsmotioniscompletelydeterministic･Theirregularityarises endogenouslyandisnotcreatedbyextemal,randomshocks･Likealimitcycle,the pathofachaoticsystemisboundedtoacertainreglOnOfstatespace･Because chaoticsystemsarebounded,chaos,likelimitcycles,canonlyariseinnonlinear systems.However,unlikelinearsystemsorlimitcycles,chaoticdynamicsdonot haveawell-definedperiod,asdoesthesimplependulumdiscussedabove･Themo- tionofachaoticsystemneverrepeats;instead,theorbitsofthesystemapproach whatisknownasastrangeattractor-asetofcloselyrelatedbutslightlydifferent orbitsratherthanaslngleclosedcurve.Furthermore,chaoticsystemshavethe propertyknownassensitivedependenceoninitialconditions･Twonearbytra- jectories,nomatterhowclose,Willdivergeexponentiallyuntilthestateofone providesnomoreinformationaboutthestateoftheotherthananyrandomlycho- sentrajectory.Sensitivedependencemeansthatthepredictionhorizonforchaotic systems-thelengthoftimeoverwhichforecastsoffuturebehaviorareaccurate- islikelytobeshortevenifourmodelofthesystemstructureandparameteresti- matesareperfect.Further,thecostofincreaslngthepredictionhorizonafixed amountbyimprovlngOurknowledgeofthecurrentstateofthesystemincreases exponentially.

Figure4-17ShowschaoticbehaviorinasimulationoftheBeerDistribution Gam e.Onlytheparametersofthedecisionruleforordershavebeenaltered',again,

FIGURE4-17 ChaosintheBeerDistributionGame

Left:Timeseriesshowlngfactoryorders.i?ight:Phaseplotshowlngordersvs.netfactorylnventory (inventorylessbacklog).

八U

t l

)

(】盲

a き＼S

l ! u

s J a p L O

^ )O i Dej

s jむ P

J 0̂J0

8 3

時』

600 700 800 900 1000 1100 -50 0 50 100

weeks FactoryNetnventory

Chapter4 StructureandBehaviorofDynamicSystems 133

theseparameterswereestimatedfromthebehaviorofanactualplayer.Likethe

limitcycle,ordersfluctuateindefinitely,inthiscasewithanamplituderanging

from0toabout50unitsperweekandanaverageperiodofabout20weeks.Un-

1ikethelimitcycle,theoscillationdoesnothavearegularamplitude,periodicity,

orshape,eventhoughtheenvironmentiscompletelyconstantandthesystemis

completelyfreeofrandomshocks･ThetrajectoryOfthesysteminstatespacefo1- 1owsawell-definedpath,butonewhichneverclosesonitself･8

Inallthreeofthesecases,dampedoscillation,limitcycle,andchaos,thefeed-

backstructureanddecisionrulesarethesame･Theonlydifferencesareinthepa-

rametersoftheorderingrulesuchasthesizeofdesiredinventoryandthe

aggressivenesswithwhichmanagersreacttothediscrepancybetweendesiredand

actualinventory.

4.4 SuMMARY

Thefeedbackstructureofasystemgeneratesitsbehavior.Mostdynamicsob-

seⅣedintherealworldareexamplesofasmallsetofbasicpatternsormodesof

behavior･Threeofthesemodesarefundamental:exponentialgrowth,goalseeking,

andoscillation.Eachofthesemodesisgeneratedbyaparticularunderlyingfeed-

backstructure.Exponentialgrowthisgeneratedbypositivefeedbackprocesses,

goalseekinglSgeneratedbynegativefeedback,andoscillationisgenerated

bynegativefeedbackwithdelays.Morecomplexpatternsofbehaviorsuchas

SIShapedgrowth,growthwithovershoot,andovershootandcollapseresultfrom thenonlinearinteractionofthesebasicfeedbackstructures.

TheprlnCiplethatthestructureofasystemgeneratesitsbehaviorleadstoa

usefulheuristictohelpmodelersdiscoverthefeedbackloopstructureofasystem.

Wheneveraparticularpatternofbehaviorisobserved,youknowwhichofthe

basicfeedbackstructuresmusthavebeendominantduringtheperiodcoveredby

thedata.Observingthatavariableofinteresthasbeenfluctuatlng,forexample,

impliestheexistenceof(atleast)onenegativefeedbackloopwithsignificanttime

delays,whichhelpstoguidethesearchfortheparticularstructures,decision

processes,andtimedelaysthatcomprlSethenegativeloop.Whilethisheuristicis

usefulasanaidtotheinitialconceptualizationprocess,modelersmustalsotake

caretosearchforandincludeintheirmodelsthefeedbackloopsandstructuresthat

havenotbeenimportantingeneratingthedynamicstodatebutthatmaybecome

activeasthesystemevolves｡

8Mosekilde(1996)providesanexcellenttreatmentofchaoticandothernonlineardynamicsin theBeerDistributionGameandawidevarietyofotherphysical,technical,andbiologlCalsystems. Strogatz(1994)providesanexcellentmathematicalintroductiontononlineardynamicsandchaos.

e蓮盲主§畠葺互ノ軸i3iIs毒嘩T3;-iifiS

Weshapeourbuildings;thereajtef;Ourbuildingsshapeus. -WinstonChurchill

Feedbackisoneofthecoreconceptsofsystemdynamics.Yetourmentalmodels oftenfailtoincludethecriticalfeedbacksdeterminingthedynamicsofour systems･Insystemdynamicsweuseseveraldiagrammlngtoolstocapturethe structureofsystems,includingcausalloopdiagramsandstockandflowmaps. Thischapterfocusesoncausalloopdiagrams,includingguidelines,pitfalls,and examples.

5.1 CAL･SALDIAGRAMNoTAT50N

Causalloopdiagrams(CLDs)areanimportanttoolforrepresentingthefTeedback structureofsystems.Longusedinacademicwork,andincreaslnglycommonin business,CLDsareexcellentfor

･Quicklycapturlngyourhypothesesaboutthecausesofdynamics;

｡Elicitingandcapturlngthementalmodelsofindividualsorteams;

･Communicatingtheimportantfeedbacksyoubelieveareresponsiblefora problem.

TheconventionsfordrawingCausaldiagramsaresimplebutshouldbefollowed faithfully.Thinkofcausaldiagramsasmusicalscores.Neatnesscounts,andidio- syncraticsymbolsandstylesmakeithardforfellowmusicianstoreadyourscore. Atfirst,youmayfinditdifficulttoconstructandinterpretthesediagrams.With practice,however,youwillsoonbesight-reading.

137

138

FIGURE5-1 Causalloop diagramnotation

PartH TわolsforSystemsThinking

Acausaldiagram consistsofvariablesconnectedbyarrowsdenotlngthe causalinfluencesamongthevariables.Theimportantfeedbackloopsarealsoiden-

tifiedinthediagram.Figure5-1showsanexampleandkeytothenotation･ Variablesarerelatedbycausallinks,shownbyarrows･Intheexample,the

birthrateisdeterminedbyboththepopulationandthefractionalbirthrate.Each

causallinkisassignedapolarity,eitherpositive(+)ornegative(-)toindicate howthedependentvariablechangeswhentheindependentvariablechanges.The

importantloopsarehighlightedbyaloopidentifierwhichshowswhetherthe loopisapositive(reinforcing)ornegative(balancing)feedback･Notethattheloop identifiercirculatesinthesamedirectionasthelooptowhichitcorresponds.Inthe

example,thepositivefeedbackrelatingbirthsandpopulationisclockwiseandso isitsloopidentifier;thenegativedeathrateloopIScounterclockwisealongwithits identifier.

Table5-1summarizesthedefinitionsoflinkpolarity.

Example

, ･･( /I主

population LB守BirthRate 竿R

Fractional BirthRate

Key

CausaILink , ･LinkPolarity

BirthRate Variable

､こ.Fl:.) (.Ln )

Q了‥二㌧

Population Van'abIe

DeathRate

Average Lifetime

LoopldentifierIPoslrtive(F7einforeing)Loop

LoopldentifE'er:Negative(Balancing)Loop

Chapter5 CausalLoopDiagrams 139

Apositivelinkmeansthatifthecauseincreases,theeffectincreasesabove whatitwouldotheJWisehavebeen,andifthecausedecreases,theeffectde-

creasesbelowwhatitwouldotherwisehavebeen･IntheexampleinFigure5-1an increaseinthefractionalbirthratemeansthebirthrate(inpeopleperyear)will increaseabovewhatitwouldhavebeen,andadecreaseinthefractionalbirthrate

meansthebirthratewillfallbelowwhatitwouldhavebeen･Thatis,ifaverage fertilityrises,thebirthrate,giventhepopulation,willrise;iffertilityfalls,the numberofbirthswillfall.Whenthecauseisarateofflowthataccumulatesintoa

stockthenitisalsotruethatthecauseaddstothestock.Intheexample,birthsadd tothepopulation(Seechapter6formoreonstocksandflows).

Anegativelinkmeansthatifthecauseincreases,theeffectdecreasesbelow whatitwouldotherwisehavebeen,andifthecausedecreases,theeffectinereases

abovewhatitwouldotherwisehavebeen.Intheexample,anincreaseintheaver- agelifetimeofthepopulationmeansthedeathrate(inpeopleperyear)willfall belowwhatitwouldhavebeen,andadecreaseintheaveragelifetimemeansthe

deathratewillriseabovewhatitwouldhavebeen.Thatis,iflifeexpectancy increases,thenumberofdeathswillfall;andiflifeexpectancyfalls,thedeathrate willrise.

Linkpolaritiesdescribethestructureofthesystem.Theydonotdescribethe behaviorofthevariables.Thatis,theydescribewhatwouldhappenIFtherewere achange.Theydonotdescribewhatactuallyhappens.Thefractionalbirthrate mightincrease;itmightdecrease-thecausaldiagramdoesn'日ellyouwhatwill happen.Rather,ittellsyouwhatwouldhappenifthevariableweretochange.

Notethephraseabove(orbelow)whatitotherwisewouldhavebeeninthe definitionoflinkpolarity.Anincreaseinacausevariabledoesnotnecessarily meantheeffectwillactuallyincrease.Therearetworeasons.First,avariableof- tenhasmorethanoneInput.Tbdeterminewhatactuallyhappensyouneedtoknow howalltheinputsarechanging.Inthepopulationexample,thebirthratedepends

TABLE5･l Linkpolarity:definitionsandexamples

Symbo一 lnterpretation Mathematics Examp一es Allelseequal,ifXincreases (decreases),thenYincreases

+ (decreases)above(below) x～ y whatI'twouldhavebeen.

Inthecaseofaccumulations, XaddstoY.

∂Y/∂X>0 Inthecaseof accumulations, I･t

Y-Jt｡(x+･-)ds+Yto

Allelseequal,ifXincreases (decreases),thenYdecreases (increases)below(above)

x～ Y whatitwouldhavebeen.

Inthecaseofaccumulations, Y- XsubtractsfromY.

∂Y/∂×<0 lnthecaseof accumulations,

仁× + .･･)ds+Yt｡

PQruOadIE.cyt一一- S ales+ Effort一~~1- Re sults

Births Population

pBo,FcuecL-㌫ sales

Frustrati蒜~~づ虹Resures

Deaths 一一~~~二由一

Population

140 PartIIToolsforSystemsThinking

onboththe丘.actionalbirthrateandthesizeofthepopulation(thatis,BirthRate-

FractionalBirthRate*Population).Youcannotsaywhetheranincreaseinthe fractionalbirthratewillactuallycausethebirthratetorise;youalsoneedtoknow

whetherthepopulationisrlSlngOrfalling.Alargeenoughdroplnthepopulation maycausethebirthratetofallevenifthefractionalbirthraterises.Whenassess- ingthepolarityofindividuallinks,assumeallothervariablesareconstant(thefa- mousassumptionofceterisparibus).Whenassessingtheactualbehaviorofa

system,allvariablesinteractsimultaneously(allelseisnotequal)andcomputer simulationisusuallyneededtotraceoutthebehaviorofthesystemanddetermine whichloopsaredominant.

Second,andmoreimportantly,Causalloopdiagramsdonotdistinguishbe- tweenstocksandflows-theaccumulationsofresourcesinasystemandtherates ofchangethatalterthoseresources(Seechapter6)･Inthepopulationexample,the populationisastock-itaccumulatesthebirthratelessthedeathrate.Anincrease inthebirthratewillincreasethepopulation,butadecreaseinthebirthratedoes notdecreasethepopulation･Birthscanonlyincreasethepopulation,theycan neverreduceit｡Thepositivelinkbetweenbirthsandpopulationmeansthatthe birthrateaddstothepopulation.Thusanincreaseinthebirthrateincreasesthe populationabovewhatitotherwisewouldhavebeenandadecreaseinthebirth ratedecreasespopulationbelowwhatitotherwisewouldhavebeen.

Similarly,thenegativepolantyofthelinkfromthedeathratetopopulationin- dicatesthatthedeathratesubtractsfromthepopulation.Adroplnthedeathrate doesnotaddtothepopulation.Adropindeathsmeansfewerpeopledieandmore remainalive:thepopulationishigherthanitwouldothenvisehavebeen.Notethat youcannottellwhetherthepopulationwillactuallybeincreaslngOrdecreaslng: Populationwillbefallingevenifthebirthrateisrislngifthedeathrateexceeds births･ToknowwhetherastockisincreaslngOrdecreasingyoumuStknowitsnet rateofchange(inthiscase,birthslessdeaths).Itisalwaystrue,however,thatifthe birthraterises,populationwillriseabovewhatitwouldhavebeenintheabsence ofthechangeinbirths,evenifthepopulationcontinuestofall.Populationwillbe fallingataslowerratethanitotherwisewould.Chapters6and7discussthestruc- tureandbehaviorofstocksandflows,

ProcessPoI'nt.･ANoteonNotation

lnsomeofthesystemdynamicsliterature,especiallythesystemsthinkingtradition (see,e.g.,Sengeetal.1994andKin1992),analternateconventionforcausaldia-

gralrlShasdeveloped.Insteadof幸or-thepolarityOfacausallinkisdenoted bysoro,respectively(denotingthesameoroppositerelationshipbetweeninde- pendentanddependentvariables):

S + x一一~1輸血.YinsteadofX一一- 曲虹 Y

0 x一一一一｢鮎.yinsteadofx一一一｢鮎.Y

Chapter5 CausalLoopDiagrams 141

Thelinkdenotedwithansisreadas"XandYmoveinthesamedirection"

whilethelinkdenotedwithanoisreadas"XandYmoveintheoppositedirec-

tion."ThusProductQualityandSalestendtomoveinthesamedirectionwhile ProductPriceandSalestendtomoveintheoppositedirection.

Thesandonotationwasmotivatedbyadesiretomakecausaldiagramseven easiertounderstandforpeoplewithlittlemathematicalbackground.Whichnota- tionisbetterishotlydebated.Richardson(1997)providesstrongarguments agalnSttheuseofsando.Henotesthatthestatement"XandYmoveinthesame direction"isnotingeneralcorrect,forthereasonsstatedabove.Thecorrectstate- mentis,"IfXincreases,Yincreasesabovewhatitwouldhavebeen."Thatis,a

causallinkisacontlngentStatementOftheindividualeffectofahypothesized change.ThevariablesXandYmaybepositivelylinkedandyetYmayfallevenas Xincreases,asothervariablesalsoaffectY.Thesandodefinitionsalsodon't

workforstockandflowrelationships.Birthsandpopulationdonotmoveinthe samedirection:adecreaseinbirthsdoesnotcausepopulationtodecreasebecause thebirthrateisaninflowtothestockofpopulation.Thecorrectdefinitionisgiven inTable511:forpositivelinkpolarity,ifXincreases,Ywillalwaysbehigherthan itwouldhavebeen;fornegativepolarity,ifXincreases,Ywillalwaysbelower thanitwouldhavebeenJnthisbookIwillusethe+and-signstOdenotelink polarity.Asamodeleryoushouldknowhowtointerpretthesandonotationwhen youseeit,butyoushouldusethe+and-notationtodenotelinkpolarlty･

5N望 Gu旧EuNESFORCAUSALLoopDIAGRAMS

5.2.1 CausationversusCorre一ation

Everylinkinyourdiagrammustrepresent(whatyoubelievetobe)Causalrela-

tionshipsbetweenthevariables.Youmustnotincludecorrelationsbetweenvar1- ables.TheLatinrootofthewordsimulate,simulwe,means"toimitate."Asystem dynamicsmodelmustmimicthestructureoftherealsystemwellenoughthatthe modelbehavesthesamewaytherealsystemwould･Behaviorincludesnotonly replicatinghistoricalexperiencebutalsorespondingtocircumstancesandpolicies thatareentirelynovel.Correlationsamongvariablesreflectthepastbehaviorofa system.Correlationsdonotrepresentthestructureofthesystem･Ifcircumstances change,ifpreviouslydormantfeedbackloopsbecomedominant,ifnewpolicies aretried,previouslyreliablecorrelationsamongvariablesmaybreakdown･Your modelsandcausaldiagramsmustincludeonlythoserelationshipsyoubelievecap- turetheunderlyingcausalstructureofthesystem.Correlationsamongvariables willemergefromthebehaviorofthemodelwhenyousimulateit･

Thoughsalesoficecreamarepositivelycorrelatedwiththemurderrate,you maynotincludealinkfromicecreamsalestomurderinyourmodels.Instead,as showninFigure5-2,bothicecreamsalesandmurderriseinsummerandfallin winterastheaveragetemperaturefluctuates.Confusingcorrelationwithcausality canleadtoterriblemisjudgmentsandpolicyerrors.Themodelontheleftsideof Figure5-2suggeststhatcuttlnglCeCreamCOnSumptlOnWOuldslashthemurder rate,savelives,andallowsocietytocutthebudgetforpoliceandprisons･

142

FIGURE5-2 Causaldiagrams mustinclude

only(whatyou believetobe) genuinecausal relationships.

PartIITわolsforSystemsThinking

lncorrect

r ' 日ceCream Murder Sales Rate

lceCream SaJes

-=t-1t-

Correct

Average Temperature

Whilefewpeoplearelikelytoattributemurderstotheoccasionaldouble-dip cone,manycorrelationsaremoresubtle,anditisoftendifficulttodeterminethe underlyingcausalstructure.Agreatdealofscientificresearchseeksthegenuine causalneedlesinahugehaystackofcorrelations:DoesvitaminCcurethecom- moncold?CaneatlngOatbranreducecholesterol,andifitdoes,willyourriskof aheartattackdrop?Doeseconomicgrowthleadtolowerbirthrates,oristhelower rateattributabletoliteracy,educationforwomen,andincreaslngcostsOfchild rearing?DocompanieswithseriousqualityImprovementprogramsearnSuperior returnsforstockholders?Scientistshavelearnedfrombitterexperiencethatreli- ableanswerstosuchquestionsarehardtocomebyandrequirededicationtothe scientificmethod-controlledexperiments,randomized,double-blindtrials,large samples,long-termfollow-upstudies,replication,statisticalinference,andsoon. Inthesocialandhumansystemsweoftenmodel,suchexperimentsaredifficult, rare,andoftenimpossible.Modelersmusttakeextracaretoconsiderwhetherthe relationshipsintheirmodelsarecausal,nomatterhowstrongthecorrelation,how hightheR2,0rhowgreatthestatisticalslgnificanceofthecoefficientsinare- gressionmaybe.AstheEnglisheconomistPhelps-Brown(197 2 ,p.6)noted, "Where,assooften,thefluctuationsofdifferentseriesrespondincommontothe pulseoftheeconomy,ltisfatallyeasytogetagoodfit,andgetitforqulteanum- berofdifferentequations‥.RunnlngregreSSionsbetweentimeseriesisonly likelytodeceive.門

5.2.2 Labe圭iflgL≡nkPo知和

BesuretolabelthepolarltyOfeverylinkinyourdiagrams.Labelthepolarityof theimportarltfTeedbackloopsillyOltii-diagrams,-tiSingthedefinitioTISillTable5-1 tohelpyoudeterminewhetherthelinksarepositiveornegative.Positivefeed- backloopsarealsocalledreinforcingloopsandaredenotedbya+orA,while negativeloopsaresometimescalledbalancingloopsandaredenotedbya-orA (Figure5-3).

Chapter5 CausalLoopDiagrams

FtGURE5-3 LabeHinkandloop polarities.

Notethatalllinks arelabeledand

looppolarity identifiersshow

whichloopsare positiveandwhich arenegative. Loopidentifiers areclockwise fortheclockwise

loops(andvice versa)[

lncorrect

sa.es.r.r .√ ( ヽ Customer Customer

Base LossRate

143

Wordof

"ouL ノノ＼ J j

Correct

sa.es.r.r ･.√ ヽ Customer

B r LossRate _i 皇

Customer R J Base

量三

Wordof

"o･uしこノ＼ = j v･

5.2.3 DeterminingLoopPo一arity TherearetwomethodsfordeterminlngWhetheralooplSpositiveornegative:the

fastwayandtherightway.

144 PartIIToolsforSystemsThinking

TheFastWay:CounttheNumberofNegativeLI'nks

ThefastwaytotellifalooplSpositiveornegativeistocountthenumberof negativelinksintheloop.Ifthenumberofnegativelinksiseven,theloopISposi- tive;ifthenumberisodd,thelooplSnegative･Theruleworksbecausepositive loopsreinforcechangewhilenegativeloopsareself-correcting;theyopposedis- turbances.ImaglneaSmalldisturbanceinoneofthevariables.Ifthedisturbance propagatesaroundthelooptoreinforcetheorlglnalchange,thentheloopISposi- tive.Ifthedisturbancepropagatesaroundthelooptoopposetheorlglnalchange, thenthelooplSnegative.Tbopposethedisturbance,theslgnalmustexperiencea netslgnreversalasittravelsaroundtheloop･Netreversalcanonlyoccurifthe numberofnegativelinksisodd.Asinglenegativelinkcausesthesignaltoreverse: anincreasebecomesadecrease.Butanothernegativelinkreversestheslgnal agaln,SOthedecreasebecomesanincrease,reinforclngtheorlglnaldisturbance. See"MathematicsofLoopPolarity"belowforaformalderivationofthisrule.

Thefastmethodalwaysworks...exceptwhenitdoesn't.Whymightitfail? Inacomplexdiagramitisalltooeasytomiscountthenumberofnegativelinksin aloop.AnditiseasytomislabelthepolarltyOflinkswhenyoufirstdrawthedia-

gram.CountlngthenumberofnegativeslgnSisunlikelytorevealthesee汀OrS.The rightmethod,Carefullytraclngtheeffectofadisturbancearoundtheloop,willof- tenrevealawronglylabeledpolarityandwillhelpyouandyouraudiencetograsp themeanlngandmechanismoftheloop,Assignlnglooppolaritytherightway

ratherthanthefastwaysavestimeinthelongrun･

TheRightWay:TracetheEffectofaChangearoundtheLoop

TherightwaytodeterminethepolarityofaloopIStOtracetheeffectofasmall changeinoneofthevariablesasltPropagatesaroundtheloop･Ifthefeedbackef- fectreinforcestheorlglnalchange,itisapositiveloop;ifitopposestheorlglnal change,itisanegativeloop.Youcanstartwithanyvariableintheloop;theresult mustbethesame.InthemarketloopsshowninFigure5-3,assumesalesfrom wordofmouthincrease.Becausethelinkfromsalesfromwordofmouthtothe

customerbaseispositive,thecustomerbaseincreases･Becausethelinkfromthe customerbasebacktosalesfromwordofmouthispositive,thesignalpropagates aroundthelooptoincreasesalesfromwordofmouthstillfurther.Thefeedbackef- fectreinforcestheorlglnalchange,sotheloopISpositive.TurningtOtheother loop,assumeasmallincreaseinthecustomerlossrate.Ifcustomerlossesincrease, thecustomerbasefails.Withalowercustomerbase,therearelreWerCustomers

whocandropout.ThefTeedbackeffectopposestheorlglnalchange,sotheloopIS negative.

Thismethodworksnomatterhowmanyvariablesareinaloopandnomatter whichvariableyoustartwith.(Identifythelooppolaritiesfortheexamplestarting withcustomerbaseinsteadofsales丘･omwordofmouth:youshouldgetthesame result).Youmayalsoassumeaninitialdecreaseinavariableratherthananinitial Increase.

Chapter5 CausalLoopDiagrams 145

EdentifyingLinkandLoopPobrity

Identifyandlabelthepolarityofthelinksandloopsintheexamplesshownin

Figure5-5.

了AttractivenessofMarket pr誓＼Price

NumberofCompetitors √一/ノ

Pressur'etoClean

FupEnvironment㌔

Environmenta】 Cleanup Quality Effort

>＼＼-｣ _ノー//

了 Cumu一ativeProduction＼＼lMarket Unit

Share Costs ㌧ー PrieeJ BankCashReserves了

Net ＼＼･＼勺Perceived withdrawals SolvencyofBankも＼一一//

MathematicsofLoopPolarity

Whenyoudeterminelooppolarlty,youareCalculatlngWhatisknownincontrol

theoryastheslgnOftheopenloopgainoftheloop.Theterm"gain"referstothe

strengthoftheslgnalretumedbytheloop:againOftwomeansachangeinavari-

ableisdoubledeachcyclearoundtheloop;agalnOfnegative0.5meansthedis-

turbancepropagatesaroundthelooptoopposeitselfwithastrengthhalfaslarge.

Thetem Hopenloop"meansthegalniscalculatedforJustonefeedbackcycleby

breaking-openlng-theloopatsomepolnt･Consideranarbitraryfeedbackloop

consistlngOfnvariables,xl,.I･,Xn.Youcancalculatetheopenloopgainatany

polnt;letxldenotethevariableyouchoose.Whenyoubreaktheloop,Ⅹ1Splitsinto

aninput,XII,andoutput,xlO(Figure516).Theopenloopgainisdefinedasthe

(partial)derivativeofxlOwithrespecttoXII,thatis,thefeedbackeffectofasmall

changeinthevariableasitreturnstoitself.Thepolarityoftheloopisthesignof

theopenloopgaln:

Polarityofloop-SGN(∂Ⅹ10/∂Xii) (5-1)

whereSGN()isthesignumorsignfunction,returning+1ifitsargumentisposi-

tiveand-1iftheargumentisnegative(iftheopenloopgainiszero,theSGN

function-0:thereisnoloop)ATheopenloopgainiscalculatedbythechainrule

fromthegalnSOftheindividuallinks,∂xl/∂xl【1:

SGN(∂xlO/∂x17)-sGN[(∂xlO/∂xn)(∂Xn/∂xn_1)(∂Xn_1/∂xn_2)･･･(∂x2/∂xII)] (5-2)

146

FdGURE5-6 Calculatingthe open-loopgaln ofaloop

PartII¶)olsforSystemsThinking

∴-I-もt Breakthe-oopatanypoint

xLx,):4fn望tracetheef changear° the一oop.

了xlO｢ .uencxLx3)4

PoJarity=SGN(∂xlO/∂xll)

∂xl0/∂xll-(∂Ⅹ10/∂Ⅹ4)(∂Ⅹ4/∂x3)(∂Ⅹ3/∂x2)(∂x2/∂xIB)

SincethesignofaproductistheproductoftheslgnS,looppolarltylSalso glVenby:

SGN(∂Ⅹ10/∂Ⅹ1Ⅰ)-SGN(∂Ⅹ10/∂X｡)*SGN(∂X｡/∂Xnー1)辛SGN(∂x｡_1/∂Xn_2) *･･･*SGN(ax2/axiI) (513)

Usingtherightmethodtodeterminelooppolaritybytraclngtheeffectofa smallchangearoundaloopisequivalenttocalculatingequation(5-3).Equation (5-3)alsoexplainswhythefastmethodworks:Sincetheproductoftwonegative slgnSisapositiveslgn,negativeopenlooppolarltyrequlreSanOddnumberofneg- ativelinksintheloop｡

AllLinksShou/dHaveUnambiguousPolan'ties

Sometimespeoplesayalinkcanbeeitherpositiveornegative,dependingono血er parametersoronwherethesystemisoperatlng.Forexample,peopleoftendraw

血ediagramontheleftsideofFigure5-7relatlngafirm'srevenuetotheprlCeOf itsproductandthenarguethatthelinkbetweenprlCeandcompanyrevenuecanbe eitherpositiveornegative,dependingontheelasticityOfdemand.Ifdemandis highlyelastic,ahigherprlCemeanslessrevenuebecausea1%increaseinprlCe causesdemandtofallmorethan1%.Thelinkwouldhavenegativepolarity.Ifde- mandisinelastic,thena1%increaseinprlCeCausesdemandtodroplessthan1%, sorevenuesrise.Thelinkwouldbepositive.Itappearsnosinglepolaritycanbe asslgned.

WhenyouhavetroubleasslgnlngaClearandunambiguouspolaritytoalinkit usuallymeansthereismorethanonecausalpathwayconnectlngthetwovariables. Youshouldmakethesedifferentpathwaysexplicitinyourdiagram.Intheexam- ple,pricehasatleasttwoeffectsonrevenue:(1)itdetermineshowmuchrevenue isgeneratedperunitsoldand(2)itaffectsthenumberofunitssold.Thatis,Reve-

nue-Price*Sales,and(Unit)SalesdependonPrice(presumablythedemand curveisdownwardsloping:Higherpricesreducesales).Theproperdiagramis

FIGURE5-7 Causa川nks musthave

unambiguous polarity.

Apparently ambiguous poLaritiesusually indicatethe

presenceof multiplecausal pathwaysthat shouldbe

represented separate一y.

Chapter5 CausalLoopDiagrams

lncorrect Correct

r ,(･or-) r ･ Price Revenue Price Revenue

＼ sa.esJメ+

147

shownontherightsideofFigure517.Thereisnownoambiguityaboutthepolar1 1tyOfanyofthelinks.

ThepriceelastlCltyOfdemanddetermineswhichcausalpathwaydominates･If demandisquiteinsensitivetoprice(theelasticityofdemandislessthanone),then thelowerpathinFigure5-7isweak,prlCeraisesunitrevenuemorethanitde- creasessales,andtheneteffectofanincreaseinpriceisanincreaseinrevenue.

Conversely,ifcustomersarequitepricesensitive(theelasticityofdemandis greaterthanone),thelowerpathdominates.Theincreaseinrevenueperunitis morethanoffsetbythedeclineinthenumberofunitssold,sotheneteffectofa priceriseisadroplnrevenue.Separatlngthepathwaysalsoallowsyoutospecify differentdelays,ifany,lneach.Intheexampleabove,thereislikelytobealong delaybetweenachangeinprlCeandachangeinsales,whilethereislittleornode- laylntheeffectofpriceonrevenue.

SeparatlnglinkswithapparentlyambiguouspolarityIntotheunderlyingmul- tiplepathwaysisafruitfulmethodtodeepenyourunderstandingofthecausal structure,delays,andbehaviorofthesystem.

EnlPioyeeMo的fation

Yourclientteamisworriedaboutemployeemotivationandisdebatingthebest waystogeneratemaximumeffortfromtheirpeople･Theyhavedrawnadiagram (Figure5-8)andarearguingaboutthepolarityofthelinks･Onegrouparguesthat thegreatertheperformanceshortfall(thegreaterthegapbetweenRequiredPer formanceandActualPerformance),thegreaterthemotivationofemployeeswill be.Theyarguethatthesecretofmotivationistosetaggressive,evenimpossible goals(soICalledstretchobjectives)toelicitmaximummotivationandeffort.The othergrouparguesthattoobigaperformanceshortfallsimplycausesfrustrationas peopleconcludethereisnochancetoaccomplishthegoal,sothelinktoemployee motivationshouldbenegative.Expandthediagramtoresolvetheapparentconflict byincorporatingboththeories.Discusswhichlinksdominateunderdifferentcir-

cumstances.Canyougivesomeexamplesfromyourownexperiencewherethese differentpathwaysweredominant?HowcanamanagertellwhichpathwaylS likelytodominateinanysituation?Wh ataretheimplicationsforgoalsettlnglnOr- ganizations?Actualandrequiredperformancearenotexogenousbutpartofthe feedbackstructure.Howdoesmotivationfeedbacktoperformance,andhow

mightactualperformanceaffectthegoal?Indicatetheseloopsinyourdiagramand explaintheirimportance.

148 PartIITわolsforSystemsThinking

Actual Performance

＼ヽ〆/// Performance Shortfall

Employee Motivation

Required Performance

5.2,4 N･3meYourLoops

Whetheryouusecausaldiagramstoelicitthementalmodelsofaclientgrouporto

communicatethefeedbackstructureofamodel,youwilloftenfindyourselftrying tokeeptrackofmoreloopsthanyoucanhandle･Yourdiagramscaneasilyover- whelmthepeopleyouaretrylngtOreach.Tbhelpyouraudiencenavlgatethenet- workofloops,it'ShelpfultoglVeeachimportantfeedbackanumberandaname.

NumberingtheloopsRl,R2,B1,B2,andsoonhelpsyouraudiencefindeachloop asyoudiscussit･Namlngtheloopshelpsyouraudienceunderstandthefunctionof eachloopandprovidesusefulshorthandfordiscussion.Thelabelsthenstandinfわr

acomplexsetofcausallinks･Whenworkingwithaclientgroup,lt'softenpossi- bletogetthemtonametheloop.Manytimes,theywillsuggestawhimsicalphrase orsomeorganization-specificjargonforeachloop.

Figure519Showsacausaldiagramdevelopedbyengineersandmanagersina workshopdesignedtoexplorethecausesoflatedeliveryfortheirorganization's

designwork｡Thediagram representsthebehavioroftheenglneerStrylngtO completeaprojectagalnStadeadline.TheenglneerScomparetheworkremaining tobedoneagainstthetimeremainingbeforethedeadline.Thelargerthegap,the

moreSchedulePressuretheyfeel･Whenschedulepressurebuildsup,englneerS haveseveralchoices.First,theycanworkovertimeJnsteadofthenormal50hours

perweek,theycancometoworkearly,skiplunch,staylate,andworkthroughthe weekend.ByburningtheMidnightOil,theyincreasetherateatwhichtheycom-

pletetheirtasks,cutthebacklogofwork,andrelievetheschedulepressure(bal- ancingloopB1).However,iftheworkweekstaystoohightoolong,fatiguesetsin

andproductivltySuffers･Asproductivityfalls,thetaskcompletionratedrops, whichincreasesschedulepressureandleadstostilllongerhours:thereinforcing BurnoutloopRllimitstheeffectivenessofovertime.Anotherwaytocompletethe workfasteristoreducethetimespentoneachtask.Spendinglesstimeoneach

taskbooststhenumberoftasksdoneperhour(productivity)andrelievesschedule

pressure,thusclosingthebalanclngloopB2･Discussionofthenameforthisloop washeated.ThemanagersclaimedtheenglneerSalwaysgold-platedtheirwork;

theyfeltschedulepressurewasneededtosqueezeoutwasteandgettheengineers tofocusonthejob.TheenglneerSarguedthatschedulepressureoftenrosesohigh thattheyhadnochoicebuttocutbackqualityassuranceandskipdocumentation

Chapter5 CausalLoopDiagrams

FIGURE5-9 Nameandnumber

yourloopsto increasediagram cfarityandprovide memorablelabels

forimportant feedbacks.

Fatigue

Schedube Pressure

苛Midnight ＼二

149

Time Remanmg r+

Workと≡て二Remamng Comp一etionRate色鼻+iurnout

一一..Productivity

oftheirwork.TheycalledittheComerCuttingloop(B2).Theengineersthenaト

guedthatcornercuttinglSSelf-defeatlngbecauseitincreasestheerrorrate,which leadstoreworkandlowerproductivltyinthelongrun:"Hastemakeswaste,Hthey said,andschedulepressurerisesfurther,leadingtostillmorepressuretocutcor-

ners(loopR2). Thefullmodelincludedmanymoreloops(section5.1providesacloselyre-

latedexample;seealsosection2.3).Thenamesgiventotheloopsbyonegroup (engineers)communicatedtheirattitudesandtherationalefortheirbehaviortothe

managersinaclearandcompellingway.Theconversationdidnotdegenerateinto adhominemargumentsbetweenmanagersshoutingthatengineersJustneedto

havetheirbuttskickedandenglneerSgrlplngthatgettlngpromotedtomanagement turnsyourbraintolfTertilizer]-themodeofdiscoursemostcommonintheorga- nizationprlOrtOtheintervention.ParticlpantSSOOnbegantotalkabouttheBurnout

Loopkickinglnandthenonlinearrelationshipsbetweenschedulepressure,over-

time,fatigue,anderrors.Thenamesfortheloopsmadeiteasytorefertocomplex chunksoffeedbackstructure.Theconceptscapturedbythenamesgraduallybegan toenterthementalmodelsanddecisionmakingofthemanagersandenglneerSin

theorganizationandledtochangeindeeplyIngrainedbehaviors.

150

FIGURE5-10 Representing delaysincausal diagrams

PartH ToolsforSystemsThinking

5.2.5 ;ndicate!nlPOrtantDe!ays弓11G訓JSaきし.∃nks

Delaysarecriticalincreatlngdynamics.DelaysglVeSystemsinertia,cancreateo s-

cillations,andareoftenresponsiblefortrade-offsbetweentheshort-andlong-run effectsofpolicies.Yourcausaldiagramsshouldincludedelaysthatareimportant tothedynamichypothesisorsignificantrelativetoyourtimehorizon.Asshownin chapterll,delaysalwaysinvolvestockandflowstructures.Sometimesitisim- portanttoshowthesestructuresexplicitlylnyourdiagrams.Often,however,itis sufficienttoindicatethepresenceofatimedelaylnaCausallinkwithoutexplic- itlyshowingthestockandflowstructure.Figure5-10showshowtimedelaysare representedincausaldiagrams.

WhentheprlCeOfagoodrises,supplywilltendtoincrease,butoftenonlyaf- tersignificantdelayswhilenewcapacitylSOrderedandbuiltandwhilenewfirms enterthemarket.SeealsothetimedelaysintheBurnoutandHasteMakesWaste loopsinFigure5-9｡

Example:EnergyDemand

TheresponseofgasolinesalestoprlCeinvolveslongdelays.Intheshortrun,gaso- linedemandisqulteinelastic:ifpricesrise,peoplecancutdownondiscretionary trlpSSOmeWhat,butmostpeoplestillhavetodrivetowork,school,andthesuper- market.Aspeoplerealizethatpricesarelikelytostayhigh theymayorganizecar- poolsorswitchtopublictransportation,ifitisalreadyavailable｡Overtimehigh pricesinduceotherresponses.First,consumers(andtheautocompanies)waitto seeifgaspricesaregoingtOStayhighenoughandlongenoughtoJustifybuying ordesigningmoreefficientcars(aperceptualanddecision-makingdelayofper-

hapsayearormore).Oncepeoplehavedecidedthatthepricewon'tdropback downanytimesoon,theautocompaniesmustthendesignandbuildmoreefficient cars(adelayofseveralyears).Evenaftermoreefficientcarsbecomeavailable,the vastmajOrltyOfcarsontheroadwillbeinefficient,oldermodelswhichareonly replacedastheywearoutandarediscarded,adelayofabout10years.Ifprices stayhigh,eventuallythedensityOfsettlementpatternswillincreaseaspeople abandonthesuburbsandmoveclosertotheirjobs.Altogether,thetotaldelayinthe linkbetweenprlCeanddemandforgasolineissignificantlymorethanadecade.As thestockofcarsontheroadisgraduallyreplacedwithmoreefficientcars,andas (perhaps)newmasstransitroutesaredesignedandbuilt,thedemandforgasoline wouldfallsubstantially-long-rundemandisqulteelastic.Figure5-llmakes thesedifferentpathwaysfortheadjustmentofgasolinedemandexplicit.

ExplicitlyportrayingthemanydelaysbetweenachangeinprlCeandthe resuitir.gcharlgeindemarldmakesiteasiei-tOSeetheworse-before-betterbehavior ofexpendituresongasolinecausedbyaprlCeincrease.ThebottomofFigure 5-llshowstheresponseofgasolinedemandandexpenditurestoahypothetical

Price Supply

Chapter5 CausalLoopDiagrams 151

unantlClpatedstepIncreaseintheprlCeOfgasoline.Intheshortrungasoline

demandisratherinflexible,sothefirstresponsetoanincreaseintheprlCeOfgas

isanincreaseingasolineexpenditures･Asthehighpricepersists,efficiency

FIGURE5-ll Differenttimede一aysintheresponseofgasolinedemandandexpenditurestoprice

Top:TheshortrunresponsetohigherprICeSisweak,whilethelongrunresponsejssubstantialasthe stockofcarsisgradua"yreplacedwithmoreefficientmode一s,andasrifestyleschange.

Bottom:ResponsetoahypotheticalpermanentunanticEPatedincreaseingasoHnepnce.Consumption s一owlydeclinesduetothelongde一aysinadjustingtheefficiencyofautomobilesandinchanglng settlementpatternsandmasstransitroutes･ExpendituresthereforeimmediatelynseandonlyIaterfaH belowtheinitialIevel:aworse-before-bettertrade一〇ffforconsumers.Ofcourse,asdemandfa川s,there

wouldbedownwardpressureonpnce,possiblylowenngexpendituresstillmore,butalsodiscouragIng furtherefficiencyImprovements.ThefeedbacktopnceisdeliberatelylgnOredinthediagram.

Gasoline

Expendjtures

Expected Short一丁erm

Price

Discretionary

CarPoo一ingand UseofExisting

+ _..′常perYear

Demandfor Gasoline

+ MassTransit

Densityof SettlementPatterns,

+ Deve60pmentofNew MassTransitRoutes

:I_- i-

EfficiencyofEb["V[〉"Vy〉Zl

r oEfffgairesn…yn-即 carsomRoad Market

Time

152

FIGURE5-12 Variab一enames shouldbenouns

ornounphrases.

FIGURE5-13 Variablenames shouldhavea clearsenseof direction.

PartIIToolsforSystemsThinking

improvementsgraduallycutconsumptlOnOfgasolinepervehiclemile,andeven- tually,settlementpatternsandmasstransitavailabilitywilladjusttoreducethe numberofvehiclemilesdrivenperyear.Inthelongrun,demandadjustmentsmore thanoffsetthepriceincreaseandexpendituresfall.FromthepointOfviewofthe consumer,thisisaworse-before-bettersituation.Thetimedelaysandthetrade-off theycreatehelpexplainwhyithasprovensodifficult,intheUnitedStatesatleast, toincreasegasolinetaxes.Althoughthelong-runbenefitsoutweightheshort-run costs,eveninnetpresentvalueterms,theyonlybegintoaccrueaftermanyyears. Governmentofficialsfocusedonthenextreelectioncampalgnjudgetheshort-run coststobepoliticallyunacceptable.Intum,theymakethisjudgmentbecausethe publicisunwillingtosacrificealittletodayforlargerbenefitstomorrow.

5.2.6 VariableNames Van'ableNamesShouldBeNounsorNounPhrases

Thevariablenamesincausaldiagramsandmodelsshouldbenounsornoun phrases.Theactions(verbs)arecapturedbythecausallinksconnectingthevari- ables.Acausaldiagramcapturesthestructureofthesystem,notitsbehavio一 mOt whathasactuallyhappenedbutwhatwouldhappenifothervariableschangedin variousways.Figure5-12Showsexamplesofgoodandbadpractice.

Thecorrectdiagramstates:Ifcostsrise,thenpricerises(abovewhatitwould havebeen),butifcostsfall,thenpricewillfall(belowwhatitwouldhavebeen). Addingtheverb"rises"tothediagrampresumescostswillonlyrise,biaslngthe discussiontowardsonepatternofbehavior(innation).Itisconfusingtotalkofa decreaseincostsrisingOrafallinpnCeincreases-areprlCeSrislng,rislngata fallingrate,Orfalling?

VanrableNamesMustHaveaClearSenseofDirectI'On

ChoosenamesforwhichthemeanlngOfanincreaseordecreaseisclear,variables thatcanbelargerorsmaller.Withoutaclearsenseofdirectionforthevariables youwillnotbeabletoassignmeaningfullinkpolarities.

OntheleftsideofFigure5-13neithervariablehasacleardirection:Iffeed- backfromthebossincreases,doesthatmeanyougetmorecomments?Arethese

lncorrect Correct

///-′ 一､､-洩 + / 一′一ー＼-凍 + CostsRise PriceRises Costs Price

lncorrect

// 一一､､-≠ + Feedback fromthe Boss

Correct

r ･ Mental Praisefr10m Attitude theBoss

Mora一e

FIGURE5-14 Choosevariables whosenormal senseofdirection

ispositive.

Chapter5 CatlSalLoopDiagrams

lncorrect Correct

153

r . r ･ Costs Losses Costs Profit

/T . r _ Criticism Unhappiness Criticism Happiness

commentsfromthebossgoodorbad?Andwhatdoesitmeanformentalattitude toincrease?ThemeanlngOftherightsideisclear:Morepraise丘.omtheboss boostsmorale;lesspraiseerodesit(thoughyoushouldprobablynotletyourself- esteemdependsomuchonyourbossフopinion).

ChooseVanlablesWhoseNormalSenseofDlrreCtionlsPosl'tive

Variablenamesshouldbechosensotheirnormalsenseofdirectionispositive. Avoidtheuseofvariablenamescontainingprefixesindicatingnegation(non,un, etc.;Figure5-14).

StandardaccountlngPracticeisProfit-Revenue-Costs,sothebettervari- ablenameisPro恥 whichfallswhencostsriseandriseswhencostsfall.Likewise,

criticism maymakeyouunhappy,butitisconfusingtospeakofrisingun- happlneSS;abetterchoiceisthepositivehapplneSS,Whichmayfallwhenyouare criticizedandrisewhencriticism drops.Thoughthereareoccasionalexcep- tions,decreasingnOnCOmpliancewiththisprinciplewilldiminishyouraudience's incomprehension.

5.2,7 ■首̀ips紬rCaLSSaFL･C10PDiagramLayout

Tomaximizetheclarityandimpactofyourcausaldiagrams,youshouldfollow somebasicprlnCiplesofgraphicdesign.

1.Usecurvedlinesforinformationfeedbacks.Curvedlineshelpthereader visualizethefeedbackloops.

2.Makeimportantloopsfollowcircularorovalpaths｡

3.Organizeyourdiagramstominimizecrossedlines.

4.Don'tputcircles,hexagons,orothersymbolsaroundthevariablesincausal diagrams.SymbolswithoutmeanlngareHchartjunk"andseⅣeonlyto clutteranddistract.Anexception:Youwilloftenneedtomakethestock andflOwstructureofasystemexplicitinyourdiagrams.Inthesecasesthe rectanglesandvalvesaroundthevariablestellthereaderwhicharestocks andwhichareflows-theyconveyimportantinformation(Seechapter6).

5.Iterate.Sinceyouoftenwon'tknowwhatallthevariablesandloopswillbe whenyoustart,youwillhavetoredrawyourdiagrams,oftenmanytlmeS ,

tofindthebestlayout.

154

FIGURE5-15 Makeintermediate

linksexpllCitto clarifyacausaJ re一ationship.

PartII ToolsforSystemsThinking

rfyouraudiencewasconfusedby

/-~ー~､--もー Market Unit Share Costs

youmightmaketheintermediateconceptsexplicitasfollows:

Cumu一ative + Production

千production +

/./ メ

Market Share

Vo一ume Experience､ -＼鶏-

Unit Costs

5.2,8 ChoosetheRightLeve弓ofAggregation Causalloopdiagramsaredesignedtocommunicatethecentralfeedbackstructure

ofyourdynamichypothesis･TheyarenotintendedtobedescnptlOnSOfamodelat thedetailedleveloftheequations.Havingtoomuchdetailmakesithardtoseethe overallfeedbackloopstructureandhowthedifferentloopsinteracLHavingtoolit- tledetailmakesithardforyouraudiencetograsptheloglCandevaluatetheplau- sibilityandrealismofyourmodel.

Ifyouraudiencedoesn'tgrasptheloglCOfacausallink,youshouldmake someoftheintermediatevariablesmoreexplicit.Figure5-15showsanexample. Youmightbelievethatinyourindustry,marketsharegainsleadtolowerunitcosts becausehighervolumesmoveyourcompanydownthelearnlngCurvefaster･The toppanelcompressesthisloglCintoaslnglecausallink.Ifyouraudiencefound thatlinkconfusing,youshoulddisaggregatethediagramtoshowthestepsofyour reasonlnglnmoredetail,asshowninthebottompanel.

Onceyou'veclarifiedthisloglCtOthesatisfactionofall,youoftencan "chunk"themoredetailedrepresentationintoasimple,moreaggregateform.The simplerdiagramthenservesasamarkerforthericher,underlyingcausalstructure.

5.2.9 D訓11号PuモAeHheLo甲信棚o OmeLargeDiagram

Short-termmemorycanhold7±2chunksofinformationatonce･Thisputsa rathersharplimitontheeffectivesizeandcomplexityofacausalmap･Presentlng acomplexcausalmapallatoncemakesithardtoseethe一oops,understandwhich ∬eimportant,Orunderstandhowtheygeneratethedynamics･Resistthetempta- tiontoputalltheloopsyouandyourclientshaveidentifiedintoaslnglecompre- hensivediagram.Suchdiagramslookimpressive-My,whatalotofworkmust havegoneintoit!Howbigandcomprehensiveyourmodelmustbe!-butarenot effectiveincommunicatlngWithyouraudience･Alarge,wall-fillingdiagrammay beperfectlycomprehensibletothepersonwhodrewit,buttothepeoplewith

Chapter5 CausalLoopDiagrams 155

whomtheauthorseekstocommunicate,itisindistinguishablefromaJackson Pollockandconsiderablylessvaluable,

Howthendoyoucommunicatetherichfeedbackstructureofasystemwithout oversimplifying?Buildupyourmodelinstages,withaseriesofsmallercausal loopdiagrams.Eachdiagramshouldcorrespondtoonepartofthedynamicstory beingtold.Fewpeoplecanunderstandacomplexcausaldiagramunlesstheyhave achancetodigestthepleCeSOneatatime.Developaseparatediagram for eachimportantloop.Thesediagramscanhaveenoughdetailinthemtoshowhow theprocessactuallyoperates.Thenchunkthediagramsintoasimpler,high leveloverviewtoshowhowtheyinteractwithoneanother.Inpresentations,build upyourdiagrampiecebypiecefromthechunks(seesections5.4and5.6for examples).

5且10 MaketheGoa!SofNegativeLoopsExplicit

Allnegativefeedbackloopshavegoals.Goalsarethedesiredstateofthesystem,

andallnegativeloopsfunctionbycomparlngtheactualstatetothegoal,thenini- tiatlngaCO汀eCtiveactioninresponsetothediscrepancy.Makethegoalsofyour negativeloopsexplicit.Figure5-16showstwoexamples.Thetoppanelshowsa negativeloopaffectingthequalityofacompany'sproduct:thelowerthequality, themorequalityimprovementprogramswillbestarted,and(presumably)thede- ficienciesinqualitywillbecorrected.Makinggoalsexplicitencouragespeopleto askhowthegoalsareformed.ThegoalsinmostsystemsarenotgiveneXOge- nouslybutarethemselvespartofthefeedbackstructure.Goalscanvaryovertime andrespondtopressuresintheenvironment.Intheexample,whatdeterminesthe

FIGURE5-16 Makethegoalsof negativeloops expHdt.

Humanagencyor naturalprocesses candetermine

goals･

Top:Thegoalof theloopIS determinedby management decision.

Bottom.･

Thelawsof

thermodynamics determinethegoal oftheloop.

Incorrect

(す

ProductOuality

真土 QuaMty

日mprovement Programs

(?'

ProductOuality 主王

Quality Improvement

Correct

＼､.i-i ;_;-- Quality ShortfaH

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DesiredProduct Quality

Room

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156 PartIIToolsforSystemsThinking

desiredlevelofproductquality?TheCEO'sedict?Benchmarkingstudiesofcom-

petitorquality?CustomerInput?Thecompany'sownpastqualitylevels?Whenthe

goalisexplicitthesequestionsaremorelikelytobeaskedandhypothesesabout theanswerscanbequicklyincorporatedinthemodel.

Makingthegoalsofnegativeloopsexplicitisespeciallyimportantwhenthe

loopscapturehumanbehavior･Butoftenitisimportanttorepresentgoalsexplic-

itlyevenwhentheloopdoesnotinvolvepeopleatall･Thesecondexamplepor- traysthenegativefTeedbackbywhichacupofcoffeecoolstoroomtemperature. Therateofcooling(therateatwhichheatdiffusesfromthehotcoffeetothesur-

roundingair)isroughlyproportionaltothedifferencebetweenthecoffeetemper- atureandroomtemperature･Thecoolingprocessstopswhenthetwotemperatures areequaLThisbasiclawofthermodynamicsismadeclearwhenthegoalisshown explicitly.

ThereareexceptlOnStOtheprlnCipleofshowingthegoalsofnegativeloops. ConsiderthedeathrateloopinFigure5-1.ThegoalofthedeathratelooplSim- plicit(andequaltozero:inthelongrun,wearealldead).Yourmodelsshouldnot explicitlyportraythegoalofthedeathlooporthegoalsofsimilardecayprocesses suchasthedepreciationofcapitalequlpment.

5.2.ll a)isモiElguishbeモW･?enA･7号lJah?nd PerceivedConditions

Oftentherearesignificantdifferencesbetweenthetruestateofaffairsandthe perceptionOfthatstatebytheactorsinthesystem.Theremaybedelayscausedby reportlngandmeasurementprocesses.Theremaybenoise,measurementerror,

bias,anddistortions･InthequalitymanagementexampleshowninFigure5-16, theremaybesignificantdelaysinassesslngqualityandinchangingmanagement's oplnionaboutproductquality･Separatlngperceivedandactualconditionshelps promptquestionssuchasHowlongdoesittaketomeasurequality?Tochange management'soplnionaboutqualityevenafterthedataareavailable?Toim- plementaqualityImprovementprogram?Torealizeresults?Besidesthelongtlme

delays,theremaybebiasinthereportingSystemCausingreportedqualitytodiffer systematicallyfromqualityasexperiencedbythecustomer.Customersdon'tfile warrantyclaimsforallproblemsorreportalldefectstotheirsalesrepresentative. Salesandrepalrpersonnelmaynotreportallcustomercomplaintstothehome Office.Theremaybebiasinseniormanagement'squalityassessmentbecausesub-

ordinatesfiltertheinformationthatreachesthem･SomeautoexecutivesareproI videdwiththelatestmodelsfortheirpersonaluse;thesecarsarecarefullyselected and丘.equentlyservicedbycompanymechanics.Theirimpressionofthequalityof theirfirm'scarswillbehigherthanthatoftheaveragecustomerwhobuysoffthe lotandkeepsthecarfor10years.Thediagrammightberevisedasshownin

Figure5-17.Thediagram nowshowshowmanagement,despltegoodinten- tions,cancometoholdagrosslyexaggeratedviewofproductquality,andyouare wellpositionedforadiscussionofwaystoshortenthedelaysandeliminatethe distortions.

FIGURE5-17

Distinguish betweenactual

andperceived conditions.

Chapter5 CausalLoopDiagrams

Biasin

Reporting System

//座軒 Product

QuaHty

㌔. Reported Product

Qua日ty

豆 Quality

lmprovement

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Product

Ouality

157

5.3 PROCESSPoINT:

DEVELOPINGCAUSALDIAGRAMSFROMrNTERVIEW DATA

Muchofthedataamodelerusestodevelopadynamichypothesiscomesfromin- terviewsandconversationswithpeopleinorganizations･Therearemanytech- nlqueSavailabletogatherdatafrommembersoforganizations,includingsurveys, interviews,particlpantObservation,archivaldata,andsoon･Surveysgenerallydo notyielddatariChenoughtobeusefulindeveloplngSystemdynamicsmodels.In-

terviewsareaneffTectivemethodtogatherdatausefulinformulatingamodel,ei- therconceptualorfわrmal.Semistructuredinterviews(wherethemodelerhasaset ofpredefinedquestionstoaskbutisfreetodepartfromthescripttOPursueaV- enuesofparticularinterest)haveproventobeparticularlyeffective.

Interviewsarealmostneversufficientaloneandmustbesupplementedby othersourcesofdata,bothqualitativeandquantitative.Peoplehaveonlyalocal, partialunderstandingofthesystem,Soyoumustinterviewallrelevantactors,at multiplelevels,includingthoseoutsidetheorganization(customers,Suppliers, etc.).Interviewdataisrich,includingdescriptionsofdecisionprocesses,internal politics,attributionsaboutthemotivesandcharactersofothers,andtheoriestoex- plainevents,butthesedifferenttypesofinformationaremixedtogether.People bothknowmorethantheywilltellyouandcaninventratlonalesandeveninci- dentstojustifytheirbeliefs,providingyouwith"data"theycan'tpossiblyknow (NisbettandWilson1977).Themodelermusttriangulatebyusingasmanysources ofdataaspossibletogaininsightintothestructureoftheproblemsituationandthe decisionprocessesoftheactorsinit.Anextensiveliteratureprovidesguidancein techniquesforqualitativedatacollectionandanalysis;See,forexample,ArgyrlSet al.(1985),Emmersonetal.(1995),GlaserandStrauss(1967),KleinerandRoth (1997),Marchetal.(1991),MorecroftandSterman(1994),VanMaanen(1988), andYin(1994).

158 PartIIToolsforSystemsThinking

Onceyou'vedoneyourinterviews,youmustbeabletoextractthecausal

structureofthesystemfromthestatementsoftheinterviewsubjects.Formulate

variablenamessothattheycorrespondcloselytotheactualwordsusedbytheper-

sonyouinterviewed,whilestilladheringtotheprlnCiplesforpropervariablename selectiondescribedabove(nounphrases,aclearandpositivesenseofdirection).

Causallinksshouldbedirectlysupportedbyapassageinthetranscript.Typically,

peoplewillnotdescribeallthelinksyoumayseeandwillnotexplicitlyclose

manyfeedbackloops.Shouldyouaddtheseadditionallinks?Itdependsonthe purposeofyourdiagram｡

IfyouaretrylngtOrepresentaperSOn'smentalmodel,youmustnotinclude

anylinksthatcannotbegroundedintheperson'sownstatements.However,you maychoosetoshowtheinitialdiagramtothepersonandinvitehimorhertoelab-

orateoraddanymisslnglinks.Peoplewilloftenmentionthemotivationforade-

cisiontheymade,Withthefeedbackeffectonthestateofthesystemimplicitly understood.Forexample,"Ourmarketsharewasslipping,SOWefiredthemarket-

1ngVPandgotourselvesanewadagency.HImplicitinthisdescrlptlOnisthebe-

liefthatanewVPandagencywouldleadtobetteradsandanincreaseinmarket

share,closingthenegativeloop.

Ifthepurposeofyourinterviewsistodevelopagoodmodeloftheproblem

situation,youshouldsupplementthelinkssuggestedbytheinterviewswithother

datasourcessuchasyourownexperienceandobservations,archivaldata,andso

on.Ⅰnmanycases,youwillneedtoaddadditionalcausallinksnotmentionedin

theinterviewsorotherdatasources･Whilesomeofthesewillrepresentbasicphys-

icalrelationshipsandbeobvioustoall,othersrequlrejustificationorexplanation.

Youshoulddrawonalltheknowledgeyouhavefromyourexperiencewiththe

systemtocompletethediagram･1

Process垂m町OVen頂門号

ThefollowlngtwoquotesareactualinterviewtranscrlPtSdevelopedinfieldwork

carriedoutinanautomobilecompanyintheUnitedStates.Themanagers,from

twodifferentcomponentplantsinthesamedivisionofthecompany,describewhy

theyieldoftheirlineswaspersistentlylowandwhyithadbeensodifficulttoget

processimprovementprogramsofftheground(RepenningandSterman1999):

Inthemindsofthe[operationsteamleaders]theyhadtohittheirpackcounts[daily quotas]･Thismeantifyouwerehavingabaddayandyouryieldhadfallen.‥you hadtorunlikecrazytohityourtarget.Ⅵ)ucouldsay,=Youaremaking20% garbage,stopthelirleandfixtheproblerrl,"aridtheywouldsay,HIcarl'thitirly packcountwithoutrunnlnglikecrazy.HTheycouldnevergetaheadofthegame.

-ManageratPlantA

Supervisorsneverhadtimetomakeimprovementsordopreventivemaintenance ontheirlines-･theyhadtospendalltheirtimeJusttrylngtOkeepthelinegolng,

iBurchillandFine(1997)illustratehowcausaldiagramscanbedevelopedfrominterviewdata inaproductdevelopmentcontext.

Chapter5 CausalLoopDiagrams 159

butthismeantitwasalwaysinastateofflux･Hbecauseeverythingwassounpre- dictable･Itwasakindofsnowballeffectthatjustkeptgettlngworse.

-Supe7VisoratPlantB

Developaslnglecausaldiagramcapturlngthedynamicsdescribedbytheinter- views.Nameyourloopsusingtermsfromthequoteswherepossible.Explainina paragraphortwohowtheloopscapturethedynamicsdescribed,Buildyourdial

gramaroundthebasicphysicalstructureshowninFigure5-18.TheNetThrough- putofaprocess(thenumberofusablepartsproducedpertimeperiod,forexample, thenumberofusablepartsproducedperday)equalsGrossThroughput(thetotal numberproducedpertimeperiod)multipliedbytheprocessYield(thefractionof

grossthroughputthatpassesinspectionandisusable).Theremainder,Gross Throughput*(1IYield),aredefective.

+ Net

Gross-√一㊥Throughput

Throughput

5.4 CoNCEPTUAuZATJONCASESTUDY:

MANAGINGYouRW oRKLOAD

Thissectionillustrates血euseofcausaldiagramstomodelanissue･Theexample showshowcausaldiagrammlngCanbeanaidtothedevelopmentofadynamichy- pothesis,alongwithidentifyingvariablesanddeveloplngarefTerencemodeshow-

1ngthedynamicsofthevariablesovertherelevanttimehorizon.

5.4.1 ProbJemDefinition

ConsidertheprocessofmanaglngyourWOrkload.Youmightbeanenglneerina productdevelopmentorganization,aconsultant,oraCEO.TokeepltCOnCrete,foI

cusonastudentmanaginghisorherworkload.Astudent(imagineyourself)must balanceclassesandasslgnmentSWithoutsideactivities,apersonallife,andsleep.

Duringthesemesteryouattendclasses,dothereadings,andhandinasslgnmentS

astheyaredue,atleastoccasionally.Youprobablytrytoworkharderifyouthink yourgradesarelowerthanyoudesireandtakemoretimeoffwhenyouaresleep-

deprivedandyourenergylevelfalls.Therearetwobasicpoliciesyoucanfollow:

(1)Theantstrategy一meverputoffuntiltomorrowwhatyoucandotoday;or (2)thegrasshopperstrategy-neverdotodaywhatcanbeputoffuntiltomorrow.

Theantworkssteadilythroughoutthesemesterasworkisassignedandnever

buildsupalargebacklogofasslgnmentS.Asaresult,theantavoidstheendofse- mestercrunch,keepstheworkweekundercontrol,andisabletostaywellrested. Becausetheantgetsenough sleep,productivityishigh,andtheanthasplentyof

160 PartIIToolsforSystemsThinking

timetopartlClpateinoutsideactivities.Theant'sgradesimprovesteadilythrough- outtheterm.

Thegrasshopper,incontrast,deferstheworkuntilthelastminute.The grasshopper'sworkweekislowatthebeginnlngOftheterm,providinglotsoftime forpartiesandoutsideactivities.Thegrasshoppercanstayreasonablywellrested desplteaheavysocialschedulebecausetheworkweekislow.Butbecausethe grasshopperdoesn'tdotheworkasfastasitisasslgned,theasslgnmentbacklog steadilybuildsupiEventually,it'scrunchtime,andthegrasshopperstartsputting inlonghours,perhapspullingafewall-nighters･Unfortunately,assleepsuffers, energyandproductivityfall.Therateandqualityofworksuffers･Gradesplummet, andthetermendsbeforethegrasshoppercanfinishallthework,perhapsleading thegrasshoppertopleadforextensionsfromthefaculty.

5且2 Edenti菅y岳mgKeyVariab暑es

ThedescrlptlOnabovesuggestsseveralvariablesimportantinamodelofstudent workloadmanagement(unitsofmeasurearegiveninparentheses):

Assignmentrate:therateatwhichprofessorsasslgnWOrkthroughoutthe term(tasks/week).

Workcompletionrate:therateatwhichtasksarecompleted(tasks/week).

Assignmemtbacklog:thenumberoftasksthathavebeenasslgnedbutnot yetcompleted(tasks).

Grades:thegradereceivedforworkhandedin(01100scale).

Workweek:thenumberofhoursspentonacademicwork,including classes,reading,homework,projects,etc.(hours/week).

Energylevel:measureshowwellrestedthestudentis.Arbitraryscalefrom O1100%wherelOO%-fullyrestedand0-comatose),

Othervariablescouldbeadded,butthissetprovidesareasonablestartlngPOlntfor conceptualizationofthefeedbackstructuregovernlngthedynamics.Asyoupro- ceed,youmayfindyouneedtorevisethelist.

5.4.3 DeveBopmg昔heRe骨eremeeMode

Figure5-19translatesthewrittendescrlptlOnSOftheant'sbehaviorintographical form(Figure5-20showsthegrasshopperstrategy)･Thesegraphsconstitutetheref- erencemodecharacterizlngtheproblem.Someitemstonote:

1.Thetimehorizonisexplicitlystated.Here,thesemesteris13weekslong.

2.Severaldifferentgraphsareusedtoavoidclutter.Thetimeaxesofeach grapharealignedsothatthetimingOfeventscanbedirectlycompared.

3.Variableswiththesameunitsareplottedonthesameaxis.Forexample,the asslgnmentandcompletionratesarebothmeasuredintasks/weekandare plottedtogether.

4.Youdon'tneedquantitativedatatocapturethedynamicsinthereference modes.Whennumericaldataareunavailableyoushouldestimatethe

Chapter5 CausalLoopDiagrams

q a aき J

ad sとS e 1

(葛 8m JSm O Li) 竜

aき望

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FIGURE5-19 Referencemode

fortheantstrategy

AssignmentRate WorkCompletionRate

Time(weeksoHhesemester) 13

AssignmentBack一og

Time(weeksofthesemester)

0 Time(weeksofthesemester)

161

(o o L ･0 ) S a P e J 9

(㌔ o o T O ) la ^ a 1 ^ 6 Ja u u

behaviorofthevariablesfromthewrittendescrlPt10nandotherqualitative

information.Scalesandrough magnitudesareprovidedwherepossible,as

theyarefortheworkweek,grades,andenergylevel･Ofcourse,when quantitativedataareavailable,血eyshouldbeused.Butdon'tomit

importantvariablessimplybecausetheyhaven'tbeenmeasuredyetor becausethedataaren'treadilyavailable.Animportantgoalofthemodeling

162

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processistheidentificationofvariablesthatshouldbemeasuredsothe necessaryemplrlCalworkcanbedone.

5.Thereshouldbeabasisinthedata(numericalorwritten)foreachfeatureof

thereferencemode.Forexample,thegraphoftheant'sgradesrisesbecause thedescrlptlOnOftheantstrategystatesthattheant'sgradesimprove steadilythroughouttheterm.Likewise,forthegrasshopperthe"termends

Chapter5 CausalLoopDiagrams 163

beforethegrasshoppercanfinishallthework"sotheassignmentbacklog, thoughfalling,remainspositiveevenasthetermends.

6.ThemagnitudesandtimlngOfvariablesshouldbeconsistentwithyour

knOwledgeofthesystemevenifthedescrlPtlOnavailabledoesnotspecify thesefeatures.Detailsmatter.Forexample,considerthegrasshopper

strategy.Theworkcompletionratemustdependonthestudent'swork effort(workweek),sothesemovetogether.However,becauseenergyand

productivltyarefallingattheend,thecompletionratedoesnotriseasmuch astheworkweekduringtheendofsemestercrunch.Tomakethiseven

moreobvious,youmightdefinethevariableProductivityexplicitly(try

sketchingitsdynamics血.omthedescriptionabove)･

7.Makesureyourgraphsareconsistentwithanystockandflowrelationships amongthevariables.Sincetheasslgnmentbacklogaccumulatestherateof

asslgnmentSlesstherateofworkcompletion,itmustberislngWhenever theasslgnmentrateexceedsthecompletionrate,andviceversa.The

relationshipbetweenthebackloganditsflOwsismostclearlyseenin thegrasshopperstrategy.Untilweek10,theasslgnmentrateexceedsthe

completionrate,sothebacklogbuildsup.Atweek10,thegrasshopper ishandinglnWOrkjustasfastasnewworkisasslgned,andthebacklog reachesitspeak.A洗erweek10,thecompletionrateexceedstheasslgnment rateandthebacklogfalls.

5.4.4 13eveEopingtheCausa=〕iagrams

NextyoumustusethedescrlPtlOnOfthesystemandreferencemodestodevelopa causalmapofthefeedbackprocessesyoubelieveareresponsibleforthedynamics.

ConsiderFigure5121･TheAssignmentRateisassumedtobeexogenous'.Once astudenthasslgnedupforasetofcourses,theassignmentrateisdetermined･ Classescansometimesbedropped,butthispossibilitylSIgnoredfornow.TheAs- slgnmentBackloglSincreasedbytheAssignmentRateanddecreasedbytheCom-

pletionRate.CompletionRate(tasks/week)isWorkweek(hoursperweek)times Productivity(taskscompletedperhourofeffort)timestheEffortDevotedtoAs-

slgnmentS･E恥rtDevotedtoAssignmentsisthee肋rtputinbythestudentcom- paredtotheeffortrequiredtocompletetheasslgnmentWithhighquality.Ifwork pressureishigh,thestudentmaychoosetocutcorners,skimsomereading,skip classes,orglVelesscompleteanswerstothequestionsinasslgnmentS.Forexam-

ple,ifastudentworks50hoursperweekandcandoonetaskperhourwithhigh qualitybutonlydoeshalftheworkeachasslgnmentrequiresforagoodjob,then

thecompletionratewouldbe(50)(1)(.5)-25taskequivalentsperweek. WorkPressuredeterminestheworkweekandeffortdevotedtoasslgnmentS･

WorkpressuredependsontheassignmentbacklogandtheTimeRemainlngtO completethework:Thebiggerthebacklogorthelesstimeremainlng,thehigher theworkweekneedstobetocompletetheworkontime.TimeremainlnglSOf coursesimplythedifferencebetweentheDueDateandthecurrentCalendarTime.

Thetwomostbasicoptionsavailabletoastudentfacedwithhighworkpressure areto(1)worklongerhours,thusincreasingthecompletionrateandreducingthe

164 PartII Toolsfol-SystemsThinking

FlGURE5-21 Basiccontrolloopsfortheassignmentbacklog

AssEgan.∑ent-＼遠来′′~一一＼二 ▲讐禁 Comp一etion+Assignment

l.Backlog

Ca一endar

Time ､< +_ Time

emaining＼ Wヽork

Pressure

-==二十 --=

＼-､嬢t喜fiosr!i冨害vmoet喜Ts

Workweek

Productivity

backlog(theMidnightOilloopBl),or(2)workfasterbyspendinglesstimeon eachtask,speedingthecompletionrateandreducingthebacklog(theCornerCut- tingloopB2)ABotharenegativefeedbackswhosegoalistoreduceworkpressure toatolerablelevel.

However,eachofthesenegativefeedbackshassideeffectsIConsiderFigure 5-22.Sustainedhighworkweekscutintosleepandthesatisfactionofotherneeds

(eating,exercise,humancompanionship,etc･),causingthestudent'sEnergyLevel tofall.Asenergylevelfalls,sotoodoconcentrationandfocus.Errorsrise.Pro-

ductivitydrops,reducingthecompletionrate-atiredstudentmustspendlonger thanawell-restedonetocompleteataskwithaglVenlevelofquality･Asthecom- pletionratefalls,thebacklogremainshigherthanitwouldotherwisebeandwork pressureintensifies,leadingtostillhigherworkweeksandstilllowerenergyand productivity･Iftheself-reinforclngBurnoutloop,Rl,dominatesthebalanclng MidnightOilloop,anincreaseinworkweekwouldactuallylowerthecompletion rateastheextrahoursaremorethanoffsetbytheincreaseinerrorsandreduction inproductivlty.

Reducingtheeffortdevotedtoeachasslgnmentalsohassideeffects･Putting lesseffortintoeachtaskdoesallowassignmentstObecompletedinlesstime butreducestheQualityofWork,loweringthestudent'sGrades･Whengradesfall

Chapter5 CausalLoopDiagrams

F【GURE5-22 Theburnoutloop

Asshgan.∑ent-＼立木′一一｢ -二"Wp.r_5 Completion+

165

Calendar

Time ＼亘 +ー Tjme

r RDue Date

emaining＼ヽ

Pressure

Workweek

relativetothestudent'saspirations,thereispressuretoboosttheeffortputinto eachtask･ThenegativeQualityControlloopB3preventseffortandqualityfrom fallingtoofarevenwhenworkpressureishigh(Figure5-23).However,theeffort

tomaintainqualityalsocreatesaninsidiouspositivefeedback･Asworkpressure forcestheworkweekup,energyleveleventuallyfalls(notethedelay),reducing grades.Thestudentrespondsbyincreaslngtheeffortputintoeachtaskinanat-

tempttoboostgradesbackupthroughthequalitycontrolloopIButincreaslngthe timespentoneachtasklowersthecompletionrate｡Thebacklogofworkrises,in- tensifyingworkpressureandleadingtostillmoreovertime,stilllowerenergy,and stilllowergrades･WhentheexhaustedstudentisTわoTiredtoThink,thepositive loopR2Operatesasaviciouscycle-effortstoboostgradesonlysucceedincreat- 1ngmoreworkpressure,longerhours,evenlowerenergy,andstilllowerquality work.

Youmaywonderwhyanyonewouldkeepworkingwhentheireffortsnotonly yieldeddiminishingreturnsbutnegativeretums.Wouldn'tthegrasshoppersrealェ izetheireffortswereactuallycounterproductive?Itispreciselywhenpeople areexhaustedthattheirjudgmentismostimpaired.Howmanytimeshaveyou continuedtoworkonaprojectWhen,atleastinretrospect,youshouldhavecalled itaday?

166 PartIIToolsforSystemsThinking

FIGURE5･23 The"tootiredtothink"loop

AssLg_T ent-1も R ate

Calendar

Time ＼東 +_Time emaining＼-束

√ ＼ - work

Assignment

l.BacklogWorkPressure

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Comp一etion+

＼1

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二言

Ifallelsefails,theexhaustedstudentcanappealtothefacultyfTorrelief,gen-

eratingRequestsforExtensions(Figure5-24)･Usually,suchrequestsareaccom- paniedbystoriesofbadluckandhardshipbeyondthestudent'scontrol:"Mydog

atemyhomework,日日Myharddiskcrashed,"HMyroommatehadanervousbreak-

down."Ifthefacultyaremovedbythesetalesoftragedyandwoe(abigif),the duedateisslipped,makingmoretimeavailableandreducingworkpressure.Be- causefacultyrarelyglVeextensionsunlesstherearegenuineextenuatlngCircum-

stances,thenegativeMyDogAteMyHomeworkloopB4isqulteWeak･Notethat slipplngthedeadline,becauseitlowersworkpressure,mayactuallycausethe

workweektofallandtheeffortdevotedtoeachassignmenttOrise,bothreducing thecomt)1etionrateandcausingWOrk1)reSSuretObuildupagain.Thesefeedbacks areresponsibleforParkinson'S(1957)famouslaw:"Workexpandstofillthetime availableforitscompletion."

Whiletherearemanyotherloopsyoucouldaddtotheframework,thesesix feedbacksjointlyexplainmostofthedynamicscreatedbytheantandgrasshopper

StrategleS･

5.4.5 Limitationsof的eCausa‖〕iagram

Causaldiagramscanneverbecomprehensive(andyoushouldn'ttry:modelingis theartofsimplification).Theyarealsoneverfinal,butalwaysprovisional.The

Chapter5 CausalLoopDiagrams

FIGURE5-24 Mydogatemyhomework-Parkinson'sLaw

AssBgan.Tent｢ -左京′一一~~､＼二 MWp.rAE Comp一etion+

167

Assignment Backlog

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MyDogAte MyHomeworkRequestsforExtensions

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Grades 十㌧･Rl2ATooTiredtoThink

Workweek

Qualityof

Productivity

mapsevolveasyourunderstandingImprovesandasthepurposeofthemodeling effortevolves.Theaccountofworkloadmanagementaboveisfarfromperfect. Herearesomeissuestoconsider:

First,thediagramdoesnotdistinguishbetweenstocksandflows.Inparticular,

itwouldbehelpfultoshowthestockandflowstructureoftheassignmentbacklog. Whatothervariablesinthismodelarestocks?

Second,someloopscouldbespecifiedinmoredetail･Forexample,thequall ltycontrolloopassumesthateffortincreaseswhengradesfallrelativetothestu- dent'saspirations.Itwouldbeclearertospecifythoseasplrationsexplicitly,for example,bycreatingavariableDesiredGradePointAverage(GPA).Effortwould thenbeaffectedbythestudent'sSatisfactionwithGrades,whichmeasuresthegap betweendesiredandactualgrades.Anexplicitgoalforgradesmakesiteasierto explorethedynamicsforstudentswithdifferentasplrationsandattitudesaboutthe importanceofgrades.Makingthegoalexplicitalsomotivatesquestionssuchas Whatdeterminesaspirationsforacademicachievement?-thatis,whatfeedback processesmightcausethedesiredGPAtovaryovertime?

Avarietyofpressuresforachievement,extemaltotheworkloadmanagement model,Putupwardpressureongradeaspirations.Suchpressuresarisefromobser- vationsofthegradesyourpeersreceive(orclaimtohavereceived),fromparents,

168

FIGURE5･ 2 5

Makingthegoalof aLoopexplicit

Addingthedesired GPAandits determinants.

PartII¶〕olsforSystemsThinking

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Orfromthe(perceived)requirementsoffutureemployersorgraduateschoolad-

missionsofficers.Figure5-25showsanotherimportantdeterminantofstudent

goals:Aspirationsadjusttopastactualachievement,formlngthenegativeGoal

Erosionloop.Manypeoplejudgewhatispossible,atleastinpart,fromwhathas

beenachieved･Erodingyourgoalsinthefaceofapersistentdiscrepancybetween

aspirationandachievementisacommonwaytoreducewhatFestinger(1957)

called"CognltivedissonanceHandhasbeenamplydocumentedinmanysituations.

ThegoalerosionloopcanbeanimportantlearnlngprocessOrmayCreateaharm-

fulself-fulfillingprophecy.Forexample,moststudentsadmittedtoeliteuniversi-

tieswereatthetopoftheirhighschoolclass.OnceenrolledinthelvyLeagueor

MIT,however,halfofthemwillbeinthebottomhalfoftheirclass.Theadjust一

meれtofgradeasplrationstoanewsituationpreventsperpetualdisappolntment,

stress,andself-doubt.Ontheotherhand,Overlyflexiblegoalscanleadtounder-

achievement･Somegrasshoppers,reflectingonhow muchmidnightoilthey

burnedattheendofthetermandthedisappolntlnggradesthosehoursledto,may concludetheyaren'tAorevenBstudentsandlowertheirasplrationstorelievethe

dissonancebetweenexpectationsandachievement.Sadly,thislessonmaybeen-

tirelyerroneous:Fewerhoursofeffort,iftheywerewellrested,mayeasilyhave

ledtohighergrades｡

PolicyAnaJys垂sWithCLquSa§D弓a§ra.PTIS

Theboundaryofthestudentworkloadmodelcouldbeextendedtoincludemany

otherfeedbackprocesses.Modifythestudentworkloaddiagramtoincludethe

followlngissues:

1･DropplngClassesinresponsetohighworkpressure,lowgrades,orlowenergy.

2.Drinkingcoffeeortakingstimulantstostayawakewhenenergylevelislow.

CIlapter5 CausalLoopDiagrams 169

3･CheatingonasslgnmentStOboostthecompletionrateandraisegrades.

4･Otherloopsyoubelievetobeimportant.

Asyouexpandtheboundaryofthemodel,askyourself:Doestheabilityofthe

modeltoexplainthedynamicschange?Doestheresponseofthemodeltopolicies

change?Aretheconclusionsoftheearlieranalysisrobusttochangesinthebound-

aryofthemodel?

5t5 ADAMSMITHウS岳NV事S旧しEHANDANDTHE

FEEDBACKSTRUCTUREOFMARKETS

AdamSmith'sinvisiblehandisoneofthemostfamousmetaphorsintheEnglish

language.Smithrealizedthatafreemarketcreatespowerfulnegativefeedback

loopsthatcausepricesandprofitstobeself-regulatlng･WhileSmithlackedmod-

erntoolssuchascausaldiagramsandsimulationmodels,thefeedbackloopsinhis

descriptionofthefunctioningofmarketsareclear.InTheTVealthofNationsSmith

arguedthatforanycommoditytherewasa"natural"priceWhichisjust"sufficient

topaytherentoftheland,thewagesofthelabour,andtheprofitsofthelcapital]

stockemployedinraising,preparing,andbringing[thecommodity]tomarket.‥=

AtthenaturalprlCe,aHcommodityisthensoldpreciselyfわrwhatitisworth,Orfor

whatitreallycoststhepersonwhobringsittomarket‥."Ⅰncontrast,theactual

marketprlCeHmayeitherbeabove,orbelow,orexactlythesamewithitsnatural

prlCeH-thatis,marketsmayatanytlmebeoutofequilibrium.

SmiththennotedhowprlCeSrespondtothebalancebetweendemandand

supply:

ThemarketprlCeOfeveryparticularcommoditylSregulatedbytheproportion betweenthequantltyWhichisactuallybroughttomarket,andthedemandofthose whoarewillingtopaythenaturalprlCeOfthecommodityI-WhenthequantltyOf anycommoditywhichisbroughttomarketfallsshortoftheeffectualdemand,all thosewhoarewillingtopaythewholevalue.Hcannotbesuppliedwiththequan- tltyWhichtheywant.Ratherthanwantitaltogether,someofthemwillbewilling toglVemore.Acompetitionwillimmediatelybeginamongthem,andthemarket prlCeWillrisemoreorlessabovethenaturalprlCe.

Similarly,whensupplyexceedsdemand,=[t]hemarketpricewillsinkmoreorless

belowthenaturalprlCe.H

ButsupplylnturnrespondstothemarketprlCe:

If...thequantitybroughttomarketshouldatanytimefallshortoftheeffectual demand,someofthecomponentpartsofitsprlCemustriseabovetheirnaturalrate. Ifitisrent,theinterestofallotherlandlordswillnaturallypromptthemtoprepare morelandfortheraislngOfthiscommodity;ifitiswagesorpro恥 theinterestof allotherlabourersanddealerswillsoonpromptthemtoemploymorelabourand stockinpreparlngandbringlnglttOmarket.Thequantitybroughtthitherwillsoon besufficienttosupplytheeffectualdemand.AllthedifferentpartsofitsprlCeWill soonsinktotheirnaturalrate,andthewholepricetOitsnaturalprlCe.

170

FIGURE5-26 Theinvisiblehand: thefeedback structureof markets

Demandresponds totherelative valueofthecom-

moditycompared tosubstitutes;

higherre一ative valueincreases

demand,bidding prlCeSuPand lowenngrelative value.Supply expandswhen profitsrise;profit dependsonprlCe relativetopro- ductioncosts

inc一udingthere- quiredreturnon capital.Greater supplybidsprlCeS down,lowerlng profits.Thepnce ofsubstitutesand

thecostofproduc- tiondetermine whatAdamSmith caHedthe"natural

pr】ce"ofthecom-

modity-theequ卜 Iibriumpnceat whichsupplyand demandareequal.

PartIIToolsforSystemsThinking

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AsimplerepresentationofthefeedbackstructureSmithdescribesisshowninFig-

ure5-26.WhentheprlCeOfacommodityrlSeSabovethenaturalprlCe,fewerbuy-

ers"willbewillingtoglVemore"andmorewillbeforcedtoHwantitaltogether.H

Thatis,asprlCerisesrelativetotheprlCeOfsubstitutes,includingallsubstitute

usesforthefundsavailabletothebuyer,consumerswillseeksubstitutesorfind

themselvessimplypricedoutofthemarket.AsdemandfallsprlCeSWillbebid

down,formlnganegativeloop.Atthesametime,higherpricesincreasetheprofit

supplierscanrealize,whichattractsnewentrantstothemarketandencourages

existlngproducerstoincreaseoutput.AsthesupplyIncreases,prlCeSarebiddown-

wards.ThesetwonegativefeedbackloopscauseprlCetOadjustuntil,intheab-

senceoffurtherexternalshocks,themarketreachesequilibrium,Withproduction

equaltoconsumptlOnandprlCeequaltoitsnaturallevel.Smithconcludes:

ThenaturalprlCe,therefore,is,asitwere,thecentralprlCe,tOWhichtheprlCeSOf allcommoditiesarecontinuallygravitating.Differentaccidentsmaysometimes keepthemsuspendedagooddealaboveit,andsometimesforcethemdowneven somewhatbelowit.Butwhatevermaybetheobstacleswhichhinderthemfrom settlinginthiscentreofreposeandcontinuance,theyareconstantlytending towardsit.

Smith'sgreatinsightwastorealizethatwhenprlCeSriseabovethenaturallevel,

producerswhoseektomaximizetheirowngalれWillcontinuetoenterthemarket

untiltheprlCeisbiddowntothepolntWherethereturnontheircapltalisnohigher

(todaywewouldaddHonariskadjustedbasisM)thanthatavailableelsewhere,re-

sultinglncompetitiveprlCeSandanefficientallocationofresourcesthroughoutso-

ciety.Hefamouslyconcludes:

Everyindividualendeavorstoemployhiscapltalsothatitsproducemaybeof greatestvalue.Hegenerallyneitherintendstopromotethepublicinterest,nor knowshowmuchheispromotlngit.Heintendsonlyhisownsecurlty,Onlyhis owngain.Andheisinthisledbyaninvisiblehandtopromoteanendwhichwas nopartofhisintention.Bypursulnghisowninteresthefrequentlypromotesthatof societymoreeffectuallythanwhenhereallyIntendstopromoteit.

Chapter5 CausalLoopDiagrams 171

Smithwasthusoneofthefirstsystemsthinkerstoshowhowthelocal,intendedly rationalself-interestedbehaviorofindividualpeoplecould,throughthefeedback

processescreatedbytheirinteractions,leadtounantlCIPatedsideeffectsforall1 0fcourse,Smith'Sconceptoftheinvisiblehandisfarmorefamousasthe

credoofmodernfreemarketcapitalism,Itisthecoreofthefaiththatmarkets knowbest.Smithhimself,however,wascarefultonotethelimitsofthemarket

feedbacksinequilibratlngdemandandsupplyatthenaturalprlCe･"Thisatleast wouldbethecaseMSmithnotes,"wheretherewasperfectliberty"-thatis,under

conditionsofperfectcompetition(freeentryandexit,freemobilityofthefactors ofproduction,andfreeexchangeofinformationondemand,supply,costs,and profits).Wheretherearemonopolies,tradesecrets,governmentregulations,barri- erstotrade,restrictionsonimmlgrationandcapitalmobility,orotherfeedbacks outsidethesimplenegativeloopscouplingsupplyanddemand,Smithnotesthat pricesandprofitsmayriseabovethenaturallevelformanyyears,evendecades･

ThefeedbackstructureforcompetitivemarketsshowninFigure5-26isqulte useful.BeglnnlngWiththegeneralframework,Onecandisaggregatetoshowthe specificadjustmentprocessesatworkinanyparticularmarketforbothdemand andsupply.Additionalfeedbacksbesidesthedemandandsupplyloopscanbe added,bothpositiveandnegative,andtheirimplicationsassessed･Thetimede- lays,ifany,inthereactionofdemandandsupplytohigherprlCeSCanbeestimated,

andtheimplicationsforthestabilityofthemarketexplored･Ifeitherthedemand orsupplyloopoperatesstronglyandswiftly(highshort-runelasticities),thenthe marketwillrapidlyreturntoequilibriumifperturbed.However,iftherearelong delaysorweakresponsesintheloops(lowshort-runelasticityandhighlong-run elasticity),thenthemarketwillbepronetopersistentdisequilibriumandinstabil- ity;randomshocksindemandorproductionwillexcitethelatentoscillatorybe- haviorofthemarket(seechapters4and20)･

NotallmarketsclearthroughprlCealone.Fewproductsarepurecommodities forwhichprlCeistheonlyconsideration:Productsandservicesareincreaslngly differentiatedandcompaniescompetetoofferthebestavailability,deliveryrelia- bility,service,functionality,termsofpayment,aftermarketsupport,andsoonLIn manymarketsprlCeSdonotchangefastenoughtoequilibratesupplyanddemand andothercompetitivevariablessuchasavailabilitybecomeimportantinclearlng themarket.Pricesmaybesluggishduetogovemmentregulation,thecostsandad一 ministrativeburdenoffrequentpriceChanges,orconsiderationsoffairness.For

example,mostpeopleconsideritunfairforhardwarestorestoraisethepriceOf snowshovelsafterastorm,eventhoughdemandmayhaveincreased(seeKahne- man,Knetsch,andThaler1986;Thaler1991).

InmanyInstitutionalsettlngSprlCedoesnotmediatemarketsatall･Most organizations,forexample,havenoprice-mediatedmarketsforoffices,parking spaces,seniormanagementattention,andmanyotherscarceresources･Inthese cases,supplyanddemandarestillcoupledvianegativefeedbacks,butresources areallocatedonthebasisofavailability,politics,perceivedfairness,lottery,

orotheradministrativeprocedures･Figure5-27showsexamplesofnon-prlCe- mediatedmarkets.Ineachcasethefeedbackstructureisasetofcouplednegative

loopswhichregulatethedemandforandsupplyofaresource･Asinthecaseof

prlCe-mediatedmarkets,theremaybesubstantialdelaysintheadjustments,1ead- 1ngtOpersistentdisequilibria.

172 PartIITわolsforSystemsThinking

FLGURE5-27 Feedbackstructureofnon-price-mediatedresourceaHocationsystems

Left:AvailabilitylSanimportantcompetitivevariablejnmanyproductmarkets,andfirmsregulate productioninresponsetoinventoryadequacyanddeliverydelay.

Right:Inservicesettings,higherservicequalitystimulatesdemand,butgreaterdemanderodesservice qualityaswaitingtimeincreases,andaccuracy,friendliness,andotherexperientialaspectsofthe serviceencounterdeteriorate.

+customer

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Adequacy ofService

TheOilCrisesofthe1970s

In1973thefirstOPECoilshockstunnedtheindustrialworld.OilprlCeSmorethan tripledinamatterofmonthsasmanyAraboilproducersembargoedshipmentsto westemnationstoretaliatefわrtheirsupportofisraelintheYonKippurwar.Many analystsbelievedmarketforceswouldbringtheprlCeOfoilbacktopre-embargo levelsinamatterofmonths,oratmostayearortwo,asdemandandsupplyre- acted｡Instead,prlCeSremainedhigh,thenroseevenhigheraslranianproduction fellinthewakeofthe1979revolution.Bytheearly1980S,manyanalystspre- dictedthatoilprlCeSWereheadedevenhigherandwouldneverretumtothelow levelsoftheearly1970S.Butafterreachingnearly$50perbarrel(in1990dollars), theprlCeOfoilcollapsedinthemid1980S.Manyoilexplorationandalternative energyprojectsWereCanceled;bankruptcywascommon.IntheUS,gasoline prlCeSinrealtermsfellbelowtheirpre-embargolevel-gasolineinthelate1990s wasoftenone-fourththeprlCeOfdesignerwater.

Startingwiththebasicmarketfeedbackstructure(Figure5-26),developa causaldiagramtoexplain(1)thefailureofmarketforcestobringpricesbackto equilibriumsoonafterthefirstoilshock(thatis,Howcouldpricesremainsohigh solong?)and(2)whypricescollapsedinthemid1980sandremainedbelowthe equilibriumlevelforsolong(thatis,Whydidn'tpricesstayhigh?),Tohelp,Figure 5-llShowssomeofthecausallinksonthedemandsideofthemarket.Figure3-4 showsUSpetroleumproduction,consumptlOn,andrealprlCeSOVertherelevant

Chapter5 CausalLoopDiagrams 173

timehorizon･Keepyourdiagramsimpleandfollowtheguidelinesforcausalloop

diagrams.

Useyourdiagramtosketchthepatternofbehavioryouwouldexpectforthe

rateofoilproductionandtherateofdrillingofnewwellsfrom 1970to1990.Also

plotcapacityutilizationforbothactivities(thatis,whatfractionofexistingwells

arepumplng,andwhatfractionofexistlngdrillrlgSareoperating,atanygiven

time).Whatdoesyourdiagramsuggestaboutthelikelydynamicsoftheworldoil

priceOVerthenextfewdecades?

SpeculativeBubbles

Notallmarketsconsistofnegativefeedbacksalone.Inmanymarketsthelocally

rationalbehaviorofindividualentrepreneurscreatespositivefeedbacksastheyIn-

teractwithoneanotherandwiththephysicalstructureofthesystem.Onecommon

exampleisthespeculativebubble.TherehavebeenmanydozensofmajorSpecu-

lativebubblesinthepastfewcenturies,fromtheinfamoustulipmaniaof1636and

SouthSeabubbleof1720tothemaniasandcrashesofthepastfewdecades,in-

cludinggold,silver,realestate,impressionistpalntlngS,andinternetstocks･2

JohnStuartMilldistilledtheessenceofthedynamicsofspeculationinthefol-

lowingpassagefromhisfamoustextPrinciplesofPoliticalEconomy,originally publishedin1848:

WhenthereisageneralimpressionthatthepriceOfsomecommoditylSlikelyto rise,fromanextrademand,ashortcrop,obstructionstoimportation,oranyother cause,thereisadispositionamongdealerstoincreasetheirstocks,inordertoprofit bytheexpectedrise.Thisdispositiontendsinitselftoproducetheeffectwhichit looksforwardto,ariseofprice:andiftheriseisconsiderableandprogressive, otherspeculatorsareattracted,who,SolongastheprlCehasnotbeguntofall,are wi11ingtobelievethatitwillcontinuerislng･These,byfurtherpurchases,producea furtheradvance:andthusariseofprlCeforwhichtherewereorlglnallysomeratio-

nalgrounds,isoftenheightenedbymerelyspeculativepurchases,untilitgreatly exceedswhattheoriginalgroundswilljustify.Afteratimethisbeginstobeper- ceived;theprlCeCeasestOrise,andtheholders,thinkinglttimetorealizetheir galnS,∬eanxioustosell.ThentheprlCebeginstodecline:theholdersrushinto markettoavoidastillgreaterloss,and,fewbeingwillingtobuylnafallingmar- ket,thepricefallsmuchmoresuddenlythanitrose.

DevelopareferencemodeflorMiil'sdescrlPtlOnOfaspeculativebubble.Begin-

ningwiththebasictwo-loopstructureforamarket(Figure5-26),developacausal

diagramgroundedinMill'stextwhichexplainsthedynamicshedescribes.Explain

brieflyhowthefeedbackstructurecorrespondstoMill'sdescrlPtlOnandhowitex-

plainsthebehavior.Giveexamplesofthephenomenon.

2perhapsthebesttreatmentofspeculativebubblesisCharlesKindleberger'S(1978)Manias, Panics,andCrashes.SeealsoGalbraith'S(1988)TheGreatCrashonthe1929stockmarketcrash.

174 PartII ToolsforSystemsThinking

TheThoroughbredHorseMarket Figure5-28showstheprlCeOftopyearlingthoroughbredsintheUSfrom1965 through1990.From1974to1984nominalprlCeSfortheseelitehorsesincreased byalmostafactorof10,toabout$450,000.Evenafterremovingtheeffectsofin- flation,therealprlCeOfatopthoroughbredincreasedbymorethanafactorof4. Pricesthencollapsed,fallingbynearly50%injust4years(inrealterms).Adapt yourdiagramofspeculativebubblestothethoroughbredhorsemarket.Addsuffi- cientdetailtospecifytheparticularbiologicalandinstitutionalfeaturesofthemar- ket.Forexample,whatarethemotivationsforowningatopracehorse?(Youcan consideraracehorsetobeaninvestmentlikeacommonstock,Withanuncertain

futurepayoffdependingonthehorse'sperformanceonthetrack,butthisisonly oneofthereasonspeopleownracehorses,andexpectedcashnowrarelyjustifies suchariskyinvestment).Howisthesupplyofhorsesincreased?Whattimedelays areinvolved?

Useyourcausaldiagramtoexplainthedynamicsofthethoroughbredprice duringthe1970sandSOS.Whydidthemarketrisesodramatically?Whydidit crashevenfaster?In1965about18,000thoroughbredswerebominNorthAmer- ica.Usingyourmodel,SketchthelikelybehaviorofthebirthrateofNorthAmer- icanthoroughbredsthrough1990.

500

400

毛8- 3300 (ちめ⊃ J=0200 :≡

100

0 1965 1970

Source.'HermannandLlnk(1990).

1975 1980 1985 1990

5息確聞aF敗e竜野a_着目ure,魚釣erSeSe室eeを毒⑳閃, amd菅的eDea抽Spj柑目

Manyrealworldmarketsareimperfectduetolimitationsofinformation,costsof entryandexit,andinflexibilityofresources.Theseimperfectionscreatefeedbacks thatsometimesoverwhelmthenegativeloopsnormallybalancingSupplyandde- mand,leadingtoinefficiencyoreventhecompletefailureofthemarket.One sourceofmarketfailureisadverseselection.

Adverseselectioncanarisewhensellersandbuyersinamarkethavedifferent informationAclassicexample,firstdevelopedbyAkerlof(1970),considersthe

Chapter5 CausalLoopDiagrams 175

usedcarmarket.Tbillustratehowadverseselectionworks,Akerlofassumedthat

theownersofusedcarsknowthetruequalityoftheircarswhilepotentialbuyers

donot.AtanyglVenmarketprlCe,OWnerS,knowlngthetruequalityoftheircars,

willofferforsaleonlythosecarsactuallyworthlessthanthemarketprice(the

"lemons")whilekeepinganycaractuallyworthmore(the"peaches").Therefore,

theonlycarsofferedforsalewillbelemons.Potentialbuyers,realizingthis,refuse

tobuy･Akerlofshowedthatinequilibriumnoonewillbewillingtobuyaused

car-themarketwillnotexist,eventhOughtherearebuyersandsellerswhowould

bewillingtotradeifbothknewwhichwerelemonsandwhichwerepeaches･3

Eachperson,behavingrationallyglVentheinformationavailabletothem,Causes

anoutcomeundesirableforall.Akerlof'sresultwasabreakthroughineconomics.

Notonlydidhismodelformthefoundationfortheimportantfieldofinformation

economics,afieldofimmenseimportanceineconomicstoday,buthealsodemon-

stratedthattheworkingsoffreemarketswerenotalwaysbenign,evenwithout

monopolypowerorcollusiveagreementsamongproducers.Adam Smithcele-

bratedmarketforcesforcreatlnganinvisiblehandleadingindividualstoHpromote

anendwhichwasnopartofltheir]intention,"anendwhich"frequentlypromotes

ltheinterests]ofsociety."Akerlofshowedthatrationalself-interestcouldlead

individualstopromote,thoughunintentionally,anendharmfultotheinterestsof

society-andthemselves.

However,Akerlof'stheory,likemosteconomicmodels,isanequilibrium

modelanddoesnotaddressthedynamicsoftheprocess･Tbexaminethedynam-

icsofadverseselectioninanimportantpublicpolicycontext,considerthemarket forhealthinsurance.

Sincethe1950S,healthcarecostsintheUShavegrownmuchfasterthanGDP

andhavelongbeenthehighestintheworld,bothinabsoluteexpendituresper

capltaandasapercentofnationalincome.Ascostsrose,sotoodidhealthinsur-

ancepremiums.FederalprogramssuchasMedicare(fortheelderly)andMedicaid

(forthepoor)werecreatedtoprovideasafetynetforthesegroups.Butrising

healthcarecostssoonoutstrlPPedfederalbenefits,andforcedtheelderlytoseek

prlVateinsurancetosupplementMedicare.AsthecostsofprlVateinsurancerose,

however,manywerefrozenoutofthemarket.Topreventhealthcarefrombank-

ruptlngthem,manystatesrequiredhealthinsurerstooffersoICalledmedigapIn-

surancetoseniorcitizensinreturnfortheprivilegeofunderwrltlngOtherbusiness

intheirstate.InMassachusetts,insurerswererequiredtooftbratleastonemedi-

gapplanprovidingunlimitedcoverageforprescrlptlOndrugs,Oneofthehighest

costsfortheelderly.Atfirst,theprogramwasverysuccessful.Inthe1980S,awide

rangeofinsurersofferedmedigapcoverageinMassachusetts,capturlngalarge

shareofthetotalseniorcitizenmarket.Thelargestprogram,Medex,Offeredby

3ofcourse,thereisausedcarmarket.Akerlof'sassumptionthatbuyershavenoknowledgeof qualitywasasimplifyingassumptlOntOmaketheexampleclear.Therealusedcarmarkethas evolvedvariousmeanstopreventmarketfailure.BuyerscangalnSOmeinformationonquality throughtestdrivesandbyhavingtheirownmechaniclookatthecar,andregulationssuchaslemon lawsandimpliedwarrantydoctrinereducethebuyer'srisk.Informationonthepastqualityofcars

offeredbyusedcardealersdeterssomefromsellinglemonstounwittingbuy?rsIThecost(intime andmoney)oftheseactivitiesisameasureoftheimpactoftheadverseselectlOnProbleminthe usedcarmarket.

176 PartIIn)OlsfわrSystemsThinking

BlueCross/BlueShieldofMassachusetts,coveredaboutone-thirdofallseniorcit- izensinthestatein1987.Premiumswerelow,about$50/month.Ⅰnthelate1980S,

healthcarecostinflationaccelerated,andunderwritershadtoraisepremiums,in- cludingthepremiumsformedigapandMedex.Inresponse,someoftheelderly wereforcedtodroptheirmedigapcoverage.Othersfoundtheycouldgetlower rateswithothercarriersorbysigninguPforplansofferingfewerbenefitsorwhich cappedbenefitsforitemssuchasprescrlPt10nS.However,onlythehealthiestse- niorswereeligiblefortheseother,cheaperplans.Thesickestoftheelderly,those sufferingfromchronicillnesses,thosewithahistoryputtingthemathighrisk-

thosewithsoICalledpre-existingconditions-Werenoteligibleforlessexpensive coverageorhealthmaintenanceorganizations(HMOs)andhadnochoicebutto staywithmedigap.Inmanycases,thecostofprescrlPtlOnSaloneforthoseelderly coveredbyMedexexceededtheirpremiumsbyhundredsofdollarseachyear.As medigaplossesmounted,premiumsgrew.Buthigherpremiumsforcedstillmore ofthecomparativelyhealthyelderlytooptoutofmedigapastheyfわundcoverage elsewhereorsimplydidwithout,bearlngtheriskofillnessthemselves･Thosere- mainingWiththeplanwere,onaverage,sickerandcostlier,forclngPremiumsup further.Figure5129showstheevolutionoftheMedexsubscriberbaseandpremi- ums.Totalsubscribersfellfromnearly300,000in1988toabout158,000in1997, whilesubscribersofthepremiumMedexGoldoptlOn,Whichprovidedunlimited coverageforprescrlPtlOnS,fellevenfaster,fromabout250,000in1988toabout 65,000in1997.Overthesame10yearspremiumsrosefromabout$50/monthto $228/month,Withfurtherincreasesprojected.Asthecustomerbaseshrankand lossesgrew,underwritersbegantowithdraw丘.omthemarket.Intheearly1990s halfadozeninsurerswrotemedigapcoverageinMassachusetts;by1997Only Medexremained.Aconsumeractivistlamented,HAshealthierpeoplecontinueto dropoutandsickerpeoplestayln,premiumscontinuetogoup,andyoucreatea deathspiral."(BostonGlobe,20January1998,A12)･

TheMedigapDea骨的Spi相月

1.Developacausalloopdiagramcapturlngthedeathspiralasdepictedin section5.5.1.Yourdiagramshouldexplainnotonlythedynamicsofthe subscriberbaseandpremiums,butalsotheprofitabilityofthemedigap market,thenumberofcarriersofferingcoverage,andthehealthstatusof thoseintheprogram･NoteanyImportantdelaysinyourdiagram･Useyour diagramtoanalyzetheimpactofthefollowlngPOlicies:

a. Requlrlngallcarriersdoingbusinessinthestatetoinsureallqualified applicants,regardlessofageorhealth.

b.Requiringallmedigapplans(all血eversionsofMedex)toprovide unlimitedcoveragefわrprescrlptiondrugs,Thegoalistopoolhealthier seniorswhogenerallyusefewerdrugsandchoosethelessexpensive Medexplanswiththesickerseniorswhousemoredrugsandoptfor MedexGold.

C. Provideasubsidytolowermedigappremiums,fundedbythestate.

Chapter5 CausalLoopDiagrams 177

d･ AllowingBC/BStodropMedex,effectivelyeliminatingallmedigap coverageinthestateofMassachusetts.

Inassesslngtheimpactofthepolicies,considertheireffectsontheinsurers,on theelderly(insuredanduninsured),andonsocietyatlarge.

2.WhatassumptlOnSaboutinfomationavailabilityandconsumerbehavior

underliethetheorycapturedinyourcausalloopdiagramofthehealth insurancemarket?HowmightthevalidityoftheseassumptlOnSbealtered,

forexample,byadvancesininformationtechnologywhichmightmakea person'sentirehealthhistoryavailabletoinsurers,oradvancesingenetic screenlngWhichmightrevealwhichpeoplewereatincreasedriskforthe

developmentofparticularillnesses?

3.Whatotherexamplesofadverseselectioncanyouidentify?Maptheir feedbackstructure.

deathsplral:subscribersandpremiumsformedigaplnsurance

nsurancefortheelderlyofferedbyBlueCross/BIueShieldofMassachusetts. unlimitedprescriptiondrugswithasmaHcopayment.OtherMedexplanslimittotal forDecemberiofeachyear.'indjcatesproposedratefor1998of$278/month.

S Jla q !)3 S qnS PueSnOLJ1

198819891990199119921993 1994199519961997

Source:BostonGlobe,20January1998,Al.

250

200

150Se≡ 0

100蔓

5.6 ExpLAjNiN13野oL!CYRES!STANCE:TRAFF忙 CoNGEST旧N

Byshowingthenetworkoffeedbackloopsinwhichpoliciesareembedded,causal diagram Sareoftenaneffectivewaytoshowhowevent10riented,open-loopmen-

talmodelsleadtopolicyresistance.Considertheproblemoftrafficcongestion. America'sroadsarechokedwithtraffic.In1995therewerenearly200millionve-

hiclesreglSteredintheUS.The1990censusreportedthatabout100millionpeo-

ple,87%ofallworkers,traveledtoworkbymotorvehicle,85%ofthemalone. Only5%usedpublictransportation.In196064%commutedbymotorvehicle. Since1970thenumberofreglSteredvehiclesgrewby70%andannualvehicle

milesgrewby90%,bothmuchfasterthanthegrowthinpopulationorhouseholds,

178

FIGURE5-30 Moreroads, moretraffic

PartIITわolsforSystemsThinking

whilepublictransportationstagnated(Figure5-30).Moreandmoreoftheaverage

person'sdaylSSpentinsideacar:ThegovernmentestimatesAmericansspend

8billionhoursperyearstuckintraffic.Thecostofdrivingincludesabout$6000

percarperyearindirectcostsanduptoanother$9400inindirect,externalized

costs.Estimatesoflostproductivityduetotrafficcongestionrangefrom$43to

$168billionperyear.TheeconomyandcultureoftheUS(andofotherauto-rich

nations)haveadaptedthemselvestothedominanceoftheauto,fromthe$40bil-

lionspentannuallylntheUStomarketautomobilestotheriseofdrive-through

fastfoods,especiallyfoodsyoucaneatwithonehand(whiletheothersteers).

Roadrageisincreasinglyrecognizedasacommonmentaldisorder,andfrustrated

drivershavetakentoshootingthosewhocutthemoffontheso-calledfreeway.

Whatwentwrong?4

5.6.1 MentalMode一sottheTrafficProblem

Thetraditionalsolutiontotrafficjamsandcongestionhasbeenroadbuilding.Fig-

ure5-31showstheopen-loopperspectiveontheproblem:Theproblemishighway

congestion;thesolutionistobuildmoreroads.

TotalVehic一eMilesTraveledintheUS

JIE!a ^ J S

aニ LN

a I U !LJa ^

U O ≡

!) ト

1920

人U

一-

Lt23と SJa6uasst2d uOu !g

1940 1960 1980 2000

TotalPassengersonUSPublicTransitSystems

1920 1940 1960

Sources:Historica一StatisticsoftheUS;Kurjan(1994)･

1980 2000

4someofthesedataappearinKay(1997),whosebookAsphaltNationdiscussesabroadrange ofsocial,cultural,economic,andenvironmentaleffectsofautomobileaddiction.SeealsoDowns (1992),Hansen(1995),andGibbs(1997).

FIGURE5-31

Open-一oopviewof

trafficcongestion

FIGURE5-32 Determinantsof

traveltime

Chapter5 CausalLoopDiagrams

Congestion BuildNew andDelays 匝･ Roads

179

Butwhathappenswhennewroadsarebuilt?Andwhereshouldyoubeginthe

developmentofacausaldiagramtoshowthefeedbackeffectsofroadconstruc-

tion?It'susuallybesttobeginbycapturlngthephysicalstructureofthesystem.

Systemsconsistofbothaphysicalstructureandthedecisionrulesusedbythepeo-

pleinthesystem(thebehavioralstructure).Thephysicalstructureisofteneasier

tovisualizeandrepresentthanthedecision-makingstructure･Additionally,con-

ceptualizationisoftenpartofagroupprocessinwhichpeoplemustsharetheir

ownmentalmodelsandreachagreementoveraslnglerepresentationJtisusually

easiertogalれagreementaboutthephysicalstructure.Thebehavioralstructureis

oftenmorecontroversial;ifyoustartthereyourgroupprocessmaygrindtoahalt

beforeyou'vereallybegun.

Agoodplacetostartforthetrafficcongestioncaseiscongestionitself.Agood

modelrequlreSaVariablethathasoperationalmeanlngandcanbemeasured.One

goodsummarymeasureofcongestionisaveragetraveltime(forthetypicaltripin

aparticularregion)･Whatdeterminestraveltime?Traveltimedependsonthebah

ancebetweenthecapacityOfthehighwaystohandletrafficandthenumberofve-

hiclesusingtheroads,denotedTrafficVolumeinFigure5-32.

Asthenumberofvehiclesontheroadsincreases,glVenthehighwaycapaclty,

theaveragetrlpWilltakelonger.AshighwaycapacltynSeS,glVenthevehiclevol-

ume,theaveragetraveltimewillfall.HighwaycapacitylSalteredbyconstruction

ofnewroads.Roadconstructionhereincludesnotonlynewroadsbutalsoim-

provementstoexistlngroadssuchasaddinglanesorincreaslngCapacitybychang-

1ngtheflowoftraffic,forexamplebyconvertingafour-wayIntersectionintoa

cloverleaf･AnyproJeCtthataugmentsthecapacltyOftheroadstocarrytraffic wouldbeincludedinthenotionofroadconstruction,atleastinthisfirstversionof

Road Construction

Highway Capacity

t､､＼- 壱

Tr.affic Volume

Travel Time

180

FJGURE5-33

Congestion leadstopolitical pressuretobuild moreroads,

reducingcon一 gestionviathe negativeCapacity ヒXPanSion feedback.

PartIIToolsforSystemsThinking

themodel(lateryoucoulddisaggregatetheconstructionofnewroadsfromwiden- ingofexistingroads,ifthatwasdeemedtobenecessaryforthepurpose).Since highwayprojectstaketime,thedelaybetweentheinitiationofaconstructionproj- ectandtheincreaseinhighwaycapacitylSexplicitlynoted.

WhendevelopingaCausalmapltishelpfultoconsidertheunitsofmeasurefor theconstructsinyourdiagram.Havingconsistentunitsisoftenagreataidtoclear thinkingaboutthedefinitionsofandrelationshipsamongthevariables.Specifying unitsandcheckinglbrdimensionalconsistencylSusefulevenwhenyourmodelis purelyconceptualandyoudonotintendtodevelopaformalsimulation.Travel timewouldbemeasuredinminutespertrip(fortheaveragetripintheregion). HighwayCapacityandTrafficVolumearemeasuredinvehicle-milesperday(a vehiclemileisonemiletraveledbyonevehicle).

Havingspecifiedthephysicalstructureofroadbuildingandhighwayconl struction,nextaskwhatdriveshighwayconstructionprograms.Theprlmarymoti- vationiscongestion:astraveltimerises,astrafficjamsbecomethenorm,asthe rushhourexpandsfromdawnthroughdusk,politicalpressuretobuildwillbuild. Figure5-33addsthelinkfromtraveltimetoroadconstruction.

Congestioncreatespressurefornewroads;afterthenewcapacityisadded, traveltimefalls,relievingthepressure.TheCapacityExpansionloop(B1)actsto reducetraveltimetoacceptablelevels.Notethat血egoaloftheloop,thedesired traveltime,hasbeenmadeexplicit.Desiredtraveltimeisthetraveltimedriv-

ersconsideracceptable(onaverage),perhaps20minutesforthecommutefrom hometowork.The1990censusfoundaverageone-waycommutingtimesforall modesandallworkersofabout22minutes,thoughmorethan17millionpeople spentmorethan40minutesgettlngtOworkandnearly2millionspentmorethan 90minutes.

Highway Capacity

Road C onstruction

年少 Capacity

＼ i E --/ --F

Traffic Volume

XPanSl0n

Tr.avel Time

㌔ Pressureto

Reduce Congestion

j -i- :iT Desired Trave一Time

Chapter5 CausalLoopDiagrams 181

5.6.2 Compensa!ingFeedback:

TheResponsetoDecreasedCongestion

Sofartrafficvolumeisconsideredtobeexogenous.ThisassumptlOnisanaccu- ratereflectionofthementalmodelsofmanypoliticians,cltyPlanners,andtrans-

portationofficials,forwhomtrafficvolumegrowsasthepopulationoftheregion growsandasthelocaleconomydevelops.Theyseetheirjobasbuildingenough

roadstokeeptraveltimeattheacceptablelevel,sopoliticalpressurestayslow,so theycanbereelected,andsotheycanservespecialinterestssuchasconstruction firms,realestatedevelopers,andthebusinesscommunityWhobenefitfromroad

buildingandwhooftenprovidelucrativejobsforthemwhentheyleaveoffice. Ifthecapacityexpansionloopweretheonlyfeedbackoperatlnginthesystem,

thenthepolicyofroadbuildingtorelievecongestionwouldworkwell:whenever trafficvolumerose,leadingtocongestionandpressurefromthecommunity,aroad buildingprogramwouldbestartedandhighwaycapacltyWOuldexpanduntilthe

pressurewasrelieved. However,trafficvolumeisnotexogenous.Toformulatethecausalstructure

determinlngtrafficflOwitisagainhelpfultoconsiderthephysicsofthesystem andtheunitsofmeasureforthevariables.Whatdeterminesthevolumeoftraffic?

Tohavetraffic,theremustbe.Hcars.Nocars,notraffic.Sothenumberofcarsin

theregionmustbeadeterminantoftrafficvolume.Trafficvolumeismeasuredin

vehicle-milesperday.Totaltrafficvolumemustthereforeequalthenumberof vehiclesinthereglOnmultipliedbythenumberofmileseachvehicletravelsper

day.Inturn,thenumberofmileseachvehicletravelsperdaylStheproductof thenumberoftripseachvehiclemakesperdayandthelengthofeachtrip.Thus, averaglngoverthevehiclepopulation,

TrafficVolume -Vehicles*AverageTripsperDay*AverageTripLength VehicleMiles/Day-Vehicles* TripS/Day * MileS/Trip

Thenumberoftripsperdayandtheaveragetnplengtharenotconstantbutde- pendonthelevelofcongestion.Iftrafficislight,peoplearemorelikelytotakead- ditionalandlongertrlpS.Whencongestionisheavy,peoplewillforegoordefer

trlpSandmakeshortertrlpS,Skippingthatquickruntothevideoshopandbuying whattheyneedatthecloseststorerathergolngOntOthemall.Likewise,thenum- berofcarsinthereglOnisnotconstant.ThenumberofvehiclesinthereglOnCan

bethoughtofastheproductofthepopulationofthereglOnandthenumberofcars perperson:Themorepeopleintheregion(andthemorebusinesses),themoreve- hiclestherewillbe.Thenumberofvehiclesperpersonorbusinessinturnisnot

constantbut(lependsontheattractivenessofdrivlng･1neattractivenessofdrivlng dependsonthelevelofcongestion(Figure5-34).

Addingtheserelationshipstothemodelclosesthreenegativefeedbackloops, allofwhichacttoincreasecongestionwhenevernewroadsarebuilt.Supposenew

roadsarebuilttorelievecongestion.Intheshortrun,traveltimefalls-thenum- berofcarsintheregionhasn'tchangedandpeople'shabitshaven'tadjustedtothe

new,shortertraveltimes.Aspeoplenoticethattheycannowgetaroundmuch fasterthanbefore,theywilltakemoreDiscretionaryTrips(loopB2).Theywill

182 PartIIToolsforSystemsThinking

FIGURE5-34 Trafficvolumedependsoncongestion,closingseveralnegativeloopsthatcausetraffic toincreasewhenevernewroadsarebuilt.

Road Construction

(,!lfCapacityHighway Capacity

Tr.affic Volume

Population andEconomic

Activityof Region

-工､

Pressureto Reduce

Trips

Tripsper Day

痩 ExtraMiles

Takethe 'Average 千千､~＼ __

estion-き-Desired ieBAT:qeuacyofAttractivenesspublicTransitofDrivingI+

Bus? TripLength+ Public

､､-- 昔二十崇 ,-:- -:蕊

Pub lic

Trans it

Fare

alsotravelExtraMiles(loopB3)｡Overtime,Seeingthatdrivingisnowmuchmore attractivethanothermodesoftransportsuchasthepublictransitsystem,some

peoplewillgiveupthebusorsubwayandbuyacartThenumberofcarsperper- son(andbusiness)risesaspeopleaskwhytheyshouldTaketheBus?(loopB4).

Allthreeoftheseloopscompensatefわranynewroadconstructionbyincreas- 1ngtrafficflow.Butroadconstructionstimulatesotherlong-termfeedbacks.The

populationoftheregionisnotexogenousbutisaffectedbytheaccessibilityofthe outlyingdistricts.Astheroadnetworkexpands,asnewfreewaysandringroads linkthecountrysidewiththecenterclty,thesizeofthereglOnWithinareasonable

traveltimegrows.Ofcourse,averagetraveltimehasanegativeeffectonthesize oftheaccessiblereglOn:Thegreaterthecongestion,thesmallertheradiusaccessi-

blewithin,say,a30-minutedriveofthecity(Figure5-35). Thelinkstothepopulationofthereg10nClosetwomorefeedbacks.Peoplebe-

gintoMovetotheSuburbs(B5).Asthepopulationofthesuburbsgrows,theauto

populationrisesaswell.Theroadsbegintofill.Trafficvolumegrowsfurtherand

Chapter5 CausalLoopDiagrams 183

FIGURE5-35 ReducedtraveltlLmeandanexpandedhighwaynetworkincreasethesizeoftheregion accessiblefromthecenter,whichexpandsthepopulationandleadstostiHmoretraffic.

Highway Capacity

(もタ Openthe Hinterlands

Moveto theBu一bs

SizeofRegion withinDesired Trave日Time

Population andEconom ic

Activityof Region

Road Construction

渚Capacity ~-㌔_≡ 77iTraffic

Vo一ume

-x-:_三､＼＼

XPanTr.avTim 与垂)scretioI Tm-ps

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==:_-LL:T=

Tripsper Day

車重 ExtraMiles

Taketh e ー Average

estion

も Desired ie:qeuacy..AttractivenesspubHcTransit

ofDrivingI+

B us? TripLength+

Pub一ic

＼寺喜 …器霊 .J paerrssSenr〆 R:drearnsSlでp

Public Transllt Fare

traveltimerisesuntiltheresultingcongestionmakesthesuburbssufficientlyunat- tractivetostopfurtherinmlgrationanddevelopment.

ThecombinedeffectofthefournegativefeedbacksB2throughB5istocom-

pensatestronglyforanydecreaseintraveltimecausedbynewroads.Ifnewhigh- wayswerebuiltandthenallconstructionstopped,therewouldbeanimmediate droplntraveltime.Butaspeoplerespondtotheirnewfoundeaseoftravel,more, longertrlpSWOuldbetaken.Morepeoplewouldabandonthebusandbuycarsto commutetowork.Thepopulationofthesuburbswouldgrow.Theseadjustments continueuntiltraveltimerisesenoughtostoptheexpansionofthesuburbsbe-

causethecommuterequiredistoolong.Thedelaysinthesenegativeloopscould causecongestiontoovershootthedesirablelevel.

Butroadconstructiondoesn'tstop･AsnewhighwaysOpentheHinterlands (loopRl),itbecomespossibletoliveinthecountrysideandcommutetoworkin thetownorcity.WhatwasonceremotefarmcotlntryOrWOOdsnowbecomesa

20minutedrivefromthecity,withitsjobs,culture,andnightlife.Wholenew

184 PartIIToolsforSystemsThlnking

communitiessprlngup,COmmunitieswherethepeoplehavetodrivenotonlyto workbutalsotothemarket,toschool,tothehomesoftheirfriendsandtheirchi1-

dren'sfriends.Theburgeonlngpopulationbringsnewdevelopment,Shops,Strlp

malls,andotherbusinessessprlngup,tumlngCOuntrySidetocondodevelopment,

pasturetoparkinglot.Allthewhile,thenumberofcarsontheroadgrows.After

someyears,trafficcongestionintheseformerlyquiettownsbecomesaterrible

problem･Politicalpressuregrowsandstillmoreroadsarebuilt.

Route128,arlngroadaroundBostonbuiltinthe1950storelievecongestion

bydivertinglong-haultrafficaroundthecentercity,rapidlyattractedlocaldrivers

andsoonprovedinadequate.Torelievethecongestionitwaswidened,fromfour

toeight,andinplaces,evenmorelanes.Instretchesthebreakdownlanewas

openedtotrafficduringrushhour(notafewhaplessmotoristshavebeenkilled whentheyhadthetemeritytousethebreakdownlaneforabreakdown).Traffic

soonfilledthesenewlanes,andtodayduringrushhourthecarscrawlalong

bumpertobumperthroughlongstretchesofroute128･Asecondringroad,Inter-

state495,wasthenbuiltanother15to20milesfartherout.Theexpandednetwork

madeevenmorecountrysideaccessible,andanotherroundofpopulationgrowth

andeconomicdevelopmentbegan.Thisself-reinforclngProcessleadstomoreand

morenewroads,pushingeverfartherintothecountryside,inavainattempttoease

congestion･ThestorylSSimilarforothercitiesintheUS,includingtheparadigm caseofcongestion-Lo§Angeles-aswellasLondon,Paris,Istanbul,Cairo,

Tokyo,Bangkok,andcountlessothercitiesaroundtheworld.

Themodelclearlyshowsthefutilityofattemptstoreducetrafficcongestion

throughroadbuilding.Itmaytakesomeyears,but,inanautomotiveversionof

Parkinson'sLaw,trafficalwaysexpandstofillthehighwaysavailableforitstravel.

TrafficvolumegrowsuntilcongestionlSJustbadenoughtodeterpeoplefromtakl

lngthatadditionaltrip,fromdrivingtoworkinsteadofridingpublictransit,Or

frommovingjustalittlefartheroutintothesuburbs･5TrafficengineersCallthisre-

action"roadgeneratedtraffic･"Hansen'S(1995)econometricstudyofUSmetro-

politanareasshowedthattheelastlCltyOftrafficvolumewithrespecttohighway

capacityWas0.9afterjust5years,thatis,alO%increaseincapacltyledtoa9% increaseintrafficwithin5years.Manyofthefeedbacksidentifiedinthemodel

operateoverevenlongerperiods,fullynegatlngtheeffectofroadconstructionon

congestion.SomeanalystsevenarguethatbyHaddingcapacitytoacrowded[high-

way]networkyoucouldactuallyslowthingsdown"(Kay1997,p.15),aphenom-

enonknownasBraess'Lawaftertheoperationsresearchanalystwhofirstcoined

it.Forexample,theM25,London'srlngroad,wasdesignedtocarrylongdistance

trafficaroundLondon.Instead,itisactuallyusedprimarilyforshorttripsbylocal

residentsandcommuters.ItsoonbecamethebusiesthlghwaylnEuropeandhas

longbeenknownas̀thelongestparkinglotintheworld',thoughcommuterson

theLonglslandExpressway,Paris'Peripherique,andtheSamDiegoFreeway

mightdisagree.Inresponse,theM25hasbeensteadily widened,alltonoavail.

Studiestypicallyfind,astheLondonTl'mesreported(10 November1997),that

5TheanalogywithParkinson'sLaw(Hworkexpandstofillthetimeavailableforitscomple- tion")ismorethanca.sual:Parkinson'SLawarisesthroughanegativefeedbackloopstructurequite similartothatgoverningtrafficcongestion･Seesection5.4.

Chapter5 CausalLoopDiagrams 185

TrafficcongestiononawidenedsectionoftheM25isnowgreaterthanbeforethe improvementtookplace,amotorlngSurveySuggests.Thewideningofastretchof themotorwayatJunction15,westofLondon,wasintendedtocurbcongestion,but thesurveyshowedthatjamsonthestretchwerenowcommonplace,althoughlast yeartrafficwasgenerallyfree-flowlng.

5.6.3 TheMassT柑mSi昔Dea抽SpiFa日 StandardeconomicanalysュsSuggeststhatadeclineintheattractivenessofagood

orserviceshouldleadpeopletoswitchtosubstitutes･Why,then,ascongestion

buildsup,don'tpeopleturntomasstransit?PartoftheanswerisshowninFig- ures-36.

Aslowertraveltimecausedbynewroadsincreasestheattractivenessofdriv-

1ng,ridershipandrevenueofthepublictransitsystemfall,Costsdon'tfallvery

much,sincemostofthecostsarethefixedcostsofprovidingservice:thebuses

mustrunwhethertheyarefulloremptyJfthetransitauthoritytriestocloseits

deficitbyCostCutting(loopB6),serviceandqualityerode.Routesareclosedand

the丘.equencyofserviceiscut.TherelativeattractivenessofdrivingrlSeSandmass

transitridershipfallsstillmore.Thedeficitwidens,leadingtostillmorecutsinthe

publictransitnetworkastheself-reinforcingRouteExpansionloopR2Operatesas

aviciouscycleofdecreasingridership,greatercuts,andstillfewerriders･

Raisingfarestobalancethetransitauthoritybudgetislittlebetter:Higherfares

increasetherelativeattractivenessofdriving,andmorepeopleabandonmasstran-

sitforcars.Ridershipfalls,andfaresmustberaisedagain,ChokingoffRidership

(loopR3).Becausemasstransitsystemshaveahighproportionoffixedcosts,they

arehighlyvulnerabletotheseself-reinforclngfeedbacks.Asroadconstructionand

autouseacceleratedinAmerica,particularlyafterthelate1940S,peopleaban-

donedtrolleys,trains,andbuses.Thesepositiveloopsbecameadeathsplralof

higherfares,reducedservice,anddeclinlngqualityuntilinmanycitiesonlythe

poorestpeople,thosewhocannotaffordtomovetothesuburbsorownacar,are

lefttoridethepublictransitsystem.Attemptstobuildupthemasstransitnetwork

tooffsetthepositiveloopsthateroderidershipthroughMassTransitCapacltyEx-

pansion(loopB7)oftenfightalosingbattleduetotheirlongdelaysandhighcosts.

Onefinalpositivefeedbackisworthadding:Theadequacyofapublictransit

systemdependsnotonlyonthescopeofthenetworkandthefrequencyofservice

butalsoonthesizeandpopulationdensityofthereglOn.Asthecountrysideisde-

veloped,thelocusofactivltyShiftsawayfromtheareaservedbyexistingmass

transit.Aspopulationdensityfalls,fewerandfewerpeoplelivenearabusorsub-

wayroute.PublictransitbecomeslessandlessusefulbecauseYouCan'tGetThere

ontheBus,leadingtostillmoredrivingandstilllowermasstransitridership,1n

anotherviciouscycle,loopR4(Figure5-37)･Thesuburbsgrowandtheadequacy

ofpublictransitfallsmuchfasterthanmasstransitcapacityCanbeadded･

Themodelaboveisstillincomplete(asallmodelsalwaysare).Onecouldadd

manymorefeedbacks.Forexample,thespreadofpopulationintothelessdensely

populatedsuburbsincreasestheaveragelengthoftrips,formingadditionalchan-

nelsbywhichcongestionrisestooffsetanygainsCausedbynewhighways.The

modeldoesnotexploreothersideeffectsoftheautomobile'srisetodominance,

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188 PartII ToolsforSystemsThinking

includingthedeaths,injuriesandcostsofaccidents,thehealtheffectsofsmogand

ozoneproduction,greenhousegasgeneration,thesolidwasteproblemposedby thediscardofmillionsofvehicleseachyear(seechapter6),andthedependenceof thehighlyautomotivenationsoninsecuresuppliesofimportedoil.Whatother feedbacksandsideeffectsdoyousee?

5.6.4 PolicyA.nalys妻S:The岩mpacto守JTechr!Obgy

Despiteitslimitationsandomissions,themodelprovidesarichexplanationforthe persistentfailureofroad-buildingprogramstoalleviatetrafficcongestion.Youcan

nowusethemodeltoassessthelikelyeffectofotherpolicies. Inthe1970sand1980S,apopularsolutionwasHOVlanes(high-occupancy

vehicle,orcarpoollanes).Theselanesarerestrictedtocarswithatleasttwooccu- pants(sometimesonlyduringrushhour).Theresult?Totheextentdriversjoined carpools,thenumberoftripsperdayfell,reducingtrafficvolumeslightly.There- sultingreductionincongestion,however,simplyencouragedotherstotaketothe roadsinsteadofmasstransit,totakeadditionaltrlpStheymightotherwisehave

foregone,andtoleaveforworkalittlelater.Thetotalvolumeoftrafficduringrush hoursdidn'tchangeandmorepeoplewerenowonthehighwaysthanbefore,fur- thererodingmasstransitridership.AndsomeenterprlSingbutimmoralmotorists tooktoridingwithinflatabledummiesinthepassengerseattofoolthepoliceand illegallytakeadvantageoftheHOVlane.

DespltethepersistentfailureofroadbuildingandinnovationssuchasHOV lanes,manytransportationplannerscontinuetopl机theirhopesontechnologlCal solutionstothecongestionproblem.ThelatestoftheseissO-calledintelligent vehicle-highwaysystems･Manyclevertechnologiesareunderdevelopment,from sensorstodetectthedistancetothecaraheadandautomaticallyadjustyourcar's speed,totranspondersormagnetsembeddedintheroadsurfacetoautomatically steeryourcar.AlreadysensorsembeddedinsomehighwaystransmitrealtimetrafJ fiedatatocarsequlPPedwithspecialreceivers･Technologistslookforwardtothe daywhentheinternet,GPS,andrealtimevehiclecontrolswillallowyourcarto

picktheoptlmalroutetoyourdestinationanddriveyoutherewhileyourelaxor readabook.Someofthesetechnologiesaredesignedtoincreasehighwaysafety. ManyaremotivatedbytheneedtoincreasehighwaycapacitylnCitieswhere

buildingnewroadsandaddingnewlanesisnolongerpossible:undercomputer control,thetechnologistspromise,carscouldzipsafelyalongat70milesperhour

onlyinchesapart,greatlyexpandingthecapacltyOfexistinghighways. Themodelshows血efutilityofthesehopes.ThereisnotechnologlCalsolution

tothecongestionproblelm.ThelmOreeffectivelythesetechnologiesirTICreaSehigh-

waycapaclty,themoretrlpSWillbetaken,themorepeoplewillbuycars,theless attractivepublictransitwillbe,andthemorecountrysidewillbedevelopedinto bedroomcommunitiesforcommuters.ThevolumeoftrafficwillswiftlyrisetOabl

sorballthenewcapacltytechnologycanyield.Wemightzipalongthefreewayat seventy,butwe'llbestuckinmuchlongerlinesattheentrancerampandonsec-

ondaryroutes.Ontheroadwaysofthefuturewemayridemoresafelyandmore comfortably,butwewon'tridemoreswiftly.

Chapter5 CausalLoopDiagrams 189

Economistsgenerallysuggestthesolutionistochargetollsthatincreaseas congestionrises(Downs1992),Whilesomeregionsareexperimentingwithtime- of-daytollsandcongestion-basedprlClnguSlngrealtimesenslngequlpment,there isconsiderablepoliticalresistancetothenotionofpayingforthefreeway,and someconcernovertheregressiveimpactoftolls,Worse,driverstendtoswitchto secondaryroadsandcitystreetswheretollsareinfeasible.

SomenationshavecometounderstandthesedynamicsandaremovlngtO reducetrafficandtheattendantpollution,accidents,anddestructionofopenland itcausesbyincreasingtraveltimes･InSeptember1997Sweden'sparliament adopted"VisionZero",apolicyaimedateliminatlngalltrafficfatalitiesbyper- mittingtownstOreducespeedlimitsto30kilometersperhourandinstallspeed bumpsandotherflowrestrictingdevices.Themodelsuggeststhesepolicieswill, inadditiontosavlnglives,encouragepeopletouseothermodessuchasbus,train, andbicycle,thusreducingthepressureforroadbuildingandthegrowthintraffic.

5.6.5 CompensatingFeedback:

TheSourceofPoljcyResistance

Thefeedbacksaffectingtrafficclearlyshowthatattemptstocontrolcongestion throughroadbuildingarevain,Anyreductionincongestionleadstomoretnpsand morecars,swiftlybuildingcongestionbackup.Whatroadconstructionactually controlsisthesizeofthemetropolitanareaandthenumberofcarsontheroad. Roadconstructioncausesthedramaticexpansionoftheurbanizedandsuburban- izedarea,thegrowthofstripmallsandparkinglots,andthedeclineoffarm ,for- est,andfield.

Thecausalstructureofthetrafficproblemillustrateshowpolicyresistance arisesinawiderangeofcomplexsystems･Road-buildingprogramsaretypicalof policiesdirectedatthesymptomofdifficulty.Policiesdirectedatalleviatlngthe symptomsofaproblemusuallyfailbecausetheytriggercompensatingfeedbacks, feedbacksthatundercuttheintendedeffectsofthepolicy･Thecompensatlngloops arisebecauseotheractors,withtheirowngoals,respondtochangesinthestateof thesysteminsuchawayastooffsettheintendedeffectsofthepolicy.Whileeach individualloopmaybeweak,thecombinedeffectcanoftencompensatecom- pletelyforanypolicydirectedatasymptomofaproblem.Directlngpoliciesat thesymptomsofaproblemisliketrylngtOSqueezeaballoontomakeitsmaller. Wheneveryousqueeze,theairpressureincreases,expandingsomeotherpartof theballoonsoitsvolumeremainsaboutthesame.

Whythendosomanypoliciesfocusonalleviatingthesymptomsofdiflficulty? Wefocusonsymptomsbecausesomuchofourexperienceiswithsimplesystems inwhichcauseandeffectarecloselyrelatedintimeandspace,inwhichsymptom andcauseareobvious.Mostofourexperienceiswithsystemsinwhichthereisa single,dominantnegativefeedback,aswhenyoureachouttograspanobjectby assesslngthegapbetweenthepositionoftheobjectandyourhand.Wethenex- trapolatetheseeverydayexperienceswithsimplesystemsintothemanagementof complexsystems.But,asJayFo汀eSter(1969,pp.9-10)notes

190 PartIIToolsforSystemsThinking

Inthecomplexsystemthecauseofadifficultymayliefarbackintimefrom thesymptoms,orinacompletelydifferentandremotepartofthesystem.Infact, causesareusuallyfound,notinprlOrevents,butinthestructureandpoliciesofthe system.‥ConditionedbyourtrainlnglnSimplesystems,weapplythesameintu- itiontocomplexsystemsandareledintoerror.Asaresultwetreatsymptoms,not causes.Theoutcomeliesbetweenineffectiveanddetrimental...Iftheattempted solutionintensifiestheproblem,wronglyattributedtoanothersource,theorganiza- tionlikelywillredoubleits"corrective"action,producingmoredifficultyandpres-

Sureforstillmoreremedialaction.Adestructivesplralbecomesestablished.

identifyingtheFeedbackStrL氾tureO官

PoF毒cyRes≠stance

L ConsiderthefailedRomanianpopulationpolicydescribedinchapter1.

Developacausalloopdiagramexplainlngthefailureofthegovernment'S effortstoincreasethebirthrate.

2.Table1-1listsanumberofcommonexamplesofpolicyresistanceinsocial,

business,andeconomicsystems.Developsimplecausaldiagramsforeach.

Useyourdiagramstoexplainwhyeachpolicyfailed･

5.7 SL糊R.･1ARY

Causaldiagramsareapowerfultooltomapthefeedbackstructureofcomplexsys-

tems.Causaldiagramscanbehelpfultoyouintheearlyphasesofaproject,When

youneedtoworkwiththeclientteamtoelicitandcapturetheirmentalmodels･

Theyarehelpfulinpresentlngtheresultsofyourmodelingworkinanontechnical

fashion.Tobeeffective,youshouldfollowtherulesforcausaldiagrams,including

selectionofvariablenames,layout,andasslgnmentOflinkandlooppolaritiesJt

isbesttobuildupdiagramsinsteps:resisttheurgetocreateaslngle,Comprehen-

sivediagram.AsinlearnlngtOreadmusic,practiceiseverything･Developyour

skillsinmapplngthefeedbackstructureofsystemsbysketchingcausaldiagrams

tocapturethefeedbacksyourecognlZeaSyoureadthenewspaperorthegreat worksofliterature.

StocksandFlows

I'mve77goodatintegralanddlHerentialcalculus,

Iknowthescientificnamesofbeingsanimalculous;

Inshort,inmattersvegetable,animal,andmineral,

IamthevefTmodelofamodernMajor-General. -W.S.Gilbert,ThePiratesofPenzance,Act1.

Thischapterintroducestheconceptofstocksandmows,acentralideaindynam- ics.Itpresentstheconceptualandmathematicaldefinitionsofstocksandflows,the diagrammlngtoolsformapplngnetWOrksofstocksandflows,andcasestudiesof theuseofstocksandflOwsinmodelingprojectsincludingautomobilerecycling andtheconstructionofpulpandpapermills.Developlngfacilityinidentifying, mapplng,andinterpretingthestockandflownetworksofsystemsisacriticalskill foranymodemsystemsmodeler.

6JI STOC葛(S,FLOWS,ANDAccuMULATlON

CausalloopdiagramsarewonderfllljytlSefulinmanysituations,TheyarewelJI suitedtorepresentinterdependenciesandfeedbackprocesses.Theyareusedef- fectivelyatthestartofamodelingprojecttOCapturementalmodels-boththose ofaclientgroupandyourown.Theyarealsousedtocommunicatetheresultsofa completedmodelingeffort.

However,causalloopdiagramssufferfromanumberoflimitationsandcan easilybeabused.Someofthesearediscussedinchapter5.Oneofthemostim-

portantlimitationsofcausaldiagramsistheirinabilitytocapturethestockand flowstructureofsystems.Stocksandflows,alongwithfeedback,arethetwocen- tralconceptsofdynamicsystemstheory.

191

192 PartIIToolsforSystemsThinking

Stocksareaccumulations.Theycharacterizethestateofthesystemandgener-

atetheinformationuponwhichdecisionsandactionsarebased･StocksgiveSys- temsinertiaandprovidethemwithmemory.Stockscreatedelaysbyaccumulatlng thedifferencebetweentheinflowtoaprocessanditsoutflowIBydecouplingrates offlow,Stocksarethesourceofdisequilibriumdynamicsinsystems.

Stocksandflowsarefamiliartoallofus.Theinventoryofamanufacturlng

firmisthestockofproductinitswarehouses.Thenumberofpeopleemployedby abusinessisastock.Thebalanceinyourcheckingaccountisastock.Stocksare

alteredbyinnowsandoutflows.Afirm'sinventorylSincreasedbytheflowofpro- ductionanddecreasedbytheflowofshipments(andpossiblyotheroutflowsdue

tospoilageorshrinkage).Theworkforceincreasesviathehiringrateanddecreases viatherateofquits,layoffs,andretirements.Yourbankbalanceincreaseswithde-

positsanddecreasesasyouspend･Yetdesplteeverydayexperienceofstocksand flows,alltoooftenpeoplefailtodistinguishclearlybetweenthem･IstheUSfed- eraldeficitastockoraflow?Manypeople,includingpoliticiansresponsiblefor

fiscalpolicy,areunclear.Failuretounderstandthedifferencebetweenstocksand flowsoftenleadstounderestimationoftimedelays,ashort-termfocus,andpolicy resistance.

6.1.i Diagramm垂ngNotatiori苧orSモocksandF一ows

Systemdynamicsusesaparticulardiagrammingnotationforstocksandflows (Figure6-1).

｡Stocksarerepresentedbyrectangles(suggestingacontainerholdingthe contentsofthestock).

｡Inflowsarerepresentedbyapipe(arrow)pointinginto(addingto)the stock.

OutflOwsarerepresentedbypipespointingoutof(subtractingfrom) thestock.

oValvescontroltheflows.

･Cloudsrepresentthesourcesandsinksfortheflows･Asourcerepresents thestockfromwhichafloworlglnatlngOutsidetheboundaryofthemodel

arises;sinksrepresentthestocksintowhichflOwsleavlngthemodel boundarydrain.Sourcesandsinksareassumedtohaveinfinitecapacityand canneverconstraintheflowstheysupport.

Thestructureofallstockandflowstructuresiscomposedoftheseelements.

Astheexampleinthefigureshows,afirm'sinventorylSaStockthataccumulates theinflowofproductionandisreducedbytheoutflowofshipments･Thesearethe onlyflowsconsideredinthemodel:unlessexplicitlyshown,otherpossibleflows intooroutofthestock,suchasinventoryshrinkageorspoilage,areassumedtobe zero.Thecloudsindicatethatthestockofrawmaterialsneverstarvestheproduc-

tionrateandthestockofproductshippedtocustomersnevergrowssohighthatit blockstheshipmentrate.

Chapter6 StocksandFlows

FIGURE6-1 Stockandflow

diagrammlng notation

Genera一Structure:

て｢7 tEtbLStock て｢7 由一.ー∠_二ゝ ∠⊥ゝ

= ] stockKey=

> Frow

X valve(RowRegulator)

○

FIowofmaterial

SourceorSink

(Stocksoutsidemode一boundary)

Valvesregulateamount / tIowmglnOrOut＼＼

flowofmaterial

Source Inflow

＼

＼ー Nameof /

fIow

Examp一e:

lnventory Production

Outf一ow

争 //

Outofstock

193

〔3 SI'nk

6且2 Ma的ema昔iea自Represenせa抽 mo甘 StocksandFlows

Thestockandflowdiagrammingconventions(originatedbyForrester1961)Were basedonahydraulicmetaphor-theflOwofwaterintoandoutofreservoirs. Indeed,itishelpfultothinkofstocksasbathtubsofwater.ThequantltyOfwater

194

FIGURE6･2 FourequlVaJent representations ofstockand 月owstructure

Each

representation contains

preciselythe Same information.

PartIIToolsforSystemsThinking

inyourbathtubatanytlmeistheaccumulationofthewaternowlnglnthroughthe taplessthewaterflowingoutthroughthedrain(assumenosplashingorevapora-

tion).Inexactlythesameway,thequantityofmaterialinanystockistheaccumu- lationoftheflowsofmaterialinlesstheflowsofmaterialout.Despitetheprosaic

metaphorthestockandflOwdiagramhasapreciseandunambiguousmathemati-

calmeanlng.Stocksaccumulateorintegratetheirflows;thenetflOwintothestock istherateofchangeofthestock.HencethestructurerepresentedinFigure6-1 abovecorrespondsexactlytothefollowlngIntegralequation:

Stock(t)- lot lInflow(S)IOutflow(S)]ds+Stock(to) (6-1)

whereInflow(S)representsthevalueoftheinflowatanytimesbetweentheinitial timetoandthecurrenttimet.Equivalently,thenetrateofchangeofanystock,its derivative,istheinflowlesstheoutflow,definingthedifferentialequation

d(Stock)/dt-Innow(t)IOutflow(t). (6-2)

Ingeneral,theflowswillbefunctionsofthestockandotherstatevariablesandpa- rameters.Figure6-2ShowsfourequlValentrepresentationsofthegeneralstockand nowstructure.ThebathtubandstockandflOwdiagramsmayappeartobelessr1g-

orousthantheintegralordifferentialequationrepresentations,buttheyarepre-

ciselyequlValentandcontainexactlythesameinformation･Fromanysystemof integralordifferentialequationswecanconstructthecorrespondingstockand flowmap;fromanystockandflOwmapwecangeneratethecorrespondingInte- gralordifferentialequationsystem.

Hydrau一icMetaphor:

曹

ノ=

StockandF一owDiagram:

lnflow

lntegralEquation:

Stock(t)- tt

Outf一ow

llnfEow(S)-Ou紺ow(S)]ds+Stock(to)

DifferentialEquation:

d(Stock)/dt-NetChangeinStock-Jnflow(I)IOutflow(I)

Chapter6 StocksandFlows 195

ProcessPoint:NotationforAccumulation

ThetraditionalnotationusedincalculusandshowninFigure6-2isoftencon-

fusingtomanypeople.Inthisbook,Iwillgenerallyrepresenttheprocessofaccu- mulationwiththeINTEGRAL()function･.

Stock-INTEGRAL(Inflow~Outflow,Stockt｡) (6-3)

TheINTEGRAL()functionisexactlyequivalenttoequation(6-1)andrepresents

theconceptthatthestockaccumulatesitsinflowslessitsoutflows,beginningWith

aninitialvalueofStockto･

6.1.3 TheContributionofStockstoDynamics

Stocksarecriticalingeneratingthedynamicsofsystemsforthefollowlngreasons (Mass1980):

1.StocksCharacterizethestateofthesystemandprovidethebasisfor aetions.

Thestocksinasystemtelldecisionmakerswheretheyare,providingthem withtheinformationneededtoact.Apilotmustknowthestateoftheaircraft

includingposition,heading,altitude,andfuellevel･Withoutknowledgeof thesestates,thepilotisflyingblindandwon'tsurvivelong.Likewise,a

firmcan'tsetitsproductionscheduleappropriatelywithoutknowledgeof theorderbacklog,thestockofinventory,thepartsstocks,thelaborforce, andotherstocks,Abalancesheetcharacterizesthefinancialhealthofa

corporationbyreportlngthevaluesofstockssuchascash,inventory, payables,anddebt.Informationaboutthesestocksaffectsdecisionssuchas

issulngnewdebt,payingdividends,andcontrollingexpensesvialayoffs.

2.Stocksprovidesystemswithinertiaandmemory.

Stocksaccumulatepastevents.Thecontentofastockcanonlychange

throughaninfloworoutflow.Withoutchangesintheseflows,thepast accumulationintothestockpersists.ThestockofleadinthepalntOf America'sinnercltyhouslngremainshightodayeventhoughleadpaintwas

bannedin1978.0mcethestockofleadpalntaccumulated,theonlywayto eliminateitisthroughexpensivedeleadingor血eeventualdemolitionofthe houslngItself.Eventhentheleadremains,eithersafelysequesteredormore likelydispersedintotheenvironmentasdust,chips,orleadleaching血･om

landfillsintowatersupplies.Likewise,thestockofozone-destroying chlorinegeneratedbyCFCswillremainintheatmospherefわrdecadeseven aftertheproductionrateofCFCsfallstozerobecausetherateatwhich chlorineisscrubbedfromthestratosphereisverylow.Stocksdon'thaveto

betangible.Memoriesandbeliefsarestocksthatcharacterizeyourmental states.Yourbeliefspersistovertime,generatlnglnertiaandcontinultyln

yourattitudesandbehaviorJfyouhaveabadexperienceonanairlineand neverflyonthatcarrieragain,yourbeliefaboutthelowqualityoftheir serviceremainsevenifthey'veimproved.

196 PartIIToolsforSystemsThinking

3.Stocksarethesourceofdelays.

Alldelaysinvolvestocks･AdelaylSaprocessWhoseoutputlagsbehindits

lnPut.Thedifferencebetweentheinputandoutputaccumulatesinastockof

materialinprocess.Thereisalagbetweenthetimeyoumailaletterandthe

timeitisreceived.Duringthisinterval,theletterresidesinastockofletters

intransit.Evenemailaccumulatesinstocksofundeliveredpacketsand

messagesresidinginthememoryofvariouscomputersbetweenthesender andreceiver.Thereisalagofseveralyearsbetweenthedecisiontobuild

newofficebuildingsandthetimetheyarereadyforoccupancy･Duringthis

intervalthereisasupplylineofbuildingsunderdevelopment,includinga

stockofproposedprojectsandastockofbuildingsunderconstruction･

Bydefinition,whentheinputtoadelaychanges,theoutputlagsbehind andcontinuesattheoldrateforsometime.Duringsuchadjustments,the

stockaccumulatingthedifferencebetweenInputandoutputchanges･Ifyou mailweddingInvitationsto1000ofyourclosestfriendsallatonce,whilethe

rateatwhichothermailisdepositedremainsconstant,thestockoflettersin

transltJumpSby1000andremainsatthenewlevelasthelettersmaketheir

waytotheirdestinations.Onlyastheinvitationsbegintoarrivedoesthe stockoflettersintransitstarttofall.Thedeliveryrateexceedsthemailing

rate,Shrinkingthestockofmailintransit,untilalltheinvitationshavebeen

delivered,atwhichpointthedeliveryrateonceagalnequalstherateatwhich

mailisdepositedandthestockoflettersintransitreturnstoitsorlglnallevel･

Perceptiondelaysalsoinvolvestocksthoughthesestocksdonotinvolve

anymaterialflows.Forexample,thebeliefofmanagersinacompany'S

¶liwanheadquartersabouttheshipmentratefromtheirSiliconValleyplant

lagsbehindthetrueshipmentrateduetomeasurementandreportingdelays･

Measurementofaratesuchasshipmentsalwaysinvolvesastock･Dueto

unpredictablevariationsincustomerorders,productavailability,and

transportation,Shipmentscanvaryslgnificantlyfromhourtohour,dayto

day,oroverevenlongerperiods.Shipmentsmustbeaccumulatedforsome

periodoftimesuchasaday,week,Ormonthtoprovideameanlngful measurementoftherate.Ifshipmentsarehighlyvolatile,thefirmwillhave

toaccumulatethemoverlongerintervalstofilterouttheshorLtermnoiseand

provideameaningfulaveragemanagerscanusetomakedecisions･In

additiontherearereportingdelaysinvolvingastockofshipmentinformation

waitlngtObeuploadedtoanddownloadedfromthefirm'scomputersystem･

Theremaybefurtherdelaysintheadjustmentoftheexecutives'beliefseven

a氏ertheyseethelatestdata.Chapter11describesthestructureanddynamics

ofdelaysindetail.

4.Stocksdecoupleratesofflowandcreatedisequilibriumdynamics｡

Stocksabsorbthedifferencesbetweeninflowsandoutflows,thuspermittlng

theinflowsandoutflowstoaprocesstodiffer.Inequilibrium,thetotal

inflowtoastockequalsitstotaloutflowsothelevelofthestockis

unchanglng.However,inflowsandoutflowsusuallydifferbecausetheyare

oftengovemedbydifferentdecisionprocesses.Disequilibriumistherule

ratherthantheexceptlOn.

Chapter6 StocksandFlows 197

Theproductionofgraindependsontheyearlycycleofplantlngand harvest,alongwithunpredictablenaturalvariationsinweather,pest populations,andsoon.ConsumptlOnOfgraindependsonhowmanymouths therearetofeed.Thedifferencebetweengrainproductionandconsumption ratesaccumulatesingrainstocks,Storedthroughoutthedistributionsystem fromfieldtograinelevatortoprocessorinventoriestomarkettokitchen cupboard.Withoutastockofgraintobufferthedifferencesbetween productionandconsumption,COnSumptlOnWOuldnecessarilyequal productionatalltimesandpeoplewouldstarvebetweenharvests.Thus JosephadvisedPharaohtostockpilegrainduringthe7goodyearsin anticlpationofthe7leanyearsduringwhichconsumptlOnWOuldexceed harvests.WhileonaveragetheproductionofgrainbalancesconsumptlOn (andlosses)asfarmersrespondtomarketpricesandinventoryconditions indetermininghowmuchtoplant,andasconsumersadjustconsumption inresponsetoprlCeSandavailability,productionandconsumptlOnare rarelyequal.

Whenevertwocoupledactivitiesarecontrolledbydifferentdecision makers,involvedifferentresources,andaresubjecttodifferentrandom shocks,abufferorstockbetweenthemmustexist,accumulatingthe difference.Asthesestocksvary,informationaboutthesizeofthebuffer willfeedbackinvariouswaystoinfluencetheinflowsandoutflows.Often, butnotalways,thesefeedbackswilloperatetobringthestockintobalance･ Whetherandhowequilibriumisachievedcannotbeassumedbutisan emergentpropertyofthewholesystemasitsmanyfeedbackloopsinteract simultaneously.Understandingthenatureandstabilityofthesedynamics isoftenthepurposeofasystemdynamicsmodel.

6d2 日der酬 y百mgStocksand『日⑳ws

Thedistinctionbetweenstocksandflowsisrecognizedinmanydisciplines. Table61lshowssomecommontermsusedtodistinguishbetweenstocksand flowsinvariousfields.Inmathematics,systemdynamics,controltheory,andre-

latedenglneeringdisciplines,stocksarealsoknOwnasintegralsorstatevariables･ Flowsarealsoknownasratesorderivatives.Chemistsspeakof71eaCtantSand reactionproducts(thestocks)andreactionrates(themows).Inmanufacturing settings,stocksandflowsarealsocalledbuHersandthroughput.Ineconomics, stocksarealsoknownaslevelsandflOwsasrates.Forexample,thecapitalstock ofaneconomyisitslevelofwealth(measuredin,say,dollars)whiletheGDPis theaggregaterateofnationaloutput(measuredinS/year).Inaccounting,balance sheetitemsarestocks,suchascash,thebookvalueofinventory,long-termdebt, andshareholderequity(allmeasuredin,e.g･,dollars).Itemsappearingonthein- comestatementornowoffundsreportareflOwswhichalterthecorresponding stocksonthebalancesheet,suchasnetrecelptS,thecostofgoodssold,long-term borrowing,andthechangeinretainedearnlngS.Theseflowsaremeasuredin S/year.Physiologicalmodelsoftenlumpdifferentstocksintoasmallnumberof compartmentsorboxesconnectedbydiffusionrates(theflows).Forexample,the stockofglucoseinahumancanberepresentedbyathreecompartmentmodel:

198

TABLE6･l Terminologyused todistinguish betweenstocks andf一owsin different

discIPIEneS

PartIITわolsforSystemsThinking

Field Stocks Flows

Mathematics,physics andeng lneerlng

Chemistry

Manufactu rlng

Economics

Accounting

Biology,physiology

Medicine, epidemiology

lntegrals,states,state variables,stocks

Reactantsandreaction

p｢oducts

Buffers,inventories Levels

Stocks,balancesheet items

Compartments

Prevalence,reservoirs

Derivatives,ratesof

change,flows Reactionrates

Throughput Rates

FEows,cashfiowor incomestatement items

Diffusionrates,flows

Incidence,infection, morbidityand mortalityrates

glucoseinthedigestivesystem,glucoseinthebloodstream,andglucoseinthein-

tracellularmatrix･Inepidemiology,prevalencemeasuresthenumberorstockof peoplewhohaveaparticularconditionatanygiventime,whileincidenceisthe rateatwhichpeoplecomedownwiththediseaseorcondition.InDecember1998 theprevalenceofHIV/AIDSworldwidewasestimatedbytheUnitedNations

AIDSprogramtobe33.4millionandtheincidenceofHIVinfTectionwasestimated tobe5.8millioIVyear.Thatis,atotalof33.4millionpeoplewereestimatedtobe HIVpositiveortohaveAIDS;therateofadditiontothisstockwas5.8million

peopleperyear(16,000newinfectionsperday)IThenetchangeinthepopulation ofHIVpositiveindividualswasestimatedtobe3.3millionpeopleperyeardueto

thedeathratefromAlDs,estimatedtobe2･5millionpeopleperyearin1998. Howcanyoutellwhichconceptsarestocksandwhichareflows?Stocksare

quantitiesofmaterialorotheraccumulations.Theyarethestatesofthesystem. TheflOwsaretheratesatwhichthesesystemstateschange.Imaglneariverflow-

ingintoareservoir.Thequantityofwaterinthereservoirisastock(measuredin, say,cubicmeters).Ifyoudrewanimaginarylineacrossthepointwheretheriver

entersthereservoir,theflOwistherateatwhichwaterpassestheline-therateof flowincubicmeterspersecond.

6 .2.1 UnitsofMeasureinStockandFlowNetworks

Theunitsofmeasurecanhelpyoudistinguishstocksfrom flows.Stocksare

usuallyaquantltySuchaswidgetsofinventory,peopleemployed,orYeninan account.TheassociatedflOwsmustbemeasuredinthesameunitspertimeperiod,

forexample,therateatwhichwidgetsareaddedperweektoinventory,thehiring rateinpeoplepermonth,ortherateofexpenditurefromanaccountin¥ノhour.Note

thatthechoiceoftimeperiodisarbitrary･Youare氏.eetoselectanymeasurement systemyoulikeaslongasyouremainconsistent.Youcanmeasuretheflowofpro-

ductionintoinventoryaswidgetsperweek,widgetsperday,orwidgetsperhour. ThestatementHThecurrentrateofproductionis1200widgetsperdayHisexactly

Chapter6 StocksandFlows 199

equlValentto山estatementthatproductionisproceedingatarateof8400widgets perweek,50widgetsperhour,5/6widgetsperminute,oreven43,800,000widgets percentury.Allarestatementsabouthowmanywidgetsarebeingproducedright now-atthisinstant.Whetherthecumulativenumberofwidgetsproducedinany glVeninteⅣalsuchasaday,week,orcenturylSequalto1200,8400,or43,800,000 dependsonwhetherthecurrentratestaysconstantoverthatinterval(oraverages outtothecurrentrate).Mostlikelyitwon't.

6.2.2 ThtTtSnapshotTest

Stockscharacterizethestateofthesystem.Toidentifykeystocksinasystem,

imaginefreezingthescenewithasnapshot.Stockswouldbethosethingsyou couldcountormeasureinthepicture,includingpsychologlCalstatesandotherin- tangiblevariables.Youcanestimatethestockofwaterinareservoirfromaset ofsatelliteimagesandtopographicdata,butyoucannotdeterminewhetherthe waterlevelisrisingOrfalling.YourbankstatementtellsyouhowmuchmoneylS inyouraccountbutnottherateatwhichyouarespendingltnow.Iftimestopped, itwouldbepossibletodeterminehowmuchinventoryacompanyhasortheprice ofmaterialsbutnotthenetrateofchangeininventoryortherateofinflationin materialsprlCeS.Thesnapshottestappliesalsotolesstangiblestocks･Theplant manager'SexpectationofthecustomerorderrateatanyInstantOrperCeptlOnOfthe sizeofinventoryarestocks,eventhoughtheyarementalandnotphysicalstocks.

Asnapshotofpeople'smentalstates,however,doesnotindicatehowfasttheyare revISlngtheirbeliefs.

Figure613listssomecommonconceptsandidentifiesthemasstocksorflows, showingtheirstockandflowstructureandunitsofmeasure･Population,Employ- ees,andDebtarestraightforward.WhyistheprlCeOfaproductastock?Prices characterizethestateofthesystem,inthiscasehowmuchyoumustpayperunit. Apricepostedonanitemremainsineffectuntilitischanged,justasthenumber ofwidgetsinaninventoryremainsconstantuntilitischangedbyaflowofpro- ductionorshipments.Eventhebidsandofferscalledoutinatradingpltatafi- nancialmarketarestocks,albeitshor t - l i vedones･.abidorofferremainsineffect

untilthetraderwi山drawsoraltersitbycryingOutanOther･ Whyistheexpectedcustomerorderrateforaproductastock?Clearly,theac-

tualcustomerorderrateisanow.TheflOwofcustomerordersaccumulatesina

backlogorstockofunfilledordersuntiltheproductcanbedelivered.However,a

manager'sbeliefabouttherateatwhichcustomerordersarebookedisastock-1t isastateofthesystem,inthiscaseamentalstate.Nooneknowsthetruecurrent orfutureorderrate.Tlhemanager'sbeliefaboutorderscan,andusuallyCLOeS,dif- ferfromthetrueorderrate(thebeliefcanbewrong).Managers'beliefsaboutthe customerorderratewilltendtoremainthesameuntiltheybecomeawareofnew

informationandupdatetheirbeliefs.TheChangeinExpectedOrderRateisthe rateatwhichthebeliefisupdated.Notetheunitsofmeasurefortheexpectedor- derrate.Liketheactualorderrate,theexpectedorderrateismeasuredinwidgets pertimeperiod(sayweeks).Theunitsofmeasurefb∫therateatwhichthebelief aboutcustomerordersisupdatedare(widgets/week)/week

200

FtGURE6-3

Examplesof stocksandflows withtheirunitsof measure

Thechoiceoftime unitfortheflows

(e.g.,days,weeks, years)isarbitrary butmustbe consistentwithina

slnglemodel.

PartH ToolsforSystemsThinking

て｢7 由一.ー Popu一ation て｢7 血,..__

(people/year)(people/year)

Borrowing (S/year)

RateofPrice

Change (S/unWyear)

Changein Expected OrderRate

(wI'dgets/weeJdweek)

(S/unit)

Expected Customer1 0rders

(widgets/week)

Repayment (S/year)

NotethattherateofprlCeChangeandthechangeintheexpectedorderratecan bepositiveornegative(pricesanddemandforecastscanriseorfall)AAnyflowinto oroutofastockcanbeeitherpositiveornegative｡Thedirectionofthearrow

(pointingintooroutofastock)definesthesignconventionfortheflow.Aninflow addstothestockwhentheflowispositive;iftheflowisnegativeitsubtractsfrom thestock.Whentheoutflowispositive,theflowsubtractsfromthestock.

Chapter6 StocksandFlows 201

!dentifyingStocksandF!ows

ArethefollowingconceptsStocksorflows?Drawastockandflowmapforeach andgivetheirunitsofmeasure.

1.Interestrate(e.g.,theprimeinterestrateorrateonthe30-yearUSTreasury bond).

2.Unemploymentrate.

Hint:Whatdoestheword"rate"meaninthesesettings?

6.2.3 ConservationofMateria一in

StockandFlowNetworks

AmajorStrengthofthestockandnowrepresentationisthecleardistinctionbe-

tweenthephysicalflowsthrough thestockandflOwnetworkandtheinformation feedbacksthatcouplethestockstothemowsandclosetheloopsinthesystem.The contentsofthestockandflOwnetworksareconservedinthesensethatitemsen-

terlngaStockremainthereuntiltheyflowout.Whenanitemflowsfromonestock

toanotherthefirststocklosespreciselyasmuchasthesecondgains.Considerthe

stockandflOwstructurerepresentingtheaccountsreceivableofafirm(Figure 6-4)･Thestockofreceivablesisincreasedbybillingsanddecreasedbypayments receivedandbydefaults.TheflOwofbillingsisconservedinthesensethatoncea

customerisbilled,theinvoiceremaiIISinthestockofreceivablesuntilitexplicitly flowsoutwhenthereceivablesdepartmentrecordsthecustomer'spaymentorac- knowledgesthatthecustomerhasdefaultedandwritesofftheaccount.Incontrast, infわrmationaboutthestockofreceivablesisnotconserved.Thecorporateac-

CountlngSystemmakesthevalueof也ereceivablesstockavailabletomany throughouttheorganization.Accesslngandusingthisinformationdoesnotuseit upormakeitunavailabletoothers.

Notealsothatwhiletheunitsofaccountspayablearedollarsand也ebュlling, payment,anddefaultmowsaremeasuredindollarspertimeperiod,thecontentsof 血estockarenotactuallydollars.Rather,thecontentofthereceivablesstockisin-

formation,specifically,aledgerordatabaseconsistlngOfrecordsofinvoicesout- standing.Toseewhy,imaginetryingtOexchangeyourfirm'sstockofreceivables forcash-youcansellthemtoacollectionagency,butonlyformuchlessthan100 cerltSOn払edollar.Thoughthecontentsofthestockofreceivablesisinformation

andnotamaterialquantity,ltisneverthelessconserved-youcannotsellaglVen

stockofreceivablesmorethanonce(notlegally,anyway).Stockscanrepresentin- formationaswellasmoretangiblequantitiessuchaspeople,money,andmateri- als.Stockscanalsorepresentintangiblevariablesincludingpsychologicalstates,

perceptlOnS,andexpectationssuchasemployeemorale,theexpectedrateofinfla- tion,orperceivedinventory.

202

FlGURE6-4 Stockandflow structureof accounts receivable

ThematerialfFow-

lngthroughthe networkisactuaHy informationabout customersandthe

amountstheyowe, Thisinformationis conserved-the

onlywayareceiv-

able,Oncebilled, isremovedfrom thestockisifthe

customerpaysor defaultsJnforma- tionaboutthesize

andcompositionof accountspayab一e, however,canbe madeavailable

throughoutthe systemandis notdepletedby uSage･

PartIIToolsforSystemsThinking

6.2.堵 S竜aモe-DeモermimedSysをems

Thetheoryofdynamicsystemstakesastate-determinedsystemorstatevariable

approach.Theonlywayastockcanchangeisviaitsinflowsandoutflows.Intum,

thestocksdeterminetheflows(Figure6-5).

Systemsthereforeconsistofnetworksofstocksandflowslinkedbyinforma- tionfeedbacksfromthestockstotherates(Figure6-6).Asshowninthefigure,the

deteminantsofratesincludeanyconstantsandexogenousvariables･Thesetooare stocks.Constantsarestatevariablesthatchangesoslowlytheyareconsideredto beconstantoverthetimehorizonofinterestinthemodel.Exogenousvariablesare stocksyouhavechosennottomodelexplicitlyandarethereforeoutsidethemodel

boundary.Forexample,inamodelofthedemandforanewvideogame,thesize ofthepotentialmarketmightdependonthepopulationbetween,say,ages4and

20･Theproductlifecyclewilllastafewyearsatmost.Overthistimehorizonthe populationbetween4and20yearsofageisnotlikelytochangesignificantlyand canreasonablybeassumedconstant.Alternatively,youcouldmodelthestockof

childreninthetargetagegroupasanexogenousvariable,uslngCensusdataand prqectionstoestimateitsvalues.Makingpopulationconstantorexogenousisac- ceptableinthiscasesincetherearenosignificantfeedbacksbetweensalesofvideo gamesandbirth,death,ormigrationrates.

6.2,5 Aux百日岳aFyVariab日es

AsillustratedinFigure6ェ6,mathematicaldescrlptlOnOfasystemrequlreSOnlythe stocksandtheirratesofchange.Foreaseofcommunicationandclarity,however,

itisoftenhelpfultodefineintermediateorauxiliaryVariables.Auxiliariesconsist offunctionsofstocks(andconstantsorexogenousinputs)･Forexample,apopula- tionmodelmightrepresentthenetbirthrateasdependingonpopulationandthe fractionalbirthrate;fractionalbirthrateinturncanbemodeledasafunctionof

foodpercaplta.TheleftsideofFigure617Showsthestructureandequationsfor

Chapter6 StocksandFlows

FIGURE6-5 State-determined

systems

Systemsevolve byfeedbackof informationfrom thestateofthe

systemtothe flowsthatalter thestates.

Left:CausaHoop representationin whichthestock andflow structureisnot

expHdt.

Right:ExpllCit stockandf一ow structureforthe samefeedback

loop.

Theequations correspondtothe stockandflow

map.Thenet rateofchange ofthestockisa functionofthe stockitself, closlngthe feedbackloop.

203

賢 √ - / l 畢

L. ＼＼ - / l ⊥ _

iS璽『璽5

StateottheSystem≡lNTEGRAL(NetRateofChange･StateoftheSystemt｡)

NetRateofChange=i(Stateof的eSystem)

themodel.TheNetBirthRateaccumulatesinthePopulationstock.Theauxiliary variablesFractionalBirthRateandFoodperCapitaareneitherstocksnorflows. Theyarefunctionsofthestocks(andexogenousinputs,inthiscaseFood).Popu- lationparticipatesintwofeedbackloops:apositiveloop(morepeople,more births,morepeople)andanegativeloop(morepeople,lessfoodperperson,lower fractionalnetbirthrate,fewerbirths).Theinclusionoftheauxiliaryvariablesdis- tlnguishesthetwoloopsandallowsunambiguousasslgnmentOflinkandlooppo-

1arities.

Theauxiliariescanalwaysbeeliminatedandthemodelreducedtoasetof equationsconsistingOnlyofstocksandtheirflows･Bysubstitutingtheequation forFoodperCapitaintotheequationforFractionalBirthRateandthensubstitutl lngtheresultintotheequationforNetBirthRate,youcaneliminatetheauxiliaries, reducingthemodeltoonewithonlyNetBirthRateandPopulation.Therightside ofFigure6-7showsthismodelanditsequations.Thoughthemodelismathemat- icallyequlValenttothemodelwithauxiliaries,itishardertoexplain,understand, andmodify.Notethatinthereducedformmodelpopulationenterstheequationfor therateofchangeofpopulationinboththenumeratoranddenominator.The polarltyOfthecausallinkbetweenPopulationandNetBirthsisnowambiguous, anditisnotpossibletodistinguishthetwofeedbackloopsinvolvingpopulation andbirths.

Theprocessofcreatlngthereducedformmodelbysubstitutionofintermedi- atevariablesintotheirratesisageneraloneandcanbeca血edoutonanymodel. However,theuseofauxiliaryvariablesiscriticaltoeffectivemodeling.Ideally, eachequationinyourmodelsshouldrepresentonemainidea.Don'ttrytoecono- mizeonthenumberofequationsbywrltlnglongonesthatembedmultiplecon- cepts･Theselongequationswillbehardlbrotherstoreadandunderstand.They willbehardforyoutounderstand.Finally,equationswithmultiplecomponents andideasarehardtochangeifyourclientdisagreeswithoneoftheideas.

204 PartIIToolsforSystemsThinking

F】GURE6-6 Networksofstocksandflowsarecoupledbyinformationfeedback.

Stocksaccumulatetheirratesofflow;informationaboutthestocksfeedsbacktoaltertherates, closlngtheloopsinthesystem.ConstantsarestockschanglngtooslowlytobemodeledexpllCitly; exogenousvariablesarestocksoutsidethemodelboundary(shownbytherectanglewithrounded corners).

Equationrepresentation:Thederivativesofthestocksindynamicsystemsare,ingeneral,nonlinear functionsofthestocks,theexogenousvariables,andanyconstants.lnmatrixnotation,theratesof changedS/dtareafunctionf()oHhestatevectorS,theexogenousvariablesUandtheconstantsC:

dS/dt-i(S,U,C) (6-4)

Forthediagrambelow,theequationfortherateofchangeofS4is

dS4/dt-f4(S3,S4,U3,C3)

Exogenous lnputl

Exogenous lnput2

Exogenous lnput3

(6-5)

6.2.6 StocksChangeOn!yThr軌唱h■rileirRates

Stockschangeonlythroughtheirratesofflow･Therecanbenocausallinkdirectly intoastock.Consideramodelforcustomerservice.Customersa汀iveatsomerate

andaccumulateinaqueueofCustomersAwaitingService.Thequeuecouldbea lineatafastfoodrestaurant,Carsawaitlngrepalratabodyshop,Orpeopleonhold

callingforairlinereservations,Whentheserviceiscompletedcustomersdepart

fromthequeue,decreaslngthestockofcustomerswaitingforservice･Therateat

whichcustomerscanbeprocesseddependsonthenumberofservicepersonnel, theirproductivity(incustomersprocessedperhourperperson),andthenumberof hourstheywork(theworkweek).Ifthenumberofpeoplewaitingforservice

increases,employeesincreasetheirworkweekastheystayanextrashift,skip lunch,orcutdownonbreaks.

Chapter6 StocksandFlows 205

FIGURE6-7 Auxiliaryvariables

Left:AsimplepopulationmodelwithauxilfaryVariables.FractionalBirthRateandFoodperCapitaare neitherstocksnorflows,butintermediateconceptsaddedtothemodeltoaidclarity.

F7ight:Thesamemodelwiththeauxiliaryvariableseliminatedbysubstitutionintotherateequation. TheJinkfromPopulationtoNetBirthRatenowhasanambiguoussFgn,apoorPractice.

Correct lncorrect

･もし-//5' Food

Population-INTEGRAL(NetBlrthRate,Populationt｡)

NetBirthRate-Population'Fractiona=∋irthRate

FractionalBirthRate-i(FoodperCapita)

FoodperCapita-Food/Popu一ation

Popu一ation-lNTEGRAL(NetBirthRate,Populationt｡)

NetBirthRate-Population'f(Food/Population)

Ihaveoftenseenpeopleinworkshopsdrawthediagramshowninthetopof

Figure6-8.TheycoITeCtlyrecognlZethattherateatwhichcustomersareprocessed

istheproductofServiceStaff,Productivlty,andWorkweekandthathigherqueues ofwaitlngCustomersleadtolongerhoursandhiringofadditionalstaff,formlng

twobalanclngfeedbacks.Butoftenpeopledrawinformationfeedbacksdirectly

fromtheworkweekandservicestafftothestockofCustomersAwaitlngService,

asslgnlngthemanegativepolarity.Theyreasonthatanincreaseintheworkweek

orstaffleveldecreasesthenumberofcustomersremainlnginthequeue,thusclos-

ingthenegativefeedbackloops.

ThecorrectdiagramisshowninthelowerpanelofFigure6% Theonlyway

customerscanexitthestockisviathedeparturerate.Thedeparturerateisthe

productofthenumberofstaff,theirworkweek,andtheirproductivity.Anincrease

inanyoftheseInputsbooststherateatwhichcustomersareprocessedandleave

thequeue.Thebalanclngfeedbacksarestillpresent:Alongerqueueofwaitlng

customersleadstolongerhoursandmorestaffandanincreaseintheprocesslng

rate.ThevalvecontrollingtheoutflowfromthestockofwaitingCustomersopens

wider,andcustomersdepartthequeueatahigherrate.Thepolaritiesoftheinfor一

nationlinksinthefeedbackloopareallPositive,butanincreaseinthecustomer departureratecausesareductioninthestockofwaitlngCustomersbecausethede-

parturerateisanoutflowfromthestock.

206

FIGURE6-8

Stockschange onlythrough theirrates.

Top:lncorrect stockandflow

mapofaservice operation.Work- week,Service Staff,andother variablescannot

directlyalterthe stockofCus-

tomersAwaiting Service.

Bottom:Corrected

diagram.The Workweek, numberofService

Staff,andProduc- tivitydrivethe CustomerDepa卜 lureRate,which decreasesthe stockofCus-

tomersAwaiting Service.

PartIIToolsforSystemsThinking

lncorrect

6.2.7 ContinuousTimeandlnstantaneousFlows

Thestockandflowperspective(anditsequivalentintegralordifferentialequation

structure)representstimeasunfoldingcontinuously.Thatis,asourexperience

suggests,timeprogressessmoothlyandcontinuously.Insystem dynamicswe

almostalwaysrepresenttilTleaSCOritinuous.EventscanhappenatalnlytilTTie;

changecanoccurcontinuously;andtimecanbedividedintointervalsasfineas onedesires.1

iInnumericalsimulationtimeisdividedintodiscreteintervals.However,theseintervalsmust besmallenoughthatthenumericalsolutionisagoodapproximationoftheunderlyingcontinuous dynamics,andmodeldynamicscannotdependonthelengthofthesolutioninterval(cuttingitin

half,e･g･,shouldnotaffectanyofyourc?nclusions)･Indiscretetimeordifferenceequationsys- temsthetimeintervalisanirreduciblemlnimllmtimedelaylneveryfeedbackloopandoftenhas alargeimpactonthedynamics.AppendixAdiscussesnumericalintegrationandtheselectionofan appropriatetimestepforyoursimulations.

Chapter6 StocksandFlows 207

AflOwatanytlmeisdefinedtobeitsinstantaneousvalue-therateatwhich waterisflowlngintoyourbathtubrightnow.Mathematically,thenetflOwtoa stock(inflowslessoutflows)istheinstantaneousrateofchangeofthestock-its derivative(thisisthemeaningofequation6-2),Noonecanmeasuretheinstanta- neousvalueofanyflow.ThegovernmentdoesnotandcannotreporttheGDPata particularmomentbutinsteadreportstheaveragerateofproductionoversome prior,finiteintervaloftime(typicallyaquarterofayear)｡Likewise,quarterlyre- portsofafirm'ssalesarethecumulativesalesduringthequarter,nottheinstanta- neoussalesrateattheendofthequarter.Duringthequartersaleslikelyvaried substantially.Salesreportsatmorefrequentintervalssuchasmonthlyoreven dailyarebetterapproximationsoftheinstantaneoussalesratebutstillrepresentav- eragestakenoversomeprior,finiteinterval.Similarly,thespeedometerofacar doesnotmeasureitsinstantaneousvelocity.Becausethecomponentsoftheveloc-

1tySensorandinstrumentationhaveinertia,thespeedometerindicatesanaverage ofthevelocityovera(short)priorinterval.

Asthelengthofthemeasurementintervalshrinks,thereportedaveragerate becomesabetterapproximationoftheinstantaneousrate,Mostspeedometersre- spondquicklyrelativetotherateofchangeofthecar'struevelocity,soforpracti- calpurposestheaveragevelocityreportedontheinstrumentpanelisthesameas theactual,currentvelocity.Ontheotherhand,thedelaysinreportingthestateof theeconomyortheprofitsofacompanyareoftenlongrelativetotheirratesof changeanddramaticallyinfluencethestabilityofthesystem.Thoughwemight developlnStrumentSforourphysicalandsocialsystemsthatshrinkthedelaysin measuringandreportingratesOfflow,Wecannevermeasuretheinstantaneous valueoftheflowsaffectinganystock.

6.2｡8 e⑳m菅岳mu⑳uSByDjvis岳b日eve帽uS QuantizedFlows

Justastimecanberepresentedasunfoldingcontinuouslyorindiscreteintervals, sotootheunitsflOwlngIntoandoutofstockscanbethoughtofeitherascontinu- ouslydivisibleorasadiscretenumbersofitems.Mostflowsareactuallyquan- tized,meanlngtheyconsistofcollectionsofindividualitemswhichcannotbe dividedintoarbitrarilysmallunits.Oiltankersarecommissionedoneatatime- itisnotmeaningfultospeakoflaunchinghalfatanker.Companyhiringconsists ofawholenumberofpeople.Eventheflowinariverconsistsofan(astronomi- callylarge)integernumberofwatermolecules.ThestockandflOwconceptand thefourequivalentnotationsshowninFigure612applywhethertheflowiscon- ceivedtobeinfinitelydivisibleorquantized.ThemetaphoroftheflOwofwater intoabathtubemphasizesoureverydayexperienceofwaterasacontinuouslydi- visiblesubstance-wearen'tconcernedwiththeidentityOftheindividualwater molecules･However,ifitwereimportanttoourpurpose,wecouldjustaseasily imaginethatthetubisfilledbyalumpyflowofindividualicecubes.Wh ethercon- tinuousorquantized,thequantltyinthestockisalwaystheaccumulationofthein- flowstothestocklessitsoutflows.

Inmanymodelsitisapproprlateandusefultoapproximatetheflowofindivid- ualitemsasacontinuousstream.Inmodelingthecashflowofalargeorganization

208 PartIIToolsfわrSystemsThinking

youusuallydonotneedtotrackindividualpayments;itisaperfectlyacceptable approximationtoconsidertheflowofrevenueandexpendituresascontinuousin

timeandcontinuouslydivisible(thoughofcoursetheaccountingdepartmentmust trackindividualpayments).Similarly,thoughorganizationshirediscrete,wholein-

dividuals,itisusuallyacceptabletoassumetheflOwsofpeoplearecontinuously divisible.Someclientsaretroubledbythefractionalpeopleyourmodelwillgen-

erate,butalmostalwaystheerrorisinsignificantcomparedtothemeasurementer-

rorinparametersincludingthenumberofemployeesthefirmactuallyhas.Since peoplecanbehiredparttime,workinjob-sharingsituations,orbeasslgnedto multipleprojects,itisquitemeaningfultospeakoffractionalemployees,measured

inFTE(FulトTimeEquivalent)people.

WhenthepurposeofthemodelrequirestraCkingtheindividualpeople,forex- amplemodelingthebehaviorofpeopleenterlngthelineatthesupermarkettode- terminetheoptlmalnumberofcheckoutcounters,thenpeoplecanbemodeledas

discreteindividualsarrivlngatdiscretepolntS;thisisaclassicmodelingparadigm inqueuingtheory(Prabhu1997;GrossandHarris1998;Papadopoulos1993),Yet eveninmanyqueulngapplications,thecontinuoustime,continuousflowapprox-

imationworksextremelywellandtheerrorsitintroducesareoftensmallcompared tomeasurementerrorandparameteruncertaintyintherealsystem.Thedecisionto

representstocksandflOwsascontinuousordiscretealwaysdependsonthepur- poseofthemodel.Forexample,ifyourpurposeistounderstandthedynamicsof priceandtheoriginofcyclesintheoiltankermarket(Seechapter20),itisfineto assumethattheratesoftankerordering,construction,andscrappagearecontinu-

ousintimeandcontinuouslydivisible.Ⅰncontrast,ifyourpurposeweretomodel thearrivalandomoadingoftankerstooptlmizeportfacilitiesyouwouldhaveto modeltheshipsasdiscreteentities.

6.2.9 WhiehM⑳東e軸gApp相aehSh⑳u日eEYouuse?

Thechoiceofmodelingtechniqueandsoftwarewilldependonwhichassumpt10nS aboutthestocksandflOwsinyoursystemareappropriatetOyourPurpose.Inall casesmakesureyourmodelingsoftwareandmethodcanincludethefeedback

processesyouconsiderimportant.Inmodelingthebehaviorofpeopleinlineatthe supermarket,forexample,youmightchoosetouseadiscretetime,quantizedflow representationandselectastochasticmodelingpackage,orevenuseaspreadsheet. Besure,however,thatyourtoolsallowyoutocapturebehavioralfeedbackssuch

asthefeedbackfromthelengthofthelinetotherateatwhichpeopleJOlntheline. Somemodelsandagreatmanyofthetheoremsinqueulngtheoryassumethatthe

rateofarrivalstoaqueuesuchasthecheckoutlineisexogenous.Peopleactually choosetoenteralinebasedonitslength(moreprecisely,theirestimateofex- pectedwaitingtime).Alonglinewillcausepeopletoswitchtoanother,defertheir

shoppingtOalesscrowdedtimeofday,orevengotoadifferentstore.Suchbalk- mgcreatesapowerfulnegativefeedbackloop:Thelongertheline,thesmallerthe arrivalrate.OmittlngSuchfeedbackprocessesfromyourmodelintheinterestsof

analyticaltractabilityorprogrammlngCOnVeniencewilloftenleadtoafatalmaw inyouranalystsandpolicyconclusions.

Chapter6 StocksandFlows 209

6.2.10 ProcessPoint:

Portray岳ngStocksandFFowsinPractice

EachofthestockandflowrepresentationsinFigure6-2(thebathtub,stockand

flowdiagram,integralequation,anddifferentialequation)containspreciselythe sameinformation.TheyareexactlyequlValent.Whichshouldyouusetodevelop andpresentyourmodels,especiallywhenyouareworkinglnateam?

TheanswerdependsonthecontextofthemodelingprqJectyouaredoingand thebackgroundofyourclientteam.Whilemanymathematicallysophisticated modelersscofFattheideaofexplainlngaCOmplexmodelusingbathtubsandpipes,

IhavemanytimesSeenOtherwisebrilliantmodelingeffortsfounderbecausethe analysttriedtoexplainamodelusingdifferentialequationsandmathematicalno- tation-orthesimulationcode-toaclientteamwithlittletechnicalbackground.

Oneoftheworstthingsaconsultantcandoishumiliatetheclient.Showingoff yourmathematicalknowledgebyusingdifferentialequations,lotsofGreekletters, andothernotationtheclientneverstudiedorforgotalongtlmeagoisasure-fire

waytoconvinceyourclientsyoucaremorefortheeleganceofyourequationsthan forhelpingthemsolvetheirproblem.

Stockandflowdiagramscontainthesameinformationasthemoremathemat-

icallyformalnotationbutareeasiertounderstandandtomodifyonthefly.Still, Someteammembersconsidereventhestockandflowdiagramformattobetooab-

stract.ihaveoftenseenclevergraphicsoftanks,pipes,andvalvesusedtoexcel-

lenteffectwithclientteams.Forexample,aconsultingprojectWithamultinational

chemicalsfirmrepresentedtheflowsofproduction,inventories,shipments,and customerstocks-alongwithcapaclty,Cash,andevenequipmentdefects-asase-

riesofpipes,valves,andtanks.Theteammemberswereabletograspthestock andflowstructurereadilysincetheywereal1familiarwiththetanksandpipesca r-

ryingmaterialsintheirplants.Infact,mostoftheclientteamwereenglneerSby

trainlngandhadplentyofbackgroundinmathematics･Yetseveralcommentedthat theyneverreallyunderstoodhowthebusinessworkeduntiltheysawthechart showlngltSStockandflowstructureastanksandpipes･

Whatifyourclientshaveevenlesstechnicaltrainlngthanthesechemicalcom- panyexecutives?Thebathtubmetaphorisoftenusedtogoodeffect,asillustrated

bythecaseofautomobileleasing(seeFigure2.4)AWhatifthestocksandflowsin yourmodelaren'tastangibleasbarrelsofoilorautomobiles?GetcreatlveJna

managementflightsimulatorofinsuranceclaimsprocessing(Kim1989;Diehl 1994),aflow oflettersarrivingtoaninboxrepresentedtheadditionofnewclaims tothestockofunresolvedclaims.LetterscontainingChecksflowedouttothecus-

tomersasclaimsweresettled.Iconsofpeoplerepresentedthestockandflowstruc- tureofclaimsadjusters(Figure619).Participantsinworkshopsusingthemodel wereabletounderstandthesystemstructuremuchbetterthanifthemoreabstract symbolshadbeenused.

Iamnotrecommendingthatyoukeeptheequationsorstockandflowdial

gramshiddenfrom yourclient･Neverhideyourmodelfromacuriousclient･You shouldalwayslookforandcreateopportunitiesforclientteammemberstolearn moreaboutthemodelingprocess;youshouldalwaysbepreparedtoexplainthe

workingsofyourmodel.

210

FIGURE6-9 Stocksandflows ofcJaimsand

claimsadjusters lnanlnSuranCe

company

PartIIToolsforSystemsThinking

撃薄 Adjusters

Turnover

ミ≡ 轟 ≡ 牽 CIaims Claims Claims Received Outstanding Sett日ed

Source.IKim1989.

AndwhilelcautionthemathematicallysophisticatedmodeleragalnStOverly technicalpresentation,theoppositeproblemcanalsoarise:someclientsareof- fendedbywhattheyconsidertobesimplisticcartoondiagramsandpreferwhat theyviewasthemoreprofessionalpresentationofstockandflowdiagramsor evenequations･Asalways,youmustgettoknowyourclientdeeplyandearlyln themodelingprocess.

Finally,acautionfb∫thosewithlesstechnicaltrainingandmathematicalback一 ground:Clientsmaynotneedtounderstandthedeeprelationshipbetweentheir bathtubandthemathematicsunderlyingstocksandflows,butyoudo.Whileyou don'tneedtobeabletosolvedifferentialequationstobeasuccessfulmodeler,you doneedtounderstandthestructureanddynamicsofstocksandflowsthoroughly andrigorously｡

6｡3 MApp日NGSTOeKSANDFLOWS

6コ3.1 WhenSh⑳uはPeaLuSaはoopD岳agramsSh㊤w StockandFlowStructure?

Causaldiagramscanbedrawnwithoutshowingthestockandflowstructureofa

system芋Or,asshowninFigure6-8ラーheycanincludethestockandflowstrlJpCtllre explicitly.Whenshouldyouincludethestockandflowstructure,andwhencan

youomitit?Generally,youshouldincludestockandflowstructuresrepresentlng physicalprocesses,delays,Orstockswhosebehaviorisimportantinthedynamics youseektoexplain･Forexample,considertheflowofaproductthroughasupply chainfromproducertoconsumer.Theproducttravelsthroughanetworkofstocks (inventories)andflows(shipmentanddeliveryrates).Thestockandflowrepre- sentationforthisprocessisshowninthetoppanelofFigure6-10.

Productionstartsaddtothestockofworkinprocess(WIP)Inventory.The ProductionCompletionRatereducesthestockofWIPandincreasesthestockof

Chapter6 StocksandFlows

FIGURE6･10 Stockandflowvs.Causaldiagramrepresentations

StockandRowRepresentationofaManufacturingProcess

Production StartRate

Wor.kin Process

lnventory Production

Completion Rate

Finished

lnventory Shipment

Rate

211

CausalLoopDiagramRepresentationoftheManufacturingProcess

/一一1-､TAL' ふ一 -~--- ､ ./一一一･-五二g 一一･一＼ー Production Workin Production Finished Shipment StartRate Process Completion hventory Rate

lnventory Rate

FinishedInventory.ShipmentstocustomersdepleteFinishedInventory.EqulV a-

1ently,thestockofWIPaccumulatesproductionstartslesscompletions,andthe stockoffinishedinventoryaccumulatesproductioncompletionslessshipments.

ThecausaldiagramrepresentationisshowninthebottompanelofFigure 6-10･Whiletechnicallycorrect,thecausaldiagrammakesithardtoseethephysi- calflowofproductthroughthesystemandtheconservationofmaterialinthe stockandflowchain.Itisoftenconfusingtointerpretthepolaritiesofthecausal linkswhentheyInvolvestocksandflows.AnincreaseintheProductionComple- tionRatecausesFinishedlnventorytoriseabovewhatitwouldhavebeenother- wise(itrisesatafasterrate),hencethepolarityofthelinkispositive.Adecrease inproductioncompletions,however,doesnotcausefinishedinventorytofall. Rather,adecreaseintheproductioncompletionratecausesfinishedinventoryto belessthanitwouldhavebeen.Youcannotsaywhetherfinishedinventorywillbe rislngOrfallingbasedonthebehavioroftheproductionratealone.Inventorywill

riseonlywhenproductioncompletionsexceedtheshipmentrate;thatis,inventory risesonlywhenweaddtoitfasterthanweremoveunitsfromit.Youneedtoknow thevaluesofalltheflowsaffectingastocktodetermineitsbehavior.Richardson (1986a,1997)carefullydocumentsthepitfallsofcausaldiagrams,mostofwhich involvethefailureofcausaldiagramstoshowthestock/flowdistinction.

Add的1gStockP.ndFlowStructuretoCausalD妻agrams

Considerthecausalloopdiagramsinchapter5･Foreach,redrawthediagram showingtheimportantstockandflOwstructurealongwiththefeedbackstructure showninthediagram.Inparticular,identifythemainstocksandflOwsinthefoil lowlngCOnCeptualizationcasestudiespresentedinchapter5:

212 PartIITbolsfわrSystemsThinking

1.Theworkloadmanagementexample.

2.Theoilindustryandhorseraclngexamples.

3.Thetrafficcongestionexample.

heachcase,considerwhethertheexplicitrepresentationofthemainstocksand

flowsenhancesyourabilitytounderstandthedynamicsofthesystemormerely clutters血ediagram.

LinkさngStet:汰andFlowS号ructurey･̂/軸 Fee軸tlCk

OftenunderstandingthedynamicsofasystemrequlreSlinkingthefeedbackloop structurewiththestockandflowstructure.Asanexample,considerthegasoline

shortagesofthe1970sJn1979theUnitedStates(andsomeotherindustrialized nations)experiencedaseveregasolineshortage.Iran'sexportsofoildroppedin thewakeoftherevolutionthere,andpetroleumprlCeSOntheworldmarketin- creasedsharply.Withinweeks,ashortageofgasolinebegan･Someservicestations foundtheirtanksemptiedbeforethenextdelivery.Drivers,rememberingthefirst oilembargoin1973andworriedthattheywouldn'tbeabletogetgas,begantotop offtheirtanks,insteadoffillinguponlywhenthegasgaugefelltowardempty･ Soon,longlinesofcarswereseenidlinginfrontofgasstations,andHSorry-No Gas"SignssproutedalongthehighwaysofAmericaasstationafterstationfound itsundergroundtankspumpeddry.Theshortagewasthetopstoryontheevenlng news-aerialfootageofcarslineduparoundtheblock,close-upsof"NoGas" slgnS,andinterviewswithanxiousdriversdominatedthenews･Insomestates, mandatoryrationlngWasimposed,includinglimltlngPurchasesto,forexample,no morethan$10worthofgas.Californiaimposedodd/evenpurchaserules:Drivers wereallowedtobuygasonlyeveryotherday,basedonwhethertheirlicenseplate numberwasoddoreven.Itseemed血atthesupplyofgasolinehadbeenslashed･

Curiously,theimpactoftheIranianrevolutionontheflowofoiltotheUSwas small.True,USoilimportsfromthePersianGulf(includingIran)fellby500,000

barrelsperdaybetween1978and1979,about3%ofUSconsumption,butimports fromothernationsincreasedby640,000barrelsperday,soimportsin1979actu- allylnCreaSedby140,000barrelsperday･Domesticproductionfellby150,000

barrelsperday,sototalsupplywasessentiallyconstant,whileconsumptionfellby about330,000barrelsperday,adropof2%from1978.Plainly,fortheyearasa whole,therewasnoshortage.ButiftheIlowofoilintotheUSwasessentially constant,whatcausedtheshortage?Wheredidthegasgo?

First,developastockandflowmapforthegasolinedistributionsystem･You neednotconsidertheentiresupplychainforgasolinebutcanfocusonretaildis- tribution.YourdiagramshouldbeginwiththeflOwofgasolinetoservicestations, thenrepresentthestockandflOwstructureforitssubsequentstorage,sale,and eventualcombustion.

Onceyou'vemappedthestockandflowstructure,identifytheinformationin-

putstotheratesofflowinyourdiagram･Assumethattherateatwhichgasolineis deliveredtoservicestationsisexogenous.ByidentifyingtheinformationinputstO

Chapter6 StocksandFlows 213

theflowsinyourstockandflowmap,youwillbecloslngsomefeedbackloops, loopswhichshouldhelpexplainwhytheshortageoccurredandanswertheques- tion,Wheredidthegasgo?Besuretoaskhowindividualdriverswouldlearn abouttheshortageandwhattheirbehaviorwouldthenbe.

Finally,uslngyourdiagram,assessthelikelyeffectivenessofthemaximum purchaseandodd/evenpolicies.Dopoliciesofthistypehelpeasetheshortageor makeitworse?Why?Whatpolicywouldyourecommendtoeasetheshortage? Explainwhyyouthinkyourpolicywouldbeeffectiveintermsofthestock/flow andfeedbackstructureofthesystem.

6.3.2 AggregatiQn喜nStockandFlowMappir!g

Theabilitytomapthestocksandflowsinasystemiscriticaltoeffectivemodel- ing.Usuallyitiswisetoidentifythemainstocksinasystemandthentheflows thatalterthosestocks.Youmustselectanapproprlatelevelofaggregationand boundaryforthesestockandflowmaps.Thelevelofaggregationreferstothe numberofinternalcategoriesorstocksrepresented.Theboundaryreferstohow farupstreamanddownstreamonechoosestorepresenttheflOwsofmaterialsand otherquantitiesinthemodel.

Toillustrate,considerthemanufacturingProcessdiscussedaboveinwhich materialflOwsfromproductionstartsthroughWIPinventorytofinishedinventory andfinallyshipmenttothecustomer.Allthevariousparts,components,andsub- assembliesareaggregatedtogetherintoasinglestockofWIP･Andthoughthefirm maycarrytensofthousandsofSKUs(stockkeepingunits),theseindividualitems areallaggregatedintoasinglestockoffinishedinventory.Formanypurposesthe aggregatepictureissufficient.However,themodelpurposemightrequiremorede- tail.Ifthepurposeinvolvedacloserlookatthemanufacturlngprocess,youCOuld disaggregatethestockofworkinprocessseriallytorepresentthedifferentstages, suchaspartfabrication,assembly,andtesting(Figure6-11)･

Thesumofthethreeintermediatestocksisthetotalworkinprocessinventory, butnowthemodeltracksthroughputatafinerlevelofresolutionandcanrepresent morepotentialbottlenecksintheproductionprocess.Notethatinboththeorlglnal, aggregatediagramandinthismoredetaileddiagramthereisnoprovisionforre- workorscrap.Allunitsstartedareeventuallycompleted-theflowofwidgets throughthesystemisconserved.Notealsothatasmaterialflowsthroughthesys-

temitistransformedfrompartstofinishedproduct.Tomaintainconsistentunits ofmeasurewemightmeasurepartsinwidgetequlValents-thatis,awidget's worthofparts.Ifnecessaryforthepurpose,youcanfurtherdisaggregatethestock andflowstructure.

ModifyingStockandFIowMaps

1.ModifythediagraminFigure6-lltorepresentthecasewhereunitsthatfail testlngareSCrapped.

2.Modifyyourdiagramtorepresentthecasewhereitemsfailingtestlngare returnedtoassemblyforrework.

214

FlGURE6111

Disaggregated stockandffow

mapfora manufacturing Process

PartII ToolsforSystemsThinking

Chapter6 StocksandFlows 215

attheplantyouaremodelingactuallyrequiresSeveraloperations:welding,grind-

1ng,andpaintlng.Observationofthegrindingoperationrevealsthatworkersdraw

partsreadyforgrindingfromabuffergeneratedbytheweldingoperation.When

grindinglSCOmpleted,thepartsareplacedinabinwhichthengoesontothenext

operation(painting)･Theweldingandpaintshopsaresimilar.Drawthedisaggre一

gatedstockandflOwmapforthepartfabricationsteptoshowthewelding,grind-

1ng,andpalntlngoperationsexplicitly.

Uptonowthediscussionhasfocusedonserialdisaggregation:howfinelyto breakdownthestagesofprocesslng.Throughout,themanydifferentpartsand

productsproducedbyatyplCalfirmareaggregatedintoaslnglechainofstocks

andflows.Inmanysituationstheprocessoccursnotonlyinseriesbutalsoin-

volvesparallelactivities.Youcouldofcoursereplicatethemainstockandflow

chainforeachproduct(manysimulationsoftwarepackagessupportarraystru c-

turesfわrthispurpose)｡Whentherearemultiple,parallelactivitiesyoumustmake

adecisionnotonlyaboutthenumberofstagesoftheprocesstorepresentbutalso

howmuchtoaggregatethedifferentparallelprocessestogether.Forexample,the

assemblyprocessforautomobilesinvolvesintegratlngthechassisandenglne.

Eachsubassemblyisbuiltonaseparateline,ofteninplantsfarfromthefinalas-

semblypolnt･Supposetheclientarguesthatyoucan'taggregateallsubcompo-

nentsintoaslngleflowofparts,butmustseparatechassisandenginefabrication

(omitthebodyforsimplicity).ThestockandflOwmapfortheassemblyprocess

mightbeshownasinFigure6-12.

Therearenowthreedistinctstockandflowchains,oneeachforenglneS,ChasI

sis,andassembledcars.Becausethethreechainsareseparate,eachcanbemea-

suredindifferentunits:englneS,Chassis,andcars.Thethreechainsarelinked

becauseeachcarbeginnlngthefinalassemblyprocessrequlreSOneenginefrom

thestockofcompletedenglneSandonechassisfromthestockofcompletedchas-

sis.Theinformationarrowsfromtheassemblyratetotheengineandchassisuse

ratesshowtheselinks.ThenumberofenglneSandchassisavailablealsodetemine

themaximumassemblystartrate,whichinturnconstrainsactualassemblystarts:

Ifeithercomponentbufferfallstozero,assemblymustcease.2Theselinks(not

shown)definetwobalancingfeedbacksthatregulatetheoutflowsfromthestocks

ofcomponentsandcouplethestockandflOwnetworks･Thediagramdoesnotrep-

resentmanyotherinformationflowsthatmustexistinthesystem(suchasthede-

terminantsofthechassisstartandcompletionrates);tryaddingthesetothemap.

Youcouldofcoursecontinuetodisaggregate.Theprocesscanbebrokendown

intomoresteps:Thepaintprocess,forexample,actuallyconsistsofmultiple

activitiesseparatedbybufferssuchaspartpreparation(solventbath),drying,

spraylngthefirstcoat,dryingintheoven,sprayingthesecondcoat,drying,and

soon,withvariousinspectionsalongtheway･Youcouldalsocontinuetheparallel

disaggregationbysplittlngtheenglneOrChassisassemblyprocessesintotheir

2FirmscanSometimesbuildincompleteunitsandaddthemisslngCOmPOnentSlater･Whena 1997Strikeshutdownacriticalsupplier,FordcontinuedtoassembleitspopularExplorer,storlng thenearlycompletedcarsuntilthemissingpartsbecameavailableandcouldberetrofitted(try modifyingthediagraminFigure6-12toaccommodatesuchretrofitting).

216 PartIIToolsforSystemsThinking

FlGURE 6 -12 Disaggre g ating para‖elactivities

Enginesin Process

Chassisin Process

Comp一eted Engines

Comp一ete d

Chassis

A ssembEies inProcess

Chassis Chassis

Comp一etion Use Rate Rate

Assembly Completlron

Rate

subassemblies.Inthelimiteachandeverypartandoperationwouldberepresented separately.Obviouslysuchamodelwouldbejustascomplexastherealsystem,at leastashardtounderstand,andquiteuseless.

Whereshouldyoustop?Howmuchdetailisnecessary?Thisisalwaysamat-

terofjudgmenttobemadebyconsideringthemodelpurposeandtheneedsofthe client.Ifthepurposeisrepresentlngthelaglntheresponseofthemanufacturlng systemtochangesindemandaspartofalargermodeloffirmstrategy,thesimpler representationisprobablyfine.IfyouseektoreenglneertheflOwofmaterial

throughtheproductionline,amoredetailedrepresentationisrequired.Itisbetter tostartwithahigh-level,aggregaterepresentationandadddetailifneededtoad-

dressthepurpose.BeginnlngWithdetailedprocessmapso氏enleadstoparalysis duetotheircomplexity,datarequlrementS,andrapidobsolescencerates.Theag一 gregatemapshowingonlyproductionstarts,WIP,production,andfinishedinven-

torylSqulteStableandremainsapproprlateevenaSthedetailsoftheproduction processchange,whileadetailedmapmaybecomeobsoleteasnewproducts,tooレ lag,Orprocesstechnologiesareintroduced.

6.乱3 Guide日ines菅orAgg帽ga抽 m

WhenisitappropriatetOaggregatedifferentactivitiestogether?Todetermine whetheractivitiestakingplaceseriallycanbeaggregated,considertheaverage

residencetimeofitemsineachstock(theaveragetimebetweenenteringandexit- ingthestock).Stockswithshortresidencetimesrelativetothetimescaleforthe

Chapter6 StocksandFlows 217

dynamicsofinterestgenerallydonotneedtoberepresentedexplicitlyandcaneL

therbeomittedorlumpedintoadjacentstocks.Forexample,inthelong-term plan-

nlngmodelsoftheUSenergysystemdevelopedbytheUSDepartmentofEnergy

(Naill1992),variousstocksofundiscoveredpetroleumandknownreservesare

explicitlyrepresentedbecausetheirlifetimesrangefromyearstodecades(atcur-

rentproductionrates).However,stocksofcrudeoilandrefinedproductsinthepe-

troleumsupplychainrepresentonlyafewmonthsofconsumptlOn.Inalong-term

modelthesestocksaretooshort-livedtorequlreexplicittreatment.Theyfluctuate

aroundtheirequilibriumvaluesasproducers,refiners,anddistributorsreactto

changesininventory.Inamodelofshort-term movementsinspotpetroleum

prices,however,thesestocksarecriticallyimportant.Agoodmodelwouldrepre-

sentthekeystocksinthepetroleumsupplychainexplicitly,perhapseveninclud-

1ngaSeparateStockfortheinventoryofgasolineatretailservicestationsandthe

inventoryofgasolineinthetanksofcarsontheroad.Ontheotherhand,ashort-

termspotprlCemodelneednotincludepetroleumreservesorundiscoveredre-

sources,asthesestockschangetooslowlytoinfluencethespotmarketoveratime

horizonofayear.

Parallelactivitiescanlegltimatelybeaggregatedtogetheriftheindividual

flowsaregovernedbysimilardecisionrulesandifthetimethedifferentitems

spendintheindividualstocksissimilar.Forexample,itisoftenapproprlatetOag一

gregatethemanypartsrequiredtomanufactureaproductintoasmallnumberof

categoriessincetheyareusuallyorderedusingthesameproceduresandtheirde-

liveryleadtimesandresidencetimesinpartsinventoriesgenerallydon'tdiffertoo

much.Incontrast,plantandequlPmentsometimesmustbedisaggregated.Their

lifetimesareverydifferent,andthedecisionrulesfornewgreen-fieldfacilitiesdif-

fersubstantiallyfromthoseusedtc･orderequlPmentforexistingfacilitiesdueto

differencesinleadtimes,costs,financlng,Permittlng,andregulatoryIssues.

Asaruleofthumb,Clientsgenerallywanttoseemoredetailinamodelthan

themodelerthinksisneeded,andmodelers,inturn,generallyoverestimatethede-

tailnecessarytocapturethedynamicsofinterest･Ofcourse,theamountofdetail

neededtocapturethedynamicsrelevanttotheclient'spurposeand也eamountof

detailneededtogivetheclientconfidenceintheresultsaretwodifferentthings.

Roberts(1977/1978)estimatedthatclientsoftenrequiretwiceasmuchdetailasthe

modelerfeelsisneededtofeelcomfortablewithandacceptamodelasabasisfor

action,andinmyexperiencethisisoftenanunderestimate･SuccessrequlreSyou

toincludethedetailnecessarytosatisfytheclient.Butthisdoesnotmeanyou

shouldacquleSCetOallclientdemandsformoredetail-youwillendupwithan

expensiveanduselessblackbox,Youmustworkwiththeclienttounderstandwhy

excessivedetailisoftenunnecessary.Often,modelsendupwithtoomuchdetail,

butastheclientgalnSCOnfidenceandunderstandingoftheimportantfeedbacks

drivlngthedynamics,theexcessstructurecanbeeliminated,resultinglnaSimpler,

moreeasilymaintained,andmoreusefulmodel(Ran°ers1980).Still,Robertsis

correct.A"Youmustprovidethelevelofdetailthatcausesltheclient]tobeper-

suadedthatyouhaveproperlytakenintoaccounthisissues,hisquestions,hislevel

ofconcerns.Otherwisehewillnotbelievethemodelyouhavebuilt,hewillnotac-

ceptit,andhewillnotuseit"(p･80)･

218 PartIIToolsforSystemsThinking

6.3.4 SystemLlynarnics岳nAct喜on:

Mode抽gLarge-Sca!eConstructionProjec官s

Aggregationofmultipleserialandparallelactivitiesiswellillustratedinamodel oflargeconstructionprqjectsdevelopedbyJackHomer(Homeretal.1993).The clientwasamultinationalforestproductscompany,Specificallythedivisionofthe

companythatdesignsandbuildspulpandpapermills.Competitionforthesmall numberofmillsbuilteachyearwasintensifyingastheindustryglobalized,andthe

firm,alreadyaleader,sawthattoremainstrongtheyhadtodramaticallyreduce thetimerequiredtodesignandbuildmills.Theirgoalwastoreducesignificantly thetotalcycletime,fromthehandshakewithacustomertothehandoffofawork- 1ngmill,withoutincreasingcosts.TheyknewtraditionalprojectmanagementteCh- nlqueSWerenotadequate:thedesignandconstructionprocessisexceedingly complex,withtightcouplingsamongthephases,andtheyhadalreadydoneallthe easythings.Theydecidedtodevelopasystemdynamicsmodeloftheentireengi- neering,procurement,andconstruction(EPC)process･

EarlymeetingsOftheprojectteamfocusedonthemodelboundaryandaggre- gation,inparticular,descrlPtlOnSOfthestockandflowstructureofatypicalpro- ject.ManyIssuesWereraised:Isthereatypicalproject?Howmuchdetailis needed?Whatactivitiescouldbeaggregatedtogether?Onememberoftheclient teamarguedthatthemodelcouldn'tbeusefulifitdidnフtrepresenteveryenglneer- 1ngdrawlng,everypurchaseorder,andeverycomponentinstalledatthesite.Ob- viously,suchamodelcouldneverbebuiltormadeuseful.Othermembersofthe clientteamarguedforasimplerapproach.Theyalreadyhadhighlydisaggregate schedulingandplannlngmodelsbasedontraditionalprojectmanagementtoolsto managethedetailcomplexityoftheprojects.Theylackedatooltomanagethedy- namiccomplexltyandinterdependenciesamongthephasesandactivitiesofthe PrOJeCtS･

Afterextensivediscussion,aninitialmodelboundaryandlevelofaggregation wereset(Figure6113).Thefigureisahigh-levelsubsystemdiagramshowinghow projectsWereaggregatedintoareasonablenumberofphases.Theoverallproject wasdividedintotwomainstockandflowchainsrepresentingP&E(processand equipment)andconstruction.Eachactivitygoesthroughdesignpreparation,re- view,anddesignrevisions.Nextsuppliersareselectedandpurchaseordersareis-

sued.Thesuppliersthenfabricatethematerialsneededforeachactivlty･Onthe constructionside,theclientfeltitwasacceptabletoaggregateallconstructionma-

terials(e.蛋.,structuralsteel,concreteforms,rebar)intoasinglecategory.The

processandequlpmentSide,however,wasdividedintothreecategories:reactor vessels,majorequipment(e.g.,largetanks,pipelines,andconveyors),andminor equipment(e.蛋.,pumps,motors,valves,andinstrumentation).Thedesign,pro- curement,andconstructionofthesetypesofequipmentareSufficientlydifferentin

scope,duration,andcostthattheycouldnotreasonablybelumpedtogether.The reactorvessels,inparticular,hadtobemodeledinmoredetailastheyarethe

largestsubassembly,almostalwaysfallonthecriticalpath,andarefrequentlya

bottleneckconstrainlngCOnStruCtionprogress.Duringconstruction,reactorves-

sels,otherequlpment,andsitepreparationsuchasfoundationsandgradingall

Chapter6 StocksandFlows 219

FIGURE6-13 Buildingapulpandpapermill

Subsystemdiagramshowrngflowsofenglneenng,Procurement,andconstructionworkinamodelof

apulpm‖constructionproject.ThediagramiHustratesthesectorboundariesandlevelofaggregation

withoutshowlngalldetails.EachblockrepresentsaproJeCtPhase,modeledwithagenericmodulewith

roughlythesamestructure.Aninternalgatecapturestheconstraintsonworkavailablewithinaphase asafunctionoftheworkcompleted.Forexample,foundationscannotbecompleteduntilsurveylng

andsitepreparationaredone;Seesection14.5.

Source:Homeretal.(1993).

mustcometogether,followedbyafunctionalitycheckout,start-upand,finally, handofFtothecustomer.

EachblockinFigure6-13representsaprojectPhase･Themodelconsistedof

agenericprojectPhasemodule,replicatedforeachblockandlinkedasshown･

Eachmodulecontainedastockandflow structureincludingtheflowsoftasks

withinthephasealongwithscheduleddeadlines,thelaborforcededicatedtothe

220

F]GURE6-14 Stockandflow structureoftasks

inaprojectphase

Simplifiedrepre- sentationofthe stockand刊Ow structureofa

phaseinthepulp millprojectmodel Determinantsof theflowsandcou-

pllngSamongthe differentphases arenotshown.

PartIIToolsforSystemsThinking

phase,workerproductivlty,fatiguelevels,elTOrrates,andcosts.Thestockand flowstructurefortaskswithinaphasemodelstheprogressionoftasksfrombase- workthroughcompletion(Figure6-14)Jngeneralthetaskstobecompletedina phasecanonlybedoneasupstreamtasksuponwhichtheydependarecompleted (therateatwhichbaseworktasksbecomeavailable).Forexample,thereactorvesI selscannotbeerectedonsiteuntiltheirfoundationsarecompleted.Likewise,not alltaskswithinaglVenphasecanbedoneconcurrently.Forexample,thedetailed designofconveyorsandpipelinesbetweenthec血ippers,reactorvessels,andpaper machinescannotbedoneuntilthehigh-levelphysicaldesignoftheplantiscom- pleted･Thesewithin-andbetween-phasedependenciesweremodeledexplicitly･ Theflowofworkfromthestockoftasksawaltlngcompletiontothestockoftasks requlnngreWOrkrepresentsthosetaskscompletedincorrectlyorrenderedobsolete bychangesinothersubsystems･Generally,errorsarenotdetectedi- ediatelyand thedelayinthediscoveryofreworkcanbesubstantial,aswhenadesignerroris notdetecteduntilconstructioninthefieldisunderway.Thediscoveryofrework movestasksthoughttobecompletebackintothestockoftasksawaltlngCOmple- tion(seeFordandSterman1998bforadetailedandfullydocumentedmodelofa multiphaseprqectsimilartotheoneusedhere;seealsotheshipbuildingprq】ect modeldescribedinsection2.3).

Themodelwassubstantiallysimplerthantheclientfirm'sdetailedproject planningmodel,whichincludedliterallythousandsofindividualactivities(high detailcomplexity)butnofeedbackloops(nodynamiccomplexity).Itwasdisag- gregatedenoughtocaptureimportantinterdependenciesamongdesign,procure- ment,andconstructionactivitiesandbetweenconstructionandthevarioustypesof

Chapter6 StocksandFlows 221

equlpment.Themodelcouldcaptureshiftsinthecriticalpaththatmightresult

frompoliciesacceleratingthefabricationofthereactorvessels,apolicyfavoredby someclientteammembers.

Itisimportanttonotethattheprocessofdeveloplngthefinallevelofaggre-

gationinvolvedanumberofiterationsandrevisions.Andthoughthemodelrepre-

sentstheprojectatahighlevelofaggregation,themodelingteamdevelopedmany

moredetaileddiagrams.Thesemoredetailedmapshelpedthemodelerandclient

teamdiscoverflawsintheirthinking,estimateparametersbetter,anddeepentheir

understandingoftheprocess.Andtheydevelopedconfidencethatthemoreaggre-

gaterepresentationinthesimulationmodelwasacceptablefわrtheirpurposeso

thesemoredetailedstockandflOwstructuresdidnothavetobeincorporatedinto themodel.

ThelevelofdetailselectedalsopermittedthemodeltobecalibratedagalnSta

widerangeofdatacollectedononeofthecompany'scurrentEPCprojects.The

modelsuccessfully(thatis,tothesatisfactionoftheclient)reproducedallrelevant

projectactivities,includingthevariousworkforcesandlaborhours,overtimeand

reworkrates,purchaseordervolumesandrevisionrates,vendorshipments,andthe

progressofvesselerectionandconstruction(Figure6-15showsanexample).

Whiletheclientsprefernottodisclosethedetailsofpolicyrecommendations,

theyviewedthemodelascredibleandusefulanddevelopedconfidence,shared

amongtheteam,thatthemodeldidagoodjobofrepresentingtheirEPCprojects.

Theyusedthemodeltoanalyzemanypoliciesandidentifiedseveralwhich,while

previouslyappearlngtObedesirable,infactgeneratedharmfulsideeffects.The

modelalsohelpedidentifypoliciesthatreducedprojectdeliverytlmeSbyatleast

30%withinafewyears.Severalofthepolicieswerenotapparenttotheclientteam

orwerehotlydebatedpriortothemodelingeffort.Themodelingprocesshelped

buildunderstandingofandconsensusaroundthesecontroversialinitiatives,help-

lngthefirmsuccessfullyimplementmanyoftherecommendations.

F日GURE6-15 SamplecomparisonofhistoricalandsimulatedbehaviorofthepulpmiHmodel

P&E-processandequlPment.

Cum.P良EDesignLaborHours一一一一●一一一一 ____Actual

ゝ Simulated

0 20

Gum.ConstructionLaborHours

____ActLJal

孤- Simulated.♂

40 60 80 100 0 20 40 60 80 100

Timeunits Timeunits

Note:TimeFSexpressedastimeunitstoprotectclientconfidentialinformation. Source:Homeretal.(1993).

222 PartIITわolsforSystemsThinking

S.3.5 SettingtheMode一Boundary:

"ChaHengirfgtheC萱ouds"

MapplngthestockandflOwstructureofasysteminvolvesimportantdecisions

abouttheboundaryofthemodel･Inreality,flowsofmaterial,people,andmoney intoastockhavetocomefromsomewhere;theflowsouthavetogosomewhere. Tokeepyourmodelsmanageable,youmusttruncatethesechainsusingSources

andsinks,representedinthestockandflowmapsby"clouds";seeFigure611. Sourcesandsinksrepresentthestockssupplyingmaterialtoorabsorbingmaterial

fromthemodeledsystem･Sourcesandsinksareassumedtohaveinfinitecapacity andcanneverconstraintheflowstheysupport.Intherealworld,thestockssup- plyingorabsorbingmowshavefinitecapacltyanddoinfluencetheflows.When youtruncateastockandflOwchainwithacloudyouaresettingtheboundaryof themodel-stocksandflowsbeyondthispolntareIgnored;youexcludeallpossi- blefeedbacksfromorinteractionswiththestocksoutsidetheboundary.

AsamodeleryoumustcriticallyexaminetheseboundaryassumptlOnS;you must,inthewordsofBan'yRichmond(1993,p.132),"challengetheclouds."Isit approprlateforyourpurposetoexcludethestocksoutsidetheboundaryofthe model?Whatfeedbacksignoredbyyourmodelmightexistintherealworld,and mighttheyaffectyourpolicyrecommendations?CanthesourcesfortheflOwsbe depletedandconstraintheinflow?Canthesinksbefilledandblocktheoutflows, backingupthesystemlikeacloggeddrain?

Considertheautomobileindustry･Astockandflowmapforautomobilepro-

ductionmightbeginwithproductionstarts,WIPinventory,production,finishedin- ventory,andshipments(Figure6-16).Drawingthemapwithasourceforthe productionstartflOwpresumesthatthesupplyofpartsisunlimitedandcannever constraintheproductionstartrate.Likewise,becauseshipmentsflowtoasink,the modelerhasassumedstocksofproductinthehandsofdealersandcustomershave noeffectonshipments･Inchallengingthecloudsyouaskwhethertheseassump- tionsarereasonable.Fortheautoindustrytheyarenot.Productionstartsrequlre theautomakertohaveanadequatestockofparts.Yetpartsstocksmayeasilybe depleted.Supplierscannotrespondinstantlytochangesinpartsorders.Largeor- dersmayoutstripSuppliercapaclty,leadingtoshortages･Astrikeatasuppliermay interrupttheflowofpartstothefirm.Attheotherend,Shipmentsofnewcarsto dealersdependonthesizeofdealerstocks.Dealersgenerallytrytomaintainabout 40to60daysofinventoryontheirlots;thisisenoughtoprovidegoodselectionfor

consumerswithoutcarrylngexcessiveandcostlyInventory.Ifstocksarelowrela- tivetotheirtargets,dealersordermorefromthemanufacturers;ifstocksarehigh,

theycutback.Figure6-17expandsthemodelboundarytocapturetheseeffects. Themodelnowrepresentsthreedistinctorganizationalentities-Suppliers,manu- facturers,anddealers.Theinventoryofpartsheldbythemanufacturerisnowex- plicit.Thesupplierhasthesamebasicstructureastheautomaker:astockof finishedinventoryandastockofworkinprocess.Attheshipmentend,manufac- turershipmentsnolongerdisappearintoasinkbutflowintodealerstocks,allowl lngyoutOmodelthepurchaserateasafunctionofthedealerinventoryandsales tocustomers.

FlGURE6･16 Initialstockand

flowmapfor theautomobi一e

industry,showlng themodel

boundary

Thesourcesand sinksforthe

flowsthrough thesystemare assumedtobe infiniteandcan

havenoimpacton thedynamics･

Chapter6 StocksandFlows

Source.･ Unlimited

supplyof ヽ

223

Absorption J Capacity

Youcouldandshouldcontinuetochallengetheboundaryofthemodel.The

modelnowallowsyoutorepresentsupplierorderprocesslng,Inventorymanage- ment,anddelivery,includingthepossibilitythatsupplierscanbecomeabottleneck

andstarveautomobileproduction･Butnowthesuppliersareassumedtohaveun- limitedpartsandrawmaterialsavailability.Isthisappropriate?Itdependsonthe modelpurpose.Youcouldcontinuetoexpandthemodelboundarybyaddingthe

supplierstothesuppliers,andtheirsuppliers,andsoon,untilyoureachedthepoint whereitisacceptabletoassumethatthesupplyofmaterialstothefarthestup- streamsupplierisunlimited.Altematively,yotlCOuldrepresenttheentireupstream supplychainbyaslngleaggregatesupplierstage.

ThemapshowninFigure6117alsoassumesthatdealersalesflOwintoasink sothereisnofeedbackfromthestockofcarsontheroadtopurchasesofnewcars.

ThisisobviouslyabadassumptlOn:Salesofnewcarsdependonthenumberand

ageofthecarspeoplealreadyhaverelativetotheirneeds･Peoplewhohavejustac- quiredanewcarareunlikelytobuyanotherforseveralyears,untiltheirloanis

paidoff,theirleaseexpires,Ortheircarisinvolvedinanaccidentandmustbere- placed(Seesection2.2).Figure6-18expandsthedownstreamendofthestockand flowmaptoincludethestockofcarsontheroad.

Youcancontinuetochallengethemodelboundary.Whathappenstothe

carswhentheyarescrapped?Inthecurrentmap,theysimplydisappear.Inreality, theydon't.InNorthAmericasome10to12millionvehiclesarescrappedper year.Roughly94%areshreddedandthesteelandsomenonferrousmetalsare

224

FdGURE6-17 Challengmgthe c一ouds

Addingasuppller anddea一ersector tothestockand flowchainfor

automobilepro- duction.Rectan一

g】eswithrounded cornersdenote theboundaries betweendifferent

organizationalen- titiesanddecision-

makingunits.

PartII¶)olsforSystemsThlnking

Supplier Seetor

Manufacturer Sector

Dealer Seetor

recovered,Oneofthehighestrecyclingfractionsofanyindustry･However,some

carsendupabandonedasdangerouseyesoresonthesideoftheroad･Andmuchof theplastic,glass,andothernonmetalmaterialsendupinlandfills,constitutlnga significantsourceofpollution(morethantwobilliondiscardedtires,mostsitting

inhugepilesacrossthecountry,havealreadyaccumulatedintheUS)･

Chapter6 StocksandFlows

FIGURE6-18 Expanded automobilemodel

Theboundarynow includesthestock ofcarsonthe road,whichfeeds backtoinf.uence salesofnewcars.

peaJer Seetor

Household Sector

225

6ど3,6 SystemDynamicsinAction二

AutomobHeReeyeI!j咽

Bythemid1990S,aslandfillsfilledandenvironmentalawarenessgrew,pressure builttorecyclemoreofthematerialincars.Germanydebatedalawthatwouldre-

quireautomanufacturerstotakebacktheiroldcarswhenpeopledereglStered

them.Pushedbytheseforces,theautoindustry,firstinEuropeandthenintheUS, begantostudywaystoincreasetherecoveryofpartsandtherecyclingofmateri- alsfromcars.

PavelZamudio-Ramirez(1996)modeledpartrecoveryandthematerialsrecy-

clinglntheUSautoindustrytohelptheindustrythinkaboutafutureofenhanced

autorecycling.Figure6-19Showsasimplifiedstockandnowstructureadapted fromthemodel.Oldorwreckedcarscaneitherbescrappedlegally(soldtoajunk-

yardordismantler)orillegallyabandoned.Thestockofabandoned,oftenburned-

out,carsisablightonthelandscapeandsignificantsourceofpollution.Thereare twooutflowsfromthestockofillegallyabandonedcars:Dismantlerswillprocess themifthevalueoftherecoverablepartsandmaterialsishighenough.Alterna-

tively,illegallydumpedcarscanbecollected(saybylocalgovemments)andtaken toshreddersforproperdisposal.Boththeseflowsarerelativelysmall,sothestock ofabandonedcarscanbuilduptohighlevelseveniftheabandonmentrateislow.

Carsheldinthedismantlers'inventoriesarestrlppedofthosepartswhose

valueexceeds血ecostofrecovery.Thesepartsenterausedpartsstockandare

thensoldtorepairshopsandusedtoreplacewonordamagedpartsonoperatlng cars･Inthismap,thepartusagerateflowsintoasink･Inactuality,thesepartsare installedincarsstillontheroadandeventuallyflowagainthroughthescrapor abandonmentrate.Sincethenumberofrecoveredpartsisverysmallrelativetothe

totalflowofmaterialsthroughthesystem,thisomissionisprobablyreasonable･

226 PartIIToolsforSystemsTllinking

FIGURE6･19 Stockandflowmapforamodelofautomobilerecycling

Thestockandflowstructureforthedevelopmentofnewvehiclep一atforms,definlngthemassand materialscompositionofcarsancHevelofdesignfordisassembly,[Snotshown.Themodelincludesa para"elstockandflowstructure(co-flow)trackingeachofthesepropertiesasvehiclesageandare eventuallyretired,dismantled,andshredded.Seechapter12.

Chapter6 StocksandFlows 227

Afterallpartsworthrecoveringareremoved,theguttedcar,nowcalledahulk, issoldtoashredder.Inthemid1990stherewereabout200ShreddersintheUS

whoprocessedroughly94%ofalldereglSteredcars･Aftershredding,thevaluable materials(principallysteelandsomenonferrousmetals)areseparatedoutforre- cycling.IftheprlCeSOftherecoveredmaterialsdon'tjustifythecost,Shredderscan

takehulksdirectlytoaland丘llandcuttheirpurchasesfromdismantlers.Whatre一 mainsaftershreddingandseparationisamixtureofplastics,glass,elastomers,and someunrecoveredmetalcalledautomotiveshredderresidue(ASR)or"fluff,"

whichisthenlandfmed.ASRisoneofthemajorenvironmentalconcernsgener- atedbythedisposalofoldcars.

Therecyclablematerialsaccumulateinaninventoryandareeventuallysoldto materialsprocessorssuchassteelmills.Theinventoryofrawmaterialsisthen

usedtomanufacturenewproducts,includingautomobiles,thushelpingtocreatea closedmaterialflOwandcuttingtheuseofnonrenewableresources.Asinthecase

ofparts,thematerialsusagerateflowsintoasinksincetheflowofrecoveredma- terialsrelativetothetotalflowofvirginmaterialsissmall.

Zamudio-Ramirez'smodelincludedarichfeedbackstructurerepresentlngthe behaviorofthevariousactorsinthesystem,includingtheautomakers,carowners, dismantlers,andshredders.Marketsforrecoveredmaterialswereexplicit.The

stockandflOwstructureforautosbeganatthedesignstagefornewmodelsand

platformsandtrackedkeypropertiesofthecarsincludingtheirmass,materials composition(ferrous,nonferrous,plastics),andthelevelofdesignfordisassembly builtintothedesign.Theseattributesweretrackedasthecarsembodyingthem

movedfromthedesignstagetomarket,age,andarethenretired,dismantled,and shredded.

Tbgathertherequireddata,Zamudio-Ramirezconductedinterviewswithvar- iousactors,includingcarmakers,dismantlers,shredders,andindustryanalystsand madeextensiveuseofvariousautoandrecyclingindustrydatabases.Someofthe

datarequired,suchasage-dependentscrapratesforcars,wererelativelyeasyto gather.Otherkeyparameterswerenot.Twocriticalrelationshipsinthemodelare

thesupplycurvesforrecoveredpartsandrecoveredmaterials･Thatis,howwillthe numberofpartsrecoveredbydismantlersvaryastheprlCetheycangetand也e costsofrecoveryv∬y?

Estimatlngthepartssupplycurveisadauntlngproblem.TheprlnClpalcostof

recoverylSthelabortimerequiredtoremoveapart･Butthetimerequiredtore- moveaglVenpartdependsonhowmanyotherpartsmustberemovedfirst.These precedencerelationshipsdependonthedesignof血ecarandthevalueofthein-

terveningparts(Cantheseatberippedoutquicklytogetatavaluablepartunderit ormustitberemovedcarefully?Shouldworkersgetatapartfrominfrontorbe- hind?).TbestimatetheserelationshipsZamudio-RamirezworkedattheVehicle

RecyclingPartnership,aconsortiumoftheliigThreeUSautomakers,dismantlers, andtherecyclingindustry.TheVehicleRecyclingPartnershipassembledacom- prehensivedatabaseofpartremovaltimesbycompletelydisassemblingavariety

oflatemodelcars.Zamudio-RamirezandhiscolleagueAndrewSpicerthende- velopedanoptimizationmodeltoestimatethesupplycurveforpartsrecoveryas

functionsofpartandmaterialsprlCeS,laborcosts,andthedesignofthevehicles･ Theoptlmizationmodeldeterminedthenumberofpartsworthrecoverlngand也e

228 PartIITわolsforSystemsThinking

optlmaldismantlingorderforanysetofprices,laborcosts,anddesignparame- ters-thesupplycurveforrecoveredparts.Theresultsoftheoptlmizationmodel werethenembeddedinthesimulationmodel.Asthedesignparametersforcars changeandtheremovaltimeforkeypartsfalls,theestimatedsupplycurvere- spondsbyrealisticallyincreaslngthenumberandtypesofpartsrecovered.

ThoughthestockandflowstructureinFigure6119issimplifiedanddoesnot showanyofthefeedbackstructuredeterminlngthevariousflowsfromthefull model,itillustratestheresponseoftheautomobileandmaterialsmarketstopoli- ciesdesignedtoincreaserecyclingofcars.

Firstconsidertheeffectofadesignfordisassembly(DFD)programdesigned toincreasethepartrecoveryrateandreducetheamountoffluffendinguplnland- fi11S･DFDcanreducethelaborcostofpartrecoverythroughbetterdesign,differ- entchoiceofpartfasteners,improvedselectionandlabelingofmaterials,andother techniques.Thefirsteffectis".nothing.Thereisalagofatleastseveralyearsbe- tweenthetimeanautomakerstartsaDFDprogramandthetimethefirstcarsde- slgnedtothosespecsrollofftheassemblyline.TheaveragecarintheUnited Statesstaysontheroadforaboutadecade,andnewcarshaveverylowscraprates (mostofthesearewrecksdeclaredtotallossesbyinsurancecompanies).Onlyaf- teradelayofmanyyearswillthestockofrecycling-readycarsbelargeenough andoldenoughforthemtoconstituteasignificantfractionofthescrappedcars purchasedbydismantlers.

Whatthenhappens?ManufacturersexpectedDFDwouldeventuallycause partandmaterialrecoverytorise,permanentlyreducingthenowofmaterialsto landfills.Instead,themodelsuggeststhenexteffectwillbeaglutofusedparts,as thepartrecoveryraterisesabovetheusedpartsusagerate.Aspartsinventories build,thepricedismantlerscangetforusedpartsfalls.Thenumberofpartsthat canbeeconomicallyrecovereddrops,andthedismantlingratedropsback.Prices continuetofalluntilthenumberofpartsrecoveredfallsenoughtobalancethe usedpartsusagerate.ThepartusageratemayrlSe,StimulatedbylowerprlCeS,but unlessthedemandforusedpartsishighlypriceelastic,thepartrecoveryratewill dropbackclosetoitsorlglnalratepriortODFD･Thedemandforusedpartsis likelytoberatherinsensitivetoprlCe.Automakersandthird-partyproducersofre- placementpartswillbereluctanttolosethelucrativepartsmarketandmaybeable toprohibittheuseofrecoveredpartsbyauthorizedservicecentersorforwarranty repalrSOrCOmpeteOnprlCeJfthedemandforusedpartsisinelastic,theprlnClpal effectofDFDmightsimplybetodepressthepriceOfusedparts,Offsettlngmost ofthebenefitofimproveddesign.

Nowconsidertheeffectofatrendtowardsmaller,lightercarswithsignifi- cantlyhigherplasticcontentandlesssteelandmetal.Suchchangesarepromoted toimprovealeleconomy,1nCreaSepartreCOVerability,anddecreasethequantltyOf fluffendinguplnlandfills.However,thestockandflOwstructuremaycausethe impactofsuchpoliciestobecountertotheirintent.TheautoindustrylSaSignifi- cantconsumerofsteel.Whennewcarsbegintouseless,therecoveryofsteel丘.om shreddingofoldhulkscontinuesatthepriorrate･ThepriceOfscrapmetalwillfall, reducingshredderprofitability.ThenumberofhulksshreddedandthequantltyOf

Chapter6 StocksandFlows 229

metalsrecoveredmayfall,andthevolumeoffluffdisposedinlandfillsmayactu- allyrise･Further,oncethescraprateofcarswithreducedsteelcontentincreases, shredderprofitcanfallfurther.Withlesssteelandnonferrouscontent,shredder revenueperhulkfalls,whilethefixedcostsofshreddingremainthesame.Zamu- dio-Ramirezfわundthatasustainedincreaseintheplasticcontentofcars,asex- pected,Wouldincreasethefractionofmaterialsrecoveredbydismantlers.Butcars withlessrecyclablemetalcouldalsodepresshulkpricesenoughtocutshredder pro恥 decreasetheshreddingrate,andactuallyincreasethenumberofabandoned carsandtheamountoffluffburiedinlandfills.

ThestockandflOwmaphelpsillustratethelongdelaysbetweenachangein thedesignofcarsandtheflowsofoldcarstolandfills,Bymakingthestocksofre- Coveredpartsandmaterialsexplicit,itiseasiertoseethatthereisimperfectcoor- dinationbetweeninflowsandoutflows,leadingtopotentialimbalancesand changesinprlCeS也atinvalidate血eassumptlOnSbehindrecyclingprograms･In- stitutionalstructuressuchasrequlrementSthatservicecentersusenewreplacement partscanoverwhelmthelogicofthemarket.Marketmechanisms,evenwhenpre- sent,arenotlikelytoworksmoothly,possiblyleadingtoinstabilityandineffi- ciency.Similardynamicshavealreadybeenobservedinthemarketforrecycled paper(Taylor1999).Supplysidestepstoincreaserecyclabilityalonearenotlikely tobeeffectiveunlessmatchedbypoliciestoincreasetheusageofrecoveredparts andmaterials･Thecollectionofrecyclablematerialsandtheactualrecyclingof thosematerialsaren't血esame仙ing.

6.4 SLBMMARY

Thischapterintroducedthestockandflowconcept.Stocksaccumulatetheirin- flowslesstheiroutflows.Stocksarethestatesofthesystemuponwhichdecisions andactionsarebased,arethesourceofinertiaandmemorylnSystems,Createde- 1ays,andgeneratedisequilibriumdynamicsbydecouplingratesofflow.Thedia- grammlngnotationforstocksandflOwscanbeusedwithawiderangeof audiencesandmakesiteasiertorelateacausaldiagramtothedynamicsofthesys- tem･Stocksaccumulate(integrate)theirinflowslesstheiroutflows.Equivalently, therateofchangeofastockisthetotalinflowlessthetotaloutflow.Thusastock andflowmapcorrespondsexactlytoasystemofintegralordifferentialequations. However,stockandflOwmapsaremucheasiertoworkwithandexplain.

Thereareseveralwaystoidentifythestocksinsystems.Inthesnapshottest youimaglnefreezingthesystematamomentoftime-themeasurablequantities (physical,informational,andpsychological)arethestocks,whileflowsarenotin- stantaneouslyobservableormeasurable.Unitsofmeasurecanalsohelpidentify stocksandflows.Ifastockismeasuredinunits,itsflOwsmustbemeasuredin

unitspertimeperiod. StocksexistlnglnSeriesinanetworkcanbeaggregatedtogetheriftheyare

short-livedrelativetothetimehorizonanddynamicsofinterest,Multipleparallel activitiescanbeaggregatedintoasinglestockandflownetworkiftheactivities aregovernedbysimilardecisionprocessesandutilizesimilarresourcesandifthe

230 PartII ToolsforSystemsThinking

residencetimesoftheitemsinthestocksissimilarenoughforthepurposeofyour model.

SourcesandsinksfortheflOwsinasystemhaveinfinitecapacity,unlike stocksintherealworld,andthusrepresenttheboundaryofthemodel.Modelers shouldalwayschallengetheseboundaryassumptlOnS,askingiftheassumptionOf infinitesupplyforsourcesandinfiniteabsorpt10nCapacityforsinksisapproprlate relativetothemodelpurpose.

i3ii{i3_畠主賓毒ぐ§!=:3ぎS極∈立至表現頭首呈ti笥~享

NaturelaughsatthedlHicultiesofintegration. -｣)ierre-SimondeLaplace(1749-1827)

ThesuccessesofthedlHerentialequationparadigmwereimpressiveand extensive.Manyproblems,includingbasicandimportantones,ledto equationsthatcouldbesolved.Apy10CeSSOfself-selectionsetin,whereby equationsthatcouldnotbesolvedwereautomaticallyoflessinterestthan thosethatcould.

-IanStewart(1989,p.39).

Chapter6introducedthestockandflOwconceptandtechniquesformapplngthe stockandflownetworksofsystems.Thischapterexploresthebehaviorofstocks andflows.Giventhedynamicsoftheflows,whatisthebehaviorofthestock? Fromthedynamicsofthestock,canyouinfTerthebehavioroftheflows?These tasksareequlValenttointegratingtheflowstoyieldthestockanddifferentiating thestocktoyielditsnetrateofchange.Forpeoplewhohaveneverstudiedcalcu-T√､ ius,theseconceptscanseemdaunting.lnfact,relatingthedynamicsofstocksand flowsisactuallyquiteintuitive;ltistheuseofunfamiliarnotationandafocuson analyticsolutionsthatdetersmanypeoplefromstudyofcalculus.

Whatifyouhaveastrongbackgroundincalculusanddifferentialequations? Itisgenerallynotpossibletosolveevensmallmodelsanalyticallyduetotheirhigh orderandnonlinearities,sothemathematicaltoolsmanypeoplehavestudiedare oflittledirectuse.Ifyouhavemoremathematicalbackgroundyouwillfindthis chapterstraightforwardbutshouldstilldothegraphicalintegrationexamplesand challengestobesureyourintuitiveunderstandinglSaSSOlidasyourtechnical

231

232 PartIIToolsforSystemsThinking

knowledge｡Modelers,nomatterhowgreatorsmalltheirtrainlnglnmathematics,

needtobeabletorelatethebehaviorofstocksandflowsintuitively,uslnggraPhi-

Calandothernonmathematicaltechniques.Thechapteralsoillustrateshowstock

andflOwdynamicsgiveinsightintotwoimportantpolicyissues:globalwarmlng andthewarondrugs.

7.1 RELAT10NS川PBETWEENSTOCKSANDFLOWS

Recallthebasicdefinitionsofstocksandflows:thenetrateofchangeofastockis thesumofallitsinflowslessthesumofallitsoutflows.Stocksaccumulatethenet

rateofchange.Mathematically,stocksintegratetheirnetflows;thenetflowisthe derivativeofthestock.

'll..虹1 S竜甜CandDynamicEqustS!tbF!'um

Astockisinequilibriumwhenitisunchanging(asystemisinequilibriumwhen allitsstocksareunchanging).Forastocktobeinequilibriumthenetrateof changemustbezero,implyingthetotalinflowISJustbalancedbythetotaloutflow.

Ifwaterdrainsoutofyourtubatexactlytherateitflowsin,thequantltyOfwater inthetubwillremainconstantandthetubisinequilibrium.Suchastateistermed

adynamicequilibriumsincethewaterinthetubisalwayschanging.Staticequl-

libriumariseswhenallflowsintoandoutofastockarezero.Herenotonlyisthe totalvolumeofwaterinthetubconstant,butthetubcontainsthesamewater,hour

afterhour.ThenumberofmembersoftheUSsenatehasbeenindynamicequilib-

riumsince1959whenHawallJOlnedtheunion:thetotalnumberofsenatorsre一

mainsconstantat100evenasthemembershipturnsover(albeitslowly).Thestock ofknownBachcantatasisinstaticequilibriumsinceweareunlikelytolosethe onesweknowof,theoddsofdiscoverlngPreviouslyunknowncantatasareremote, andBachcan'twriteanynewones.

7.1.2 CalculuswithoutMathematics

Tbunderstanddynamics,youmustbeabletorelatethebehaviorofthestocksand flowsinasystem.Giventheflowsintoastock,whatmustthebehaviorofthe

stockbe?Giventhebehaviorofthestock,whatmustthenetrateofchangehave been?Thesequestionsarethedomainofthecalculus.Calculusprovidesrulesto answerthesequestionsmathematicallyprovidedyoucancharacterizethebehavior ofthestocksorflowsasmathematicalfunctions.Calculusisoneofthemostbeau-

tifulandusefulbranchesofmathematicsbutonefartoofewhavestlJIdiedHfiappilyラ

theintuitionbehindtherelationshipbetweenstocksandflOwsisstraightforward anddoesnotrequlreanymathematicsJfyouareshownagraphofthebehaviorof

theflowsovertime,youcanalwaysinferthebehaviorofthestockThisprocessis knownasgraphicalintegration.Likewise,fromthetrajectoryOfthestockyoucan

alwaysinferitsnetrateofchange,aprocessknownasgraphicaldlHerentiation. Integrationanddifferentiationarethetwofundamentaloperationsinthecalculus.

Table711providesthedefinitionsgraphicallyandinplainlanguage.

Theamountaddedtoastockduringanytlmeintervalistheareaboundedby thecurvedefiningItsnetrateOfchange.Why?Considerthebathtubmetaphor

Chapter7 DynamicsofStocksandFlows

TABLE7-1 日ntegrationanddifferentiation:definitionsandexamples

233

Integration Differentiation

Stocksaccumulateorintegratetheirnetflow. ThequantityaddedtoastockoveranyinteⅣal istheareaboundedbythegraphofthenetrate betweenthestartandendoftheinteⅣal.The

finalvalueofthestockistheinitialvalueplusthe areaunderthenetratecurvebetweentheinitia一 andfina=jmes.

lntheexamplebelow,theva山eoHhestockat timetl-Sl.Addingtheareaunderthenetrate curvebetweentimestlandt2increasesthe stocktoS2.

(au J!lJSl!u n )

att2t] la N

0 2

･ー

(s l!u n )q 3 0

tl モ2

Theslopeofalinetangenttoanypointofthe trajectoryOfthestockequalsthenetrateof chan9eforthestockatthatpoint.Theslopeof thestocktrajectoryistheden'Vativeofthestockl

hltheexamplebelow,theslopeofthestock trajectoryattimetlisRl,SOthenetrateattl -

Rl.Attimet2,theslopeofthestockislarger,so thenetrateatt2-R2isgreaterthanRl.The stockrisesatanincreasmgrate,Sothenetrate ispositiveandincreaslng.

( a

∈!

l !

un )

a l

jl a

(sl!u n ) 羊 UO IS

again･Howmuchwaterisaddedtothetubinanytlmeinterval,suchasbetween

timetlandt2inTable7-1?Dividetheentireintervalintoanumberofsmallerseg-

ments,eachsmallenoughthatthenetnowofwaterisnotchanglngSlgnificantly duringthesegment(Figure7-1).ThelengthofeachsegmentiscalledHdtHfor

"deltatime."HowmuchwaterflOwsinduringeachsmallintervalofdurationdt?

Thequarltityaddedistilenetnow duringtheirlterVal,sayR,muitipliecLDy 11

thelengthoftheinterval,thatis,theareaoftherectangledtperiodswideand

良units/periodhigh:

Quantityaddedduringintervaloflengthdt- R * dt (Units) -(Units/Time) (Time) (7-1)

Notetheunitsofmeasure:Theflowinunitspertime,accumulatedforaperiodof

timeyieldsthequantltyaddedtothestock･

Touseaconcreteexample,supposet1-1minuteandt2-2minutes.The questionishowmuchwaterflowsintothetubduringthatminute.Dividethe

234

FIGURE711

Graphical integration

Dividetimeinto smallintervalsof

一engthdt･Each rectang一erepre-

sentstheamount

addedduringthe intervaldt,assum-

lngthenetrateR. atthattimere-

mainsconstant

duringtheinterval. Theareaofeach

rectangleisR,dt. Thetotaladdedto thestockbetween

tlandt21Sthenthe sumoftheareas

oftherectang一es. Dividingtimeinto smallerincrements increasesthe

accuracyofthe approximation･

PartIITわolsforSystemsThinking

(a ∈ !tJsl!u n )

alt2tJla N

( s

l!u n ) q UOI

昔1 t2

minuteupintoSixlOISeCOndintervalsandassumetheflOwisconstantthroughout

eachoftheseintervals.Ifatthestartofthefirstintervaltheflowwas6litersper minute(thatis,0.1liters/second),thentheamountaddedwouldbe(0.1liters/sec-

ond)(10seconds)-lliter.AtthestartofthesecondlOISeCOndinterval,theflow

hasincreased,perhapsto7liters/minute,orabout0.117liters/second.Theareaof

thesecondrectangleisthen1.17liters.Calculatingtheareaofallsixrectangles

andaddingthemtogetherglVeSanapproximationofthetotalvolumeofwater

addedduringtheminute.Theapproximationisn'tperfectbecausethenetflOwis

actuallychangingduringeach6-secondinterval･InFigure7-1,theflowisactually

rislng,SOthecalculatedvalueofthestockwillbetoosmall.Toincreasetheaccu-

racyoftheapproximation,simplydividetimeintoevenfinerintervals,increaslng

thenumberofrectangles.Computersimulationsintegratethestocksinthemodel

inpreciselythisfashion;themodelermustchoosethetimestepdtsothattheap-

proximationisacceptableforthepurpose･1Ⅰnthelimit,asthetimeintervalbe-

comesinfinitesimal,thesumoftheareasofalltherectanglesbecomesequaltothe

totalareaunderthenetratecurve.CalculusprovidesformulasthatglVetheexact

areaunderthenetrate-providedthenetratecanbeexpressedasacertaintypeof

mathematicalfunction.ButwhetherthenetratecanbeintegratedanalytlCallyor

not,theamountaddedtoastockisalwaystheareaunderthenetrate.Graphicalin-

tegrationistheprocessofestimatlngthatareafromagraphofthenetrate.

7.1.3 GraphicaHntegration

Toillustrategraphicalintegration,considerthemostbasicstockandflowsystem:

aslnglestockwithoneinflowandoneoutflow･Assumetheflowsareexogenous- therearenofeedbacksfromthestocktoeitherflow.Supposetheoutflowfromthe

lTheproceduredescribedaboveisknownasEulerintegrationandisthemostcommonlyused methodfornumericalsimulation.OthermethodssuchasRunge-Kuttaintegrationusemoresophis-

ticatedmethodstoestimatetheareaandselectthetimestep.SeeAppendixA.

Chapter7 DynamicsofStocksandFlows

FJGURE7-2

Graphical integration: examp一e Whiletherate

stepsupandsteps down,thestock risesandremains

atahigherleveL Notethedifferent unitsofmeasure fortherateand stock.

柿0

(p uo u a s J

sl!un )

き

0 ]L

laN

400

竜宮 300

き桟 200 100

0蓮華 ∃ 0 10 20 30

Time(seconds)

235

stockiszero･Supposealsothattheinflowtothestockfollowsthepatternshown inFigure7-21Theinnowbeginsatzero･Attime10theinflowsuddenlylnCreaSeS to20units/second,remainsatthatlevelfわr10seconds,thenstepsbackdownto zeroJftheinitiallevelofthestockis100units,howmuchisinthestockattime 30,andwhatisthebehaviorofthestockovertime?

Table7-2Showsthestepsinvolvedingraphicalintegration.Applyingthese stepstoFigure712,firstmakeasetofaxesforthestock,linedupunderthegraph fortheflows.Nextcalculatethenetrate.Sincethereisonlyoneinflowandone outflow,andsincetheoutflowiszeroatalltimes,thenetrateofchangeofthe stock(TotalInflowITotalOutflow)simplyequalstheinflow.Initially,thestock hasavalueofloounits.Betweentime0andtime10,thenetflowiszerounits/ second,sothestockremainsconstantatitsinitialvalue.Attime10,thenetrate

JumpstO20units/Secondandremainstherefor10seconds.Theamountaddedis theareaunderthenetratecurve(betweenthenetratecurveandthezeroline).

Sincetherateisconstant,theareaisarectangle20units/secondhighand10sec- ondslong,sothestockrisesby200units,glVlngatotallevelof300unitsbytime 20･BecausethenetratelSpositiveandconstantduringthisinterval,thestockrises linearlyatarate20units/second(theslopeofthestockis20units/second).

Attime20,theinflowsuddenlyceases.Thenetrateofchangeisnowzeroand remainsconstant,andthestockisagainunChanglng,t壬10ughnowatthelevelof 300units.

Notehowtheprocessofaccumulationcreatesinertia:thoughtheraterisesand fallsbacktoitsorlglnallevel,thestockdoesnotreturntoitsorlglnallevel.Instead, itremainsatitsmaximumwhenthenetratefallsbacktozero.Inthisfashion,

Stocksprovideamemoryofallthepasteventsinasystem.Theonlywayforthe stocktofallisforthenetratetobecomenegative(fortheoutflowtoexceedthein-

flow)ANotealsohowtheprocessofaccumulationchangedtheshapeoftheinput. TheinputisarectangularpulsewithtwodiscontinuousJumps;theoutputisa smooth,continuouscurve.

236

TABLE7-2

Stepsingraphical integration

PartII ToolsforSystemsThinking

1.Calculateandgraphthetotalrateofinflowtothestock(thesumofall inflows).Calculateandgraphthetotalrateofout刊owfromthestock(the sumofa"outflows).

2,Calculateandgraphthenetrateofchangeofthestock(thetotaHnflowless thetota一outflow).

3.Makeasetofaxestographthestock.Stocksandtheirflowshavedifferent unitsofmeasure(ifastockismeasuredinunitsitsflowsaremeasuredin unitspertimeperiod).Thereforestocksandtheirflowsmustbegraphedon separatescales.Makeaseparategraphfor帥estockunderthegraphfor theflows,withthetimeaxeslinedup.

4.Plottheinitialvalueofthestockonthestockgraph.Theinitialvaluemust bespecified;itcannotbeinferredfromthenetrate,

5lBreakthenetfJowintointervalswiththesamebehaviorandcalculatethe

amountaddedtothestockduringtheintervalSegmentsmightbeintervals inwhichthenetrateisconstant,changlngllnearFy,OrfoIIowIngsomeOther pattern.Theamountaddedtoorsubtractedfromthestockduringa

segmentistheareaunderthenetratecurveduringthatsegment･For exampFe,doesthenetflowremainconstantfromtimetltOtimet2?Efso, therateofchangeofthestockduringthatsegmentisconstant,andthe quantityaddedtothestockistheareaoHherectangledefinedbythenet ratebetweentlandt2.1日henetrateriseslinearlylnasegment,thenthe amountaddedistheareaofthetriangle.Estimatetheareaunderthenet

ratecurveforthesegmentandaddittothevalueofthestockatthestartof thesegment.Thetotalisthevalueofthestockattheendofthesegment. Plotthispointonthegraphofthestock.

6.Sketchthetrajectoryofthestockbetweenthestartandendofeach segment.Findtheva山eofthenetrateatthebeglnnlngOfthesegment. fsitpositiveornegative?lfthenetflowispositive,thestockwinbe increaslngatthattime.lfthenetflowisnegative,thestockwHlbe deereasmg.ThenaskwhetherjtisrislngOrfalllngatanincreaslngOr

decreaslngrate,andsketchthepatternyouinferonthegraph.

lfthenetrateispositiveandincreaslng,thestockincreasesatan

increasl'ngrate(thestockacceleratesupward).

lfthenetrateispositiveanddecreaslng,thestockincreasesata

decreasingrate(thestockisdeceleratingbutstillmovingupward).

lfthenetrateisnegativeanditsmagnitudeis/Increasing(thenetrateis

becomingmorenegative),thestockdecreasesatan/'ncreasingrate,

lfthenetrateisnegativeanditsmagnlJtudeisdecreasing(becomingless negative).thestockdecreasesatadecreasingrate1

7.Wheneverthenetrateiszero,thestockisunchanglng.Makesurethat

yourgraphofthestockshowsnochangeinthestockeverywherethenet rateiszero.lfthenetrateremainszeroforsomeinterval,thestock remainsconstantatwhatevervalueithadwhenthenetratebecamezero.

Atpointswherethenetratechangesfrompositivetonegative,thestock reachesamaximumasitceasestoriseandstartstofa川.Atpointswhere

thenetratechangesfromnegativetopositive,thestockreachesa minimumasitceasestofallandstartstorise.

8.Repeatsteps5through7untildone.

Chapter7 DynamicsofStocksandFlows

FIGURE7･3 Theaccumulationprocesscreatesdelays. Notetheone-quartercyclelagbetweenthepeaksofthenetflowandthepeaksofthestock.

(LJt u O ∈

＼ S l !u

n )Sき O lj

lntlow Outfto

Y W--㌔

)

『雨 …己~~~~~~

＼㌔ _メ㍉ j ㌔ _i

0 3 6 9 12 24 36 48

Time(months)

237

NowconsidertheflOwsspecifiedinthetoppanelofFigure713.Theoutflow

isconstantat100units/month,1DuttheinflowFluctuatesaroundanaverageofloo

withaperiodof12monthsandanamplitudeof±50units/month.Atthestart,the inflowisatitsmaximum.Assumetheinitialvalueofthestockis500units.

Sincetheoutflowisconstant,thenetinflowisafluctuationwithamplitude

±50units/monthandameanofzero.Thestockbeginsatitsinitialvalueof500

units,butsincetheinflowisatitsmaximum,thestockinitiallyriseswithaslope of50units/month.However,thenetflowfallsoverthefirst3months,sothestock

increasesatadecreasingrate.Atmonth3thenetflowreacheszero,thengoesneg- ative.Thestockmusttherefわrereachamaximumatmonth3.Theamountadded

tothestockinthefirst3monthsistheareaunderthenetratecurve.Itisnoteasy

238 PartIITわolsforSystemsThinking

toestimatetheareafromthegraphbecausethenetratecurveisconstantlychang-

1ng.Youcouldestimateitbyapproximatlngtheareaasasetofrectangles,asde- scribedabove,thoughthiswouldtaketime.Usingsimulationtocarryoutthe accumulationshowsthatalittlelessthan100unitsareaddedtothestockbythe timethenetratefallstozeroatmonth3.

Frommonth3tomonth6,thenetrateisnegative.Thestockistherefore falling.Justaftermonth3,thenetratelSJustbarelynegative,Sotherateofdecline ofthestockisslight.Butthemagnitudeofthenetrateincreases,Sothestockfalls atanincreasingrate.At6months,thenetratehasreacheditsminimum(mostneg- ative)valueof-50units/month.Thestockisdecliningatitsmaximumrate;there isaninflectionpolntinthetrajectoryOfthestockatmonth6.

Howmuchdidthestocklosebetweenmonth3andmonth6?Assumingthe fluctuationinthenetrateissymmetrical,thelossJustbalancedwhatwasgainedin thefirst3months,reducingthestockbacktoitsinitiallevelof500units.

Frommonth6tomonth9,thenetflowremainsnegative,sothestockcontin-

uestofall,butnowatadecreaslngrate.Bymonth9thenetflowagalnreaches zero,sothestockceasestofallandreachesitsminimum.Againusingtheassump- tionofsymmetry,thequantltylostfrommonths6to9isequaltothequantltylost frommonths3to6,Sothestockfallstoaleveljustabove400units.

Frommonths9to12thenetflowispositive,sothestockisrising.Duringthis timethenetraterises,sothestockincreasesatanincreasingrate,endingwitha slopeof50units/monthasthenetratereachesitsmaximum.Again,thestockgalnS thesameamount,recoverlngItsinitiallevelof500unitsexactlyatmonth12.Be- yondmonth12thecyclerepeats.

TheexampleillustratesthewaylnWhichtheprocessofaccumulationcreates delays,Theinputtothesystemisafluctuationwitha12-monthperiodreachingIts peakattime-0,12,24,...months.Thestock,oroutputofthesystem,alsofluc-

tuateswitha121mOnthperiodbutlagsbehindthenetinflowrate,reachingIts peaksatt-3,15,27,‥.months.ThelaglSpreciselyone-quartercycle.Thelag arisesbecausethestockcanonlydecreasewhenthenetflowisnegative.Ifthenet flowispositiveandfallstozero,thestockincreasesandreachesitsmaximum.

AnalyticalIntegrationofaFluctuatlrOn

TheexampleinFigure7-3canbemadepreciseuslngalittlebasiccalculus.The stockSistheintegralofthenetrateR.Assumingthenetflowisacosinewithpe- riod12monthsandamplitude50units/month,R=50cos(2Trt/12),then

s-lRdt-l50cos(2Tu12)dt-50(12/2T)sin(2Tu12)+StD (7-2)

Thestockfollowsasinewavewiththesameperiodandamplitude(12/2¶)times thatofthenetflow.Thedelaycausedbytheaccumulationprocessiseasilyseen sincesin(0)=cos(0-¶/2):

S-50(12/ユ′汀)cos(2′汀t/12-¶/2)+St｡ (7-3)

ThestockfollowsthesametrajectoryaSthenetflowbutwithaphaselagof7T/2 (one-quartercycle).Equation(7-2)alsoshowsthattheamplitudeofthestockis (50units/month)*(12months/2Tr)-96units,Sothestockfluctuatesbetween

about404and596,asseeninthefigure.

Chapter7 DynamicsofStocksandFlows 239

GraphicaHntegration ConsiderastockwithasingleinflowrateRlandsingleoutnowrateR2･Drawthe

behaviorofthestockgiventheratesRlandR2ShownineachpanelofFigure7-4. Theinitialvalueofthestockis100unitsinbothcases.Donotuseacomputer.The

polntistodevelopyourintuitionaboutstocksandRowsandyourabilitytorelate theirbehavior.Usingsimulationdefeatsthatpurposeandwilltakelongeraswell.

lnflow♂ Outf一ow〆

15 20

肋減 Tjkjg494tOu紺ow

-∴こ.::./.:㌔

｢-一■̀■■■■■~~匡匡 ′- - - ■-

5 10 15 20

7.1.4 GraphicalDifferentiation

Theinverseofintegrationisdifferentiation,thecalculationofthenetrateof

changeofastockfromitstrajectory.Givenagraphofastock,itisalwayspossi-

bletoinferthenetrateofchangeandplotit.Asinthecaseofintegration,thereare

analyticmethodstocalculatethenetrateofastocklfthefunctiondescribingthe

stock'spathisknown.However,inmostdynamicmodelsnoanalyticfunctionfor

thestocksisknown,Soyoumustdeveloptheskillofgraphicaldifferentiation･

Graphicaldifferentiationisstraightforward･Simplyestimatetheslopeofthe

stockateachpolntintimeandplotitonagraphofthenetrate.Figure7-5provides

anexample.

240

FIGURE7-5

Graphica一 differentiation

PartII ToolsfわrSystemsThinking

(sl !

u n )q U

(日石 a ÂJS tl.un ) a te t] laN

疏 Q + '.tJ1

-●●.､～Q /I〃′ u)ご巴 y)忠: .i■■＼0l.0＼⑳ 令 ¢ ⊂コ ⊂コ＼ ≠

ち ea,,/ Oくつ⊂)▼ー ⊂l⊂>⊂I▼■ ･､萎由I

5weeks

10 20 30 40

Time(weeks)

Theinitialstockis2000units.Forthefirst10weeksthestockdeclineslin-

early,Sothenetrateduringthisintervalisnegativeandconstant.Thestockfalls from2000to1000unitsin10weeks,sothenetrate(theslopeofthestock)is

-100units/week.Atweek10thestocksuddenlystartsincreaslng.Drawlngaline tangenttothestockcurveattime10givesanestimateoftheslopeof200units/ week.Thenetratethereforestepsup丘･om-100units/weektheinstantbefわrethe startofweek10to+200units/weekjustafteritstarts.Fromweeks10to20the

stockincreasesatadecreasingrate,SOthenetrateispositivebutfalling.Attime 20thestockreachesamaximumsothenetrateiszero.Therearenokinksor

bumpsinthestocktrajectory,implyingasteady,lineardeclineinthenetratefrom 200units/weekinweek10tozeroinweek20.Fromweek20toweek30thestock

isfalling.Byweek30itisfallingrapidly;theslopeofalinetangenttothestock trajectoryatWeek30hasaslopeof-200units/week.Again,therearenokinksin thetrajectory,SOthenetratedeclineslinearlyfromzeroinweek20to1200units/ Weekinweek30.Atweek30thestocksuddenlystopschanglngandremainscon-

stanta氏erwards.Thenetratesuddenlystepsupfrom-200tozerounits/Weekand remainsatzerothereafter.

GraphicaldifferentiationofastockrevealsonlyItsnetrateOfchange.Ifthe stockhasmultipleinflowsandoutflowsitisnotpossibletodeterminetheir

Chapter7 DynamicsofStocksandFlows 241

individualvaluesfromthenetratealone:afirm'sstockofcashremainsconstant

whetherrevenuesandexpendituresbothequal$1millionperyearor$1billion peryear･

Graphica一Differentiation

ThetrajectoryOfastockisshowninFigure7-6.Determinethebehaviorofitsnet ratebygraphicaldifferentiation.Donotuseacomputer.

0 5 10 15 20

7.2 SYsTEM r3yh!AMiCSJNAcT10N:GLOBALWARM州G

Muchofthepowerofthesystemdynamicsperspectivecomes血.omunderstand- 1nghowtheprocessofaccumulationcreatesdynamics,evenbeforeconsidering thefeedbackscouplingthestocksandtheirflows.Toillustrate,considerglobal Warmlng･

Istheearthwarmlng?IsthewarmingCausedbyemissionsofgreenhousegases (GHGs)causedbyhumanactivity?Howmuchwarmingislikelyoverthenext century?Whatchangesinclimatepatterns,rainfall,growingSeason,Storminci- denceandseverlty,andsealevelmightensue,andhowmuchdamagewouldthese changescausetohumanityandtootherspecies?Thesequestionsaredifficultto answer,andlegltlmatescientificdebatesabouttheimpactofanthropogenicGHG emissionscontinue.

Despitethescientificuncertainty,severalfactsarenotindispute.Thetemper- atureattheearth'ssurface-theland,loweratmosphere,andsurfacelayerofthe ocean(theso-calledmixedlayer,thetop50to100meters,wheremostsealifeex- ists)-isprimarilydeterminedbythebalanceoftheincomingsolarradiationand theoutgolngreradiatedenergy.Theearthisawarmmasssurroundedbythecold ofspaceandlikeallsuchmassesemitsso-Calledblackbodyradiationwhosefre- quencydistributionandintensitydependsonitssurfacetemperature.Thewarmer themass,themoreenergyltradiatesJncomlngSOlarenergywarmstheearth･Asit warms,moreenergylSradiatedbackintospace.Thetemperaturerisesuntilthe earthisJustWarmenoughfortheenergyradiatedbacktospacetobalancethein- comlngso一arenergy.

242 PartIIToolsforSystemsThinking

Theamountofenergyradiatedbackintospacedependsonthecompositionof theatmosphere.GHGssuchascarbondioxideandmethanetrapsomeoftheen- ergyradiatedbytheearth,insteadofallowlnglttOescapeintospace･Thusanin-

creaseinGHGscausestheearthtowarm.Theearthheatsupuntiltheenergy escaplngthroughtheatmospheretospacerisesenoughtoagainbalancethein- comlngso一arenergy.GreellhousegasesreducetheemissivltyOftheatmosphere enoughtowarmthesurfaceoftheearth(includingtheoceans)toalife-sustaining averageofabout15oC(59oF).WithoutGHGsintheatmosphere,themeanglobal temperaturewouldbeabout-17oC(lop)andablanketoficewouldperpetually covertheearth.

Naturalprocesseshavecausedtheconcentrationofcarbondioxide(CO2)in theatmospheretofluctuatesignificantlyovergeologicaltime,andsurfacetemper- atureshavefluctuatedwithiLHumanactivityhasnowreachedascalewhereitcan affecttheseprocesses.AsshowninFigure7-7,therateofanthropogenicGHG emissionshasbeengrowlngeXPOnentiallysincethebeglnnlngOftheindustrial age.AtmosphericconcentrationsofCO2andotherGHGsincludingnitrousoxide (N20),methane(CH4),Chlorofluorocarbons(CFCs),hydrofluorocarbons(HFCs), perfluorinatedcarbons(PFCs),andothershavebeengrowingexponentially,with concelltrationsofCO2,N20,andCH4upby30,15,and145%,respectively,since 1800.Meanglobalsurfacetemperaturehasbeenrising,thoughnotinasteadypat- tern.Comparedtothelate1800S,averageglobaltemperaturesareabout0.5toloC wamertoday.Bycomparison,themeanglobaltemperatureduringthelasticeage, whensheetsofice1000feetthickcoveredmuchofthenorthernhemisphere,was about50ccolderthantoday.

Debatecontinuesaboutthedynamicsoftheglobalclimatesystem,itsresponse toforcingbyhumanactivlty,andtheconsequencesofariseinglobalmeantem- perature.Thepublicdiscussionhasbeenpolarizedbywell-financedcampaigns todiscountthescience.Nevertheless,consensusisemerging.In1995,theUN sponsoredlntergovernmentalPanelonClimateChange(IPCC)concludedthat globalwamlngWasindeedoccurrlng,andthathumanactivltyWasresponsible, statlng"Thebalanceofevidencesuggestsadiscerniblehumaninfluenceoncli- mate"(IPCC1996).ThroughtheUNFrameworkConventiononClimateChange (UNFCCC)variousnationsarenegotiatinglimitstoGHGemissions,thoughcom- plianceremainselusive.

Simulationmodelsofvarioustypesaretheprlmaryresearchtooltoexplore theseissues.Theenormouslydetailedgeneralcirculationmodels(GCMs)calcu-

lateclimateatfinelyspacedintervalscoverlngtheentiresurfaceoftheearth,but takeGHGemissionsasexogenousInputs.Attheotherextreme,so-Calledinte- gratedclimate-economymodelsclosesomeofthefeedbacksamongthehuman economy,carbonemissions,andglobalclimatebuttreatthecarboncycleandcli一 mateasglobalaggregateswithasmallnumberofstocks･TわmFiddaman(1997) analyzedmanyofthemostwidelyusedclimate-economymodels,identifyinga numberofproblemsandinconsistenciesinthem.Forexample,thewidelycited DICEmodel(Nordhaus1992a,1992b)violatesthelawofconservationofmassby

assumingthatasignificantfractionofcarbonemissionssimplydisappear(Nord- hausassumedtheyflOwintoasinkoutsidethemodelboundary).Fiddaman(1997)

Chapter7 DynamicsofStocksandFlows

FlGURE7-7 GHGemissions, concentration,

andglobalmean

temperature

()｡

a ĴS uO 1

3 !)ta Luu O !H !g )

u o !s

s!Luu N

o3 0 g

ua6 o doJLJluV

( s

u o I D !J

ta uJu OM !g

)

o 3 U EJ

a LIds o∈lV

1900 1950 2000

1800 1850 1900

(U O N .0 - 0ト･ 0 9 6 L )

^ le Lu O u V 巴 nl e Ja d u J a

a 3

t?lJn S u t= a M

lt2

q O 一9

243

1800 1850 1900 1950 2000

Sources:DatafromtheCarbonDioxidelnformationAnalysisCenter(CDIAC),OakRldgeNational

Laboratory(http://cdEaC.eSd.ornI.gov/trends/trends.htm)lEmissions:Keeling(1997).Emissionsin- cludecarbonfromburnlngfossilfuelsonlyandexcludesotherGHGsandchangesincarbonflux

from,e;g.,deforestationCO2irlatmosphere:SipleStat10nlCeCOredatarNefteletal.19941.Mauna

Loagasrecorderdata(Keelingetal.1997);concentratEOninppmvconvertedtobilliontonslntotal

atmosphere.Globalmeansurfacetemperatureanomaly:Jones,Wigley,andWrlght(1997)andAnge" (1997),resca‡edso1960-70,E0,2oC.

developed amodelthatcorrectstheseand otherdefectsin common climate-

economymodelsandlinkedittoamodeloftheeconomyandenergysystem･The

modelsectorswerebasedontherelevantscientificknowledgeoftheglobalcarbon

cycleandclimatesystem andcarefullycalibratedtotheavailabledata.

244 PartIIToolsforSystemsThinking

Despltethedifferencesamongthemodels,allshowtheclimatesystemtoposI sessenormousinertia.ChangesinGHGemissionsonlyslowlyshowuplnChanges inglobaltemperatureandclimate,andthechangespersistformanydecades.To illustrate,Figure7-8ShowsanextremeconditionstestusingFiddaman'smodel.In thesimulation,anthropogenicCO2emissionsfollowtheirhistoricalpaththrough themid1990S,remainconstantuntil2000,andthenfalltozeroafter2000.Sur-

prlSlngly,thoughtherateofCO2emissionsfallstozerointheyear2000,mean globaltemperaturecontinuestoriseforaboutthreemoredecades.Itthenfalls veryslowly.

ThestockandflOwstructureresponsibleforthecounterintuitiveresultthat temperatureriseseventhoughemissionsfalltozeroisshowninFigure7-9.The leftsideofthefigureportraystheglobalcarboncycle;therightsideportraysthe globalheatbalance.BurnlngfossilfuelsaddsCO2tOtheatmosphere.Thereare severaloutflowsfromthestockofatmosphericC02･HigheratmosphericCO2con- centrationincreasestherateatwhichCO2isconsumedbyaquaticlifeordissolves intothemixedlayeroftheocean.Eventually,CO2takenupbythesurfacelayer diffusestodeeperwaters,boththroughoceancurrentsandasdetritusfromaquatic lifesinks.Thetransferofcarbontothedepthsisslow,andmixingbetweenthesur- faceandabyssalwatersisweak,somanycarboncyclemodelsdisaggregatethe watercolumnintoanumberofdistinctstatesandmodelthetransferofcarbon

betweenadjacentlayersexplicitly.Fiddaman'smodelutilizes10layers,enoughto capturetheslowadjustmentofabyssalCO2concentrationstochangesinCO2in themixedlayer.

IncreasedatmosphericCO2COnCentrationalsostimulatesuptakeofcarbonby terrestrialplants(thefluxofCo∑tObiomass).Carboninbiomasscanbereleased backintotheatmospherethroughresplrationandmetabolicactivltyOfanimaland bacteriallifeandbyfire(naturalandhuman-caused)･Asbiomassdecays,thestock ofcarbonstoredinsoilincreases(thefluxofcarbonfrombiomasstosoilhumus).

Thecarboninhumuscanbetakenupdirectlyintobiomassasplantsgroworcan bereleasedintotheatmospherethroughdecay.

NotethatthemodelrepresentstheinflowofCO2tOtheatmospherefromthe burningOffossilfuelsasflOwingfromanunlimitedsourcewheninfacttheflow drawsdownthecaIもOnsequesteredinglobalstocksoffossilfuels.Similarly,血e modeldoesnotcapturetheconversionofcarboninhumusortheabyssallayerof theoceanintonewstocksoffossilfuels.Althoughthedynamicsofglobalwarm- 1ngWillplayoutoverthenextseveralcenturies,thistimehorizonissoshortrela- tivetothemillionsofyearsrequiredtoformoil,gas,andcoalthatthesecarbon flowscanbesafelyignored.

TherightsideofFigure7-9showsthestockandflowstructurefortheheat balanceoftheearth'ssurface,atmosphere,andoceans.Thesurfaceandatmos- phere,includingthesurfacelayeroftheocean,absorbincomlngSOlarenergyand radiateheatbackintospace.Heatisalsotransferredbetweenthesurfacelayerand thedeepocean,thoughatslowrates.Therateofheattransferbetweensurfaceand deepoceandependsonthetemperaturedifferentialbetweenthedifferentlayers, creatlngtwonegativefeedbackswhichseektoequilibratethetemperaturesofthe differentlayers.Similarly,netradiativeforcingisthedifferencebetweenthein- ComlngSOlarenergyandtheenergyradiatedfromthewarmearthbackintospace.

Chapter7 DynamicsofStocksandFlows

FIGURE7-8

Globaltempera- tureriseswellafter GHGemissions falltozero.

Simulatedemis- sionsfa‖tozero in2000.Mean

surfacetempera- turecontinuesto

riseforroughly 20years･

(Lt

20ĴSu O }

U Tl a

LuuO ≡

!g )

su o !s

s!uU e O

u36Od

JLIIuV 2025 2050

■ー■■-■■-■-■-■一一■

( p u no J

6 q oE 2

q a ^ O q

e 3 0)

^ It 2u JO uV 巴

nlt2 J a d

∈ al

a 3

t=- ･]n S u t2 3 m

-t2

q O 19

1975 2000 2025 2050

1950

Source.IFiddaman(1997).

2000 2025 2050

245

Thewarmerthesurface,themoreenergylSradiatedbackintospace,Coolingthe earthandformlnganothernegativeloop.TheconcentrationofC02andother GHGsincreasesnetradiativeforcingbyreducingtherateatwhichenergylSradi-

atedbackintospaceforanyglVenSurfacetemperature.

Thediagram(thoughnotthefullmodel)deliberatelyomitsmanyadditional feedbacksaffectingtheratesofcarbonflowandheatexchangeaswellascou- plingstootherbiogeochemicalcycles.Knowledgeofthenatureandstrengthof

themanyfeedbackscouplingclimate,carboncycle,andhumanactivitylSStill evolving.SomeofthesefeedbacksarenegativeandmayoffsetGHGemissionsor

246 PartII TわolsforSystemsThinking

FIGURE7-9 Stockandflowdiagramofgtobalcarboncycleandheatba一ance

BurnlngfossilfuelsaddsCO2tOtheatmosphere,increasmgnetradiativeforclnguntilthetemperature oftherand,oceansurface,andatmosphererisesenoughtobalancereradiationofenergyintospace withincomlnglnSOlation,Thediagramdeliberatelyomitsmanyofthefeedbacks,bothpositiveand negative,amongthecarbonstocksandglobalmeantemperature.Flowswitharrowheadsatbothends canbepositiveornegative(e.g.,NetRadiativeForcingcanbeaninflowofheattotheatmosphereor anoutflow).Thesolidarrowheadindicatesthepositivedirectionoftwo-wayflows,

Source:AdaptedfromFiddaman(1997).

Chapter7 DynamicsofStocksandFlows 247

warmlng･Theseincludeincreasedcarbonuptakebybiomass,stimulatedbyhigher CO2concentrations,andincreasedcloudcoverfromenhancedevaporation,re- flectlngmoreincomlngSunlighttospace.Particulateaerosolsfromfossilfuelcon-

sumption(airpollutionandsmog)alsoincreasereflectionofincomingsolar

radiationandmayaccountfortheslowerthanexpectedrateoftemperatureriseob- servedintheNorthernHemisphere.

Amongthepositivefeedbacksdrivingclimatechangearechangesinsurface

albedo:Warmlngreducesthewintersnowcoverandshrinksthehighlyreflective polaricecaps,thusincreasingheatabsorptlOnandleadingtofurthermelting,less

snowcover,andstillgreaterabsorptlOn･Scientistsexpectthispositiveloopwill causemuchgreaterwarmlngatthepolesthaninthetroplCSandmorewamlngln winterthansummer･Thawingofpermafrostmayreleaselargequantitiesof methanefromdecayoforganicmatter,increaslngtheconcentrationofGHGsand

leadingtofurtherwarminglnanotherpositiveloop.Increasedevaporationfrom warmerlandandsurfacewatersmaybeself-reinforclngSincewatervaporisa

powerfulGHG･Atpresentitisnotknownwhetherthenegativeorpositivefeed- backsdominatethedynamicsnorhowthedominanceoftheloopsmightchangeas variousnonlinearitiescomeintoplay.However,Gouldenetal.(1998)studiedthe northernborealforestofCanadaandfoundthatwarminghasresultedinnetcarbon

fluxtotheatmosphereasC02releasedfromdecayofthawedbiomassoutweighed increasedcarbonuptakebyplants.Forthatbiome,atleast,thepositivefeedbacks

appeartodominatethenegativeloopofincreasedbioticactivity. TheimpactofwarmlngOnSealevelmayalsobedrivenbypositivefeedback.

ThehugeWestAntarcticIceSheet(WAIS)consistsofaflOatingtongueattached toalargericemasssoheavyltrestsOnbedrockbelowsealevel.TheWAISholds

alotofwater:"Ifitmeltedawaylnagreenhouse-warmedworld,itwouldraiseall theworld'soceansby5meters"(拡err1998,p.17).IfwarmerseascausetheWAIS

tothin,itwillrisefartherofftheseabed,exposlngmoreOftheicetomeltingand acceleratingthinninglnapositiveloop.Astheedgethins,thehighericeonthe Antarcticlandmassflowsfasterintothesea,whereitisexposedtothewarmerwa-

ters,furtherspeedingmeltinginanotherpositivefeedback.Rignot(1998)notes thataglacierwithH[t]hisconfigurationistheoreticallyunstablebecausearetreat

ofitsgroundingline(wheretheglacierstartstofloat)wouldbeself-perpetuating andirreversible"andshowsthatthegroundinglineofthePineIslandglacierfeed- 1ngtheWAISisretreatingat1.2±0.3kilometersperyear.Icecoresshowthat

withinthepastl･3millionyears,‖atatimeperhapsnotmuchwarmerthantoday, theWAISwastedawaytoascrapandfloodedtheworld'scoasts"(Kerr1998,

p･17)IIcecoredatafromGreenlandalsosuggestthepaleoclimaterepeatedly warmedandcooled,WithcorrespondlngChangesinsnowfall,overtimescalesof

onlydecades･Theserapidchangessuggestpositivefeedbacksmayhavedomi- natedclimatedynamicsingeologicallyrecenttimes.

Itwilltakeyearsofresearchtodiscoverallthefeedbacksthatdrivetheclimate

anddeterminethelikelyeffectsofgreenhousewarmlng.Nevertheless,thestock

andflOwstructureoftheglobalcarboncycleandheatbudgetexplainssomebasic featuresofthedynamics.ThestockandflOwstructureshowshowitispossiblefor

248 PartIIToolsforSystemsThinking

theglobaltemperaturetoriseevenafterhumanGHGemissionsfalltozero.When emissionsfalltozerotheinflowstothestockofatmosphericcarbonfallbelowthe outnows.ThereforethestockofCO2intheatmospherepeaksandbeginstofall. TheconcentrationofC021ntheatmospherefallsonlyslowly,however｡First,血e uptakeofcarbonbybiomassfallsastheconcentrationofCO2intheatmosphere declines,whileCO2continuestoflOwintotheairfromburnlnganddecayofbi0- massandhumusstocks.Second,asatmosphericCO2falls,thefluxofcarbonfrom theairtothemixedlayeroftheoceanfalls,whilethefluxofcarbonfromtheocean totheairincreases･Thesecompensatoryresponsesslowthedeclineofatmospheric CO2SOthat50yearsafterhumanemissionsstopcompletely,theconcentrationof C02inthemodelatmospherehasfallenbackonlytoits1990level.

Theheatcontentofthesurfacelayerrisesaslongasincomlngradiationex- ceedstheheatradiatedbacktospaceortransferredtothedeepocean.Though fallingaftertheyear2000,globalatmosphericCO2COnCentrationsremainhigh enoughtoreducetheenergyradiatedbacktospacebelowincomlnglnSOlation. DecliningatmosphericCO2after2000meansglobalmeantemperaturegrowsata diminishingrate.Byabout2030thesurfacehaswarmedenoughandtheconcen- trationofCO2intheatmospherehasfallenenoughforinsolationtobebalanced againbytheearth'sblack-bodyradiationandtherateofheattransfertothedeep ocean.Notethatglobalmeantemperaturefallsonlyslowlyafter2030,First,the slowdeclineofGHGconcentrationsafter2000slowstheincreaseinradiative

emissivity.Second,duringthewarmestdecadeswhenthesurfacetemperatureex- ceededthetemperatureofthedeepocean,heatflowedfromthesurfacelayertothe deep.Asthesurfacelayercools,heatstoredinthedeepoceannowflowsbackto thesurface,slowingatmosphericcooling.

ThestockandflOwstructureofthecarboncycleandheatbalanceexplainsthe seemlnglyparadoxicalresultthattemperaturescanriseevenwhenemissionsfall. Thereareseverallessons.First,globalwarmingCannotbeprovenordisprovenby correlatlngemissionsandtemperature:thedynamicsaretoocomplexforsuch naivecommonsenseapproaches.Second,thefullimpactofpastemissionshasnot yetbeenobserved.Theoceansandterrestrialcarbonstockshavebeenabsorbing carbonoutoftheatmosphereathigherrates,Suppresslngtheriseinatmospheric CO2COnCentrations.Andasthesestocksincrease,theirabsorptlOnCapaCltydimin- ishes.TheimpactoffutureemissionsonatmosphericCO2mayWellbelargerthan thatobservedinthepast.Third,theinertiaofthesystemmeansfurtherwarmlng andclimatechangearealreadyunderway.Actiontohaltwarmlngmustbetaken decadesbeforewecanknowwhattheconsequencesofwarmingWillbeandbefore scientificcertaintyaboutthedynamicsoftheglobalclimatecanbegained.

Mostimportant,tnestockandFlowStructureOftheglobalClimatemeansSta- bilizlngemissionsnearcurrentrateswillnotstabilizetheclimate.Figure7-10 showsasimulationinwhichemissionsarestabilizedin1995.Theconcentrationof

atmosphericCO2COntinuestorise,morethandoublingby2300.Globalmeansur- facetemperaturerisesbyabout3oC.ManyindustrializednationsagreedattheRio conferenceontheenvironmenttostabilizetheirGHGemissionsat1990levels,

and38industrializednationsagreedatthe1997KyotoconferenceoftheUNFCCC toreduceemissionsby2012toabout95%of1990rates.ButtheUSSenatede- claredthetreatydeadonarrival.Implementationremainselusive;slgnlngatreaty

Chapter7 DynamicsofStocksandFlows

FIGURE7-10

StabilizlngGHG emissionsdoes notstabi一izethe climate.

StabilizlngGHG emissionsat1995 1evelscausesaト

mosphericCO2

concentrationsto

doubleby2300, whHemeanglobal surfacetempera-

tureincreases about3oC.Even

underthepro- posedKyoto agreement,global emlSS10nSare

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isonething,actuallyreducingemissionsanother.Mosttroubling,theemissionsof

rapidlydeveloplngnationssuchasChinacontinuetogrowathighexponential rates.TheUSEnergylnformationAdministrationforecastin1997thatGHGemis-

sionsfromdevelopingnationswouldnearlydoubleby2015,accountlngforthe

largemajorityoftheworldtotal(Malakofr1997). Whiledifferentclimatemodelsdifferintheirdetailsandintheirestimatesof

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qulreSaSubstantialdeclineintherateofGHGemissions･Theworldhasyettoface

uptotheinexorablelogicOfthestocksandflowsoftheglobalclimatesystem.

250 PartIIToolsforSystemsThinking

7.3 SYsTEMDYNAM!CSINAcT10N:TtlEWARONDRUGS

Inthe1980stheuseofcocaineincreaseddramatically.Ascocainespread,crime,

violence,andhealthproblemsgrewexponentially.TheUnitedStatesdeclareda

warondrugs.Anewfederalagency,theWhiteHouseOfficeofNationalDrug

ControIPolicy(ONDCP),headedbytheHdrugczar,"wasappointedtooversee也e

campalgn.Penaltiesforpossession,saleanduseofdrugswerestiffened･Billions

werespenttoincreaseenforcement,especiallytoreducethenowofcocaineinto theUS,estimatedbytheONDCPtobe550to660metrictonsin1989｡Thefocus

ofthewarondrugswasprimarilythesupplyside:slashingtheproductionofco-

caine,chokingoffsmugglingIntotheUS,andstiffeningpenaltiesforpossession

andsale,Onthedemandside,kidsweretoldto"JustsayNO.H

Diditwork?Inthelate1980sthedatatoldaconflictingstory.Somedrugdata

showedimprovement.ThroughtheHNationalHouseholdSurveyH(NHS)and

HHlghSchoolSeniorSurveyH(HSSS),thegovernmentregularlyaskspeopleabout

theiruseofalcoholanddrugs.Tbassesstrendsinincidenceandprevalence,也e

surveysaskwhetherpeoplehaveeverusedcocaine,whetherthey'veuseditinthe

lastyear,andwhether血ey'veuseditinthelastmonth･Figure7-llshowsNHS

dataforthe虫.actionofpeoplerespondingthattheyhaveusedcocaineinthepast

month.Accordingtothesurveys,cocaineusewasfallingsharply,withlessthan

1%ofthepopulationreportlngpastmonthcocaineusein1990,downfrom3%in

1985.ThedroplnreportedusecoincidedwithasharplnCreaSeintheseizurerate,

tomorethan75metrictonsperyear(Figure7-11).Thewarondrugsseemedtobe

working.,citingthesedata,theadministrationcalledforevenmoremoneytofinish

thejob.

However,otherindicatorsshowedtheproblemwasgettlngWOrSe･Arrestsfor

possessionandsaleofcocaine,thenumberofemergencyroomvisitsassociated

withcocaine,andthenumberofcocaine-relateddeathsallshowedexponentialin-

creases,whilethepurltyOfcocaineonthestreetwasgrowlngandthestreetprlCe

wasfalling(Figure7-ll).Bythesemeasures,cocaineusewasupsharplyand

availabilitywasgrowlng.Critics,Citlngthefailureofprohibitioninthe1920sand

1930S,arguedthatinterdictioncouldneverworkandcalledforstrongerdemand-

sidemeasures(MacCounandReuter1997review血edebate).Othersarguedthat

decriminalizationwouldeliminatethecrimeproblem causedbyuseofillegal

drugsandallowthegovernmenttoregulatepurltytOpreventaccidentaloverdoses･ Muchofthedebatefocusedonwhichdataserieswererightandwhichwere

wrong.Thestakeswerehigh:Besidestheissuesofpublichealthandsafety,the

drugwarwasprosecutedanddataserieswerecollectedbyanalphabetsoupof

federalandstateagencies,incltldingtheFBI,DEA,SAMHSA,NIJ,NIDA,DEPB,

ONDCP,and CIA･2EacharguedfortheprlmaCyandcorrectnessofitsdataand

2FederalBureauofInvestigation,DrugEnforcementAgency,SubstanceAbuseandMental HealthServicesAdministrationoftheDepartmentofHealthandHumanServices,National InstituteofJustice,NationalInstituteonDrugAbuse,DrugEnforcementPolicyBoard,Officeof NationalDrugControlPolicy,andCentralIntelligenceAgency･

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drug-enforcementprogramsastheystruggledtogalnalargershareofmorethan $10billionperyeardevotedtothewarondrugs.

Supportersoftheinterdictionstrategyarguedthatthesurveydatadirectly

measuredwhatcounts-theuseofdrugs-whileotherindicatorswereindirect. Theyarguedthatrisingarrestratesandseizuresreflectedgreaterenforcement,not

greaterdruguse,andwerethereforeaslgnOfsuccess;fallingprices,rlSlngPurity, andthesurgeinmedicalemergenciesanddeathssimplyreflectedthesubstitution ofmorepotentcrackforthelesspurepowderform.Criticsofinterdictionandthe

surveydataarguedthatdrugusersarelesslikelythanlaw-abidingcitizenstobese-

lectedfororparticipateinthesurveys･Manycocaineusersarelikelytodenythey usedrugswhenthegovernmentasks.Defendersofthesurveyspointedtotheso- phisticatedsamplingmethodstheyusedtoaccountforpossibleunderrepresenta-

tionofcertainsubpopulations･TheyguaranteedanonymltytOSurveyrespondents andclaimedthatwhileH[t]hevalueofself-reportsobviouslydependsonthehon- estyandmemoryofsampledrespondents[,r]esearchhassupportedthevalidityof self-reportdatainsimilarcontexts"(SAMHSA1994).

Inthelate1980S血eNationallnstituteofJusticecommissionedastudytore- solvetheapparentparadoxofdecliningmeasuresofcocaineuseandrislngCOn-

sumptlOn,Crime,arrests,anddeaths.Aspartofthestudy,asystem dynamics modelwasdevelopedtointegratethedemandandsupplysidesofthemarket (Homer1993,1997).Thefullmodelconsistedofseveralhundredequationsand includedadetailedrepresentationofthestockandflowstructureofusers,along

withthefeedbacksam ongdifferentmarketactors,themarket,andthecriminaljus- ticesystem.

Figure7112Showsasimplifiedrepresentationofthestockandflowstructure forthedifferentcategoriesofdrugusersrepresentedinthemodel.TheNHScon-

sidersallpersonsage12andovertobepotentialdrugusers･Aspeopleinthisage groupfirstexperimentwithcocainetheymovefromthe"neverused"population tothestockofactivecasualusers(thosewhohaveusedcocaineinthepastmonth butarenotaddicted).Somecasualusersfindtheycannotcontroltheircocainecon-

sumptlOnandbecomecompulsiveusers.Activeusers,bothcasualandcompulsive,

canstop,becoming"transitionalusers"(thosewhohaveusedcocaineinthepast

year,butnotinthepastmonth),Transitionaluserscanrelapse,becomingactive usersagain.Afterayearwithoutanycocaineuse,transitionalusersarereclassified

asex-users･Someex-usersrelapse,becomingactiveusersagain･Othersqultper- manently.Thereare,ofcourse,deathratesoutofeachstock,bothfromdrug- relatedcausesandallothersources｡

Thefullmodelhasamorecomplexstockandflowstructurethanshown

inFigure7-12,explicitlydistinguishingbetweencasualandcompulsivetransi-

tionalandex-usersandbetweenusersofpowderandcrackcocaine.Themodel

accountedforescalationfromcasualtocompulsiveuseandforswitchingbetween powderandcrack.Thisdisaggregationwasnecessarybecausetheprobabilities ofmovingfromonestatetoanotherdependontheformandintensltyOfuse. Compulsiveusersarelesslikelytoquitandmorelikelytorelapse,andcrackusers

aremorelikelytoescalatefromcasualtocompulsiveuseandsufferhigherre- lapserates.

Chapter7 DynamicsofStocksandFlows

FlGURE7-12 Cocaineuse: stocksandf一ows

253

Source:AdaptedfromHomer(1993).

Notethatthecategoriesofuseinthemodelcanbedirectlycomparedtothose usedinthesurveys.Thetotalnumberofactiveusers,bothcasualandcompulsive,

forbothpowderandcrack,isthenumberofpeoplewhohaveactuallyusedcocaine inthepastmonth.Thesumoftheactiveusersandthetransitionalusersisthetotal

numberwhoactuallyusedcocaineinthepastyear.Finally,thesumofactive,tran- sitional,andex-usersisthetotalnumberwhohaveeverusedcocaine.

Whatarethedeterminantsoftheinitiationrate-whatcausespeopletouseco-

caineforthefirsttime?Studiesshowmostpeoplebeginusingdrugsthroughpeer influence-byobservlngOthersuslngdrugsandthroughtheirmembershipinso- cialnetworksinwhichothersusedrugs(thatis,byhangingwiththewrong crowd)･Asmorepeoplestartusingcocaine,thesocialnetworksofusersexpand, bringingStillmorenonusersintocontactwiththedrug,inapositivefeedback

processanalogoustothespreadofaninfectiousdisease(chapter9)･Thestrength ofthesocialexposurefeedbackdependsonthesocialauraofthedrug:howchic cocaineisperceivedtobe(isthisthedrugtheopinionleaders,thebeautifulpeo-

ple,areusingthisyear?).Thepositivefeedbackalsodependsonwhethercurrent

254 PartIIToolsforSystemsThinking

andpotentialusersviewthedrugasbenign-isltPerceivedtoofferagoodhigh withoutnegativeeffectssuchasaddiction,badtripsortheriskofsuddendeath?

Pricehasacomparativelymodesteffect,atleastinhighersocioeconomicgroups, becausehigh priceandscarcltyCOnfersocialstatusonthosewhocanprovidethe drugfわrfriendsatpartiesorintheworkplace.Inthemid1970S,asthecocaine epidemicbegan,cocainewasviewedasabenign,nonaddictivedrugposlnglittle healthrisk.Itbecamethein-groupdrugofchoiceamongcertainprofessional elites･Theentertainmentindustryreinfわrcedthechicimageofthedrug･Allthese self-reinforcingprocessesarecapturedbytheWordofMouthloopRlinFig- ure7-13.

Thedynamicsofthemarketreinforcedthegrowthoftheepidemic.Ascon- sumptionincreased,thesupplysideofthemarketbecamemuchmoreefficient. PricedeclinedandpurltylnCreaSed.Thegrowlngscaleoftheindustrycreatedhuge incentivesfortechnologlCalandorganizationalinnovationbyproducersandsmug- glers･Theintroductionofcrackcocainein198lwasthemostimportant,butfar fromtheonly,technicalinnovationinthemarketAsinmanylegltlmateindustries, growthledtoproductionandespeciallydistributionscaleeconomies.Horizontal andverticalmarketintegrationthroughthecocainecartelscutcostsandledto moreconsistentproductquality.Growlngexperienceledtoasubstantiallearnlng curveasharvestlng,Production,smuggling,distribution,andmoneylaundering operationswereimproved･Thesescaleandlearnlngeffectscreatedadditionalpos- itivefeedbacksleadingtowideravailability,greaterpurlty,andlowerprlCeS,mak- ingcocainea耽)rdableandaccessibletoall(loopR2)･

Aslongaspeopleperceivedthehealthandlegalrisksofcocainetobesmall, thesepositivefeedbacksdominatedthesystem.Cocaineusemushroomed,spread- 1nggradually血.ommiddleandupperincome,trend-consciouspopulationsonthe eastandwestcoaststoeverysocialandincomelevelineverystateofthecountry.

Whythendidthedatashowsuchalargedroplntheincidenceofcurrentco- caineuseafter1985?Supportersoftheinterdictionstrategycreditedtheadminis- tration'ssupply-sidepolicy.Theyarguedthatenhancedenforcementincreasedthe fractionofcocaineseized,cuttingtheavailabilityofthedrug(thebalancingSup- plyDisruptionloopB1)andthataggressivelyarrestingandincarceratingpushers andusershelpscleanuptheStreets(thebalancingloopB2)･Boththesenegative loops,itwasargued,cutdruguse,asindicatedbythesurveydata.

However,stockandflowstructurefordrugusersshowedthatthesurveydata couldnotbecorrectandweresubstantiallyunderstatingtheprevalenceofdrug use･Inadditiontoaskingaboutpastmonthuse,theNHSasksrespondentsifthey haveusedcocaineinthepastyearandiftheyhaveeverusedcocaine.Homercare- fuiiydisaggregatedtheuserpopulationintostockscorrespondingtothesecate- goriessothemodelcouldbedirectlycomparedtothedata.

Figure7-14showstheNHSdataforthefractionofthepopulationwhore- spondedaffirmativelywhenaskediftheyhadeverusedcocaine.Notethatthe reportedever-used-cocainepopulationpeaksin1982atabout12%andfallsto aboutlo啄by1988.

ThelifetimecocaineprevalencedatainFigure7114istheratiooftheever- usedpopulationtothetotalpopulation(thosewhoneverusedplusthosewhoever used)ATheinflowtothetotalstockofpeoplewhohaveactuallyusedcocaineisthe

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initiationrate.Theonlyoutflowisdeath.Theonlywaythestockofpeoplewho

haveeverusedcocainecandeclineisforthedeathrateofcurrentandpastusersto

exceedtheinitiationrateofnewusers･3Yetthesurveydatareporteda3･2%drop

inthenumberofpeoplewhohaveeverusedcocainefrom 1982to1988.Evenif

therateatwhichpeopletriedcocaineforthefirsttimefelltozeroin1985-even

ifeveryman,woman,andchildintheUSwhohadneverusedcocaineJustsaid

NO!,somethingnoteventheadministrationbelieved-mortalityratesoftheever-

usedpopulationaretoosmalltocausethereporteddeclineinthenumberofpeo-

plewhohaveevertriedcocaine.Evenwiththemostoptlmisticestimatesforthe

declineintheinitiationrate,itisphysicallyimpossibleforthestockofpeoplewho

haveeverusedcocainetofallasquicklyasthesurveyssuggested･4

Whythendidthereportedincidenceofusefallsodramaticallya氏er1985?

Therearetwomainreasons.First,thesurveyspresumethattheirsamplesareprop-

erlystratified,thatis,thattherepresentationandresponseratesofsubpopulations

(suchasdifferentgeographic,ethnic,racial,andsocioeconomicgroups)aread-

justedtomatchtheproportionofthesegroupsintheoverallpopulationandthat

anyunderrepresentationisconstantthroughtime.Heavydrugusers,however,are

muchlesslikelytobeinterviewedforthesurvey.ThoughtheNHSmethodology

attemptedtoadjustforthisunderrepresentation,theycautionedthat

Prevalenceestimatesforspecificsubgroupsaresometimesbasedonmodestto

smallsamplesizes,whichmayleadtosubstantialsamplingerror‥.[T]hisreport

doesnotpresentestimatesforsomesegmentsoftheUSpopulationthatmaycon-

tainasubstantialproportionofdrugusers,suchastransientsnotresidinglnShelters

3InprlnCIPle,thelifetimeprevalencefractioncouldfanifthoseintheever-usedpopulationemi- gratedfromtheUStoothercountrleSataratemuchhigherthanthatofthosewhohaveneverused cocaine.Theserates,however,arenegligible.Forthesurveytobecorrecttherequiredoutmlgration ofdruguserswouldgreatlyexceedalloutmlgrationfromtheUS.

4Theprobleminthesurveydataisworse.TheNHSreportedadropinthefractionofthepopul lationthathaseverusedcocaine.Thedeclineinrelativelifetimeprevalencewouldrequlrethe

deathrateofformercocaineuserstogreatlyexceedthedeathrateofthosewhohaveneverused cocaine,Thedifferenceindeathrates,however,isverysmall,partlyduetothelowexcessmortall ltyOfactiveusersandlargelybecausemostmembersoftheever-usedpopulationnolongeruse cocaineandexperiencemortalityratesaboutthesameasthenever-usedpopulation･

Chapter7 DynamicsofStocksandFlows 257

(e.g.,usersofsoupkitchensorresidentsofstreetencampments)andthoseincarcer- atedincountyjailsorStateandFederalprisons(SAMHSA1994).

Thatis,fewfederalworkersarewillingtoknockonthedoorsofacrackhouseto

asktheoccupantswhethertheyuseillegaldrugs･Consequently,activeandespe-

ciallycompulsiveusersareunderrepresentedinthesurveys.Becausethesepopu-

1ationsgrewrapidlylnthe1980S,thesurveyssystematicallyunderestimatedthe

growthincocaineuse.

Second,andmoreimportantly,1nCreaSlnglegalriskscausedalargerfraction

ofcurrentandespeciallyformeruserstodenytheyeverusedcocaine･Inplainlan-

guage,morepeopleliedabouttheirpastcocaineuse.Thechangingdistributionof

cocaineusersanddeclinlngSOCialacceptanceofcocaineledtosystematicunder-

estimationofcocaineprevalenceinthesurveydata.

Byintegratingalltheavailabledataintoaconsistentandunifiedframework,

themodelprovidedmoreaccurateestimatesofdrugusethanwereavailableprevi-

ously.Modelestimatesoftheever-usedpopulation(alongwiththeothercategories

ofdruguse)Werederivedtobeconsistentwithotherdemographic,crime,health,

prlCe,andpuritydata,constrainedbythestockandflOwstructureofthepopulation

andepidemiologlCalandmedicaldataonhealthrisks.Understalldingthedynam-

icsofthestocksandflOwsofusershelpsreconciletheapparentlycontradictory

data.Figure7115comparesthemodel'sbehaviorforreportedlifetimeuseagalnSt

thesurveydata,alongwiththemodel'sestimateoftheactualever-usedpopulation.

Theactualpopulationofpastusersmusthavecontinuedtogrowbecausethenum-

berofpeopletryingcocaineforthefirsttimeexceededthedeathrateofthosewho

hadevertriedit.Theavailability,purlty,anduseofcocainewereinfactincreaslng

throughoutthelate1980sdespitethebillionsspentonenforcementandsupply reduction.

InhindsightitseemsqulteObviousthatthestockofpeoplewhohaveeverused

cocainecannotdeclineasrapidlyasthedatasuggested,Sothesurveydatashould

immediatelyhavebeenchallenged.Buthindsightisalwayscrystalclear.Thefact

remainsthatthedatawerenotchallenged.Instead,thegovemmentusedthesurvey

datatotakecreditforwinningthedrugwar,tojustifyinterventionintheaffairsof

othernations,andtolobbyfortougherpenalties,greaterpowersforlawenforce- mentagencies,moreprlSOnS,andmoreresourcestodefendthebordersoftheUS

agalnStthethreatofforeigndrugs.

Perhapstheadministrationknewthedataoverstatedthereductionindmguse

anduseditcynicallytomanipulatepublicopinionandthecongress･Eveniftrue,

itilnmediatelybegsthequestionofwhyothersingovemment,alongwiththeme-

dia,policyanalysts,andthepublicatlargedidnotrecognlZetheflawinthedata.

Theadministration,congress,andthemediaallfocusedonthedatashowing

recentuse-theNHSpastmonthorpastweekdata,alongwiththeHSSS-rather

thanlifetimeuse･Recentuseprovidesabettersnapshotofcurrentdrugtrends,and

showedthelargestdecline,makingthecasemostfavorabletotheadministration.

However,thedatashowingdeclineinrecentuseconfoundedtheactualdecline

inusewiththeincreaseinunderreportlng.Thetwosourcesofdeclinecannotbe

disentangledfromtherecent-usedatabecausetherecentuserstockcandropas

peoplequit;likewise,pastusersageoutofthehighschoolseniorpopulation･Itis

258

FJGURE7-15 Simulatedvs.

actualpopulation oflifetimecocaine users

Notethatwhilethe

suⅣeydatashow adroplntheever- usedpopulation after1982,the modelestimates fortheactua一

populationof thosewhohave everusedcocaine

continuetorise, thoughata dJrminishingrate. lncreaslnglegal risks一edtoalarge increaseinthe fractionoHormer userswhodenied theircocaineuse.

PartIIToolsforSystemsThinking

(u o !tt2 一n

d o d -o u o Fto t2J I ) a

U u a Ht2 ^ a J d

1976 1980

Source.-Homer(1993,1997).

1984 1988 1992 1996

Onlybyexplicitlyaccountingforthestockandflowstructureofdruguse-forthe inexorableaccumulationofusersintotheever-usedpopulation-thatthetwocom-

petingSOurCeSOfdeclineincurrentusedatacanbeseparated.Unfortunately,the abilitytounderstandbasicstockandflowrelationshipsisfartoorareinoursoci- etytoday,evenamongmanyprofessionalpolicyanalysts.

7L3.1 TheCocaineEpidemica熊er1990

Themodelshowedpersuasivelythatthesurveydatasignificantlyunderestimated cocaineuseandhighlightedthefailureofthesupply-sidestrategy.AsMacCoun

andReuter(1997,p.47)putit,"Theprobabilityofacocaineorheroinsellerbeing incarceratedhasrisensharplysinceabout1985butthathasledneithertoincreased prlCenorreducedavailability.MHowever,acloselookatthesimulationinFigure 7-15showsthatbythelate1980sthenumberofpeoplewhohadeverused

cocaine,thoughstillrising,wasgrowingatadiminishingrate･Thereforetheini- tiationratemusthavebeenfalling.Bythemid1990S,theepidemicbegantoabate: thegrowthofcocaine-relatedmedicalemergenciesanddeathsslowed;arrestsfell

slightly.TheONDCPestimatednetimportsin1995atbetween421and513metric tons,with98metrictonsseized,leavlngnetcocaineavailableonthestreetsof Americaataboutthree-quartersthe1989level.Themodel,Orlglnallydeveloped inthelate1980S,forecastthesedramaticshiftsincocaineusequitewell(Fig- ure7-16).

Notethatthepoint-by-pointfitofthemodelinthe1990sisn'tperfect,andyou

shouldrIAOtexpectittobe.Simulatedarrestsare,toohigh,andthemodeldoesnot trackthetemporarydipincocainerelatedmedicalemergenciesin1990-91.Never- theless,themodel'sabilitytocapturetheturningPOlntintheepidemic,from

exponentialgrowthtogradualdecline,isqulteremarkable,consideringthatthe simulationsshowninFigure7-16Werebasedondataavailableonlythrough1989. Theonlyexogenousinputsaffectlngmodelbehaviorafter1990arethetarget population(thoseage12andover)andtheprevalenceofmarijuanause(aproxy

forsocialtoleranceofdrugs).Changesindata-reportingsystemsanddefinitions werenotincluded.

Chapter7 DynamicsofStocksandFlows

FIGURE7･16 Simu一atedvs. actualcocaine

epidemic

Dashedlines, data;solidlines, model.

J e a p̂

一

d o a d p u e s

n o u ト

1976 1980 1984 1988 1992 1996

J t2 a ^ P

Ld o ¢d p u 2 S n

O LJI

1976 1980 1984 1988 1992 1996

(u o !tt21nd od

0 u

O! I

U tぶ ) aO u a一｡ ^ a

1976 1980

Source:Homer(1993,1997).

1984 1988 1992 1996

259

AddingadditionalexogenousinputsCOuldimprovethefittothedata.But modelsshouldnotbetunedtofitdatabyintroducingexogenousvariableswhose

solefunctionistoimprovethecorrespondenceofmodeloutputtodata･Exogenous variablesmustbejustifiedbysignificantrealworldevidenceindependentoftheir

potentialcontributiontohistoricalfit.Further,Variablesinvolvedinanyfeedback loopsjudgedtobepotentiallysignificantrelativetothemodelpurposemustbe

capturedaspartofthemodel'sendogenousstructureandcannotbeusedasexoge- nousInputstOimprovehistoricalfit.

260 PartIITわolsforSystemsThinking

Whilethemodelshowsthatthesurveydataoverestimatedthedeclineinco- caineuse,model-generatedestimatesoftheactualnumberofactiveusers,while

remainingSignificantlyhigherthantheestimatesreportedinthesurveys,doshow adecline.Thefieldresearchandmodelresultsshowedthedroplncocaineusewas

notcausedprimarilybytheSupplyDisruptionLoopBlinFigure7-130rbythe CleanuptheStreetsloopB2,assupportersoftheinterdictionpolicyclaimed. Rather,theexponentialgrowthofcocaineusewaseventuallyhaltedbytwonega-

tivefeedbacksinvolvingpublicperceptlOnSOfcocaine'shealthandlegalrisks. First,cocaineisnotthebenignsubstanceitwasthoughttobeinthe1970S.Aspeo- plebegantoexperienceorhearabouttheNegativeHealthandSocialEffectsofthe

drug,theybecamelesslikelytostartandmorelikelytostop(balancingloopli3in Figure7-13).Second,growinglegalrisksofdruguseduetohigherarrestratesand

longersentencesdecreasedthewillingnessofpeopletostartandincreasedtheqult rate-theFearofArrestreducedusage(balancingloopB4)･Asthepopulationof activeusersbegantofall,thesocialexposureofnonusersalsofell,Weakeningthe

reinforcingWordofMouthloop(Rl). Unfortunately,bothofthesenegativeloopsinvolvelongdelays.First,thereis

alagbetweengrowthincocaineuseandtheincidenceofhamfulhealthandlegal

effects.Astheinitiationrategrewexponentially,sodidthestockofactivecasual users.Thestockofcompulsiveusersalsoroseexponentially,thoughwithasub-

stantiallag.Thelaginthegrowthofthecompulsiveuserpopulationisimportant becausecompulsiveusersaremorelikelytoexperienceseverehealtheffects(es- peciallyastheyturntocrack)andmorelikelytocommitdrug-relatedcrimesin-

cludingpushingthedrugtofinancetheirownhabits.Thustheexponentialgrowth incocaine-relatedcrime,arrests,medicalemergencies,anddeathslagsbehindthe growthofthecasualuserpopulation,whichinturnlagsbehindtheinitiationrate.

Thereisafurtherlaglntheperceptionbythepublicofthetruehealtheffects ofcocaine.Mostpeopledon'treadtheNewEnglandJournalofMedicineorthe AnnalsofAddictiontolearnaboutthehealthrisksofillegaldrugs.Instead,Public

perceptlOnSOfriskarestronglyconditionedbypersonalexperience,personal acquaintancewithsomeoneharmedbycocaine,andmediareportsofhigh-profile individualswhowerearrestedfor,injuredby,ordiedfromcocaineuse,suchasthe

comedianRichardPryor,whowasseverelyburnedwhilefreebasing,ortheUni- VersltyOfMarylandbasketballstarLenBias,whodiedofacuteheartfailurewhile

doingcocainetocelebratehisselectionasatopdraftpickbytheBostonCelticsof theNationalBasketballAssociation.

Thestrengthofallthesechannelsofpublicawarenessthereforelagsbehind

thepopulationofactiveusersdrivingthegrowthoftheepidemic･Exponential growthincocaineusedideventuallyreducethesocialacceptabilityofthedrugand thustheinitiationrate.However,thestockofactiveuserslagswellbehindtheini- tiationrate.Thestockofactiveuserswillriseaslongasinitiationexceedstherate

atwhichpeoplestopuslng,andthestockofcompulsiveusersincreasesaslongas theescalationrateexceedstherateatwhichcompulsiveusersstop.Thedynamics

ofthestockandflOwstructureinevitablymeanthatthepopulationofdrugusers, especiallythecompulsiveusersresponsibleformostofthecrimeandhealthef- fects,continuestogrowevenaftertheinitiationratepeaksandfalls.Thedelayen-

suresthatthereinforcingsocialexposureandwordofmouthfeedbacksdominate

Chapter7 DynamicsofStocksandFlows 261

thenegativeriskperceptlOnloopsintheearlyyearsoftheepidemic,leadingtoa laterandhigherpeakforincidenceandprevalence.

Still,bythelate1980S,nearlyeverycommunltyhadexperiencedthearrest,in-

jury,Ordeathofatleastoneofitspromislngyoungpeople,Slowlystrengthening thenegativefeedbacksthatslowtheinitiationrate.Ironically,thecocaineepidemic didnotabatebecauseinterdictionmadethedruglessavailable;onthecontrary,the

datashowedgrowlngaccessibility,purity,andaffordabilitythroughoutthe1980S. instead,theveryabundanceofcocaine,byleadingtoalargeincreaseinpersonal

knowledgeofitsharmfuleffects,ledpeopletoturnawayfromthedrug･Nolonger chic,StrlPPedofitssocialauraandbenignimage,thosewhocravedescapefrom theworldturnedfromcocainetootherdrugs.Thus,thecocaineepidemicwasul-

timatelyself-1imltlng. ThefeedbackstructureoutlinedinFigure7-13isqultegeneralandappliesto

anyharmfuldrug,legalorillegal.Thepositivefeedbacksgeneratinggrowthinus-

ageactswiftly,whilethenegativefeedbacksthatdeterusage,particularlypublic recognltlOnOfadrug'sharmfuleffects,areonlyperceivedslowly.Theresultisthe

characteristicboomandbustpattemfordruguse･Eachnewornewlypopulardrug generatesawaveofnaiveenthusiasminwhichusersextolitsbenefits,onlytodis-

coverasthepopulationofusersgrowsandmorepeopleescalatetocompulsiveuse thatthedruglSn'tasbenignaspeoplewereledtobelieve.

Infact,thecocaineepidemicofthe1980swasnotthefirst.Asimilarboomand bustincocaineuseoccurredinthelate1800S.Itbeganwithmedicinaluse,asco-

cainewaspraisedbythemedicalcommunlty,includingFreudinhisfamous1884 paper"OnCoca,"asacureforoplumaddiction,alcoholism,fatigue,depression, nervousness,timidity,impotence,andseasickness,amongothercomplaints.Foll

lowlngtheclassicpattern,cocainemovedintomoregeneralandrecreationaluse, becomlnganIngredientinCoca-ColaandsomeclgaretteS.Asusespread,avaiレ

abilityandpurityIncreased;insteadofinjectingOrdrinkingthepreparation,pow-

derforsnortingbecamepopular.Soontheharmfuleffectsbegantobeexperienced, observed,andreportedinthemedicalandpopularpress.Bytheearly1900S,co- caineusehadspread丘･omsocialelitestolowersocialclasses.Communitiesacross

thecountrystruggledtodealwithcompulsiveusers(knownas"cokefiends"),and "by1914theAtlantapolicechiefwasblaming70percentofthecrimes[inthecity] oncocaine"(GrinspoonandBakalar1985,p.38).Inresponse,legalrestrictions

andprohibitionsgrewincreaslnglysevere;in1922congressdefinedcocaineasa narcoticandbannedimportationofcoca;by1931everystatehadrestricteditssale andmostmadepossessionacrime.Cocaineusefellfromitspeakandremained

lowas1)eOl)1eturnedtootherdrugs,untilthecurrentel)idemicbegan.Similar

wavesofdrugusehavebeenrepeatedlyobservedfortheopiates,forpsychedelics, andforvariousstimulantsandbarbiturates.

Whileepidemicsofanyparticularillegaldrugareultimatelyself-limiting(if

thedrugisharmfulenough)peoplehavealwayssoughtoutmind-alteringsub- stances.Evenasonedrugfallsoutoffavor,newepidemicsbegin,centeredonnew

drugsforwhichthereisasyetnoexperienceofharmfuleffectsoronolddrugsfor

whichthehard-wonknowledgeofharmgainedbyprlOrgenerationshasfaded

fromcollectivememory.Themodestdeclineincocaineuseinthe1990sledtoan

increaseintheuseofotherdrugs,includingmarijuana,methamphetamine,and

262 PartIIToolsforSystemsThinking

mosttroubling,aresurgenceofheroinuse,morethan20yearsafterthelastwave

ofheroincrested,Thislatestheroinepidemicwasstimulatedbytheusualself-

reinforcingwordofmouthandmediafeedbacks,includingtheglorificationof

"heroinchic"inpopularcultureandCalvinKleinunderwearads･5

7.4 SuMMARY

Thischaptershowedhowstocksandflowsgeneratedynamics.Theprocessofac-

cumulationisequlValenttointegrationincalculus.Theamountaddedtoastockin

anyperiodisequaltotheareasweptoutbythenetrateofchangeinthestockover

thatperiod.Conversely,theslopeofthetrajectoryOfastockatanytlmeisitsde-

rivative,thenetrateofchange.Graphicalmethodsforintegrationanddifferentia-

tionwereintroduced.Giventhebehaviorovertimefortheratesaffectingany

stock,youcandeducethebehaviorofthestock;glVenthetrajectoryOfthestock

youcandeduceitsnetrateofchange,allwithoutuseofcalculus.Theabilitytore-

1atestocksandflowsintuitivelyisessentialforallmodelers,eventhosewithex-

tensivemathematicstrainlng,becausemostrealisticmodelshavenoanalytlCal

solutions.Examplesshowthatunderstandingthedynamicsofstocksandflows,

evenwithoutfeedback,canyieldinsightintoimportantproblems.

5Furtherreading:ShreckengostdevelopedamodelfortheUSCIAtoestimateheroinimports byintegratingprevalence,crime,price,purity,andotherdata(GardinerandShreckengost1987). Shreckengost(1991)appliestheframeworktococaine･Levin,Hirsch,andRoberts(1975),inThe PersistentPoppy,developasystemdynamicsmodelofheroinuseandabuseinacommunitybased onacasestudyofthesouthBronx.Theyusethemodeltoexploreavarietyofpolicyoptionsin-

cludingdemand-sidepolicies,increasedenforcement,andmethadonemaintenance.SeealsoLevin,

Hirsch,andRoberts(1978).Richardson(1983)developsasimplemodeltoexplainwhyaggressive

policeefforttoseizestreetsuppliesofheroinactuallyIncreasesdrug-relatedcrime･G61uke,

Landeen,andMeadows(198la,1981b)developedamodelofaddictivebehavior,focusingon alcoholism.HolderandBlose(1987)developamodelofcommunitylevelpolicyresponsesto alcoholism.Homeretal.(1982)presentasystemdynamicsmodelof(tobacco)smokingand analyzeavarietyofpolicies.

C呈osi王1g音量はf_}榊声:_-i!き-naIf_13_呈eSポ ●

S畳mp旦eS息丁眠息覗TeS

AmathematicaltheoTTISnottObeconsideredcompleteuntilyouhavemadeit

soclearthatyoucanexplainittotheji'rstmanwhomyoumeetonthestreet. -DavidHilbert

Ihopetoshow.‥thatmathematicalnotationcanbekeptclosetothevocabulafT

ofbusiness,･thateachvariableandconstantinanequationhasindividual

meanlngtOthepracticingmanager,･thattherequiredmathematicsiswithinthe

reachofalmostanyonewhocansuccessfullymanageamoderncorporation. lJayW.Forrester(IndustrialDynamics,1961,p.9)

Thischapterformalizestheconnectionbetweenstructureandbehaviorbylinking feedbackwithstockandflOwstructuresIThefocusisthesimplestfeedbacksys- tems,thosewithonestock(knownasfirst-ordersystems).Linearfirst10rdersys- tems(definedinthischapter)Cangenerateexponentialgrowthandgoal-seeking behavior.Noniirlearityir.firsLL-Ordersystemscausesshiftsinthedominantloops, 1eadingforexampletoS-ShapedgrowthThechapteralsointroducestheconcept ofaphaseplot-agraphshowinghowthenetrateofchangeofastockisrelated tothestockitself-andshowshowdynamicscanbederivedfromthephaseplot withoutcalculusordifferentialequations.

8tl F旧ST-ORDERSYsTEMS

Chapter4discussedthebasicmodesofbehaviorgeneratedbycomplexsystems andthefeedbackstructuresresponsibleforthem.Themostfundamentalmodesare

263

264 PartIIToolsforSystemsThinking

FIGURE8-1 Growthandgoalseeking:structureandbehavior

;.:;;ta_Sニ毒 hcrease

R･atL

) ′ヽyl ofthe

System

+ Stateofthe

Action ~+

Goal

(Desl]red StateofSystem)

exponentialgrowthandgoalseeking.Positivefeedbackcausesexponential

growth,andnegativefeedbackcausesgoal-seekingbehavior(Figure8-1).

Thesimplestsystemthatcangeneratethesebehaviorsisthe丘rst-order,linear

feedbacksystem.Theoyderofadynamicsystemorloopisthenumberofstate

variables,orstocks,itcontains.Afirst10rdersystemcontainsonlyonestock.Lin-

earsystemsaresystemsinwhichtherateequationsarelinearcombinationsofthe

statevariablesandanyexogenousinputs.

ThetermHlinear"hasaprecisemeanlngindynamics:inalinearsystemthe

rateequations(thenetinflowstothestocks)arealwaysaweightedsumofthestate

variables(andanye呆ogenousvariables,denotedUj):

dS/dt=NetInflow=alSl+a2S2+ ･･･+ anSn+blUl+b2U2+ ･･･+bmUm(811)

wherethecoefficientsalandb,areconstants･Anyotherformforthenetinflowsis nonlinear.1

8.2 PosmvEFEEDBAeKANDExpoNENTEALGROWTH

Thesimplestfeedbacksystemisafirst10rderpositivefeedlDaCkioop･lnafirst-

ordersystem,thereisonlyonestatevariable(stock),denotedherebyS･Thestate

ofthesystemaccumulatesitsnetinflowrate;inturn,thenetinflowdependsonthe

lForexample,formulationsforthenetinflOwsuchasal*Sl*S2,al*Sl/S2,OrMAX(0,al*Sl) areallnonlinear.Theterm"nonlinear"isoftenusedinothersenses,forexampletodescribethe nonchronologlCalnarrativestructureofnovelssuchasCortazar'SHopscotch･ThetermHnonlinearH inthesecontextsactuallymeans"nonsequential"andhasnothingtodowiththetechnicalmeanlng oflinearlty.

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 265

stateofthesystem(fornow,assumenoexogenousinputs).Ingeneral,thenetin-

flowisapossiblynonlinearfunctionofthestateofthesystem:

S-INTEGRAL(NetInflow,S(0)) (8-2)

NetInflow-f(S). (8-3)

Ifthesystemislinear,thenetinflowmustbedirectlyproportionaltothestateof

thesystem:

NetInflow-gS (8-4)

wheretheconstant蛋hasunitsof(1/time)andrepresentsthe丘'actionalgrowthrate ofthestock.2

Figure8-2shows血estructureofthissystemasacausaldiagramandalsoasa

setofequations.Asexamples,considertheaccumulationofinterestincomeintoa

bankaccountorthegrowthofapopulation.TheprlnClpalandprevailingInterest

ratedeterminetheinterestpayment;populationandthefractionalnetbirthrate determinethenetbirthrate.3

Whatwillthebehaviorofthesystembe?Section8.2.1usesbasiccalculusto

solvethedifferentialequation;thesolutionistheexponentialfunction

S(t)-S(0)exp(gt) (8-5)

whereS(0)isthevalueofSattheinitialtimet-0･Thestateofthesystemgrows

exponentiallyfromitsinitialvalueataconstantfractionalrateofgpertimeunit･

8.2.1 AnalyticSoJution紬!.the

LinearF室rsトOrderSystem

Tosolvethedifferentialequationforthefirst10rderlinearsystem,dS/dt-gS,first

separatevariables,toobtain

普 -gdt

Now,integratebothsides

I;-Igdt

toget

ln(S)-gt+c

wherecisacoriStant.TakirlgeXPOrientiaisofbothsidesgives

(8-6)

(8-7)

(8-8)

2Inthegeneralcaseofamultistatesystem,theratesofchange,dS/dt,areafunctionf()ofthe

statevectorSandanyexogenousvariablesU:dS/dt-i(S,U)･Inalinearsystem,theratesare

linearcombinationsofthestatesandexogenousvariables:dS/dt-AS+BUwhereAandBare matricesofcoefficients.Forgoodtreatmentsoflinearsystemtheory,see,e･g･,Ogata(1997)and Karnopp,Margolis,andRosenberg(1990).

3Representlngpopulationgrowthasafirsトorderprocessassumesthereisnodelaybetween birthandtheabilitytoreproduce,apoorassumptionformammals,butreasonableformany unicelllllarandothersmallorganisms.

266 PartIIToolsforSystemsThinking

FIGURE8-2 Firsトorder,linearpositivefeedbacksystem:Structureandexamples

GeneralStructure

dS/dt≡NetlnflowRate≡gS

Examp一es

Netlnterestlncome

=lnterestRate★Principa一

NetBirthRate

=Fractiona一NetBirthRate★Population

S-C*exp(gt) (8-9)

wherec*isexp(C).ThevalueofSattheinitialtime,whenexp(gt)-1,isbydefi- nitionS(0),soc*mustequalS(0).Substitutionyieldseciuation(8-5)三

8.2.2 Graph;capSohjtionofthe

LinearF喜rst-OrderPosii;veFeedbackSystem

Youdonotneedcalculustosolvetheequationforthefirst-orderlinearsystem. Youcanalsodeduceitsbehaviorgraphically･Figure8-3showsathirdrepresenta- tionofthestructureofthesystem:aphaseplot-agraphshowlngthenetrateasa functionofthestateofthesystem.Thegraphshowsthatthenetinflowrateisa straightlinestartlngattheorlglnWithpositiveslopeg.

FIGURE8-3 Phaseplotfor thefirst-order,

linearpositive feedbacksystem

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures

dS/dt=NetlntlowRate=gS

(a ∈ !tJst!u n )

a lE!t] NtO l-u 〓 aN

ot＼＼ StateoftheSystem(units)

267

Unstable

EquihLbrium

Notethatifthestateofthesystemiszero,thenetinflowisalsozero.Zerois

anequilibriumofthesystem:nosavlngS,nOinterestincome;nopeople,nobirths.

However,theequilibriumisunstable:addanyquantltytothestockandtherewill

nowbeasmall,positivenetinflow,increaslngthestateofthesystemabit.The

greaterstateofthesystemleadsnowtoaslightlygreaternetinflowandastill

largeradditiontothestock.Theslightestdeparturefromtheequilibriumleadsto

furthermovementawayfromtheequilibrium,justaSaballbalancedexactlyatthe

topofahill,ifdisturbedevenslightly,willrolleverfasteraway丘.omthebalance

polnt.Thegreaterthestateofthesystem,thegreaterthenetinflow:thisispre-

ciselythemeanlngOfthepositivefeedbackloopcouplingthestockanditsnetin-

flow.Inthegeneralcasewherethephaseplotofastatevariablecanbenonlinear,

thestateofthesystemwillgrowwheneverthenetrateisanincreasingfunctionof

thestock.Anequilibriumisunstablewhenevertheslopeofthenetrateattheequi-

libriumpolntispositive.

Becausetherateequationintheexampleislinear,thenetincreaserategrows

exactlyinproportiontothestateofthesystem.Everytlmethestateofthesystem

doubles,sotoowillitsabsoluterateofincrease.Therefore,thetrajectoryOf

thesystemintimeshowsanever-increaslngacceleration.Figure8-4showsthetra-

jectoryOfthefirst-orderlinearpositivefeedbacksystemonthephaseplotandasa

ofthesystemis1unit.ThearrowsalongthephaseplotshowthattheflOwofthe

systemisawayfromtheunstableequilibriumpolnt.Fromanynonnegativestartl

lngpOlnt,thestateofthesystemgrowsatanever-acceleratlngrateaSitmoves

alongthelineNetInflow-gS･4Theacceleratinggrowthiseasilyseeninthetime

4Thesystemfssymmetricfornegativevaluesofthestatevariable･IfS(0)<0,Swillbecome evermorenegatlVeatexponentialrates.Inmostsystems,however,thestatevariablesarerestricted tononnegativevalues(therecanbenonegativepopulations).

268 PartII TわolsforSystemsThinking

FIGURE8-4 Exponentialgrowth:structure(phaseplot)andbehavior(timeplot)

Thefractionalgrowthrateg-0.7%/timeunit.lnitialstateofthesystem-1unitlPointsonplotshow everydoubling(10timeperiods)

Structure

( a

Lu !tJ選

u n ) JVLO llu〓 a N

128256 512

StateofSystem(units)

1024

( s l !u

n) u a l S ^ S

a L lt i O

a l e l S

Behavior

0 200 400 600 Time

800 1000

tln flo

w(u ni t s

Jtime )

domain.Theslopeofthestatevariableateverypointisexactlyproportionaltothe

quantltylnthestock,andthestateofthesystemdoublesevery100timeperiods (Seesection8.2.3).

NotethatchanglngthefractionalgrowthratechangestheslopeofthelineNet Inflow-gSandthereforetherateofgrowth,butnottheexponentialshapeofthe Curve.

8.2.3 ThePowerofPositiveFeedback:

DLRtJb軸gTimes

Beforecontinulng,trythefollowingChallenge.

Paper『0日dimg

Takeanordinarysheetofpaper.Folditinhalf･Foldthesheetinhalfagain.Thepa- perisstilllessthanhalfamillimeterthick.Ifyouweretofoldit40moretimes, howthickwouldthepaperbe?Ifyoufoldeditatotalof100times,howthick

woulditbe?Giveyourintuitiveestimate,withoutusingaCalculator.Giveyour 95%upperandlowerconfidenceboundsforyourestimates(thatis,arangeofes-

timatesyouare95%sureincludestherightanswer.Your95%confidenceboIJind

meansyoubelievethereisonlya5%chancethecorrectanswerfallsoutsidethe

upperandlowerboundsyougive)･Askyourfriendsandfamilytotrythechallenge aswell,notlngdowntheiranswersandconfidencebands.

TheRuleof70

Positivefeedbackloopsarethemostpowerfulprocessesintheuniverse.Their powerarisesfromthefactthattherateofincreasegrowsasthestateofthesystem

Chapter8 CloslngtheLoop:DynamicsofSimpleStructures 269

grows.Whenthefractionalnetincreaserateisconstant,positivefeedbackleadsto

exponentialgrowth.Exponentialgrowthhastheremarkablepropertythatthestate

ofthesystemdoublesinafixedperiodoftime,nomatterhowlargeitis.Intheex-

ampleinFigure8-4,thestateofthesystem doublesevery100timeperiods･It takes100timeperiodstogrowfromtheinitialvalueof1to2unitsandonlyloo

timeperiodstogrowfrom 1000to20000rfrom 1billionto2billion･Anyquan-

titythatgrowsbypositivefeedback,thatdoublesinafixedperiodoftime,gets

verylargeafterJustafewdoublings.

Youcanreadilydeterminethedoublingtimeforanyexponentialgrowth

process.Todososolveequation(815)fortheintervaloftimetdthatsatisfiesthe

equationwhenthestockhasreachedtwiceitsinitialvalue:2S(0)-S(0)exp(gtd). Theresultis

td-1n(2)/g (8-10)

wheretdisthedoublingtime.5Thenaturallogof2-0.6931… Roundingln(2)

to0.70andexpresslngthefractionalgrowthrateinpercentpertimeperiodgives

theRuleof70:

td-70/(loo雷). (8-ll)

Thusaninvestmentearning7%/yeardoublesinvalueafter10years･6Asshownin

Figure4-2,theaveragegrowthrateofrealGDPintheUSoverthepast100years

hasbeen3.4%/year,sothedoublingtlmeisroughly20years.Thepast200years

havewitnessed10doublings,increaslngthesizeoftheUSeconomybyroughlya

factorofonethousand(210-1024).

8.2適 M岳spereep色盲oms⑳菅EXp⑳mem骨iaLEGr⑳Wをh WhiletheRuleof70issimpleandeasytoapply,theimplicationsofexponential

growtharedifficulttograspintuitively.Wagenaar(1978)andWagenaarand

Sagaria (1975)studied people'sability to extrapolate exponentialgrowth

processes.Theyfoundpeoplegrosslyunderestimatedtherateofgrowth,tending

toextrapolatelinearlyinsteadofexponentially.Thatis,wetendtoassumeaquan-

tltyIncreasesbythesameabsoluteamountpertimeperiod,whileexponential

growthdoublesthequantitylnafixedperiodoftime･Whenthegrowthrateand

forecasthorizonaresmall,linearextrapolatiOnisareasonableapproximationto

5Dividingequation(8-5)throughbyS(0)yields2- exp(gtd).Thatis,thedoublingtimeisin- dependentoftheinitialsizeofthestock･Takingthenaturallogofbothsidesanddividingthrough bygglVeStd-1n(2)/g.

6TheRuleof70isbasedontheassumpt10nthatthegrowthprocessiscontinuousintime･In theinvestmentexample,theassumptlOnisthatinterestiscompoundedcontintlOuSly･Compounding atdiscreteintervalsreducestheeffectiveyieldandlengthensthedoublingtlmeJndiscretetime, equation(815)nolongerholds;insteadthestatevariablelSgivenbyS(t)-S(0)(1+g/p)Ptwhere

pisthecompoundingperiod(forexample･p= 12formonthlyc?mpoundingwhengistheinterest rateperyear).ThedoublingtimeofthediscretetimeprocessisglVenbytd-ln(2)/(pln(1十g/p))･

Sinceln(l+g/p)記g/pforsmallg/p,theRuleof70remainsチgoodapproxiplationofdiscrete timepositivefeedbackprocessesaslongasthecompoundingIntervalisrelatlVelyshortcompared tothedollblingtlme.Forexample,aprocessgrowlngatarateOf7%/yearcompoundedonlyan- nuallydoublesin1 0.24yearscomparedto9.90yearswhencompoundingiscontinuous(usingthe exactvalueofln(2)tocalculatetd).Inthelimitaspぅ co,(1+g/p)(pt)- exp(gt).

270 PartIITわolsforSystemsThinking

exponentialgrowth.However,asthegrowthrateincreasesorthefわrecasthorizon

lengthens,theerrorsbecomehuge,

Howthickdidyouthinkthesheetofpaperwouldbeafterfoldingit42times?

After100times?Mostpeopleestimatethepaperwillbelessthanameterthick

(3.3feet)evenafter100fわlds.Infact,after42foldsthepaperwouldbe440,000 kilometersthick-morethanthedistancefromtheearthtothemoon!Andafter

100folds,thepaperwouldbeanincomprehensiblylmmenSe850trilliontimesthe distancefromtheearthtothesun!7

Theunderestimationofexponentialgrowthisapervasiveandrobustphenom-

enon.Wagenaarandcolleaguesfoundthattheunderestimationwasrobusttothe

presentationofthedataintabularvs.graphicform.SurprlSlngly,showingmore

datatendstoworsentheunderestimation,andtrainlnglnmathematicsdidnothelp

(WagenaarandTimmers1979).

Thecounterintuitiveandinsidiouscharacterofexponentialgrowthcanbeseen

byexaminlngltoverdifferenttimehorizons.Figure815Showsapositivefeedback

processgrowlngeXpOnentiallyataconstantrateof0.7%/timeperiod,withfour

differenttimehorizons.BytheRuleof70,thedoublingtimetd- lootimeperi-

ods･Overatimehorizonofone-tenththedoublingtlme,growthisimperceptible.

Overatimehorizonofonedoublingtime,thegrowthappearstobeclosetolinear.

Over10doublings,theacceleratlngCharacterofexponentialgrowthisclearlyvis-

ible.Over100doublings,itappearsthatnothinghappensatalluntilabout90%of

thetimehaspassed.Manypeople,examinlngthebehavioroverthelongtlmehori-

zon,concludethattheremusthavebeenadramaticchangeinthestructureofthe

systemaroundtime9000.Infact,thesameprocessofaccumulationpoweredby

positivefeedbackisoperatlngthroughouttheentirehistory,butonlythelastfew

doublingsarenoticeable.

Ofcourse,norealquantltyCangrowforever.Becauseexponentialgrowthdou-

blesinafixedtimeinterval,positivefeedbackprocessesapproachtheirlimits

rapidlyandoftenunexpectedly.Meadowsetal.(1972,p.29)illustratewithanold Frenchriddle:

SupposeyouownapondonwhichawaterlilylSgrOWlng.Thelilyplantdoubles insizeeachday.Ifthelilywereallowedtogrowunchecked,itwouldcompletely coverthepondin30days,chokingofftheotherformsoflifeinthewater.Fora longtlmethelilyplantseemssmall,andsoyoudecidenottoworryaboutcuttlng

itbackuntilitcovershalfthepond.Onwhatdaywillthatbe?Onthetwenty-ninth day,ofcourse･Youhaveonedaytosaveyourpond･8

7Eachfolddoublesthethickn essofthepaper･AtypicalsheetofpaperisaboutO･1mmthick･ Aftertwofoldsitis0.4mmthick;afterfivefolds,just3.2mm.After42doublingsthethickness hasincreasedbyafactorof242;岩4･4triilion･MultiplyingbytheinitialthicknessofO･1mmand convertlngtOkilometersgivesathicknessof440,000km.After100foldsthethicknesshasin- creasedbyafactorof2100-1127xlO30lMultiplyingbytheinitialthickness,convertlngtOkilome- ters,anddividingbythemeanearth-solardistanceof93millionmiles-149millionkmglVeSa thicknessof852×1012timesthemeansolardistance-morethan1billionlight-years･Ofcourse, youwouldneedaverylargesheetofpapertocarrytheexperimentthrough.

8Infact,thelilypadwouldbemicroscopicformuchofthe30days･Initiauythelilycoversonly 93×10-8%ofthepond'sarea･Itreaches1%oftheareaonlyafterthe23rdday.

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271

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272 PartIIToolsforSystemsThlnklng

Asvariouslimitsareapproached,nonlinearitiesalwaysweakenthepositiveloops

andstrengthenthenegativefeedbacksuntiltheexponentialgrowthhalts.These

nonlineareffectsareillustratedbyanotherfamousstoryaboutexponentialgrowth.

AstoldbyMeadowsetal.(1972,p.29):

ThereisanoldPersianlegendaboutaclevercourtierwhopresentedabeautiful chessboardtohiskingandrequestedthatthekingglVehiminreturn1grainof riceforthefirstsquareoftheboard,2grainsforthesecondsquare,4grainsforthe third,andsoforth.Thekingreadilyagreedandorderedricetobebroughtfrom hisstores.Thefourthsquareofthechessboardrequired8grains,thetenthsquare took512grains,thefifteenthrequired16,384,andthetwenty-firstsquaregavethe courtiermorethanamilliongrainsofrice.Bythefortiethsquareamillionmillion ricegrainshadtobebroughtfromthestorerooms.Theking'Sentirericesupply wasexhaustedlongbeforehereachedthesixty-fourthsquare.

Infact,thetotalquantltyOfriceonall64squareswouldhavecoveredallofmod-

erndayIrantoadepthofmorethan5feet.

8.2.5 ProcessPoint:OvercomingOverconfidence

ConsideragalnyouranswerstOthepaperfoldingchallenge･Notonlydopeople

underestimatethethicknessofthepaper,butthecorrectanswersfalloutsidetheir

95%confidenceboundsalmostallthetime.Thatis,peoplearegrosslyoverconfi-

dentintheirjudgments.

Overconfidenceisoneofthemostrobustjudgmentalbiasesdocumentedinthe

psychologicalliterature.Inacarefulreview,ScottPlous(1993)writes,HNoprob-

leminjudgmentanddecisionmakinglSmoreprevalentandmorepotentiallycaト

astrophicthanoverconfidence."

Overconfidencemeanstheconfidenceboundspeopleprovidearoundtheires-

timateofanunknownquantityaretoonarrow,CauSlnganunexpectedlyhighrate

ofincorrectpredictions.LichtensteinandFischoff(1977)foundthatpeoplewere

65%to70%confidentofbeingrightinanswerlngaVarietyofquestionswhenin

facttheyansweredcorrectlyatonlyaboutthechancerateof50%.Suchresults

havebeenreplicatedinawiderangeoftasksandwithexpertsaswellasnovices.

Lichtenstein,Fischoff,andPhillips(1982)reviewedstudiestotalingnearly15,000

judgmentsandfoundthatpeople'S98%confidenceboundscontainedthecorrect

responseonly68%ofthetime-anerrorrate16timesgreaterthanexpected.

Extensivestudyoftherelevantissuecanactuallyworsenoverconfidence.Os-

kamp(1965)Showedthatthemoreinformationpeoplereceivedaboutanissue,the

moreconfidenttheybecame-whileaccuracydidnotimprove.Financialincen-

tivesdonotreduceoverconfidence:Insomestudiessubjectsweregiventheopt10n

ofbettingontheiranswersattheoddstheyestimatedforbeingcorrect.Theycon-

sistentlylostmoney.

situationsinwhichpeople'sconfidenceboundsareapproximatelycorrectare

rare･Weatherforecastersandprofessionalcardplayersareamongthefewgroups

whosejudgmentshavebeenfoundtobewellcalibrated.Thesearenarrowly

boundedcontextswheretherelevantfactorsarewellknown･Thousandsofrepe-

titionsprovidefeedbackenablingthemeteorologistandgamblertolearnfrom

experience.TheseconditionsdonotholdformostdynamicallycomplexsettlngS ,

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 273

includingjudgmentsaboutthelikelybehavioroffeedbacksystems:thecausal

structure,relevantvariables,andparametersarehighlyuncertainandlargelyun-

known(seechapter1).Inmostsocialandbusinesssituationsthetimedelaysareso

longthereislittleornochancetolearnfromexperience;bythetimefeedbackis

availableitwillbetoolatetotakeeffectiveaction･ManylnVeStOrSandmoney

managersduringthegreatbullmarketsofthe1920sand1980S-90sneverexperi-

encedamarketcrashandunderestimatedthelikelihoodofdecliningshareprices.

Andforissuessuchasglobalclimatechangetheworldmustadoptpoliciesre-

gardingemissionsofgreenhousegasesdecadesbeforethefullimpactofhuman

activityOnglobalclimatewillbeknown.Overconfidencemeansyouwillproba-

blybuytoolittleinsuranceandarelikelytowakeuponedaytofindyouhavein-

sufficientcoverage･BeforetheChallengerexplosionNASAestimatedtheriskof

catastrophiclaunchfailureat1in100,000･9

Asanillustrationthatexpertsarefarfromimmunetooverconfidence,consider

thedebateoverglobalwarming｡TheeconomistWilliamNordhaus(1994)con-

ductedasurveyofdistinguishedexpertsonglobalclimatechangetoassesstheir viewsonthelikelyeconomiceffectsofglobalwarmlng.Nordhausaskedthepanel

toestimatethelossofgrossworldproduct(GWP)Causedbyvariousamountsof

warmlng.Theresultsshowedahugegulfbetweentheestimatesofthescientists

comparedtotheeconomists･ScientistsestimatedtheprobabilityofaHhigh-

consequenceevent"(acatastrophicchangeinclimatecuttingGWPby25%or

more)as20to30timesmorelikelythantheeconomistsdid.Estimatesofthemost

likelyreductioninGWPweresimilarlybimodal,Withscientistsgenerallyestimat-

1nglargeimpactsandeconomistsgenerallyestimatlngSmallorevenpositiveim-

pactsofwarmlngOntheglobaleconomy.NooneknowswhichgrouplScorrect.

Whatisstriking,however,isthesmallrangeofuncertaintyeachexpertallowed.

Eachprovided90%confidencebandsaroundtheirbestestimates,yetinmany

casestheserangesweresosmalltheyexcludedthemajorityOftheotherexperts' views.Economists,whotendedtopredictsmalleffects,tendedtohavethenarrow-

estconfidencebands.Oneeconomistwrote,"Itisimpossibletocontemplatewhat

societywillbelikeacenturyfromnowastechnologychanges"yetestimatedthat

a30Criseinglobalmeantemperatureby2090wouldproduceachangeinGWP

rangingfrom-2%to+1%,Oneofthesmallestrangesofferedbyanyrespondent.

OvercomlngOVerCOnfidencerequiresgreaterhumilityaboutthelimitsofour

expertise.Severaltechniquescanhelp.Listallthereasonsyouroplnioncouldbe

wrong･Trytoidentifytheimplicitassumpt10nSOfyourmentalmodelandconsider

howtheoutcomemightchangeifdifferentassumptionsWereused.Becauseiden-

tifyingthehiddenbiasesinourownmentalmodelsisdifficult,itisespeciallyvalu-

abletosolicitthejudgmentsandopinionsofadiversegroupofpeople,especially

thosewithoppositeviews.Yourcriticswillusuallybefarmoreeffectiveinhelpl

lngyouCalibrateandimproveyourjudgmentthanyour丘.ユends-seekoutandweト

cometheirviews.YoushouldbeespeciallysuspectofstatementsthatsomethinglS

absolutelycertain,inevitable,withoutdoubt,oraoneinamillionchance,espe-

ciallyifthesituationinvolveshumanbehaviororifpeople'sjudgmentsrequlre

9ofcourse,NASA'sestimatecouldhavebeencorrectandtheChallengerdisaster,Just extraordinarilybadluck.WhileloglCallypossible,Carefulstudiesofthedisasterbeliethatview.

274 PartIIToolsforSystemsThinking

mentalsimulationofdynamicallycomplexsystems･Whenassesslngtheconfi- denceintervalsprovidedbyformalmodelsorstatisticalanalysisofdata,remem-

berthattheconfidenceboundsprovidedbystatisticalmodelsmeasureonlythe

uncertaintyduetosamplingerror,andnotthatduetospecificationerror(errorsin

themodelboundaryandinthemaintainedhypothesesofthestatisticalmethod).

TheselattersourcesoferroraretyplCallymuchlargerthanuncertaintyduetosam-

plingerror･Whenformalmodelsareavailable,conductextensivesensitivitytests,

notonlyoftheresponsetoparametricuncertaintybutalsotouncertaintyaboutthe

modelboundary,feedbackstructure,andotherstructuralassumptlOnS.

8.3 NEGATIVEFEEDBACKANDExpoNENTIALDECAY

Firstl0rderlinearpositivefeedbacksystemsgenerateexponentialgrowth.First-

ordernegativefeedbacksystemsgenerategoal-seekingbehavior.Whenthesystem

islinear,thebehaviorispureexponentialdecay.

ThefeedbackstructureresponsibleforexponentialdecayisshowninFig-

ure8-6.As examples,considerthedeathrateofapopulationorthedepreciationof

anasset.Inbothcases,thenetoutflowisproportionaltothesizeofthestock.The

equationforthenetrateofchangeofthestockis

NetInnow--NetOutflow--dS (8112)

wheredisthefractionaldecayrate(itsunitsare1/time)AThereciprocalofthefrac-

tionaldecayrateistheaveragelifetimeofunitsinthestock(seechapter11ondel

laysforaproof).

Todeducethebehaviorofthelinear,first10rdernegativefeedbacksystemnote

thatequation(8-12)isthesameasequation(8-4)exceptthatthenegativeofthe

fractionaldecayratereplacesthefractionalnetincreaserate.Thesolutionisthere-

foreglVenbythesameexponentialfunction,with-dreplacingg:

S(t)-S(0)exp(-dt) (8-13)

Figure8-7showsthephaseplotforthefirst10rderlinearnegativeloopsystem.The

netrateofchangeofthestockisnowastraightlinewithnegativeslope-d.Asbe-

fore,thepointS-0isanequilibrium:wheretherearenopeople,therecanbeno

deaths;whenthevalueofanassethasdeclinedtozero,nofurtherdepreciationcan

betakenUnlikethepositivefeedbackcase,theequilibriumisstable.Increaslng

thestateofthesystemincreasesthedecayrate,movlngthesystembacktoward

zero.Asystemwithastableequilibriumislikeanorangerestlngatthebottomof

abowl.Ifyoupushtheorangeupthesideofthebowlandreleaseit,itrollsback

downuntilitcomestorestagalnatthebottom.Deviationsfromtheequ111Drlum

areself-correcting.

Figure8-8Showsthedynamicsofthesystemonboththephaseplotandinthe

timedomain.The丘.actionaldecayrateintheexampleis5%/timeperiod,andthe

initialstateofthesystemis100units･Initially,thedecayrateis-5units/timepe-

riod･Thedecayrateisdirectlyproportionaltothestateofthesystem,soasthe

stateofthesystemdeclines,sotoodoesthedecayrate.Theflowofthesystem,de-

notedbyarrowsinthephaseplot,isalwaystowardthestableequilibrium.Thedots onthephaseplotshowthelocationofthesystemevery10timeunits.Notehow

FtGURE8-6 Firsトorderlinear

negativefeedback: structureand

examples

FIGURE8-7 Phasep一otfor exponentialdecay via‖nearnegative feedback

Chapter8 ClosingtheLoop:DyI-amicsofSimpleStructures

GeneralStructure

Netln刑owRate =-NetOut朋owRate=-dS

d Fractional

DecayRate

Examples

275

DepreciationRate =BookValue/AssetLifetime

NetlntlowRate=-NetOuttlowRate≡-dS

0(au !tJst!u n )

a tt2t] き O lIu J la N

276 PartIITわolsforSystemsThinking

FIGURE8-8 Exponentialdecay:structure(phaseplot)andbehavior(timeplot)

Thefractionaldecayrated-5%/timeunit.Initialstateofthesystem-100units.

Structure

( a

∈!I J S l ! u n ) N L O[iu〓

0 20 40 60 80 100 StateofSystem(units)

( s l !u

n ) u Ja lS ^ S O L

Jl10 a l t2 t S

Behavior

StateoHheSystem (leftscale)

Netlnflow (rightscale)

N e 〓 n f l

(u コit s J t i m e )

20 40 60 Time

theadjustmentisrapidatfirstandfallsovertime.Thestateofthesystemfallsata

diminishingrateasitapproacheszero･

Theexponentialdecaystructureisaspecialcaseofthefirst10rderlinearnega-

tivefeedbacksystem.Asdiscussedinchapter4,allnegativefeedbackloopshave

goalsJnthecaseofexponentialdecay,suchasthedeathrateanddepreciationex-

amples,thegoalisimplicitandequaltozeroJngeneral,however,thegoalsof

negativeloopsarenotzeroandshouldbemadeexplicit.Figure8-9showsthegen-

eralstructureforthefirst10rderlinearnegativefeedbacksystemwithanexplicit

goal.Examplesincludetheprocessbywhichafirmadjustsitsinventoryorwork-

forcetothedesiredlevel.PossibledelaysinchangingProductionorhiringnew

workersareIgnored.Includingsuchdelayswouldaddadditionalstockstothe model.

Inthegeneralcase,thecoITeCtiveactiondeterminingthenetinflowtothestate

ofthesystemisapossiblynonlinearfunctionofthestateofthesystem,S,andthe desiredstateofthesystem,S*:

NetInflow-i(S,SX). (8-14)

Thesimplestformulation,however,isforthecorrectiveactiontobeaconstant

fractionpertimeperiodofthediscrepancybetweenthedesiredandactualstateof

thesystem:

Netlnflow -Discrepancy,/AT-(S*-S),/AT (8-15)

wheretheparameterATisknownastheadjustmenttimeortimeconstantforthe loop.Notetheunitsofequation(8-15):thenetinflowhasdimensionsofunits/time

period･Thediscrepancybetweenthedesiredandactualstateofthesystemhasdi一

mensionsofunitsIForexample,ifthedesiredinventoryofafirmis100unitsand

currentinventorylSOnly60units,thediscrepancyis40units.Theadjustmenttime

representshowquicklythefirmtriestocorrecttheshortfall:ifthefirmseeksto

correcttheshortfallquickly,theadjustmenttimewouldbesmall.Forexample,the

firmmaysettheadjustmenttimetoAT-1week,meanlngthattheywouldcorrect

Chapter8 ClosingtheLoop:DynamicsofSimpleStmctures

FlGURE819 Firsトorderlinearnegativefeedbacksystemwithexplicitgoals

GeneralStructure

S★ DesiredStateof

theSystem

Examp一es

lnventory Desired

hventory

AdustmentTime

･=--I-I -:I_=: 千AdustmentTime

NetHiring

AdustmentTime

W -

1nventory

･ef Tim.:au

｣警

Shortfall +

Labor

dS/dt≡Netln¶owRate

=Discrepancy/AT =(S★ -S)/AT

277

ProductionRate

InventoryShortfaH/AT (Desiredlnventory-1nventory)/AT

Desired LaborForce

一〆 ---

Shortfall +

NetHiringRate =LaborShortfall/AT

=(DesiredLabo卜Labor)/AT

theinventoryataninitialrateof40units/week.Beingmorecautiousandsetting AT-2Weekswouldentailaninitialnetinflowof20units/week,andaneven

moreaggressivefirmmightsetAT-0.5weeks,leadingtoaninitialnetinflowof

inventoryof80units/week.Ofcourse,thesecorrectiveactionscausetheinventory

shortfalltodiminish,reducingthenetinflowovertimeuntilthediscrepancylS

eliminated.Thediscrepancycanbenegative,aswhenthereisexcessinventory;ln

thiscasethenetinflowisnegativeandthestateofthesystemfalls.

278

FIGURE8-10

Phaseplotfor firsトorder一inear

negativefeedback systemwith expllCitgoal

FIGURE8-ll

Exponential approachtoagoal

Thegoalisloo units.Theupper curvebeglnSWith S(0)-200;the lowercurvebeglnS withS(0)-0.The adjustmenttime inbothcasesis 20timeunits.

PartII n)OlsforSystemsThinking

Thereciprocaloftheadjustmenttimehasunitsofl/timeandisequivalentto

thefractionaladjustmentrate,Correspondingtothefractionaldecayrateintheex-

ponentialdecaycase.Thephaseplotforthesystem(Figure8-10)showsthatthe

netinflowratetothestateofthesystemisastraightlinewithslope(I1/AT)and

equals0whenS-S*･Thebehaviorofthenegativeloopwithanexplicitgoalis

alsoexponentialdecay,butinsteadofdecaylngtOZero,thestateofthesystem

reachesequilibriumwhenS-S*･

Iftheinitialstateofthesystemislessthanthedesiredstate,thenetinflowis

positiveandthestateofthesystemincreases,atadiminishingrate,untilS-S*･If

thestateofthesystemisinitiallygreaterthanthegoal,thenetinflowisnegative

andthestateofthesystemfalls,atadiminishingrate,untilitequalsthegoal.The

flowofthesystemisalwaystowardthestableequilibriumpointatS-S*(Fig- ures-ll).

NetlnflowRate=-NetOutf一owRate=(S★-S)/AT

∈ !t

Jsl!u n )

al e t

]き Ol-u〓 a N

60 80 100

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 279

8.3.1 TimeConstantsandHatトLives

Justasexponentialgrowthdoublesthestateofthesysteminafixedperiodoftime,

exponentialdecaycutsthequantltyremainlngbyhalfinafixedperiodoftime.

Thehalf-lifeofanexponentialdecayprocessiscalculatedinthesamefashionas

thedoublingtime.Thesolutiontoequation(8-15)is

S(t)-Sx-(Sr - S(0))exp(-t/AT) (8-16)

Inequation(8-16)S*-S(0)istheinitialgapbetweenthedesiredandactualstates

ofthesystem.Thetermexp(-t/AT)decaysfrom 1to0astimeincreases;itis

thefractionoftheinitialgapbetweendesiredandactualstatesremainlngatany

timet･Theproduct(S* - S(0))exp(-t/AT)isthereforethecurrentgapremaining

betweenthedesiredandactualstates.Whenthetermexp(-t/AT)hasdecayedto

zerothestateofthesystemequalsthegoal(Figure8-12).

Thehalf-lifeisglVenbythevalueoftime,th,Whichsatisfies

O.5-exp(-th/AT)-exp(-dt) (8-17)

wherethe虫.actionaldecayrated- 1/AT.Solvingforthyields

th=ATln(2)-1n(2)/d2;0.70AT-70/(100d) (8-18)

Thehalf-lifeisglVenbythesameRuleof70characterizingexponentialgrowth

Equivalently,thehalfllifeisgivenby70%oftheadjustmenttime.10

EachtimeperiodequaltoAT,thegapremainingfallstoexp(-AT/AT)-37%

ofitsinitialvalue,and1-exp(-AT/AT)-63%ofthegapiscorrected.Whyisn't

theentiregapcorrectedafteronetimeconstanthaspassed?Fromequation(8115)

theinitialrateofchangeofthestateofthesystemis(S*-S(0))/AT,thatis,theini-

tialgapdividedbytheadjustmenttime.Iftheinitialrateofadjustmentremained

constant,theentiregapwouldbeeliminatedafterATtimeunits(notethatthetan-

genttothestateofthesystemattime0justeliminatesthegapafteroneadjustment

time;seeFigure8-12).However,thenetrateofchangeofthestateofthesystem

doesnotremainconstant･Asthestateofthesystemapproachesthegoal,thegap

remainingfalls,andsotoodoesthecorrectiveaction.Thenegativefeedbackgrad-

uallyreducestheadjustmentrateasthegoalisapproached.

ThetableatthebottomofFigure8112showsthefractionofthegapremaining

fordifferentmultiplesoftheadjustmenttime.Afteroneadjustmenttime,63%of

theinitialgaphasbeencorrected･Aftertwoadjustmenttimes,thestateofthesys-

temhasmoved86%ofthewaytothegoal.Afterthreeadjustmenttimes,thead-

justmentis95%complete.Technically,thegapISneverfullycorrected;thereis

alwayssomesmallfractionofthegapremainlngatanyfinitetime.However,for

allpracticalpurposesadjustmentiscompleteafterthreetofouradjustmenttimes

havepassed･11

10Takinglogsofbothsidesgivesln(0.5)--th/ATorth-ln(0.5)*AT-ln(2)*AT.

llAfterfouradjustmenttimes,thegapremainlnglSjust2%,aquantltyoftensmauerthanthe

accuracywithwhichthestateofthesystemcanbemeasured.ControlenglneerSSpeakofasystem's settlingtime,definedasthetimerequiredforasystem,afterashock,tosettlewithinasmal1per- centageofitsequilibriumvalue.

280 PartII Tわolsfb∫SystemsThinking

FrGURE8-12 Relationshipbetweentimeconstantandthefractionofthegapremaining

Rateequationforfirstorderlinearnegativeloopsystem:

NetlnflowRate≡-NetOuttlowRate=(S★-S)/AT

S(t)

Stateot

theSystem

Stateot

theSystem

6u !u ! E? ∈ atJd t29 一E2!l!u l -O uO !)3t2Jj

AnalyticSolution:

S ' - (S'-S(0)) ' exp(-I/AT)

i= :電=i i≡ 琵 =i

Desired

Stateof

theSystem

Desired

Stateof

lnitial

Gap

Fractionof . lnitialGap

Remaining

ヽ一一一ヽ′.............′ theSystem GapRemaining

l 1-expT(-1/AT,

1-ex(-2/AT) 1-exp2lAT)---: -- - - 二二: l

ヽ p(｢1′AT,

exp(

1AT 2AT

Time(multiplesofAT)

FractionoflnitialGap

Remaining

FractionofInitialGap Corrected

0 T

5 7

0 7 4

0 3

. 1

･1 0

二二

二

)

ー

)

一

【

ー

(

ー

(

P nL P

i -exp(-0) 1-exp(-1)

1-exp(-2)

1-exp(-3)

1-exp(-4)

1-exp(-5) 3

3 7

6 8

0 0

二

二二

二

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 281

GoaトSeekingbehavior ConsiderthelaborforcestructureinFigure819.Assumethenethiringratefora

firmisproportionaltothegapbetweenthedesiredandactualworkforce･Without uslngacomputerOrCalculator,Sketchthebehavioroftheworkforceandnethiring rateforthefollowlngSituations･

i.Thedesiredworkforceincreasesfrom1000to2000atweek4,thensteps

downto1500atweek12(Figure8-13).Assumetheworkforceadjustment timeAT-4Weeksandtheactualworkfbrceinitiallyequalsthedesired workforce.

2.Repeatstep1forthecasewherethelaborforceadjustmenttimeAT- 2weeks.

3.Sketchtheworkforceandnethiringrateforthecasewherethedesired workforceincreaseslinearlybeginninginweek4(Figure8-14)･Assumethe

l l l 】 lDesiredLaborForce

0 2 4 6 8 10 12 14 16 18 20 22 24

( q aa NVa

l d

oad)

let] 6 u!

)

H laN

0 2 4 6 8 10 12 14 16 18 20 22 24

Time(weeks)

282 PartIIToolsforSystemsThinking

laborforceadjustmenttimeAT-4weeks.Doestheworkforceeventually

equalthedesiredworkforce?Whyorwhynot?

DesiredLabl orFoFie

0 2 4 6 8 10 12 14 16 18 20 22 24

(qaaきP

l d

oa d

)

ate t] Bu!

)

H l a

0 2 4 6 8 10 12 14 16 18 20 22 24

Tjme(weeks)

8.格 MuL7日PkE-』00PSysTEMS

Thediscussionuptonowtreatedpositiveandnegativefeedbackinisolation.What

isthebehaviorofafirst-ordersystemwhenthenetrateofchangeisaffectedby

bothtypesofloop?Considertheexampleofapopulation(Figure8-2).Disaggre一

gatethenetbirthrateintoabirthrateBRandadeathrateDR.Thenetrateof

changeforthesystemisthen

Population-INTEGRAL(NetBirthRate,Population(0))

NetBirthRate-BR-DR

Considerthelinearcasewherethefractionalbirthrateisaconstant,denotedb,and

thefractionaldeathrateisalsoconstant,denotedd.Thenetbirthrateisthen

NetBirthRate-bp-dP-(b-d)P (8-21)

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 283

Figure8-15Showsthephaseplotforthesystem･Onlythreebehaviorsarepos- sible.Iftheenvironmentcontainsabundantresources,birthswillexceeddeaths

(b>d),andthepopulationgrowsexponentiallywithoutlimit･Altematively,births

anddeathsmightexactlyoffseteachother(b-d),andpopulationisinequilib-

rium.Finally,theenvironmentmightbesoharshthatdeathsexceedbirths(bくd),

FIGURE8･15 Alinearfirst-

ordersystem cangenerate onlygrowth, equilibrium,

ordecay.

S a le tJ LJle a 凸 P

ue LJtJl!g

S a le tj LJlt2a 凸 P ue

LJt !g

S al t= t

j LJl

E!aCIP

u p L J亡 !g

Structure(phaseplot) > Behavior(tlmedomain)

b>d b BirthRate 1

NetBirthRate

l b-d

Popu一ation

Population

BirthRate

NetBirthRate

Population

0 Time0 Time

ExponentialDecay

Time

284 PartIIn)OlsforSystemsThinking

andpopulationdeclinesexponentiallytozero.Becausethesystemislinear,the fractionalnetbirthrateisaconstant,independentofthesizec･fthepopulation,

丘Xedfわralltimeoncethevaluesofbanddarechosen･Thebehaviorofthesystem isthesum,orsuperposition,ofthebehaviorsgeneratedbytheindividualloops. Becausethesystemislinear(banddareconstants),thedominanceofthetwo

loopscanneverchange･Thepopulationwillgrowwithoutbound,remainconstant, ordecaytoextinction.

ThesuperpositionpropertylStrueOflinearsystemsofanyorderandcom-

plexity.Aslongasalltherateequationsinasystemarelinear,therelativeimpoト tanceofthedifferentfeedbackloopscanneverchange-therecanbenoshiftsin loopdominance.Superpositionmeanslinearsystemscanbeanalyzedbyreduction totheircomponents.Asaresult,linearsystems,nomatterhowcomplex,canbe solvedanalytically,adistinctadvantageinunderstandingtheirdynamics.

However,realisticsystemsarefarfromlinear.Thebehaviorofthelinearpop- ulationgrowthsystemshowswhy.Becausethedominanceofthefeedbackloops canneverchange,thepopulationcanonlygrowforever,remainconstant,orgoex- tinct.Realpopulationsintroducedintoanewhabitatwithabundantresourcesgrow atfirst,thenstabilizeorfluctuate.Therelativestrengthofthepositiveandnegative loopsmustthereforeshiftasapopulationgrowsrelativetothecarrylngCaPaCltyOf theenvironment.Inrealsystems,theremustbeshiftsinfeedbackloopdominance,

andthereforetheremustbeimportantnonlinearitiesinallrealsystems. Unfortunately,manymodelershaverestrictedtheirattentiontomodelsthatcan

beexpressedaslinearsystemssothattheycanapplythepowerfultoolsoflinear systemstheory,whilemakingtheheroicassumptlOnthatthelinearapproximation isreasonable.Infairness,therelianceonlineartheoryandtheavoidanceofnon-

1inearsystemswasJustifiablepriortOthedevelopmentofcomputersimulationbe- causeanalyticalsolutionstononlineardynamicsystemscannotingeneralbe found.EarlytheoristsofdynamicsystemsmadetheassumptionOflinearitybe- causeitwastheonlywaytomakeprogress.Evenaftertheadventofcomputer simulation,however,toomanymodelersandmathematicianscontinuedtostress lineartheoryandbuildlinearmodels.Thetendencytotreateverysystemasalin- earnailbecausethehammeroflineartheorylSSOpowerfulhashamperedthede- velopmentofrealisticandrobustmodelsofcomplexity･

Ofcourse,thetriumphoflinearmethodshasneverbeencomplete.EvenprlOr tothecomputereraseveralimportantnonlinearmodelsweredeveloped,mostno- tablyVerhulst'sfamous1844logisticpopulationgrowthmodel(Seesection9.1)

andtheequallyfamousLotka-Vblterrapredatorl)reymodel(Lotka1956).Andthe qualitativetheoryofdynamicsystemsdevelopedbyPoincargandotherstoanalyze thethree-bodyproblemincelestialmechanicsisfundamentaiiynonlinear(see

DiacuandHolmes1996foranontechnicaltreatmentofthehistoryandtheory).In thepastfewdecadestherehasbeenanexplosionofinterestin,theoriesof,and datasupportlngtheimportanceofnonlinearbehaviorinallbranchesofdynamics (theriseofsoICalledchaosorcomplexitytheory).Still,YoshisukeUeda,whodisI coveredchaosinanonlinearoscillatorasagraduatestudentinthelate1950S,was

unabletogethisworkpublishedforoveradecadebecausehisadvisors,steepedin lineartheory,assertedthathismeasurementsandanalystsmustbewrongbecause they…knewHthatsystemscouldnotgeneratethestrangenonlinearbehavior

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 285

(chaos)thattodaywerecognizeasubiquitousinphysical,biological,andother

systems(seeUeda1992).

Linearanalysisremainsanimportanttool.Oftenasystemisclosetolinearin

acertainneighborhoodandcanbeusefullyanalyzedbylinearization,thatis,by

approximatingthenonlinearrateequationsataparticularoperatingpoint(setof

statevariablevalues)withthebestlinearapproximation.Andagreatdealofim-

Portantintuitionaboutdynamicscomesfromunderstandingsimple,linearsystems,

suchasthefirst10rderlinearsystemsresponsibleforexponentialgrowthanddecay-

Still,understandingthedynamicsofrealsystemsrequlreSnOnlinearmodels.

8u5 NoNuNE.ARF旧ST10RDERSysTEMS:S-SHAPEDGROWTH

NorealquantltyCangrowforever.Everysysteminitiallyexhibitingexponential

growthwilleventuallyapproachthecarrylngCaPaCltyOfitsenvironment,whether

thatisthefoodsupplyforapopulationofmoose,thenumberofpeoplesusceptl-

bletoinfectionbyavirus,Orthepotentialmarketforanewproduct.Asthesystem

approachesitslimitstogrowth,itgoesthroughanonlineartransition血.om a

reglmeWherepositivefeedbackdominatestoareglmeWherenegativefeedback

dominates.Theresultisoftenasmoothtransitionfromexponentialgrowthtoequl -

1ibrium,thatis,S-shapedgrowth(Seechapter4).

Inrealsystems,thefractionalbirthanddeathratescannotbeconstantbutmust

changeasthepopulationapproachesitscarrylngCapaClty.Hencetheequationfor thenetbirthratebecomes

NetBirthRate-BRIDR-b(P/C)p-d(P/C)P (8122)

wherethefractionalbirthanddeathratesbanddarenowfunctionsoftheratioof

thepopulationPtothecarryingCapacityC･Fornow,assumethecarrylngCaPaClty

isfixed-neitherconsumednoraugmentedbytheactivityOfthepopulation,Fig-

ure8-16Showsthecausaldiagramforthesystem｡

FIGURE8-16 Causaldiagram forpopulation growthinafixed environment

ち. @jDF:aa諾oRna誌Fractiona一BirthRate Aヲ】＼ーー

Population/ CarryingCapacity

草~ CarryJng Capacity

) .

286 PartIIToolsforSystemsThinking

NonlinearBirthandDeathRates

Beforecontinulng,Sketchagraphshowingthelikelyshapeofthefractional

birthanddeathratesforapopulationasitapproachesitscarryingcapacity(Fig-

ure8-17)｡Thecarryingcapacityisdefinedasthepopulationthatcanjustbesup-

portedbytheenvironment.Besuretoconsiderextremeconditions(thatis,what

willthefractionalbirthanddeathratesbeforveryloworverylargepopulations?).

Fromyourestimates,drawthefractionalnetbirthrate(thedifferencebetweenthe

fractionalbirthanddeathrates).

(¢ ∈ 空し )

S a t e ∝

L Jl t2 a

P u t2 LJt L ! g

uO !10e JId

Population/CarrylngCapacity (dimensionless)

Whenpopulationdensity(theratioP/C)issmall,bothfractionalbirthrateand

lifeexpectancyshouldbeattheirbiologicalmaxima.Aspopulationgrows,re-

sourcespercapitadecline.Fractionalbirthrateandlifeexpectancymustfall.Do

theydeclineimmediately?Insomecases,evensmallreductionsinresourcesper

capltacouldcauseadeclineinfertilityandlifeexpectancy.Forotherresources,

suchasfood,individualscannotconsumemorethanacertainamount,Sofractional

birthanddeathratesshouldremainconstantaslongasresourcespercapltaexceed

themaximum eachindividualCanconsume.Reducingavailablefoodfrom 10 timesmorethanneededto5timesmorethanneededhasnoimpactsinceeachin-

dividualstillgetsalltheycanconsume･12Inthiscasethefractionalbirthanddeath

ratesremainconstant-uptoapolnt-aSP/Cincreases･Onceresourcespercaplta fallbelowacertainlevel,thefractionalbirthratefallsandthefractionaldeathrate

increases.Bydefinition,thecarryingCapacitylSthepopulationthatcanJustbe

supportedbytheresourcesavailable,Sothefractionalbirthratemustequalthe

12Theassumptionthatexcessfoodhasnoimpactonfertilityormortalityholdsonlyifthe

organismsinquestioneatonlywhattheyneedanddonotgorgethemselveswhenasurplusis available･Forthehumanpoptllation,incontrast,anabundantfわodsupplyanddietrichinanimal proteinandfattendstoleadtoobesityandsignificantlyhighermorbidityandmortality.Insucha case,theeffectoffoodpercapltaOnthefractionaldeathratewouldactuallyrisewhenfoodper capltaexceedsacertainlevel.

Chapter8ClosingtheLoop:DynamicsofSimpleStructures 287

fractionaldeathratewhenP/C-1.Ifthepopulationweretoriseabovethecarry-

ingCapacity,thebirthfractionwouldcontinuetofallandthedeathfractionwould continuetorise.Asp/Ccontinuestoincrease,thebirthfractionmustfalltozero

andthedeath丘.actionmustrisetoaverylargevalue.Therefore,asshowninFig-

ure8-18,thefractionalnetbirthratewillbepositiveforP<C,equalzerowhen

P-C,andfallbelowzeroatanincreaslngrateWhenpopulationexceedsthe

carrylngCapaCltyOftheenvironment.Whilethenumericalvaluesfortheserela-

tionshipswoulddifferfordifferentpopulations,theirqualitativeshapeisnotin doubt.

Nextconstructthephaseplotforthesystemusingthesenonlinearfertilityand

lifeexpectancyrelationships.ThebirthanddeathratesarenowcurvesglVenbythe

productofthepopulationandfractionalbirthanddeathrates(Figure8-19).First,

notethatthepointP=0isanequilibrium,asinthelinearsystem.Sincethefrac-

tionalbirthrateremainsnearlyconstantwhenpopulationissmallrelativetothe

carryingcapacity,thebirthrate(inindividuals/timeperiod)isnearlylinearfわr

PiC.Aspopulationdensltyrisesandthefractionalbirthratefalls,thebirthrate,

whilestillgrowlng,riseswithashallowerandshallowerslope･Atsomepolnt,the declineinthefractionalbirthratereducestotalbirthsmorethantheincreasein

sheernumbersincreasesthem,andthebirthratereachesamaximum.Sincethe

fractionalbirthratefallstozeroforhighpopulationdensities,sotoothetotalbirth

ratemustapproachzero.Likewise,thedeathraterisesnearlylinearlyforPiC,

butasgreaterpopulationdensitybooststhefractionaldeathrate,thetotaldeath

rateincreasesatanincreasingrate.

TurnlngtOthedynamics,imaglnetheinitialpopulationissmallrelativetothe

carrylngCapacity.ThenetbirthraterisesnearlylinearlyforPiC･Thebehavior

ofthesysteminthisregimeWillbenearlypureexponentialgrowth.Aspopulation

densityIncreases,thenetbirthratecontinuestorise,butatashallowerandshal-

lowerslope.Thepopulationcontinuestogrowatanincreasingrate,butthefrac-

tionalgrowthrateissteadilydiminishing.Atsomepolnt,thenetbirthratereaches

amaximum.ThispolntCOmeSatalowerpopulationdensitythanthepeakinthe

birthratesincedeathsareincreaslngatanincreaslngrate･Thepeakofthenetbirth

ratecurveonthephaseplotcorrespondstotheinflectionpolntinthetrajectoryOf

FIGURE8･18 Nonlinear

relationship between

populationdensity andthefractional

growthrate

(む u J!)[L )

Sat t2 ∝

LJIe a e l P u 佃

LJI Jl ! g

一e u O !tO eJLL

Population/CarrylngCapacity (dimensionless)

288

FIGURE8-19 Phasep一otfor non‖near

populationsystem

Arrowsshowdi- rectionoHlow.

Positivefeedback

dominatesthesys- teminthereg10n wherethenetbirth

ratehaspositive slope;negative feedbackisdomi- nantwherethenet

birthratehasneg- ativeslope.The maximumnetbirth rateoccursatthe

point(P/C).nf,the inflectionpointin thetrajectoryOf population･

Population/CarrylngCapacity (dimensionFess)

populationinthetimedomain(thepointatwhichthepopulationisrisingatits

maximumrate).Beyondtheinflectionpoint,theincreaseinpopulationdensityre- ducesthenetbirthratemorethantheincreaseintotalpopulationsizeincreasesit.

Thenetbirthrate,whilestillpositive,drops,fallingtozeroJustWhenthepopula-

tionequalsthecarrylngCapaClty.IfthepopulationexceededthecarrylngCapaClty,

resourcespercapltaWOuldbesoscarcethatdeathswouldexceedbirths,andthe

populationwouldfallbacktowardthecarryingCaPaClty･TheequilibriumatP-C isthereforestable.

Figure8-20Showsthebehaviorofthesystem overtimefortwocases:

(1)whentheinitialpopulationismuchsmallerthanthecarryingcapacityand

(2)whentheinitialpopulationismuchlargerthanthecarryingcapacity.When

P(0)iC,thenetbirthrateisincreasinginthepopulation.Aslongastheslopeof

thenetbirthratecurveinthephaseplotispositive,thesystemisdominatedbythe

positivefeedbackloopandpopulationgrowsexponentially･Unlikethelinearsys-

tem,however,theslopeofthenetbirthratecurveisnotconstant,Sothegrowthis

notapureexponential.Instead,thefractionalgrowthratefallsaspopulation

grows.Populationgrowthreachesitsmaximumwhenthepopulationreachesthe

valuedenoted(P/C)Imf,theinflectionpointinthetrajectoryofthepopulation.At

thatpolnttheslopeofthenetbirthratecurveiszero;thepositiveandnegative

loopsexactlyoffsetoneanother.Aspopulationcontinuestogrow,theslopeofthe

netbirthratecurveinthephaseplotbecomesnegative;forP/C>(P/C)1nf,thesys-

temisdominatedbynegativefeedback.Becausethenetbirthratehasanegative

slopeinthisreglOn,theequilibriumpointatP-Cisstable,Apoptllationlessthar)

thecarrylngCapaCltyWillgrowatadiminishingrateuntilitreachesthecarrylng

capacity;apopulationlargerthanthecarrylngCaPaCltyWillfalluntilitreachesthe

carryingCapacityfromabove.

8.5.1 Forma‡De伽 itiomo菅LoopDom岳mamee

Thephaseplotshowstheorlginofthetermspositiveandnegativefeedback.Posi-

tivefeedbackdominateswhenevertherateofchangeofthestatevariableis

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures

FtGURE8-20 Nonlinear

populationgrowth: timedomain

Top:P(0)iC; Populationfo"ows anS-shaped trajectory,With 州 ectionpointat (P/C).nf.

Bottom:P(0)>,C,

thepopulation rapidlydecays backtothestable

equilibriumat P-C.

Thetimeaxisin bothsimulationsis

thesame;ve｢lical sca一esdiffer.

n CJHu岬

^ 1!3t 2d

t20 6u !̂

Je3 J

uO !t e r n

d od

0 2

A )!o e

de 3 6 u!̂ ヒ

3J u O !te P

do d

N e t

B ir t h R a t e

289

increaslnglnthestatevariable,thatis,aslongastheslopeofthenetrateofchange

asafunctionofthestatevariableispositive.Negativefeedbackdominateswhen-

everthenetrateofchangeisdecreaslnglnthestatevariable,thatis,aslongasthe

slopeofthenetrateisnegative.

Thisobservationleadstoaformaldefinitionofloopdominanceforfirst-order

systems(Richardson1986b,1995):

莞 (<:

0=⇒Positivefeedbackdominant 0⇒Nonetfeedbackfromstatetorate

0⇒Negativefeedbackdominant

(8-23)

where

s- 慧

DeterminingWhetherasystemisdominatedbypositiveornegativefeedbackis

moredifficultinhigher10rdersystemsbecausealoopwithtimedelayscanhavea

weakshort-runbutlargelong-runeffect.Kampmann(1996)providessomemethl

odstodeterminethedominantloopsinmultiloop,highordersystems;seealsoN.

Forrester(1982)andMojtahedzadeh(1997).

290 PartIIToolsforSystemsThinking

8,5.2 First10rdeFSysモemst=annotOsciiEate

Asafinalobservationonthegeneralnonlinearfirst10rdersystem,consider

whetherafirstl0rdersystemcanoscillate.Section8.4demonstratedthatthelinear

first-ordersystem cangenerateonlyexponentialgrowth,decay,orequilibrium.

Nonlinearfirst-ordersystemsgeneratemorecomplexdynamics,butcanneveros-

cillate,nomattertheformofthenonlinearity･Toseewhy,considerthephaseplot

forthefirsトordersysteminFigure8119.Tooscillate,thestatevariablemustgo

throughperiodsofincreasefollowedbyperiodsofdecrease.Therefore,thenetrate

ofchangeinthephaseplotmustcrossfrompositivetonegativevalues,atleastin

oneplace｡However,anypolntWherethenetrateofchangeiszeroisanequilib-

riumofthestatevariable.Sincefirst10rdersystemshaveonlyonestatevariable,

everysuchpolntisanequilibriumforthesystemaswell.Everyequilibriumpolnt

iseitherstable(theslopeofthenetratecurveintheneighborhoodoftheequilib-

riumisnegative)orunstable(positiveslopeintheneighborhoodoftheequilibrium

point).13Ifafirst10rdersystemisdisturbedfromanunstableequilibrium,itwilldi-

verge丘.omit,eitherwithoutbotlnd(notoscillating)Oruntilitapproachesastable

equilibriumpolntWhereallchangeceases.Thereforetooscillate,asystemmustbe

atleastsecondorder,meanlngtheremustbeafeedbackloopwithatleasttwo stocksinit.14

8｡6 SuMMARY

Thischapterexploredthedynamicsofsimplesystems,specifically,first10rder

linearsystemsISyStemSWithonlyonestock(statevariable)andinwhichtherates

offlOwarelinearfunctionsofthesystemstate.Thesesimplesystemsarethebuild-

1ngblocksoutofwhichallmodelsarebuiltandfrom whichmorecomplex

dynamicsemerge･First-orderlinearpositivefeedbacksystemsproducepureexpO -

nentialgrowth.Exponentialgrowthhastheremarkablepropertythatthestateof

thesystem doublesinafixedperiodoftime,nomatterhow largeitis.The

doublingtlmeCharacterizesthestrengthofthepositiveloop.Similarly,first-order

linearnegativefeedbacksystemsgenerateexponentialdecaytoagoal･Thedecay

rateischaracterizedbythehalfllife,thetimerequiredforthegapbetweenthestate

ofthesystemandthegoaltobecutinhalf.Thechapteralsointroducedthephase

13Ifthenetrateofchangeiszerooverafiniteintervalinstatespace,thesepolntShaveneutral staDlllty;adisturlDanCeLWithinthatrange)CausesneitheraresILOralLiveilOitdivergerltChangeilltlr.e netrate,JustaSaballplacedanywhereonaflatsurfacewillremainatthatpolnt.

14Technically,first-ordersystemscannotoscillateprovidedtimeistreatedcontinuously･Firstl ordersystemsindiscretetimecanoscillate.Forexample,theloglSticmap,thefirst-ordernonlinear

discretetime禦apX(t+1)-kx(t)(1IX(t)),Where0≦k≦4andO<x(0)<1,notonlyoscil- latesforcertainValuesofk,butgeneratesperioddoublingandchaosaswell.However,thestate-

mentthatoscillationrequlreSafeedbackloopwithatleasttwostocksisstillvalid:indiscretetime models,thetimestepbetweeniterationsconstitutesanirreducibletlmedelaylneveryfeedback loop.Everytlmelagcontainsastockwhichaccumulatestheinflowtothedelaylessitsoutflow. EverydiscretedynamicsystemcanbeconvertedintoanequlValentcontinuoustimesystemby introducingalagequaltothetimestepateveIYStateVariable,increaslngtheorderofthesystem (seeLow1980foranexample).

Chapter8 ClosingtheLoop:DynamicsofSimpleStructures 291

plot,ausefultooltoanalyzethedynamicsofsystemsgraphically,withouttheuse ofcalculus.

AnalysISOfthephaseplotsforfirst10rdersystemsshowsthatinsystemswith

morethanonefeedbackloop,thedynamicsdependonwhichloopisdominant.In

linearsystems,thedominanceofthedifferentloopscanneverchange.Thuslinear

first10rdersystemscanonlyexhibitthreebehaviors:exponentialgrowth(whenthe

positiveloopsdominate),exponentialdecay(whenthenegativeloopsdominate),

andequilibrium(whentheloopsexactlyoffsetoneanother).Nonlinearfirst-order

systemscanexhibitSIShapedgrowthbecausethedominantfeedbackloopsshiftas

thesystemevolves.AsthepopulationapproachesitscarrylngCapacitythepositive

loopsdrivinggrowthweakenandthenegativeloopsrestrainlnggrowthstrengthen,

untilthesystemisdominatedbynegativefeedback,andthepopulationthen

smoothlyapproachesastableequilibriumatthecarrylngCapaClty.

§-Silia盲準尋iI-;ぞ串W睦;互声量dem量gs千言i-1即ち~主音享和 Ii75主熟呈§畳紙き員n封もe Growもhi)fNew喜〉ro戚ue息S

EveZTthingthatrisesmustconverge.

-FlanneryO'Connor

Asseeninchapter8,positivefeedbackcreatesexponentialgrowth.Butnoreal quantityCangrowforever.Everysysteminitiallydominatedbypositivefeedbacks eventuallyapproachesthecarrylngCapaCltyOfitsenvironment.Asthelimitsto growthapproach,thereisanonlineartransitionfromdominancebypositivefeed- backtodominancebynegativefeedback.Undercertainconditions,theresultis S-shapedgrowth,wherethegrowlngpopulationsmoothlyapproachesequilibrium. ThischaptershowshowS-shapedgrowthcanbemodeled,withapplicationstothe diffusionofinnovations,thespreadofinfectiousdiseasesa.-.dcomputerViruses, thegrowthofthemarketfornewproducts,andothers･Avarietyofimportantand widelyusedmodelsofS-Shapedgrowthareintroducedandanalyzed,theuse ofthesemodelsforforecastlngisdiscussed,andextensionstothemodelsare presented･CasesexaminedincludethespreadofmadcowdiseaseandHIVand thegrowthofthemarketsforhigh-techproductssuchascomputersandconsumer servicessuchascabletelevision.

295

296 PartIIITheDynamicsofGrowth

9.1 MoDEuNGS-SHAPEDGROWTH

Thenonlinearpopulationmodeldevelopedinchapter8isqultegeneral･Thepop- ulationinthemodelcanbeanyquantitythatgrowsinafixedenvironment,forex- ample,thenumberofadoptersofaninnovation,thenumberofpeopleinfectedby adisease,thefractionofanygroupadheringtoanideaorpurchasingaproduct,

andsoon.Ifthepopulationisdrivenbypositivefeedbackwhenitissmallrelative toitslimits,thentheresultingbehaviorwillbeSIShapedgrowth,providedthere

arenosignificantdelaysinthenegativefeedbacksthatconstrainthepopulation.If therearedelaysintheresponseofthepopulationtotheapproachingcarrylngCa- paclty,thebehaviorwillbeS-Shapedgrowthwithovershootandoscillation;ifthe

carrylngCapacitylSconsumedbythegrowlngPOPulation,thebehaviorwillbe overshootandcollapse(Seechapter4).Conversely,wheneveryouobserveasys- temthathasexperiencedS-shapedgrowth,youknowthatinitiallythebehavior wasdominatedbypositivefeedbackloops,butasthesystemgrew,therewasa nonlinearshifttodominancebynegativefeedback.

9.i.1 Logl-SttlcGrowth

Asillustratedinthenonlinearpopulationgrowthexampleinchapter8,thenet fractionalgrowthrateofthepopulationPmustfallfromitsinitialvalue,pass

throughzerowhenthepopulationequalsthecarrylngCapacityC,andbecomeneg- ativewhenP>C.Consequently,thephaseplotofthenetbirthratemusthavea shaperoughlylikeaninvertedbowl:Netbirthsarezerowhenthepopulationis

zero,risewithincreaslngpopulationuptoamaximum,falltozeroatthecarrylng capaclty,andcontinuetodrop,becomnglnCreaSlnglynegative,whenpopulation

exceedsthecarrylngCaPaCity･However,thereareaninfinitenumberoffractional netbirthratecurves,andhencephaseplots,satisfyingthesegeneralconstraints･An importantspecialcaseofSIShapedgrowthisknownaslogisticgrowth,orVerhulst growth,afterFran90isVerhulstwhofirstpublishedthemodelin1838(see Richardson1991).

TheloglSticgrowthmodelpositsthatthenetfractionalpopulationgrowthrate

isa(downwardsloping)linearfunctionofthepopulation･Thatis,

NetBirthRate-g(P,C)p-gU IP/C)P (911)

whereg(P,C),thefractionalgrowthrate,isafunctionofthepopulationandcarry- ingcapacityandg*isthemaximumfractionalgrowth(thefractionalgrowthrate

whenthepopulationisverysmall)･Thelogisticmodelconformstotherequire- mentsforSIShapedgrowth:thefractionalnetgrowthrateispositiveforP<C,

zerowhenP-C,andnegativeforP>C･TheloglSticmodelhassomeadditional characteristics.Rearrangingequation(9-1)gives

NetBirthRate-g決(1-P/C)p-g帯p-gti'p2/C (9-2)

Thefirsttermg*pisastandardfirst-orderlinearpositivefeedbackprocess;the secondterm,一g*p2/C,isnonlinearinthepopulationandrepresentstheever-

Strongernegativefeedbackcausedbytheapproachofthepopulationtoitscarry- lngCapaClty･

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts297

Whendoesthenetgrowthratereachitsmaximum?IntheloglSticmodelthe

netbirthrategivenbyequation(9-2)isaninvertedparabolawhichpassesthrough

zeroatthepolntSP-0andP-C.Becauseaparabolaissymmetricaroundits

peak,themaximumnetbirthrateoccurswhen

P.nf-C/2 (9-3)

wherePinfisthevalueofpopulationwherethenetgrowthrateisatamaximumand

thereforetheinflectionpointinthetrajectoryOfthepopulation･1Themaximumnet

growthrateoccurspreciselyhalfwaytothecarrylngCaPaCity･Figure9-iplotsthe

fractionalgrowthrate,phaseplot,andtimedomainbehaviorfortheloglSticmodel.

TheloglSticmodelisimportantforseveralreasons･First,manyS-Shaped

growthprocessescanbeapproximatedwellbytheloglSticmodel,despitethere-

strictionthattheinflectionpolntoccursatPreciselyC/2.Second,theloglSticmodel

canbesolvedanalytically.Finally,theloglSticmodel,thoughintrinsicallynon-

1inear,Canbetransformedintoaformthatislinearintheparameterssoitcanbe

estimatedbythemostcommonregressiontechnique,ordinaryleastsquares(See section9.3.1).

9.1u2 AnaFyticSolutionof的eLogistkEquation

Thoughitisnonlinear,thelogisticmodelshowninequation(9-1)canbesolved

analytically.Firstseparatethevariables,thenintegrate:

J薄 -恒

Rearrangingtheleft-handsidegives

I詰 -Ilg･詩 ]dP-fg*dt lntegratlngbothsidesyields

ln(P)-1n(C-P)-gxt+c

wherecisaconstant.SincebydefinitionP(t)-P(0)whent-0,

1n(P)-1n(CIP)-g串t+ln(P(0))一1n[C-P(0)].

Takingexponentialsyields

P P(0)exp(g*t) (C-p)~ C-p(o)

whichcanberearrangedas

P(t)-

I･[iSrl]exp仁g*t)

(9-4)

(9-8)

(9-9)

lThemaximumnetbirthrate,andthereforetheinfectionpolntinthepopulation,occurswhen

∂[g(P,C)*P]/∂p-g祥一2gxP/C-0.

SolvingforPyieldsPl｡f-C/2.

298

FIGURE9-1

Thelogisticmodel

Top:Thefractional growthratede-

clineslinearHyas

populationgrows.

Middle:Thephase plotisaninverted parabola,symmeト ricabout(P/C)-

0.5.Bottom:Popu- lationfollowsan

S-shapedcuⅣe withinflection

pointat(P/C)-

0.5;thenetgrowth ratefollowsabeH-

Shapedcurvewith amaximumvalue

of0.25Cpertime periodlThetime axisisscaledso

thatlunit-1/g', Withtheinf一ection

pointcenteredat timeh-0.

PartIII TheDynamicsofGrowth

a l t2 t J L ft JUt O Jg

la N 届

u O EtO e Jlj

a l e t ]

LJlJVtO J I

ta N

( s

s a lu

O !S u a ∈ !P )

^ l!3 e d t2 3

u ! ^ JLe O ＼u O !le ln d o d

Ne t

B irth

R a t

e J C

a r

ryin g

C a p a

c i t y

(

一 ≧

∃

Population/CarrylngCapacity (dimensionless)

-4 -2

orequlValentlyas

P(t) 1+ exp卜 g H(t - h)]

O Time

2 4

(9110)

wherehisthetimeatwhichthepopulationreacheshalfitscarrylngCa-

pacity;settingP(h)- 0.5Cinequation(9-10)andsolvingforhyieldsh-

ln[(C/P(0))-1]/g*.Equations(9-9)and(9-10)∬etwoformsoftheanalyticsolu-

tiontotheequationforlogisticgrowthgivenbyequation(9-i).

Chapter9 S-ShapedGrowth:Epidemics,InnovationDimlSion,andtheGrowthofNewProducts299

9.1.3 0therCommonGrowthMode一s

Duetoitssimplicityandanalytictractability,theloglSticmodelisthemostwidely

usedmodelofS-shapedgrowth.However,therearemanyothermodelsof

S-shapedgrowth.Thesemodelsrelaxtherestrictiveassumptionthatthefractional

growthratedeclineslinearlyinthepopulation.Thesegrowthcurvesareingeneral notsymmetric.

TheRichardscurveisonecommonlyusedmodel(Richards1959).In

Richards'modelthefractionalgrowthrateofthepopulationisnonlinearinthe population:

･etBinhRate-芸 -諾㌔ [1-(E)mー1] (9111)

Whenm-2,theRichardsmodelreducestotheloglStic.Othervaluesofmcause

thefractionalgrowthratetobenonlinearinthepopulation(trysketchingthefrac-

tionalgrowthrateasafunctionofpopulationfordifferentvaluesofm).Thesolu-

tionoftheRichardsmodelis

P(t)-C(1Ikexp(-gSt))1/(1-m) (9112)

wherekisaparameterthatdependsontheinitialpopulationrelativetothecarryl lngCapaClty･

AspecialcaseoftheRichardsmodelistheGompertzcurve,glVenbythe

Richardsmodelinthelimitwhenm -1.Notethatwhileequation(9-12)isun- definedwhenm-i,

1illl(Xa- 1)

a→O a -1m(Ⅹ) (9-13)

sotheGompertzcurveisglVenby

P(t)-Cexp(-kexp(-gxt)). (9114)

IntheGompertzmodel,thefractionalgrowthratedeclineslinearlyintheloga-

rithmofthepopulation,andthemaximumgrowthrateoccursatP/C-0.368.

AnothercommonlyusedgrowthmodelisbasedontheWeibulldistribution:

P(t)-C(1-exp卜(Vb)a]) (9-15)

wherea,b>0areknownastheshapeandscaleparameters,respectively.Thecase

a-2isknownastheRayleighdistribution･

TheRichardsandWeibullmodelsprovidethemodelerwithanalytically

tractablegrowthfunctionsthatcanrepresentavarietyofnonlinear血.actionalnet

increaserates.However,thereisnoguaranteethatthedatawillconfom totheas-

sumpt10nSOfanyoftheanalyticgrowthmodels.Fortunately,withcomputersimul

lation,youarenotrestrictedtousetheloglStic,Gompertz,Richards,Weibull,or

anyotheranalyticmodel.Youcanspecifyanynonlinearrelationshipforthefrac-

tionalbirthanddeathratessupportedbythedataandthensimulatethemodelto

exploreitsbehaviorovertime.

300 PartIIITheDynamicsofGrowth

9.l.4 TestingtheLogisticN!odel

ToillustratetheuseoftheloglSticmodel,considertheexamplesofS-shaped

growthinFigure419.Figure912showstheresultoffittingtheloglSticmodeltothe dataforthegrowthofsunflowers.ThebestfitloglSticmodelmatchesthesun-

flowerdatareasonablywell,thoughitunderestimatesthegrowthinthefirstmonth andoverestimatesitlater.ThesediffTerencessuggestabetterfitmightbegalned

throughuseofadifferentgrowthmodel,suchastheRichardsmodel,inwhichthe fractionalgrowthrateisnonlinearinthepopulation･Section9･3･lprovidesaddi-

tionalexamples.

9R2 DYNAMICSOFDISEASE:MoDEuNGEpIDEMECS

EpidemicsofinfectiousdiseasesoftenexhibitSIShapedgrowth･Thecumulative numberofcasesfollowsanSIShapedcurvewhiletherateatwhichnewcasesOCI

currisesexponentially,peaks,thenfallsastheepidemicends･Figure9-3Shows thecourseofanepidemicofinfluenzaatanEnglishboardingschoolin1978･The

epidemicbeganwithasingleinfectedstudent(patientzero)･Thefluspreads throughcontactandbyinhalationofvirus-ladenaerosolsreleasedwheninfected individualscoughandsneeze.Thefluspreadslowlyatfirst,butasmoreandmore studentsfellillandbecameinfectious,thenumbertheyinfectedgrewexponen-

tially,Duetotheclosequartersandthushighrateofexposure,abouttwo-thirdsof

thepopulationeventuallybecameill,andtheepidemicendedduetothedepletion ofthepoolofsusceptiblepeople.Figure9-3alsoshowsthecourseofanepidemic ofplagueinBombayin1905-6.ThebehaviorisqulteSimilar,despitethediffer-

encesintimeframe,mortality,andotheraspectsofthesituation.Thepathogen

doesnothavetobeabiologicalagent-epidemicsofcomputervirusesfollowsim- ilardynamics.

9.2.1 AS血pヨeM◎deを⑳曹Em甘ee竜岳ousDisease

Figure914Showsasimplemodelofinfectiousdisease.Thetotalpopulationofthe communltyOrregionrepresentedinthemodelisdividedintotwocategories:those susceptibletothedisease,S,andthosewhoareinfectious,I(forthisreasonthe

FtGURE9-2

Thegrowthof sunflowersand thebestfit

logisticmodel

0 14 28 42 56

Days 70 84

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts301

modelisknownastheSImodel).Aspeopleareinfectedtheymovefromthesus-

ceptiblecategorytotheinfectiouscategory.TheSImodelinvokesanumberof

simplifyingassumptions;Section9.2.2developsamorerealisticmodel.First,

FIGURE9･3 Dynamicsofepl-

demicdisease

Top:Influenza

epidemicatan

Englishboarding

school,January

22-February3, 1978.Thedata

showthenumber

ofstudents

confinedtobedfor

influenzaatany

time(thestockof

symptomatic

individuals). Soul℃e:BrJtI'shMedl'CaI

Journal,4March1978, p.587･

Bottom:Epidemic

ofp一ague,Bom-

bay,India190516r Datashowthe

deathrate

(deaths/week). Source:Kermackand McKendrick(i927, p714)lForfurtherdisI cussionofbothcases, seeMurray(1993).

FIGURE9-4 Structureofa

simplemodelof

anepidemic

B州1S,deaths,

andmigrationare omittedsothe

totalpopulationis aconstant,and

peop一eremain infectious

indefinitely.

(】苛

aき P

一d o ad )s u

tea凸

1/24 1/26 1/28 1/30 2/1 2/3

0 5 10 15 20 Weeks

25 30

302 PartHITheDynamicsofGrowth

births,deaths,andmigrationareIgnored.Second,oncepeopleareinfected,they remaininfectiousindefinitely,thatis,themodelappliestochronicinfections,not acuteillnesssuchasinfluenzaorplague.

TheSImodelcontainstwoloops,thepositiveContagionloopandthenegative Depletionloop.Infectiousdiseasesspreadasthosewhoareinfectiouscomeinto contactwithandpassthediseasetothosewhoaresusceptible,increaslngthein- fectiouspopulationstillfurther(thepositiveloop)whileatthesametimedeplet- ingthepoolofsusceptibles(thenegativeloop).

TheinfTectiouspopulationlisincreasedbytheinfectionrateIRwhilethesus- ceptiblepopulationSisdecreasedbyit:

Ⅰ -INTEGRAL(IR,Io) (9-16)

S-INTEGRAL(-IR,N-Io) (9117)

whereNisthetotalpopulatio汀inthecommunltyandI｡istheinitialnumberof infectiouspeople(asmallnumberorevenasingleindividual).Tbformulatethe infectionrate,considertheprocessbywhichsusceptiblepeoplebecomeinfected.

Peopleinthecommunityinteractatacertainrate(theContactRate,C,mea- suredinpeoplecontactedperpersonpertimeperiod,or1/timeperiod)･Thusthe susceptiblepopulationgenerateScencounterspertimeperiod.Someoftheseen-

countersarewithinfectiouspeople.Ifinfectiouspeopleinteractatthesamerateas susceptiblepeople(theyarenotquarantinedorconfinedtobed),thentheproba- bilitythatanyrandomlyselectedencounterisanencounterwithaninfectiousin- dividualisI/N.Noteveryencounterwithaninfectiouspersonresultsininfection. Theinfectivlty,i,ofthediseaseistheprobabilitythatapersonbecomesinfected aftercontactwithaninfectiousperson.Theinfectionrateisthereforethetotal numberofencountersScmultipliedbytheprobabilitythatanyofthoseencounters iswithaninfectiousindividualI/Nmultipliedbytheprobabilitythatanencounter withaninfectiouspersonresultsininfection:

IR-(ciS)(Ⅰ/N) (9-18)

Thedynamicscanbedeterminedbynotlngthatwithoutbirths,deaths,ormlgra-

tion,thetotalpopulationisfixed:

S+Ⅰ-N (9-19)

Thoughthesystemcontainstwostocks,itisactuallyafirst-ordersystembecause oneofthestocksiscompletelydeterminedbytheother･SubstitutlngNIIforS in(9-18)yields

IR-(C)(i)I(1-Ⅰ/N) (9-20)

Equation(9-20)isidenticaltoequation(9-1),thenetbirthrateinthelogistic model.Anepidemic,inthismodel,growsexactlylikeapopulationinafixeden- vironment.ThecarrylngCapaCltyisthetotalpopulation,N.IntheSImodel,once aninfectiousindividualarrivesinthecommunlty,everySusceptiblepersoneven- tuallybecomesinfected,Withtheinfectionratefollowlngabell-shapedcurveand

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts303

thetotalinfectedpopulationfollowlngtheclassicSIShapedpatternoftheloglStic curve(Figure9-1).Thehigherthecontactrateorthegreatertheinfectivity,the

fastertheepidemicprogresses. TheSImodelcapturesthemostfundamentalfeatureofinfectiousdiseases:the

diseasespreadsthroughcontactbetweeninfectedandsusceptibleindividuals.Itis theinteractionofthesetwogroupsthatcreatesthepositiveandnegativeloops andthenonlinearltyreSPOnSible氏)rtheshiftinloopdominanceasthesusceptible

populationisdepleted.Thenonlinearltyarisesbecausethetwopopulationsare multipliedtogetherinequation(9118);ittakesbothasusceptibleandaninfectious

persontogenerateanewcase･

9.2.2 Mode!ingAcutehfection:TheS旧 Mode!

WhiletheSImodelcapturesthebasicprocessofinfection,itcontainsmanysim- plifyingandrestrictiveassumptlOnS.Themodeldoesnotrepresentbirths,deaths,

ormlgration.Thepopulationisassumedtobehomogeneous:allmembersofthe communityareassumedtointeractatthesameaveragerate(therearenosubcul- turesorgroupsthatremainisolatedfromtheothersinthecommunltyOrWhosebe- haviorisdifferentfromothers).Thediseasedoesnotalterpeople'slifestyles:

infectivesareassumedtointeractatthesameaveragerateassusceptibles.Thereis nopossibilityofrecovery,quarantine,orimmunization.

AlltheseassumptlOnSCanberelaxed.Thesusceptiblepopulationcanbedis- aggregatedintoseveraldistinctsubpopulations,Orevenrepresentedasdistinctin- dividuals,eachwithaspecificrateofcontactwithothers.Anadditionalstockcan

beaddedtorepresentquarantinedorvaccinatedindividuals･Birthanddeathrates canbeadded.Randomeventscanbeaddedtosimulatethechancenatureofcon-

tactsbetweensusceptiblesandinfectives. ThemostrestrictiveandunrealisticfeatureoftheloglSticmodelasappliedto

epidemicsistheassumptionthatthediseaseischronic,Withaffectedindividuals

remaininginfectiousindefinitely.Consequently,onceevenaslngleinfectiousin-

dividualarrivesinthecommunity,everySusceptibleeventuallybecomesinfected. Whiletheassumptionofchronicinfectionisreasonableforsomediseases(e.g.,

herpessimplex),manyinfectiousdiseasesproduceaperiodofacuteinfectiousness andillness,followedeitherbyrecoveryandthedevelopmentofimmunityOrby death.Mostepidemicsendbeforeallthesusceptiblesbecomeinfectedbecause

peoplerecoverfasterthannewcasesarise.KermackandMcKendrick(1927)de- velopedamodelapplicabletosuchacutediseases.Themodelcontainsthree

stocks:TheSusceptiblepopulatiorl,S,theIr.fectio-uspopuiatior.,I,andtheRecov- eredpopulation,良(Figure9-5).LongknownastheSIRmodel,theKermack- McKendrickformulationiswidelyusedinepidemiology.Thosecontractlngthe diseasebecomeinfectiousforacertainperiodoftimebutthenrecoveranddevelop

permanentimmunity.TheassumptlOnthatpeoplerecovercreatesoneadditional feedback-thenegativeRecoveryloop.Thegreaterthenumberofinfectious

304 PartIIITheDynamicsofGrowth

FIGURE9-5 StructureoftheSIRepidemicmodel

Peopleremaininfectious(andsick)foralimitedtime,thenrecoveranddevelopimmunity･

individuals,thegreatertherecoveryrateandthesmallerthenumberofinfectious

peopleremainlng･AllotherassumptlOnSOftheorlglnalSImodelareretained･2

Thesusceptiblepopulation,asintheSImodel,isreducedbytheinfectionrate.

Theinfectiouspopulationnowaccumulatestheinfectionratelesstherecoveryrate

RRandtherecoveredpopulation良accumulatestherecoveryrate:

S-INTEGRAL(-IR,N-ⅠO- Ro)

Ⅰ-INTEGRAL(IR-RR,Io)

良 -INTEGRAL(RR,Ro)

Theinitialsusceptiblepopulationisthetotalpopulationlesstheinitialnumberof

infectivesandanyinitiallyrecoveredandimmuneindividuals.

Therecoveryratecanbemodeledseveralways･IntheSIRmodel,theaverage

durationofinfectivity,d,isassumedtobeconstantandtherecoveryprocessisas-

sumedtofollowafirst-ordernegativefeedbackprocess:

RR-Ⅰ/d. (9-24)

Theaveragedurationofinfectivity,d,representstheaveragelengthoftimepeople

areinfectious.Theassumptionthattherecoveryrateisafirst10rderprocessmeans

2IntheSIRmodeltherecoveredpopulationisoftentermed"Removals"andtherecoveryrateis

thencaiiedtheremovairate.ManyappilCationsofthemodelinterprettheremovalrateasthesum ofthoserecoveringfromthediseaseandthosewhodiefromit･However,thisinterpretationisin- correct,sincethosewhodiereducethetotalpopulation,whileintheSIRmodelthetotalpopulation isconstant.Theaggregationofdeathsandrecoveriesintoasingleflowofremovalsandaslngle stockofcumulativeremovalsisusuallyJustifiedbyargulngthatmortalitylSOftenasmallfraction ofthetotalpopulation.Evenwhenthisistrue,itisbadmodelingpracticetoaggregatethelivlng withthedead,sincetheirbehaviorisoftenquitedifferent.Inthiscase,thosewhorecovercontinue

tointeractwiththeremainingSusceptibleandinfectiouspopulations,whilethosewhodieusually donot.

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts305

peopledonotallrecoverafterexactlythesametime,butratheraglVenpopulation

ofinfectiousindividualswilldeclineexponentially,withsomepeoplerecoverlng

rapidlyandothersmoreslowly･3Theinfectionrateisformulatedexactlyasinthe

SImodelinequation(9-18).

9.2.3 Mode=∋ehavior:TheTippingP13ht Unlikethemodelsconsideredthusfar,thesystemisnowsecond-order(thereare

threestocks,butsincetheysumtoaconstant,onlytwoareindependent).However,

itisstillpossibletoanalyzeitsdynamicsqualitatively.First,unliketheSImodel,

itisnowpossibleforthediseasetodieoutwithoutcauslnganepidemic.Ifthein-

fectionrateislessthantherecoveryrate,theinfectiouspopulationwillfall.Asit

falls,sotoowilltheinfectionrate.Theinfectiouspopulationcanthereforefallto

zerobeforeeveryonecontractsthedisease. Underwhatcircumstanceswilltheintroductionofaninfectiousindividualto

thepopulationcauseanepidemic?Intuitively,foranepidemictooccur,theinfec-

tionratemustexceedtherecoveryrate;ifso,theinfectiouspopulationwillgrow,

leadingtostillmorenewcases.If,whileeachpersonwasinfectioustheypassed

thediseaseontoexactlyonemoreperson,thenthestockofinfectiveswouldre-

mainconstantsincetheinfectionratewouldbejustoffsetbytherecoveryrate.

Therefore,foranepidemictooccur,eachinfectivemust,onaverage,passthedis-

easeontomorethanoneotherpersonprlOrtOreCOVerlng.

Thequestionofwhetheranepidemicwilloccurisreallyaquestionabout

whichfeedbackloopsaredominantwhenthediseasearrivesinacommunlty.Ifthe

positivecontaglOnloopdominatestherecoveryanddepletionloops,thenthein-

troductionofevenaslngleinfectiveindividualtoacommunltytrlggerSanePl-

demic.Theinfectionratewillexceedtherecoveryrate,Causlngtheinfectionrate

togrowstillfurther,untildepletionofthepoolofsusceptiblesfinallylimitsthe

epidemic.If,however,thepositivelooplSWeakerthanthenegativeloops,anep1-

demicwillnotoccursinceinfectiouspeoplewillrecoveronaveragefasterthan

newcasesarise.ThenumberofnewcasescreatedbyeachinfectivepriortOtheir

recovery,andthereforethestrengthofthedifferentloops,dependsontheaverage

durationofinfectionandthenumberofnewcaseseachinfectivegeneratesper

timeperiod.ThehigherthecontactrateorthegreatertheinfectivltyOfthedisease,

thestrongerthepositiveloop.Likewise,thelargerthefractionofthetotalpopula-

tionsusceptibletoinfection,theweakerthedepletionloop.Finally,thelongerthe

3whiletheassumptionthatremovalsarefirst10rderisreasonableinthesimpleSIRmodel, thecourseofmanydiseasesismorecomplexandthedelaybetweeninfectionandremovalisoften notexponential(ifagroupwereallinfectedatonce,theremovalratewouldbesmallinitially,then buildtoapeakbeforetaperingoff)･Chapter11discusseshowdifferenttypesofdelayscanbemod- eledindepthandshowshowmodelerscanselectrobustformulationsfordelaystomatchthedata fordifferentdistributions.

306 PartIH TheDynamicsofGrowth

averagedurationofinfection,theweakerthenegativerecoveryloopandthemore

likelyanepidemicwillbe･4

ForanyglVenpopulationofsusceptibles,thereissomecriticalcombinationof

contactfrequency,infectivlty,anddiseasedurationJustgreatenoughfortheposi-

tivelooptodominatethenegativeloops.ThatthresholdisknownasthetlPPlng

point･BelowthetippingPOlnt,thesystemisstable:ifthediseaseisintroducedinto

thecommunity,theremaybeafewnewcases,butonaverage,peoplewillrecover

fasterthannewcasesaregenerated.Negativefeedbackdominatesandthepopula-

tionisresistanttoanepidemic｡PastthetipplngpOlnt,thepositiveloopdominates.

Thesystem isunstableandonceadiseasearrives,itcanspreadlikewildfire-

thatis,bypositivefeedback-limitedonlybythedepletionofthesusceptible

population.

Figure9-6showsasimulationofthemodelwherethesystemiswellpastthe

tlpplngpoint.ThepopulationofthecommunltylS10,000andinitiallyeveryoneis

susceptibletothedisease.Attimezero,asingleinfectiveindividualarrivesinthe

community.Theaveragedurationofinfectionis2days,andinfectivltyis25%.

TheaveragecontactfrequencylSSixpeopleperpersonperday.Eachinfective

thereforegenerates1.5newcasesperdayandanaverageofthreenewcasesbefore

theyrecover.Thepositiveloopthereforedominatesandtheepidemicquickly

spreads.Theinfectionratepeaksatmorethan2000peopleperdayaroundday

nine,andatitspeakmorethanone-quarterofthepopulationisinfectious.Thesus-

ceptiblepopulationfallsrapidly,anditisthisdepletionofpotentialnewcasesthat

haltstheepidemic.Bythetenthday,thenumberofsusceptiblesremainlnglSSO

lowthatthenumberofnewcasesdeclines.Theinfectiouspopulationpeaksand

fallsaspeoplenowrecoverfasterthannewcasesarise･Thesusceptiblepopulation

continuestofall,thoughataslowerandslowerrate,untiltheepidemicends.

Inlessthan3weeks,asingleinfectiousindividualledtoamassiveepidemicin-

volvingnearlytheentirecommunity.Notethatafewluckyindividualsnevercon-

tractthedisease.Unlikethechronicinfectionmodelinwhicheveryoneeventually

contractsthedisease,intheSIRmodeltheepidemicendsbeforethesusceptible

populationfallstozero.Thestrongerthepositiveloop,however,thefewersusI

ceptiblesremainattheendoftheepidemic.AlsonotethatunliketheloglStic

model,thebehaviorisnotsymmetric･.theinfectiouspopulationrisesfasterthan itfalls.

4TheSIandSIRmodelswereorlglnallyformulatedasdeterministicsystemsrepresentlngthe averagecontactrateandabstractlngfromtheindividualencountersamongmembersofthepopula- tion,KeeplnmindthatthedeterministicformulationisamodelingassumptlOn,aPPrOPrlatein somesitlJ-ationsa!ldnotapproprlateinothers(particlllarly,Wbe!Hhepopulationsaresmallorthe

varianceinthedistributionofcontactrates,infectivity,andrep?verytimeislarge).Themodelsare easilygeneralizedtoincorporateStOChasticencounters,infectlVlty,andrecovery,eitherbyadding randomvariationtotherateequationsoftheSIRmodelorbyrepresentlngthemembersofthepop- ulationasdiscreteindividualsandspecifyingdecisionrulesfortheirinteraction(anagenトbased model).Incorporatingtheserandomeffectsmeanstherewillbeadistributionofpossibleoutcomes foranysetofparameters.Thesharpboundarybetweenanepidemicandstabilitydefinedbythetip- plngpOlntinthedeterministicmodelsbecomesaprobabilitydistributioncbaracterizlngthechance anepidemicwilloccurforanygivenaverageratesOfinteraction,infectivlty,andrecovery.Like- wise,theSIandSIRmodelsassumeahomogeneousandwell-mixedpopulation,whileinrealitylt iso鮎nimportanttorepresentsubpopulatioI-SandthespatialdimlSionofanepidemic.Forspatial modelsofthespreadofdiseaseandotherrefinements,seeMurray(1993).

Chapter9 S-ShapedGrowth:Epidemics,ⅠnnovatlonDi軌sion,andtheGrowthofNewProducts307

Toillustratethetipplngpoint,Figure9-7showsthesusceptiblepopulationin

severalsimulationsofthemodelwithdifferentcontactrates･Theotherparameters areidenticaltothoseinFigure9-6.Atthetippingpoint(twocontactsperperson

perday),thenumberofnewcaseseachinfectivegenerateswhileinfectiousisjust equaltoone(2contactsperpersonperday*0125probabilityofinfection*2days ofinfectivity).Contactsataratelessthantwoperpersonperdaydonotcausean

FIGURE9-6 Simulationofan

epidemicinthe SIRmode一

Thetotal

populationis 10,000.The contactrateis

6perperson perday,infectivity is0.25,and averageduration ofinfectivityfS 2days.The initialinfective

populationisi, andalTothers

areinitially susceptible,

FIGURE9-7

Epidemic dynamics fordifferent contactrates

Thecontactrate isnotedoneach

cuⅣe;allother parametersare asinFigure916.

(

^ t2 P P

do a d )

s a l

e E

^ O U a t l

Pu t=

u O

!83a l u E

(a ld o a d ) uo !l e

P d o d aJ q!

l d

ao s

m…

(a Fd oa d ) u o !te p d o d a一 q! t d

aos n s

0 4 8 12 Days

16 20 24

0 4 8 12 Days

16 20 24

10 04 S

y 3 Da

02 50 60

308 PartIIITheDynamlCSOfGrowth

epidemic.Whenthecontactraterisesabovethecriticalthresholdoftwo,thesys-

tembecomeunstable,andanepidemicoccurs.Thehigherthecontactrate,the strongerthepositivecontaglOnlooprelativetothenegativerecoveryloop,andthe fastertheepidemicprogresses.Further,thestrongerthepositiveloop,thegreater thepopulationultimatelycontractlngthedisease.Anychangethatincreasesthe strengthofthepositiveloopswillyieldsimilarresults･Anincreaseininfectivlty strengthensthepositiveloopandisidenticalinimpacttoanincreaseincontactfre- quency.Anincreaseinthedurationoftheinfectiousperiodweakenstherecovery loopandalsopushesthesystemfartherpastthetlPPlngPOlnt･

ExphringtheS旧 ModeI

SimulatetheSIRmodelundervariouscombinationsofparameters.Whatde- termineswhetheranepidemicwilloccur?Whatdeterminesthefractionofthe populationremaininguninfectedinequilibrium?Why?

TheexacttlpplngpOlntintheSIRmodelcaneasilybecalculated.Foranepidemic tooccur,theinfectionratemustexceedtherecoveryrate:

IR>RR=⇒ciS(Ⅰ/N)>Ⅰ/d

orequlValently,

cid(芸)>1

(9-25)

(9-26)

Inequation(9-26),theproductofthecontactrateandinfectivityisthenumberof infectiouscontactspertimeperiodeachinfectiouspersongenerates.Multiplying bytheaveragedurationofinfection,d,yieldsthedimensionlessratiocid,known asthecontactnumbey:However,notallthesecontactswillbewithsusceptibles,so notallwillresultinanewcase.Thenumberofinfectiouscontactsthatactually

resultintheinfectionofasusceptiblepersondependsontheprobabilitythatthe infTectivesencountersusceptibles.Assumingthepopulationishomogeneous,the probabilityofencounterlngaSusceptibleisglVenbytheprevalenceofsusceptibles inthepopulation,S/N.Theexpressioncid(S/N)isalsoknownasthereproduction

ratefortheepidemic｡Equation(9-26)thereforedefinesthetippingpointorthresh oldatwhichanepidemicoccursinapopulationandisknownasthethresholdthe- oreminepidemiology.

Notethatthecontactnumbercanbelargeifinfectivltyishighorifthedur a-

tio王10finfectionislong.Theduratio王.l_OftheinfFIXtioIJSperiodfordiseasessuchas measlesandchickenpoxisveryshort,amatterofdays,butthesediseaseshave highcontactnumbersbecausetheyareeasilyspreadthroughcasualcontact｡h contrast,thecontactrateandinfectivityofHIVaremuchlower(HIVcannotbe spread血roughcasualcontactbutonlythroughsexualcontactorexchangeof bloodorbloodproducts).Nevertheless,thecontactnumberforHIVishighamong thosewhoengageinriskybehaviorsbecausethedurationofinfectionissolong. TheincubationperiodprlOrtOthedevelopmentofclinicalsymptomsofAIDSav- eragesabout10years(Seesection9.2.7).

Chapter9 S-ShapedGrowth:Epidemics,ⅠnnovationDi軌sion,andtheGrowthofNewProducts309

Figure9-8showshowthetipplngpOlntdependsontheparameters.Thecurve

istheboundarybetweenstableandunstablereglmeS.Totheleftofthecurve,the

systemisstableandthereisnoepidemicbecausetheinfectivity,contactrate,du-

rationofinfection,andfractionofsusceptiblesinthepopulationaretoolow.Tothe

rightofthecurve,thesystemisunstable,andthereisanepidemic.

9.2.4 ⊆mmun章ZationandtheEradicationofSmaHpox

Theexistenceofthetippingpoint(equation(9-26))meansitistheoreticallypos-

sibletocompletelyeradicateadisease.EradicationdoesnotrequireaPerfect

vaccineanduniversalimmunizationbutonlytheweakerconditionthattherepro- ductionrateofthediseasefallandremainbelowonesothatnewcasesariseata

lowerratethanoldcasesareresolved.Thestockofinfectiouspeoplewillthende-

cline,furtherreducingtheinfectionrate,untilthepopulationbecomesdisease-free.

Formanydiseases,itisdifficultorimpossibletoachieveormaintainthiscondi-

tionduetohighinfectivlty,theexistenceofreservoirsofthediseaseoutsidethe

humanpopulation(asinmalariaorLymedisease,bothofwhichhaveanimal

hosts),ortherapidinfluxofsusceptiblepeoplethroughbirths,migration,orthe

decayofimmunlty.

Smallpox,however,isdifferent.Smallpoxwasonceoneofthemostdeadly

diseasesandendemicthroughouttheworld.TheinfectivltyOfsmallpoxishigh,

butthedurationofinfectionisshort.Survivorsacquiredlong-livedimmunlty.

Mostimportant,thesmallpoxviruscannotsurviveoutsideahumanhost-there arenoanimalorotherreservoirstoharborthevirus.Theseconditionsmeantthat

thedevelopmentofaneffectivevaccine,deployedsufficientlybroadly,couldre-

ducetheinfectionratebelowtherecoveryrateandeliminatethevirus,evenifnot

everypersoncouldbeimmunized.

Thehistoryofsmallpoxeradicationiswellknown:EdwardJennerdeveloped

thefirsteffectivevaccinein1796.DespitethesuccessofJenner'svaccine,ittook

manyyearsforvaccinationtobeaccepted;smallpoxwasstillamajorCauseOf

deathatthestartofthe20thcentury.Bythe1950S,duetoimprovementsinpublic

healthprogramsandintheeffectivenessandshelf-lifeofthevaccine,smallpox

FIGURE9-8

Dependenceof thetipplngPOint onthecontact numberand

susceptible population

( s s o l u

O IS u a ∈ !P )

(p !3

)L む q

Lu.n N IDe t u O

cid(S/N)=1

Epidemic (unstab一e;positiveloopdominant)

NoEpidemic stable;ne

Susceptib一eFraction,ofPopulation(S/N) (dimensl0nless)

310 PartIIITheDynamicsofGrowth

hadbeeneradicatedinmostoftheindustrializedworld.Inthemid-1960S,the

WorldHealthOrganization(WHO)Coordinatedavigorousworldwidecampaignto trackthedisease,immunizethesusceptible,andquarantinethesick.Thelast knownnaturallyoccurringCaseWasreportedin1977inSomalia.In1978,some smallpoxvirusescapedfromaresearchlabinEnglandandcausedtwocases,one

fatal･Sincethennofurthercaseshavebeenreported,and,inoneofthegreatesttri- umphsinthehistoryofmedicine,thenationsoftheworlddeclaredin1980that smallpoxhadbeeneradicatedfromtheearth

Almost.DuringtheColdWar,boththeUSandSovietUnionmaintained

stocksofsmallpoxvirusaspartoftheirbiologicalwarfareprograms.Thoughboth nationsslgnedthe1972BiologicalWeaponsConventionbanningbioweaponsand biowarfareresearch,theycontinuedtomaintaintheirstocksofsmallpox,andthe SovietUnioncontinuedbiowarfareresearchinviolationoftheConvention.While

thesesmallpoxstocksaremaintainedinthehighestsecuritybiocontainmentlabs,

thereisnaturalconcemthatthevirusmightescape,accidentally,throughterrorism,

orinwar.AWHOpanel,afterlongandsometimesacrimoniousdebate,recom-

mendedin1994thatallUSandRussianstocksofthevirusbedestroyedbyJune 1999.However,manyanalystsbelieveterroristsornationssuchaslraqandNorth

KoreamayhaveacquiredsmallpoxfromtheformerSovietUnion.Becausepeople nolongerreceivesmallpoxvaccinations,andbecausetheimmunityCOnferredby

childhoodvaccinationdecays,muchoftheworld'spopulationtodayissusceptible. Thereleaseofsmallpoxfromthesestockscouldtriggeramassivepandemic.Inre- sponse,PresidentClintonorderedUSsmallpoxstocksbepreservedforresearch,

andWHOsuspendeditsattempttohavedeclaredstocksofsmallpoxdestroyed.

TheEffic領CyOfhlLmuniZa如 FT.甲相gTamS

Equation(9-26)andFigure9-8showhowthevulnerabilityofapopulationtoepi- demicdependsontheparametersoftheSIRmodel.Manyinfectiousdiseasesare highlycontaglOuSanditisnotfeasibletoreducethecontactnumber.IInmuniza-

tion,wherevaccinesareavailable,canbehighlyeffectivenotonlyinprotecting theimmunizedindividualsbutalsoinmovinganentirepopulationbelowthetip- pingpoint.Forexample,poliohasallbutvanishedinnationswithstrongpublic healthprogramsandWHOhopestoeradicateitworldwidewithinafewyears.

1.Effectivenessofimmunizatiom｡

Thecontactnumberforpolioisestimatedtoberoughly5to7(Fine1993).

Whatfractionofthepopulationmustbevaccinatedtoensurethatno epidemicwilloccur?AssumethevaccineislOO%effective.Nowconsider measlesandpertussis(whoopingcough),diseaseswhosecontactnumbers

areestimatedtobe12to18(Fine1993).Whatfractionofthepopulation mustbevaccinatedtoensurenoepidemicwilloccur?Whatfractionmustbe vaccinatedifthevaccineisonly90%effective?Whydomeaslesand

pertussispersistwhilepoliohasbeeneffectivelyeliminated? Next,simulatetheSIRmodelwiththeparametersinFigure9-6(C-6,

i-0･25,d-2,N- 10,000),butassumethat50%ofthepopulationhas

Chapter9S-ShapedGrowth:Epidemics, InnovationDi軌ISion,an dtheGrowthofNewProducts311

beenimmunized(Settheinitialrecoveredpopulationtohalfthetotal

population). Whatistheeffectonthecourseoftheepidemic?Whatfraction ofthepopulationmustbeimmunizedtopreventanepidemic?

2 . Effectivenessofquarantine.

Examinetheeffectivenessofquarantineasapolicytopreventanepidemic. Todoso,mo difytheSIRmodeltoincludeastockofquarantined

individuals. (i)Assumepeoplearequarantinedonlyaftertheyexhibitsymptoms,so

thequarantinerate(therateofinflowtothequarantinedpopulation)

flOwsfromtheinfectiouspopulationtothequarantinedpopulation. Formulatethequarantinerateasfollows. Assumeittakesacertain

periodoftime, denotedtheQuarantineTime, toidentifyinfectious

peopleandmovethemtoaquarantinearea. Furぬer,assumeon lya fractionoftheinfTectiouspopulation, denotedtheQuarantineFraction, isidentifiedasinfectiousandwillingorabletobequarantined. Be

sureyourformulationforthequarantinerateisdimensionallycon- sistent･ Assumequarantinedindividualsrecoverfromthediseasewith

thesameaveragedurationofinfectivltyaSthosenotquarantined･ (ii)Quarantinedindividualsarenotcompletelyremovedfromcontactwith

therestofthepopulation(duringanepidemicofsmallpoxin18thcen- turyBoston, forexample, thesickwerequarantinedbutstillpermitted

toattendchurchonSunday). Modifytheequationfortheinfectionrate toincludethepossibilitythatquarantinedpeoplecomeincontactwith

susceptiblesatacertainrate, denotedtheQuarantineContactRate. AssumetheinfectivltyOfquarantinedindividualsisthesameasthat forotherinfectives. Howdoestheadditionofastockofquarantined individualsalterthefeedbackstructureoftheSIRmodel?

(iii)AssumetheQuarantineTimeishalfaday,an dusetheparametersfor

thesimulationinFigure9-6(C-6, i-0. 25 , d-2, N-10, 000) ･ Assumethequarantineisperfect,So thattheQuarantineContactRate iszero. RunthemodelforvariousvaluesoftheQuarantineFraction andexplaintheresultingbehavior･ Whatfractionoftheinfectious populationmustbeqtlarantinedtopreventanepidemic?Nowassume thatthecontactrateofquarantinedindividualsishalfthenormal

contactrate. Whatfractionmustnowbesequesteredtopreventan

epidemicandhowfastmustpeoplebemovedtoquarantineoncethey becomeinfectious?Exploretheresponsetootherparameters, includ1 1rI_gPar tialimmllnizationofthepoptllation･ Comparetheefficacyof

immunizationtoquarantineinpreventingOrSlowlngepidemics. What

policyconsiderationswouldinfluenceyourchoiceofthesepoliciesin differentsituations?

3 . Lossofimlnunity.

Forsomediseases, ilnmunltylSnotpe-anent, butdecaysovertime, 1eavlng formerlyimmunePeoplesusceptibletoreinfection. Modifythemodelto incorporatelossofimmunity. Assumeimmunitydecaysataratedetemined byaconstantaveragedurationofimmunity･ Runthemodelfordifferent

312 PartHI TheDynamicsofGrowth

valuesoftheaveragedurationofimmunlty,Whatistheimpactonthe dynamics?Underwhatconditionswillthediseasebecomeendemicinthe population?Whatistheequilibriumreached,andwhy?Whatimpactdoes lossofimmunityhaveontheeffectivenessofimmunization?Ontheability toeradicateadisease?Why?

9.2t5 Herd貞mmunはy lntherealworld,apopulationisrepeatedlychallengedbyexposuretodi恥rent diseases.Infectiousindividuals,unwittinglycarrylngthedisease,mayarrivefrom othercommunities.Thespreadoftheblackdeathin14thcenturyEuropewasac-

celeratedbyextensivetradenetworkswithotherreglOnS,thehighrateoftravelof pilgrims,andbytheflightoftheterrifiedandunknowinglyinfectedtotownsasyet unexposed.Susceptibleindividualscanalsocomeintocontactwithotherreser- voirsofthedisease,suchascontaminateddrinkingwater(asincholera),orani-

mals(bubonicplagueisnotonlytransmittedfrompersontopersonbutbyfleas whopasstheplaguebacillusfrominfectedratstopeople)ASomepathogensmutate andcrosstheso-calledspeciesba汀ier,Jumpingfromanimalreservoirstohuman populations(asoccursininfluenzaandlikelyoccurredwithHIV,outbreaksofthe Ebolavirus,andapparentlywithBovineSpongiformEncephalopathy(BSE)- madcowdisease).Ifthecontactrate,infectivity,anddurationofinfectionare smallenough,thesystemisbelowthetipplngpointandstable･Suchasituationis knownasherdimm unity(Fine1993)becausethearrivalofaninfectedindividual

doesnotproduceanepidemic(thoughafewunluckyindividualsmaycomeincon- tactwithanyinfectiousarrivalsandcontractthedisease,thegroupasacommunity isprotected).However,changesinthecontactrate,infectivity,ordurationofill- nesscanpushasystempastthetipplngpOlnt.

Figure9-9Showshowchangesinthereproductionratecandramatically changetheresponseofapopulationtoexposure.Inthesimulation,thepopulation ischallengedevery50daysbythearrivalofaslngleinfectedindividual.Thepop- ulation,infectivlty,anddurationofinfectionareidenticaltothoseinFigure916 (10,000,0.25,and2days,respectively).However,thecontactrateisassumedto increaselinearlyovertime,beginnlngatZero.Thecontactratemightincreaseas populationdensltygrowsOraSChangesinsocialstructuresorculturalpractices bringpeopleintomorefrequentcontact.Therapidurbanizationoftheindustrial revolution,forexample,increasedthecontactrateandincidenceofepidemicsfor

manydiseases. Duringthefirst500days,thereproductionrate(themum-berofnewcasesgen-

eratedbyeachinfectivepriortorecovery)islessthanone,thenegativeloopsdom- inate,andthesystemisbelowthetlPPlngPOlnt.Thereisnoepidemic:Every50 daysaninfectiousindividualarrives,butanypeopleinfectedbythispersonre- coverbeforetheycanreplacethemselvesinthepoolofinfectives.Thepopulation enjoysherdimmunity.Atday500thetipplngPOlntiscrossed.NowthecontaglOn loopdominates,andthenextinfectiouspersontoarrivetriggersanepidemic.The epidemicendsafterthesusceptiblepopulationfallsenoughforthedepletionand recoveryloopstooverpowerthecontaglOnloop.Byaboutday600thedeclinein

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts313

FlGURE9･9

Successiveepl- demicwavescre-

atedbyincreaslng contactrate

Every50days thepopulation ischa"engedby thearrivalofasin-

gleinfectrlousIlndl-I vjduaLAtfirst,the

populationhas herdimmunity. Thecontactrate

l'ncreaseshlnearly fromzero,increas-

lng的ere一ativere- productionrate andeventually causmgawaveof epidemics･

(a 一do ad ) u o .rt t2 1

n d o d al q

.Ilda o s n s

1500 2000

thesusceptiblepopulationreducesthereproductionratebelowoneandthenega-

tiveloopsonceagaindominatethepositivecontagionloop.Thoughinfectedindi-

vidualscontinuetoarriveat50-dayintervals,thesystemhasbecomestableagaln.

However,thecontactratekeepsrlSlng,lnCreaSlngthestrengthofthecontagion

loop･Byday800,thecontaglOnloopISOnceagaindominant.Thearrivalofthe

nextinfectiouspersontrlggerSanotherepidemic.SincethereareevenfewersusI

ceptiblesthistimearound,itisabitmilder･Byday1100thedepletionofthesus-

ceptiblepoolhasonceagalnOVerWhelmedthecontaglOnloopandthereproduction

314 PartIII TheDynamicsofGrowth

ratefallsbelowone.ThecommunitylSOnceagalnresistanttoepidemic,untilthe contactraterisesenoughtopushthereproductionrateaboveoneagain,trlggerlng thethirdwaveofinfection.

Inthissimpleexampletheperiodicepidemicsarisefromtheassumedsteady riseinthecontactrate.Successivewavesofepidemicsareinfactobservedfor manyinfectiousdiseases,perhapsmostnotablymeasles.Priortotheintroduction ofmassimmunizationinthe1960S,industrializednationssuchastheUSandUK

experiencedlargeamplitudemeaslesepidemicsaboutevery2years.Duetoim- munizationprograms,theamplitudeofthecyclesismuchreducedtoday,but血e tendencytowardcyclicwavesofmeaslespersists.Incontrasttotheexample above,thecontactrateformeaslesremainsreasonablyconstant.Thecyclicchar- acteroftheepidemicsarisesfromtheinteractionofherdimmunltyWithpopulation growth･Eachepidemicincreasestheimmunefractionofthepopulationenoughto conferherdimmunlty,PreVentlnganotherepidemicthefollowlngyear.Iiowever, duringthistimethepopulationofsusceptiblesincreasesaschildrenareborn. Eventually,thesusceptiblefractionofthepopulationrisesenoughtopushthesys- tempastthetipplngpOlntagaln,andthenextepidemicbegins.TheSIRmodelcan easilybeextendedtoincludetheagestructureofthepopulation,includingbirths anddeaths(Seechapter12)･Withrealisticparametersthesemodelsgenerateper- sistentoscillationsindiseaseincidenceasthesystemrepeatedlycyclesaboveand belowthetlpplngpOlnt.

Thereproductionrateforaninfectiousdiseaseisnotsolelyamatterofthevir- ulenceandotherbiologlCalattributesofthepathogen･Itisstronglyinfluencedby socialstructuresandthephysicalinfrastructureofacommunity.Thecontactrate obviouslyrepresentsthenatureofsocialstructuresinthecolnmunity:Thecontact rateinruralcommunitieswithlowpopulationdensitiesislowerthanthatofhighly urbanizedpopulations.TheinfectivltyOfadiseaseisonlypartlydeterminedbybil ologicalfactors.Casualcontactandinhalationcanspreadinfluenza,whileHIVcan onlybecontractedthroughexchangeofbloodorotherbodyfluids(abiological factor).Butinfectivityisalsostronglyaffectedbysocialpracticesandpublic healthpolicies,suchastheavailabilityofcleanwater,theprevalenceofhand washing,orthefrequencyofcondomuse.

9E.2･6 棚4.7Jt.･･汗噂 PaSH:､,i:-I:-{'T矩沖巧キヨFr,h音: MadCowDisease

TheepidemicofBSEormadcowdiseaseinGreatBritainduringthe1990sillus-

trateshowchangesintechnicalandsocialstructurescanpushapopulationpast血e tlpplngpoint.Priorto血eepidemic,theincidenceofBSEandrelateddegenerative neurologicaldiseasessuchasscrapie(insheep)andCruetzfeldt-JacobDisease (CJD,inhumans)wasextremelylow.Butbetween1985and1997,approximately 170,000casesofBSEwereconfirmedintheUK,andalmostonemillioncattleout

ofatotallivestockpopulationofaboutllmillionwereestimatedtobeinfected (Prusiner1997).BSE,scrapie,andCJDprogressivelyand,atpresent,irreversibly destroybraintissue;symptomsincludeuncontrollabletremor,disorientation,loss ofmotorandcognitivefunction,andultimatelydeath.

≡

∫ 一

■

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts315

ThecauseofBSEisstilldebated.MostscientistsbelieveBSEiscausedbyprト

ons,abnormalproteinsthatarehypothesizedtoreplicateeventhoughtheydonot

containanyDNAorRNA.BiologistStanleyPrusinerreceivedthe1997Nobel

Prizeforhispioneering(andstillcontroversial)workonprions(seePrusiner1997

forfurtherdetailsonprionsandBSE).OthersbelieveBSE,scrapie,andCJDare

causedbyanasyetundetectedandpossiblynoveltypeofvirus.

SinceBSEisnotthoughttobedirectlycommunicablefromanimaltoanimal,

thepositivecontagionfeedbackdidnotexistundertraditionalanimalhusbandry

practices.Howthendidtheepidemicarise?Toreducecostsoverthepastfew

decades,Cattleproducersbegantosupplementthedietsoftheirherdswithmeat

andbonemeal(MBM)preparedfromtheoffalofslaughteredlivestock,including

sheep,cattle,pュgs,andchickens.Tbreducecostsfurther,anewprocessfわrprepa-

rationofMBMwasintroducedinthelate1970S.Thenewprocessinvolvedlower

temperaturesforrenderingoffalintofeedpelletsandleftmorefatintheproduct. ItisthoughtthatthischangeallowedBSEtoentertheUKcattlepopulation

throughMBMmadefromsheepinfectedwithscrapie.Initssearchforlowercosts

thelivestockindustryconverteditsherds丘.omherbivorestounwittlngCannibals

andcreatedapathwayforinfectedcattleto"contact"susceptibles,thusclosingthe

contagionloop.ThepracticeoffeedingMBMtocattledramaticallyboostedthere-

productionrateforBSEinthecattlepopulationandpusheditwellabovethetip-

plngpoint.Further,whereasmostdiseasesarecommunicatedonlybyclosecontact

betweeninfectedandsusceptibleindividualssothatepidemicstendtobegeo-

graphicallylocalized,MBMwasdistributedallovertheUK,allowlngaSlnglein-

fectedanimaltopassBSEtoothershundredsofmilesaway.

Theepidemic(Figure9-10)spreadrapidly,muchfasterthanmedicalknowl-

edgeofitorthereactionsofpublichealthauthorities.Bythemid1980SBritish

publichealthofficialsknewtherewasanewdiseaseafflictingthecattleindustry.

BSEwasfirstidentifiedastheculprltOnlyln1986.Therewasafurtherdelayof

severalyearsbeforetheUKbannedtheuseofMBMasafeedsupplement.Dueto

First

HistopathoEogICal Confirmation

∩)

ウ]

ー

LJlu O M

J a

d sasE! U

6 6 6 L

96 6 L

卜66L 96 6 L

S 6 6 L

寸

6 6 L

6 6 LN66L

L 6 6 L

O 6 6 L

696 L

996L ト96 L

996 L

の96 L

Month/YearofClinicalOnset

Source:UKMlnistryofAgriculture,FisherleS,andFood,<www.maff.gov.uk/anlmalh/bse/ bse-Statistics/Ieveト4-epidemhtmL>,3August1999.

316 PartIIITheDynamicsofGrowth

thelongIncubationdelay,however,confirmedcasescontinuedtorisethrough 1992,decliningonlyasanimalsininfectedherdsweredestroyed.Bythen,how- ever,BritishbeefwasbannedbytheEuropeanUnionandshunnedthroughoutthe world.Worse,manyscientistsfearthatBSEhasbeenpassedfromcontaminated beeformilktothehumanpopulation.By1998,23confirmedanduptoadozen possiblecasesofanewvariantofCJD(nvCJD)hadbeenidentified,allintheUK orFrance.Thenewvariant,unliketraditionalCJD,primarilystrikesyoungpeople. BecauseCJDhasaverylongincubationtime(yearstodecades),itisnotyet knownwhetherthesenvCJDcasesrepresentanisolatedgrouporthefirstcasesof ahumanepidemiccausedbyconsumptlOnOfBSEcontaminatedbeef.Manysci- entistsfearthatBSEhascrossedoverfromthelivestocktothehumanpopulation andmaynowbegintospreadthroughexchangeofbloodproducts.InJuly1998 theUKgovernmentauthorizeditsNationalHealthServicetoimportbloodplasma fromnationsapparentlyfreeofBSEafteritwasdiscoveredthattwoofthevictims ofnvCJDwereblooddonors,PotentiallythreateningtheintegrltyOfUKblood suppliesandvaccinespreparedfrombloodproducts.

Extemd摘g昔的eS8円掴⑳de日

TheSIRmodel,usefulasitis,invokesanumberofrestrictiveassumptlOnS.Like theSImodelofchronicinfection,theSIRmodeldoesnotincorporatebirths, deaths,ormlgration;assumesthepopulationishomogeneous;doesnotdistinguish betweenpersonsremovedfromtheinfectiouspopulationbyrecoveryandthede- velopmentofimmunltyOrbydeath;andassumesimmunltylSpermanent.

Mostimportantly,themodelassumesthereisnoincubationperiod.Individu- alsinfTectedwithadiseaseintheSIRmodelimmediatelybecomeinfectious.Inre-

ality,mostdiseaseshavealatency,orincubationperiod,andpeoplebecome infectiousbeforeexhibitinganysymptomsofillness･Peopleexposedtochicken poxbecomehighlyinfectiousseveraldayspriortOtheemergenceofsymptoms, some14to21daysafterinitialexposure,ManypeopleinfectedwithHepatitisA starttoexhibitsymptomsaboutamonthafterinfectionbutbecomehighlyinfec- tiousabout2weeksearlier.TheaverageincubationperiodforHIV(thetimebe- tweeninfectionwithHIVandthedevelopmentofAIDS)foradultsnotreceiving treatmentisabout10years･Thelatencyperiodbetweeninfectionandtheappear- anceofsymptomsforHepatitisCisevenlonger-averaglngperhaps15years. SomefourmillionpeoplearethoughttobeinfectedwithHepatitisCintheUS, andwhileabout15%spontaneouslyrecover,inmanyothercasesthediseaseeven- tuallyproducesirreversibleandoftenfatalliverdamage･He†)atitisCisspreadby⊥ exchangeofbloodproductsbutonlyrarelythroughsexualcontact･

ModifytheSIRmodelbydisaggregatlngthestockofinfectiousindividuals intotwocategories:AsymptomaticInfectivesandSymptomaticInfectives.Thein- fectionratemovespeoplefromthesusceptiblecategoryintotheasymptomatic infectivepopulation,thatis,peoplewhoareinfectedwiththediseasebutdo notyetexhibitanysymptoms.Aftertheincubationperiod,peoplebegintoexhibit symptoms(typicallywhileremaininginfectious)andmoveintothesymptomatic

Chapter9S-ShapedGrowth:Epidemics7 InnovationDiffusion,an dtheGrowthofNewProducts317

infectivecategory. Assumethattherateatwhichpeoplebecomesickisafirst- orderprocesswithaconstantaverageincubationperiod.

SusceptiblepeoplecancontractthediseasebycomlnglntOCOntaCtWitheither symptomaticorasymptomaticinfectives. Thecontactrateandinfectivityfor asymptomaticandsymptomaticindividualsoftendiffer. Oncepeoplefallill(be- comesymptomatic)theyoftenreducetheircontactratewiththeoutsideworld,e i- thertoavoidinfectingOthersorsimplybecausetheyaretoosicktofollowtheir normalroutine｡ Asymptomaticindividuals, incontrast,usua llydonotknowthey areinfected, donotexhibitanysymptoms,an dcontinuetocontactothersattheir normalrate･ Similarly,t heinfectivltyOfadiseasepriortOtheemergenceofsymp- tomsisoftendifferentfromtheinfectivltyaftersymptomsappear. Inmeasles, forexample,peop learemostinfectiousfrom5dayspriortO5daysaftertheapI pearanceofthecharacteristicrash. Modifytheformulationfortheinfectionrateto capturethedifferingcontactratesandinfectivitiesofthesymptomaticandasymp- tomaticinfectivepopulations.

Runthemodelforahypotheticaldiseasewithanincubationperiodsimilarto chickenpox. Becausetheincubationperiodfわrchickenpoxis14to21days,as- sumeanaverageof18days. Assumetheaveragedurationofillnessis4days. Set thecontactrateforasymptomaticinfectivestofourperpersonperday, butbecause thoseexhibitingsymptomsremaininbedinself-imposedquarantine,se tthecon- tactrateforthesymptomaticpopulationtoonlyoneperpersonperday. Assumein- fectivltyis0. 25forbothasymptomaticandsymptomaticpopulations. Alsoassume aninitialpopulationof10, 000 , allofwhomareinitiallysusceptibleexceptforone asymptomaticinfectiveperson.

Runthemodelanddescribetheresults. Howdoestheinclusionofanincuba-

tionperiodaffectthedynamics?Bythetime1%ofthepopulationexhibitssymp- toms,w hatfractionofthesusceptiblepopulationremainsuninfected?Howmany susceptiblesremainbythetimelo啄ofthepopulationhasbecomesick?Whatis theimpactofanincubationperiodontheeffectivenessofquarantine?Youcan simulateaperfectquarantinepolicybysettlngthecontactrateforthesymptomatic

populationtozeroorincludethequarantinestructuredevelopedabove. Explore theresponseoftheepidemictodifferentincubationtimesandinfectivities. What istheeffectofalongincubationperiodonthecourseofanepidemicandtheabill 1tyOfapopulationtoenjo

herdimmunity?

PoII'cyAnalys/'S:Just-in-Timelmmunizalion Evaluatetheeffectivenessofapolicyof"just-in-time(JIT)vaccination, "thatis, VaccinatlngPeopleonlvafterevidenceofanepidemicappears. ManvI)eODleonly

_/ getflushotswhentheybelievethefluintheirareaisparticularlyseverethatyear. Similarly,somevacc inesaresoexpensiverelativetotheincidenceofinfectionthat theyarenotroutinelyglVen. Whenpreviouslyunknowndiseasesstrike,vacc ines cannotbemadeuntilafterthediseaseemergesandisidentified. Theappearance

ofnewcomputervirusesleadstofranticeffortsbyprogrammerstocomeup withcountemeasures, buttheresultingHvaccines"arenotavailableuntilafterthe

virusisidentified. TheBritishgovernment'sbanontheuseofMBMasafeed

318 PartIIITheDynamicsofGrowth

supplementforcattleisroughlyequlValenttoapolicyofJITimmunization.The banreducedthenumberofinfectiouscontactsbyremovlngthevectorforBSE

fromthedietofthecattleatriskonlyafterthescientificevidencethatMBMwas

thesourceoftheepidemicbecamecompellingenough,andthepublicoutcrygreat enough,toovercome也epoliticalresistanceofthecattleindustry.

TomodelaJITvaccinationpolicy,CreateanImmunizationRatethattransfers

peoplefromthesusceptiblepopulationtoanewstock,theimmunizedPopulation. (Keepingtheim unizedpopulationseparatefromtherecoveredpopulationmakes

lteasytodeterminehowmanypeopleultimatelygetthedisease.)Formulatethe immunizationratesothatthevaccinationprogramisdeployedonlyafteracertain numberofcaseshavebeendiagnosed:

Immunization Rate

(

0ifSymptomaticPopulationく ThresholdforVaccinationProgram

VaccinationRate*VaccineEffectiveness otherwise

VaccinationRate-FractionVaccinated*SusceptiblePopulation TimetoDeployVaccine

(9-27)

(9-28)

Theimm unizationrate(theactualrateatwhichpeopledevelopimmunityfromthe vaccine)differsfromthevaccinationratebytheeffectivenessofthevaccine.Once theprogramisdeployed,ittakesacertainamountoftime,theTimetoDeployVac- cine,tocarryouttheprogram･Thevaccinationprogrammayonlyreachafraction ofthepopulationaswell.Notethatbecausethesusceptiblescannotbedistin一 guishedfromtheasymptomaticinfectivesorrecoveredpopulations,theentire populationwouldhavetobeimmunized(withthepossibleexceptionofthesymp- tomaticinfectivesforwhomvaccinationwouldnotbeeffective).Consequently, thecostsoftheprogramdependonthetotalnumbervaccinated.However,those whohavealreadyrecoveredfromthediseaseremainimmunesotheystaylnthe poolofrecoveredindividuals.Theformulationalsoassumesthatthevaccineis ineffectiveforthosewhohavealreadybeeninfected,sothereisnoflowfromthe asymptomaticinfectivepopulationtotheimmunizedpopulation.

TotesttheeffectivenessofaJITimmunizationprogram,makethestrongas- sumptionsthatavaccinewithlOO%effectivenessisavailableandthatthefraction ofthepopulationvaccinatedisloo瑞.Further,assumethattheentirepopulation canbevaccinatedinJuSt2days,Oncethethresholdhasbeenreachedandthedeci- siontodeploythevaccinehasbeenmade.Theseconditionsareunlikelytobe

achievedinrealitybutprovideastrongtestofthepotentialforJITvaccination strategleStOaddressacuteinfectiousdisease.

ExploretheeffectivenessoftheJITvaccinationpolicybyrunningthemodel

forvariousthresholds,startlngWithathresholdof5%ofthetotalpopulation.What

fractionofthetotalpopulationeventuallygetsthedisease?Howdoesthatcompare tothecasewithoutJITvaccination?WhatifthethresholdwereJust1%oftheto-

talpopulation(100cases)?Wh atistheeffectivenessofJITvaccinationwhenthe vaccineisonly95%effective,only80%ofthepopulationisimmunized,andifthe

delayindeployingthevaccinationprogramis1week?Commentonthetypesof diseasesforwhichJITvaccinationislikelytobeeffectiveandthosesituationsin whichitwillbeineffective.Besuretoconsiderthesocialaswellasbiologicalde-

terminantsofcompliancewithacrashvaccinationprogram･

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts319

9.2.7 Mode!ingtheHⅣ/A旧SEpidemic

Sofarthehypotheticaldiseasesexaminedhavebeenhighlyinfectious,acutein-

fections(similartochickenpoxormeasles)thatgeneraterapid,short-livedepi-

demics.Overthecourseofsuchanepidemic,itisreasonabletoassumethatthe

contactrateandotherparametersareconstants-theepidemicdevelopstoofastfor

slgnificantchangesinpeople'sbehaviororforresearchonpreventionortreatment

tocometofruition.TheseassumptionsarenotaPPrOPrlatefordiseasessuchas

HIV/AIDSwheretheincubationtimeislong.Figure9-11showstheincidenceand

mortalityofAIDSintheUSfrom 1984through1996;Figure9-12Showsthe

prevalenceofAIDSamongadultsintheUS･5

ThedatashowimportantshiftsinthedynamicsoftheepidemicintheUS.In-

cidenceofclinicalAIDS(indicatedbytheAIDS-OIcurveinFigure9-11)grew

steadilyuntilabout1995andhasdeclinedsignificantlysince.Mortalityclosely

followsincidenceandexhibitsanevenlargerdecline･ThedeclineinmortalityexI

ceedsthatinincidenceduetothedevelopmentoftherapleSincludingAZTand,

mostimportantly,theso-CalledmultidrugcocktailsorHAART(highlyactiveantト

retroviraltherapy).Overallincidencehasdeclinedduetoareductioninnewcases

transmittedbymalehomosexualcontactandsharingofdirtyneedlesbyintra-

venousdrugusers(incidenceamongwomenandduetoheterosexualcontactwas

stillrisingasIwrotethis).NotethatevenbeforetheintroductionofHAART,how-

ever,thegrowthoftheepidemicwasnotapureexponential,aswouldbeexpected

ifthecontactrateorinfectivltyWereconstant.Instead,thefractionalgrowthrate

ofAIDSincidencedeclinedastheepidemicspread.

Despitethegreatstridesintreatments,theimprovlngOutlookfortheHIVepi-

demicinthewealthynationsisonlypartofthestory.Thereisasyetnoeffective

vaccine,andthelong-runeffectivenessandsideeffectsofHAARTremainun-

known.Moreimportantly,HAARTisexceedinglycostlyand,inmanynations,

simplyunavailable.TheincidenceofHIVinfectiongloballycontinuestoriseand

inmanynationshaslongsincepassedthecrisispolnt.Thescaleoftheepidemicis

almostimpossibletocomprehend.TheWHOestimatedthatin1997aboutone-

quarteroftheentirepopulationofZimbabwewasinfectedwithHIV;incidencein

muchofAfricaandsomeotherdevelopingnationsisestimatedtoexceedl0%.Ten

millionpeoplehavealreadydiedofAIDSinsub-SaharanAfrica,andwithoutdra一

maticchangesinaccesstotreatmentanddrugs,20millionmorepeoplearepro-

jectedtodie.Mortalityandmorbidityfrom HIVandAIDSinmanyofthese

nationshaveoverwhelmedthehealthcaresystems.TheWHOestimatesthatin

1990therewerefewerthan200hospitalsand1400doctorsinallofZimbabwe,a

nationofmorethan1imillion.Lifeexpectancyisfalling.Despitethedeclinein

AIDS-relatedmortalitylnsomeOftheaffluentnationsoftheworld,theHIV/AIDS

pandemicisfarfromover.TheWHOreportedthatin1998AIDSwasthefourth

largestcauseofdeathworldwide,upfromseventhin1997.

5DespltethemassiveeffortandcarefulworkoftheCDC,thedataarehighlyuncertainandare adjustedinseveralwaystoovercomevariouslimitationsintheUSsurveillanceandreportlng system.ThedefinitionsofAIDShavechangedovertheyearsasunderstandingofthediseasehas improved.DataonHIVincidenceandprevalenceareevenlesscompleteandreliable.Readersare urgedtoconsultthefullHIV/AIDSSurveillanceReportsandreferencesthereinfordetails.

320

FLGURE9･ll lncidenceand

mortalityofAIDS intheUS

"Estimatedincidence

ofAIDS,AIDS- opportunisticiHness (A旧S一〇1),and deathsinpersons withAIDS,adjusted fordelaysinreport- fng,byquarter-year ofdiagnosis/death, UnitedStates, 1984-1996[quar= terlydatareportedat annualrates].

Estimatedincidence ofAIDSincludes

personsdiagnosed uslngthe1993ex-

pandedsurveiHance casedefinition

lwhichcountsHN' personswithse- verelysuppressed immunesystems eventhoughtheydo notyetsufferfrom opportunisticinfec-

tions;theodddefini- tionisnowtracked

bytheincidenceof AFDS-Ol,whichpro- videsamorecon-

sistentestimate ofincidenceover

time]HHPointson thefigurerepresent quarter一yIncidence 【rescaledtoannual rates];linesrepre- sentsmoothedinci- dence.Estimated incidenceofAIDS, estimatedAIDS-OIs, anddeathsareall

adjustedforde一ays inreportjng･Esti- matesarenotad-

justedforincomplete reportingofcases･"

PartIIITheDynamicsofGrowth

(Jt2a ^ J a ld o

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satEZtJ le n u u V IE! ^

)!IEZu O M P U u aP !3 u

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O 6 6 L

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Source:USCentersforDiseaseControlandPrevention,H/仰 IDSSurvel'IIanceFPepoll,Midyear 1997edltl0∩,VOl.9(no.1),flgUre6andcaption,p.19

Tbinterpretthedataanddevelopamodel,itisusefultoreviewthenatureand

courseofHIVandAIDS.TheprogressionofHIV/AIDScanbedividedroughly

intothefollowingCategories:AfterinitialinfectionwithHIV,thevirusreplicates

rapidly,stimulatinganimmuneresponseincludingtheproductionofHIVISPeCific

antibodies･ThecommonclinicaltestforHIVdoesnotdetectthepresenceofthe

virusitselfbutrathertheantibodiesindicatingthepresenceofsufficientvirusto

triggertheimmuneresponse.Thereisadelayofseveralweeksto6monthsbefore

thebodyproducessufficientantibodiestoyieldapositiveresultfromanHIVtest.

Priortoseroconversion(thepointatwhichaninfectedpersonbeginstotestposi-

tive),infectedpeoplecantransmitthevirustoothersbutwillnottestpositive.Af-

terseroconversion,thereisalonglatencyperiodduringwhichtherearenoclinical

symptoms.Thelengthoftheincubationperiodvarieswidely.Themedianincuba-

tionperiodisestimatedtobeabout10yearsinpreviouslyhealthyadults,thoughit

isshorterforchildren,theelderly,andthosewithpriorhealthproblems(Cooley,

Myers,andHamill1996).Eventually,theviruscompromisestheimmunesystem

soseverelythatthepatientbeginstosufferfromawiderangeofopportunisticin-

fectionssuchaspnuemocystispnuemoniaandKaposi'ssarcoma,whichleadtothe

diagnosisofAIDS.

PriortothedevelopmentofHAART,themortalityratewasextremelyhigh.

About93%ofallthosediagnosedprlOrtO1986intheUShaddiedbytheendof

1996.Themeansurvivaltimefromthetimeofdiagnosis,intheabsenceoftreat-

mentwithHAART,isabout10to12months,though,aswithincubation,survival

timesvarywidely･6Thelong-runeffectivenessofHAARTisstillunknown･While

itcanreducetheviralloadbelowdetectablelevelsinsomepatients,HAARTdoes

6TheclinicalandepidemiologlCa1literatureonHIV/AIDSisenormousandevolvesrapidly. AgoodsourceofinformationandreferencesisavailableattheHIVInSitewebsitedevelopedby theUniversityOfCalifomiaatSamFrancisco,くhttp:仙ivinsite.ucsf.edu>.

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts321

FIGURE9-12 Prevalenceof AIDSinthe UnitedStates

"AduIts/ adolescents

livTngWithAIDS, byquar【er, January1988 throughJune 1996,adjustedfor reportingdelays, UnitedStates"

S 凸一 V Lf

t! ^

6 u!̂ ! 1

a ld o a d

000002

■■■

■l

Quarter-Year

Source.BUSCentersforDiseaseControlandPrevention,HIV/AIDSSurveillance

Repol1,1996,vol.8(no.2), p.1.

notcompletelyeliminateHIVfromthebody(Cohen1998).Peoplewhodiscover

theyareHIV十canbeginHAARTandothertreatmentsprlOrtOtheemergenceof

symptomsandaremorelikelytoaltertheirbehavior.Notallthosewhoareatrisk

aretested,ofcourse,soformanypeoplethefirstindicationthattheyareHIV'

ComeswhentheydevelopsymptomsofAIDS.

ModeHぎ1gHIVIA旧S

A.StockandnowstructureoftheHIV/AIDSepidemic.

BasedonthedescriptlOnabove,developastockandflowdiagram

representlngtheprogressionofindividuals丘.omsusceptiblethroughthe

variousstagesofHIVinfectionandAIDS.Includeastockofcumulative

deaths･IntheSIRmodelthepopulationisassumedtobehomogeneous,a

verypoorassumptionformodelingHIV/AIDS.Manyepidemiological

modelsofHIV/AIDSdisaggregatethepopulationintoseveralcategoriesthat

representthedifferentmodesoftransmission(primarilyhomosexualcontact,

heterosexualcontact,andintravenousdruguse),aswellasgender,age, socioecono王血:star17,SヲreglOn,andperhapsothercategories17Thesegroups

overlapandinteract,Creatlnganintricatefeedbackstructureandavery

complexmodel.Forthepurposeofthischallenge,donotdisaggregatethe

population.Afteryoudevelopaslngleaggregatemodel,youcanconsider

disaggregationtocapturethedifferentriskybehaviorsandtheirinteractions.

7TherearedozensofpublishedepidemiologlCalmodelsofHIV/AIDSandothersexually transmitteddiseases.GoodstartingpointsincludeAnderson(1994),GarnettandAnderson(1996), HeidenbergerandRoth(1998),andRobertsandDangerfield(1990)･TheentireMay-June1998 issueofInte癖 ces(28[3])wasdevotedtomodelingAIDS,includingpolicyissuessuchasneedle exchanges,vaccinedevelopment,andHIVscreenlng･

322 PartIIITheDynamicsofGrowth

A.FeedbackstructureoftheHIV/AIDSepidemic.

Onceyouhavedevelopedthestockandflowmap,addthefeedbackstructure

fortheratesbyfollowlngtheassumptlOnSOftheextendedSIRmodelabove, includingtheinfectionrate,rateofseroconversion,AIDSdiagnosisrate,and deathrate,

OverthetimeframeforthedevelopmentoftheAIDSepidemic,the parametersoftheSIRmodelsuchasthemortalityrateandthecontactrate

betweensusceptiblesandthevariouscategoriesofHIV+individualscannot beconsideredconstant.Modifyyourcausaldiagramtoincorporatefeedbacks

youbelieveareimportant.Besuretoconsiderthefollowing:

I.Theaveragecontactratemayfallaspeoplebecomeawareoftheriskof HIVandthewaysinwhichitcanbetransmitted;thatis,somepeoplemay reduceorabstainfromuseofintravenousdrugsorsexualcontact.

2.TheinfectivltyOfcontactsdependsonpeople'sbehavior.Safersex practicesandtheuseofcleanneedlesbyIVdruguserscanreducethe infectivltyOfthosecontactsthatdooccur.Theuseofsafersexpractices andcleanneedlesinturndependsonpeople'sawarenessoftheriskofHIV infectionanditsconsequencesandontheavailabilityofinformationand resourcesaboutthesepractices｡Inturn,theavailabilityofinformationabout safersexandtheimportanceofneedlecleanlng,alongwithcondomsand cleanneedles,dependsonsocialattitudesandpublichealthprogramsin themedia,schools,andothercommunltyOrganizations.

3,ResearchanddevelopmentintotreatmentssuchasHAARTcanreduce themortalityrate.Theavailabilityofthesetreatmentsdependsonthe extenttowhichtheyarereimbursablethroughhealthinsuranceandon thewillingnessofpeopletogettestedforHIV.Manypeopleareunwilling tobetestedeveniftheyknowtheyareatrisk,outoffear,frequentlywell founded,thattheymaybestigmatized,includingthepossibilitytheymight losetheirjobs,homes,andfriends.

Inrepresentingchangesinpeople'sbehavior(e｡g.,changesincontactrates andinfectivity),considerhowpeoplemightbecomeawareoftheexistence, severlty,andrisksofHIVanddifferentbehaviors.DotheyreadtheNew

EnglandJournalofMedicineorgettheirinformationthroughwordof mouthorpersonalacquaintancewithsomeonesufferingfromAIDS?How dopeoplejudgetheriskofinfectionandtheconsequencesofinfection?

PeoplearemuchmorelikelytocontractthecommoncoldthanHIVbuta coiddoesnotinspirethedreadHIVdoes.Whatinformationsourcesare ordinarypeopleexposedto,andhowpersuasivearetheseininducing changesinbehavior?Whatistheroleofsocialattitudestowardthe behaviorsthroughwhichHIVcanbetransmitted?Whatistheroleof governmentpolicies?Besuretoconsiderthetimedelaysinthefeedbacks youidentify.

UseyourcausaldiagramtoexplainthedynamicsoftheAIDS epidemicintheUS.Inparticular,explain,intermsofthefeedbackstructure ofthesystem,whythefractionalgrowthrateoftheepidemicfellinthe

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts323

earlyyears.Explainthedeclineinincidencebeginnlngabout1995andthe

evensteeperdeclineinmortality.Explainwhythenumberofpeoplelivlng

withAIDScontinuestoincrease(Figure9-12).

TreatmentssuchasHAARTholdthepromisetoconvertHIVinfection

fromadeathsentencetoachronicinfectionwithlowmortality.Basedon

yourdiagram,whatchangesinbehaviormightariseasasideeffectofthe

developmentofHAART?Howmightthesechangesaffectthecontactrate

orinfectivity?Wouldthesefeedbacksincreaseordecreasetheincidenceof

HIVinfection?Explain.Whatarethepublichealthimplicationsof successfultreatmentssuchasHAART?

C.SimulatingtheHIV/AIDSepidemic.

DevelopaformalmodeloftheHIV/AIDSepidemicbasedonthestructureyou

identifyabove.Todosoyouwillneedtouseanumberofnonlinearbehavioral

functions(e.g.,tocapturethewayperceptionsofriskalterthecontactrateor

infectivity).Guidelinesforthedevelopmentofsuchnonlinearfunctionsare

foundinchapter14.Work(atleastinitially)withasingleaggregatestockand

flowstructure,anddonotdisaggregateyourmodelintosubpopulations.Sim-

ulateyourmodelunderatleasttwoconditions:(1)ontheassumptionofnobe-

havioralchangeandnoimprovementintreatmentsand(2)includingthe

feedbacksyouidentifiedinpartBthatmightleadtochangesinthecontact

rate,ininfectivlty,andinmortality.Explaintheresults.Testthepolicyrecom-

mendationsyouidentifiedinpartB･DiscussthepolicylmPlications･8

9.3 lNNOVAT10NDIFFUStONASINFECT10N:

MoDELtNGNEW IDEASANDNEW PRODUCTS

ThediffusionandadoptionOfnewideasandnewproductsoftenfollowsS-shaped

growthpatterns.Whatarethepositivefeedbacksthatgeneratetheinitialexponen-

tialgrowthofasuccessfulinnovation,andwhatarethenegativefeedbacksthat

limititsgrowth?Considerthespreadofcabletelevision(Figure4-9).Thegrowth

ofthepopulationofcabletelevisionsubscriberscannotbeexplainedbythebirth

ofchildrentoexistingCablesubscribers,thoughtheoffspringofheavyTVview-

ersdotendtogrowuptobecollChpotatoes･Whatthenarethepositiveloopsre-

sponsibleforthegrowthofthecableindustry?

Thespreadofrumorsandnewideas,theadoptionofnewtechnologleS,andthe

growthofnewproductscanallbeviewedasepidemicsspreadingbypositivefeed- backasthosewhohaveadol)tedtheinnovation"infect"thosewhohavenot.The

conceptofpositivefeedbackasadriverofadoptionanddiffusionisverygeneral

andcanbeappliedtomanydomainsofsocialcontagion(e.g.,thefeedbackstruC-

tureofthecocaineepidemicdescribedinsection7.3).Arumorspreadsasthose

whohaveheardittellthosewhohavenot,whothengoontotellstillothers･New

ideasspreadasthosewhobelievethemcomeintocontactwiththosewhodonot

8Forthepurposeofthischallengeitisacceptabletomodelthetransitions血･omonecategoryof infectedindividualtothenextasfirst-orderprocesses.Morerealisticmodelsrepresenttheincuba-

tionandmortalitydistributionsderivedfromemplricalstudiesmoreaccuratelythroughtheuseof higher-orderdelays(seechapter11).

324 PartIIITheDynamicsofGrowth

andpersuadethemtoadoptthenewbelief･Thenewbelieversintumthenpersuade

others･Asearlyadoptersofnewtechnologyandearlypurchasersofanewproduct

exposetheirfriends,families,andacquaintancestoit,somearepersuadedtotrylt

orbuyitthemselves･Inallthesecases,thosewhohavealreadyadoptedtheprod-

uct,ideaortechnologycomeintocontactwiththosewhohavenot,exposlngthem

toitandinfectingsomeofthemwiththeidea,orthedesiretobuythenewproduct

andfurtherincreaslngthepopulationofadopters･Anysituationinwhichpeople

imitatethebehavior,beliefs,orpurchasesofothers,anysituationinwhichpeople

jumpOnthebandwagon,describesasituationofpositivefeedbackbysocialcon-

taglOn･Ofcourse,oncethepopulationofpotentialadoptershasbeendepleted,the adoption(infection)ratefallstozero.9

Inthecabletelevisioncase,importantfactorsinahousehold'sdecisiontosub-

scribe(assumingcableisavailableinthecommunity)includefavorablewordof

mouthfromthosewhoalreadysubscribeandpositiveexperiencesviewlngCableat

thehomesoffriendsandfamily.Peoplehearaboutprogramsonlyavailableonca-

bleandfeeltheymustsubscribetobehipandknOwledgeableamongtheirpeersin

schoolorattheworkplace･Additionally,peoplemaysubscribetokeepupwiththe

Joneses,thatis,tomaintainorenhancetheirstatus(ortheirperceptionoftheirsta-

tus)amongtheirpeergroup.Allofthesechannelsofawarenessandmotivations

foradoptioncreatepositivefeedbacksanalogoustothecontaglOnlooplnthebasic epidemicmodel.

Figure9-13adaptstheSIepidemicmodel(section9.2.1)tothecaseofinno-

vationdiffusion.Theinfectiouspopulationnow becomesthepopulationof

adopters,A-thosewhohaveadoptedthenewideaorpurchasedthenewproduct.

Thesusceptiblepopulationbecomesthepoolofpotentialadopters,P.Adoptersand

potentialadoptersencounteroneanotherwithafrequencydeterminedbythecon-

tactrate,C･Unlikeinfectiousdiseases,Wordofmouthencountersthatmightlead toadoptioncouldoccurbytelephone,mail,email,orotherremotemeansanddo

notrequlrePhysicalproximity.Asininfectiousdisease,noteveryencounterresults

ininfection.Theproportionofcontactsthataresufficientlypersuasivetoinduce

thepotentialadoptertoadopttheinnovationistermedheretheadoptionfraction

anddenotedi(sincetheadoptionfractionisanalogoustotheinfectivityofadis-

easeintheepidemicmodel).

Theequationsforthesimpleinnovationdiffusionmodelareidenticaltothose

fortheSImodelofchronicinfectiondescribedin9･2･1･Usingtheterminologyln

Figure9-13,themodelis

A-INTEGRAL(AR,Ao) (9-29)

p-INTEGRAL(-AR,N-A｡) (9-30)

AR-°ip(A/N) (9-31)

AsintheSImodel,thetotalpopulationNisconstant:

P+A-N (9-32)

9Theliteratureondi軌ISionofnewproductsandofsocialandtechnicalinnovationsishuge･ AgoodplacetostartisEverettRogers(1995),DIHusionoflnnovations,aclassicoriginally publishedin1962.Fordiffusionmodelsappliedtothesalesofnewproducts,seeParker(1994) andMahajan,Muller,andBass(1990).

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts325

FIGURE9-13

Adoptionofanew ideaorproductas anepidemic

Potentialadopters comeintocontact

withadopters throughsocial interactions. Afractionofthese contactsresu一tin

infection,thatis, adoptionoHhe newideaor

purchaseofthe newproduct･ Compareto Figure9-4･

TheinterpretationisthesameasintheSImodel･Peopleintherelevantcom一

munltyCOmeintocontactatarateofcpeopleperpersonperday･Thetotalrateat

whichcontactsaregeneratedbythepotentialadopterpoolisthencP･Thepropor-

tionofadoptersinthetotalpopulation,A/N,givestheprobabilitythatanyofthese

contactsiswithanadopterwhocanprovidewordofmouthabouttheinnovation･

Finally,theadoptionfraction,i,istheprobabilityofadoptiongivenaCOntaCtWith

anadopter.Asbefore,theseequationsconstituteanexampleoftheloglSticgrowth modeldiscussedinsection9.1.1.ThebehaviorofthemodelistheclassicS-Shaped

growthofthelogisticcurve(Figure9-1)･

9.3NI TheLogはticMode!ofEnnov甜onDiffusion:

EXampヨes

ThediffusionofmanynewproductsfollowroughlyloglStictraJeCtOries･Asanex-

ample,Figure9-14showssalesoftheDigitalEquipmentCorporatioIIVAX11/750

minicomputerinEurope(Modュs1992)･TheVAXserieswasaverysuccessfulline

ofminicomputers.Theysoldforabout$100,000to$150,000aunit,dependingon

whichperipherals(suchastapedrives)wereincluded,anexcellentvaluecom-

paredtothemainframesoftheday･Typicalcustomerswerelargecompanies,

researchorganizations,anduniversities,whousedthemfordataprocesslngappli-

cationsandtosupportscientificandenglneerlngcomputationinR&Dlabs,prod-

uctdevelopmentdepartments,andacademicresearch.The11/750wasintroduced

in1981.Salesfollowtheclassicbell-shapedproductlifecycle,peakinglnmid

1984.Theproductwaswithdrawnfromthemarketaround1989･Accumulated

salesfollowanS-Shapedpath.SincetheusefullifetimeoftheVAXislongcom-

paredtothetimehorizonfortheproductlifecycle,itisreasonabletoassumethat

fewunitswerediscardedpr10rtO1989whentheproductwaswithdrawnfromthe

market.Thereforecumulativesalesisagoodmeasureoftheinstalledbase･

TofittheloglSticproductdiffusionmodeltotheVAXsalesdata,assumethe

totalpopulationN-cumulativesalesby1989(about7600units)･Theremaining

parameterofthemodel,representlngtheproductofthecontactrateandadoption

326

FIGURE9-14 Salesofthe

DigitalEqulPment CorporationVAX ll/750inEurope

Top:Salesrate (quarterlydata

atannualrates). Bottom:Cumula-

tivesales(roughly equa日othe instaHedbase).

PartIIITheDynamicsofGrowth

1981 1983 1984 1986 1988

8000

6000

のllll■ ■≡ 4000 =〉

2000

1981

SouJ℃e:ModJS(1992,p.58).

1983 1984 1986 1988

fraction(ci),Canbeestimatedeasilybylinearregression.10First,recallfromequa-

tion(9-8)thatthesolutiontothelogisticequationcanbeexpressed(usingthevari-

ablenamesfortheinnovationdiffusionmodelabove)as

a R exp(got, (9-33,

whereAisthenumberofadopters(theinstalledbase),A｡istheinitialinstalled

base,Nisthetotalequilibriumorfinalvalueofadopters,andgoistheinitialfrac-

tionalgrowthrateoftheinstalledbase,whichattheinitialtimewhenthereare

veryfewadoptersisequaltothenumberofinfectivecontacts(ci).Takingthenat-

urallogofbothsides,

ll-,lR ]-irllR ]IgotL (9134,

yieldsarelationshipthatislinearintheparametersandcanbeestimatedbyordi-

naryleastsquares.NotethatsinceN -A-P(thedifferencebetweenthetotal

10sincetheadoptionratedependsontheproductofthecontactrateandinfectivlty,Ci,these parameterscannotbeestimatedseparatelyfromsalesdata.However,marketresearchtechniques suchastestmarkets,focusgroups,surveys,andsooncanhelpthemodelerdevelopestimatesof theadoptlOnfractionandcolltaCtrate.Forforecastingpurposes,Onlytheproductciisneeded.

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts327

populationandthenumberofadoptersisthenumberofpotentialadopters),equa-

tion(9-34)Canbewrittenmoreintuitivelyasafunctionoftheratioofadoptersto

potentialadopters(A/P):

･n(; )-ln(% ) I g ot (9135,

Equation(9-34)or(9-35)isknownasthelogistic(orsimply,logit)transformation.

Figure9-15ShowstheloglttransformationoftheVAXsalesdata,alongwiththe

estimatedlinearregression･Thedataareclosetolinear,whichindicatesexcellent

correspondencetotheloglSticmodel.ThebottompanelsofFigure9-15Compare

theestimatedloglSticcurvetothesalesandinstalledbasedata.

WhilethelogisticinnovationdiffusionmodelfitstheVAXsalesdataqulte

well,theestimationofthemodelwasretrospective:theentiresaleshistorywas

used,andtheestimationmethodrequiredknowledgeofthefinalvalueofthein- stalledbase.Inmostbusinesssituations,however,theclientswanttoknowthe

likelygrowthpathprospectively,whenthemarketpotentialisnotknown,Sothey

candecidewhetherthemarketwillbebigenoughtojustifyentryandplanstrategy

forcapacityacquisition,prlClng,marketing,andsoon･Onewaytofitthelogistic

growthmodeltodataprlOrtOSaturationistoestimatetherateatwhichthefrac-

tionalgrowthratedeclineswithgrowingpopulation.Recallfromequation(9-1)

thatthefractionalgrowthrateoftheloglSticmodeldeclineslinearlyasthepopul

lationgrows.Figure9-16Showsthefractionalgrowthrateincabletelevisionsub-

scribersintheUS,alongwiththebestlinearfit(Calculatedbyordinaryleast

squares).Asexpected,thefractionalgrowthratedeclinesasthepopulationgrows,

thoughthereisconsiderablevariationaroundthebestlinearfit.TheloglSticgrowth

pathimpliedbytheseparametersfitsthedatawellthrough1994andpredicts amaximumofabout74millionhouseholdssubscribingtocable,reachedshortly after2010.

Thereis,however,considerableuncertaintyinthisprediction.First,thereis

uncertaintyregardingthebestfittinglinearfractionalgrowthrate･Theactualfrac- tionalgrowthratevariessubstantiallyaroundthebest恥 Otherparametersforthe

straightlinewillfitnearlyaswellyetyieldlargedifferencesinthemaximumnum- berofsubscribersandtimetosaturation.Second,thebestfitwasestimatedforthe

period196911994;prlOrtO1969thefractionalgrowthratewasmuchhigher.This

istypicalofgrowthprocesses:Thefractionalgrowthrateearlyinthehistoryofa

newproductorinnovationisoftenveryhighsincethepopulationofadoptersisso

small(andofcourse,whenanewproductisintroducedthegrowthrateforthefirst

reportingperiodisinfinite).Changingthehistoricalperiodoverwhichthelogistic

modelisestimatedwillthereforechangethebestfitparametersandtheforecast.

Third,theloglSticmodelpresumesalineardeclineinthefractionalgrowthrateas

thepopulationgrows.Thereis,however,nocompellingtheoreticalbasisforlin-

earlty･Othershapesforthefractionalgrowthratecurvewillyieldverydifferent predictions.Tbillustrate,Figure9-17ShowsthecabletelevisiondataagalnStthe

bestfitofboththelogisticandGompertzcurves(equation(9114)).TheGompertz

curvefitsthedataaboutaswellasthelogisticcurvebutsuggestscontinuedgrowth

tonearly150millionsubscribersin2020,doublethefinallevelpredictedbythe

loglSticmodel.

328

FIGURE9-15

Fittingthelogistic modelof innovation diffusion

Top:Applylngthe logittransforma-

tion(equation (9-35))Showsthat thelogoftheratio ofadopterstopo-

tentialadopters overtimeisvery closetolinear.The

bestfitisfoundby linearregression. M/'ddle:Estimated andactualin- StaHedbase

(adopters)using theestimatedpa- rameters.Bottom:

Estimatedand actualsales

(adoptIlonrate) uslngtheesti- matedparameters.

PartIIITheDynamicsofGrowth

( s s a 一 u O !S u a

∈ !P )

s J a

ld o p v

一e !l u a lO

d JSJaldo p v

1981

8000

6000

の･- '≡ 4000 =)

2000

1983 1984 1986 1988

1981 1983 1984 1986 1988

Estimated ､､4-一一一salesRate

SalesRate

1981 1983 1984 1986 1988

9.3.2 P椅eeSSPO棚 :H岳S昔8㌢岳eaEF岳菅andModeHvlaヨ岳d岳電y

TheloglSticmodeliswidelyusedtoexplainandpredictthedi軌lSionofinnova-

tions,thegrowthofpopulations,andmanyotherphenomena.Marchetti(1980)and

Modis(1992),amongmanyothers,havefitthelogisticcurvetoawiderangeof

data,fromthecompositionsofMozarttotheconstructionofGothiccathedrals.

Thelogisticcurvecanfitdataforawiderangeofgrowthprocessesreasonably

well.ButyoushouldnotusetheloglSticmodel10ranymodel-asacurvefitting

procedureforblackbox(atheoretical)forecasting･Thelogisticmodeloftenworks

wellbecauseitincludesthetwofeedbackprocessesfundamentaltoeverygrowth

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,and也eGrowthofNewProducts329

FIGURE9-16 Fittingthelogistic modeltodatafor UScableTV subscribers

Top:Estimated andactual

fractionalgrowth rateofcab一e subscribers, Bottom:Actual subscribersvs. subscribers

projectedfrom theestimated

growthrate･

FlGURE9-17 Predictedcable subscribersdiffer

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LogisticMode]+

1950 1960 1970 1980 1990 2000 2010 2020

process:apositiveloopthatgeneratestheinitialperiodofacceleratlnggrowthand

anegativefeedbackthatcausesthegrowthtoslowasthecarryingCaPaCltylSaPI proached･Anysystemgrowingbypositivefeedbackmustincludethesetwotypes ofloops,couplednonlinearly;anygrowthmodelmustbecharacterizedbyafrac-

tionalgrowthratethatultimatelydeclinestozeroasthepopulationapproachesits carrylngCapacity.However,asdiscussedabove,theloglSticmodelmakesrestric-

tiveassumptlOnSaboutthenatureofthegrowthprocess･AdvocatesoftheloglStlc modeloftenpresentevidenceselectivelytoshowhowwellthemodelfitscertain

330 PartIIITheDynamicsofGrowth

databutomitthemanyothergrowthprocessesforwhichitdoesnot.Thesame

considerationsapplytoallotherslngleequationgrowthmodelssuchasthe RichardsorWeibullfamily.

TheabilityoftheloglSticmodeltofitawiderangeofgrowthprocessesalso

illustratesseveralimportantlessonsaboutthevalidityofmodelsingeneraLFirst, thecontrastbetweentheforecastsoftheloglSticandGompertzmodelsfortheca-

bletelevisioncaseshowninFigure9-17Showsthatdifferentdiffusionmodelscan

producewildlydifferentpredictionswhilefittingthedataequallywell･Theability tofitthehistoricaldatadoesnot,therefore,provideastrongbasisforselectlng

amongalternativehypothesesaboutthenatureorstrengthofdifferentfeedbacks thatmightberesponsiblefわrasystem'sdynamics･

Second,gettlngmoredatadoesnotsolvetheproblem.Estimatingtheparame- tersofdifferentgrowthmodels,andhencethetrajectoryOfgrowth,byeconomet- rictechniquesrequlreSalongenoughsetoftimeseriesdatatoprovidestable parameterestimatesandtodiscriminateamongthedifferentgrowthmodels･Ina reviewofinnovationdiffusionmodelsfornewproductsalesforecasting,Mahajan,

Muller,andBass(1990)notethat"bythetimesufficientobservationshavedevel- opedforreliableestimation,itistoolatetousetheestimatesforforecastlngPur- poses,"Bythetimecabletelevisionhasprogressedfarenoughtodiscriminate betweenthelogisticandGompertz(andpossiblyother)models,somuchofthe di軌ISionlifecyclewillbepastthatthemodelwillnolongerbeuseful･Thewildly differentforecastsofcablediffusionaregenerated40yearsaftertheintroduction ofcable,a氏erabouthalfthehouseholdsintheUShadalreadyadoptedit,andwell

aftertheentrytotheindustryofformidablecompetitors･ Third,amainpurposeofmodelinglStOdesignandtestpoliciesforimprove-

ment.Todoso,theclientmusthaveconfidencethatthemodelwillrespondtopoli-

ciesthesamewaytherealsystemwould.Fittingthelogisticcurve(oranymodel) toadatasetdoesnotidentifythespecificfeedbackprocessesresponsibleforthe dynamics.Theabilityofamodeltofitthehistoricaldatabyitselfprovidesnoin-

formationatallaboutwhetheritsresponsetopolicieswillbecorrect･ Toillustrate,notethattheloglSticmodel,likeallfirst10rdergrowthmodels,

presumesthatth eadopterpopulationorinstalledbasemovessteadilyupward･The numberofad o p terscanneverdecline.Yetthehistoryofnewproductsandnew technologleS is repletewithinnovationswhosepatternofemergenceisboomand bustorfluctu ation.ItiseasytoimagineCrediblescenariosinwhich,forexample,

cabletelevisionu sedeclines,includingrislngprlCeS,declinlngqualityofpr0-

grammlng, lnC rea SlngcompetitionfromnewtechnologiesSuchasdigitalsatellite broadcastsand th einternet,andevenadeclineintelevisionviewing(well,perhaps

thatlastoneisn'tc redible).Yetthelogisticmodel,andall丘rstordermodels,can

nevergenerateany th ingbutgrowth･Thesemodelsdonotincludetherichfeedback structureneeded to g eneratemorecomplexandrealisticpatternssuchasovershoot andoscillationo r o v ershootandcollapse｡

Innov ationd iffu sionusuallyInvolvesmanypositivefeedbacksdrivinggrowth

besidesw o rd o f m o u th(seechapter10forexamples)･Forexample,theavailability ofthird-p a rty so 氏 w a reisapowe血ldriverofproductattractivenessfb∫computers･ Inturn,th ird -p a rty d ev eloperswillwritesoftwareforthoseplatformstheybelieve havetheg reatestm a rk etpotential.Thusthelargertheinstalledbaseofaparticular

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts331

computer(suchastheVAX),themoresoftwarewillbewrittenforit,themoreat-

tractiveitbecomestopotentialcustomers,andthelargertheinstalledbasewillbe･ Thepositivesoftwareavailabilityloop(andmanyothers)Canstimulategrowthjust asthewordofmouthloopcan.Becausetheseotherpositiveloopsareomittedfrom

thesimpleinnovationdiffusionmodel,statisticalestimatesofthestrengthofthe wordofmouthloopwillreflecttheimpactofallpositiveloopscontributingtothe

growth.Theimportanceofwordofmouthwillbegreatlyoverestimatedwhileat thesametimethestrengthofalltheomittedloopsisassumedtobezero･The modelwouldindicatethatagoodpolicytostimulatetheearlygrowthofthemar-

ketwouldbetostrengthenwordofmouth(say,bysponsoringconferencesorhir- ingkeyopinionleadersasspokespeople).However,thebestpolicymayactually betostimulatesoftwareavailabilitybypartnerlngWiththird-partydevelopers. Suchamodelwillnotyieldreliablepolicyrecommendationsdespitetheexcellent historicalfit.AmodelmayfitthedataperfectlyforthewrongreasonsI

Isitdifficulttooveremphasizetheimplicationsformodelersandclients.The abilityofamodeltoreplicatehistoricaldatadoesnot,byitself,indicatethatthe modelisuseful.Andfailuretoreplicatehistoricaldatadoesnotnecessarilymean amodelshouldbedismissed.Theutilityofamodelcannotbejudgedbyhistorical fitalonebutrequiresthemodelertodecidewhetherthestructureanddecisionrules ofthemodelco汀eSpOndtotheactualstructureanddecisionrulesusedbythereal peoplewithsufficientfidelityfortheclient'spurpose･Todosorequiresthemod- elerandclienttoexaminetheassumptionsOfthemodelindetail,toconductfield studiesofdecisionmaking,andtoexplorethesensitivltyOfmodelresultstoplau- siblealternativeassumptions(amongothertests)･Determiningwhetheramodel providesasoundbasisfordecisionmakinglSneveramatterOnlyofstatisticaltest- 1ngOrhistoricalfitbutisessentiallyandunavoidablyavaluejudgmentthemod- elerandclientmustmake.

Unfortunately,clientsandmodelersfrequentlygivehistoricalfittoomuch weight.JudgingtheappropriatenessOfthemodel'sstructure,itsrobustness,andits sensitivltytOassumptionstakestime,whilehistoricalfitcanbedemonstrated quickly.GraphsshowingaClosefitbetweendataandmodelaredramaticand compelling.Clientsaretooeasilyswayedbysuchgraphsandbyimpressivetables ofR2andotherstatistics･Modelers,evenwhentheyknowbetter,toooftenover-

emphasizestatisticsshowinghowwelltheirmodelsfitthedatatopersuadetheau- diencethatthestronghistoricalfitofthemodelmeansitmustbecorrect.

Youshouldnotconcludefromthisdiscussionthathistoricalfitisunimportant

orthatyoudonotneedtocompareyourmodelstothenumericaldata･Onthecon- trary,comparlngmodeloutputtonumericaldataisapowerfulwaytoidentifylim- itationsorflawsinmodelformulations.Butthereisaprofounddifferencebetween

usinghistoricaldatatoidentifyflawssoyourmodelscanbeimprovedandusing historicalfittoassertthevalidityofyourmodel.Inthelattercase,showinghow wellthemodelfitsthedataisadefensivemaneuverdesignedtoprotectamodel andthemodelerfromcriticismandsealstheclient-andmodeler-offfromlearn-

1ng.Intheformercase,thehistoricalfitisusedtofindproblemsandstimulate learning.Examininghistoricalfitshouldbepartofalargerprocessoftestlngand

modelimprovementdesignedtoyieldamodelsuitableforpolicydesignanddeci- sionmaking(Seechapter21).

332 PartIIITheDynamicsofGrowth

9.3.3 TheBassDiffusionMode一

Oneoftheflawsinthelogisticmodelofinnovationdiffusionisthestartupprob1

len.Inthelogistic(andtheothersimplegrowthmodelsincludingtheRichards

andWeibullfamilies),zeroisanequilibrium:thelogisticmodelcannotexplainthe

genesisoftheinitialadopters.Priortotheintroductionofcabletelevision,the

numberofcablesubscriberswaszero;prlOrtOthefirstsalesoftheVAXminicom-

puter,theinstalledbasewaszero.Whengrowthprocessesbegin,positivefeed-

backsdependingontheinstalledbaseareabsentorweakbecausetherearenoor

onlyafewadopters.Initialgrowthisdrivenbyotherfeedbacksoutsidethebound-

aryofthesimplediffusionmodels.Thereareseveralchannelsofawarenessthat

canstimulateearlyadoptionofnewinnovationsbesideswordofmouthandrelated

feedbackeffectsthatdependonthesizeoftheadopterpopulation.Theseinclude

advertising,mediareports,anddirectsalesefforts.

FrankBass(1969)developedamodelforthediffusionofinnovationsthat

overcomesthestartupproblem.TheBassdiffusionmodelhasbecomeoneofthe

mostpopularmodelsfornewproductgrowthandiswidelyusedinmarketing,

strategy,managementoftechnology,andotherfields.Basssolvedthestartupprob1

1embyassumlngthatpotentialadoptersbecomeawareoftheinnovationthrough

externalinformationsourceswhosemagnitudeandpersuasivenessareroughly constantovertime.

TheorlglnalBassmodelwasintroducedprimarilyasatoolforforecastlng

salesofnewproducts,andBassdidnotspecifythenatureofthefeedbacksatthe

operationallevel.Thepositivefeedbackisusuallyinterpretedaswordofmouth

(socialexposureandimitation)andtheexternalsourcesofawarenessandadoption

areusuallyinterpretedastheeffectofadvertising(Figure9-18Showsthefeedback

structureofthemodelwiththisinterpretation).11

InFigure9-18thetotaladoptionrateisthesumofadoptlOnSresultingfrom

wordofmouth(andimplicitlyotherpositivefeedbacksdrivenbythepopulationof

adoptersortheinstalledbaseoftheproduct)andadoptionsresultingfromadver-

tislngandanyotherexternalinfluences.Adoptionsfromwordofmoutharefor-

mulatedexactlyasinthelogisticinnovationdi軌 sionmodel(equation(9-31)).

Bassassumedtheprobabilitythatapotentialadopterwilladoptastheresultofex-

posuretoaglVenamountOfadvertislngalldthevolumeofadvertisingandother

externalinfluenceseachperiodareconstant.Thereforetheextemalinfluences

causeaconstant血.actionofthepotentialadopterpopulationtoadopteachtimepe-

riod.Hencetheadoptionrate,AR,is

AR-AdoptionfromAdvertislng+AdoptionfromWordofMouth (9-36)

AdoptlOnfromAdvertising-aP (9137)

1iTheorlglnalmodel,incontinuoustime,wasspecifiedasdA/dt-AR-aP+bPA,where aandbwereparameterstobeestimatedstatisticallyfromthedataonsalesoradopters.Bass(1969) didnotexplicitlydiscussthefeedbackloopstructureofthemodelorspecifywhattheprocessesof adoptionWereOPerationally,1nSteadcallingtheminnovationandimitationOthersrefertothetwo loopsasexternalandinternalinfluencesonadoptlOn.Themodelwasalsocriticizedforomittlng economicandothervariablesthataffecttheadoptiondecisionsuchasprlCeOradvertislngeffort (seethechallengesbelow;seealsoBass,Krishnan,andJaln1994).

Chapter9 5-ShapedGrowth:EpidemicsJnnovationDiffusion,andtheGrowthofNewProducts333

FIGURE9-18 TheBassdiffusion model

Themode一 includesan externa一sourceof awarenessand

adoption,usuaHy interpretedas theeffectof

advertising,

AdoptionfromWordofMouth-ciPA/N (9-38)

wheretheparametera,advertlSlngeffectiveness,isthefractionaladoptionrate

fromadvertising(1/timeperiod).

Thetwosourcesofadoptionareassumedtobeindependent.Collectlngterms,

themodelcanbeexpressedmorecompactlyas

AR-aP+ciPA/N (9-39)

Whenaninnovationisintroducedandtheadopterpopulationiszero,theonly

sourceofadoptionwillbeexternalinfluencessuchasadvertlSlng.Theadvertislng

effectwillbelargestatthestartofthediffusionprocessandsteadilydiminishas

thepoolofpotentialadoptersisdepleted.

PhaseSpaceof的eBassDi甘fusionMode目

LiketheloglSticgrowthmodel,theBassmodelhastwostocks.However,because

P+A-N,Onlyoneofthesestocksisindependent,andthemodelisactuallyfirstl

order.UsingthefactthatP-N -A,expressequation(9-39)intermsofthe

adopterpopulationA.Drawthephaseplotforthemodel(agraphshowingthe

adoptionrateasafunctionoftheadopterpopulation)ADrawthephaseplotforthree

conditions:(i)advertisingeffectivenessiszeroandalladoptionoccursthrough

wordofmouth,(ii)wordofmouthiszero(ci-0)andalladoptionoccursthrough

advertising,and(iii)bothadvertisingandwordofmouthcontributetoadoption･

WithoutuslngSimulation,usethephaseplottosketchthebehaviorovertime

oftheadopterpopulation,potentialadopterpopulation,andadoptionrateforeach ofthethreecasesabove.HowdoesadvertlSlngalterthepolntatWhichloopdom-

inanceshiftsfrompositivetonegativefeedback?Howdoesadvertislngaffectthe

timlng,Symmetry,andotheraspectsofthedynamicscomparedtotheloglStic model?

334 PartIIITheDynamicsofGrowth

Afteryouhaveansweredthesequestions,buildandsimulatethemodeltotest yourintuition.Runthemodelforthethreecasesabove,andtryothercombinations

ofparameterstoexploretherangeofbehaviorsthemodelcangenerate.

9.3.4 BehavioroftheBassMode一

TheBassmodelsolvesthestartupproblemofthelogisticinnovationdiffusion

modelbecausetheadoptionratefromadvertisingdoesnotdependontheadopter population.Whentheinnovationornewproductisintroduced,theadoptlOnrate consistsentirelyofpeoplewholeanedabouttheinnovationfromexternalsources

ofinfo-ationsuchasadvertising.Asthepoolofpotentialadoptersdeclineswhile

theadopterpopulationgrows,thecontributionofadvertisingtOthetotaladoption ratefallswhilethecontributionofwordofmouthrises.Soon,wordofmouthdom-

inates,andthedimlSionprocessplaysoutasintheloglSticdi乱sionmodel. Asanexample,consideragaintheVAXll/750salesdata(Figure9-14).To

modeltheVAXproductlifecyclewiththelogisticdiffusionmodelitwasneces- sarytostartthesimulationaftertheproductwasintroduced,Sothattherewasa

nonzeroinstalledbase.AcloselookatFigure9-15ShowsthatthepureloglStic modelunderestimatessalesduringthefirstyearandahalf,andoverestimatessales atthepeak,consistentwiththehypothesisthatinitialadoptlOnSWereStimulated notbywordofmouthorotherpositivefeedbacksbutbyexternalsourcesofaware-

nesssuchasmarketingeffort.Figure9119ComparesthebehavioroftheBass modeltotheloglSticdiffusionmodelandtheVAXsalesdata.Asinthesimulation

oftheloglSticmodel,thetotalpopulationNisassumedtobe7600units.Advertis- 1ngeffectiveness,a,andthenumberofcontactsresultinglnadopt10nfromwordof

mouth,ci,wereestimatedbyregressiontobe0.011peryearand1.33peryear,re- spectively.ThecontributionofsalesfromadvertisingtOtotalsalesissmallafter

thefirstyear,asseeninthebottompanelofFigure9-19.Nevertheless,thismod- estchangeinthefeedbackstructureofthedi軌lSionprocessimprovesthemodel's

abilitytofitthesalesdata,bothinthefirst2yearsandatthepeak.Mostimportant, theinclusionoftheadvertlSlngeffectsolvesthestartupproblemoftheloglStic model.

TheBassmodelisasignificantandusefulextensionofthebasicloglStic

modelofinnovationdi軌sion･Themodelitself,orvariantsofit,isbroadlyap- plicabletoawiderangeofdiffusionandgrowthphenomena,andthereisalarge literatureapplyingtheBassmodelandrelatedmodelstoinnovationdi軌sionand salesofnewproducts(see,e.g.,Mahajan,Muller,andBass1990andParker1994 forreviews).

Cr岳t蔓quingtheBassDiffusionModel

EventhoughtheBassmodeloftenworkswell,themodelinvokesanumberofre-

strictiveassumptlOnS.ListasmanyassumptionsOftheBassmodelasyoucan.In-

cludeassumptlOnSexplicitintheformulationofthemodelandassumptlOnSthat areonlyimplicit,especiallythoseconcernlngaggregationandthemodelboundary (particularlyeffectsandfeedbacksomittedfromthemodel).

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts335

FIGURE9-19 TheBass

andlogistic diffusionmodels

comparedto actua一VAXsales

8000

6000

の t≡ 4000 =1

2000

LogisticMoS ノミ〇二喜sslMode.'∴こpp＼ CumulativeSales

1981 1983 1984 1986 1988

i. 2000 (q dJ>･li=:Fu).t= ⊂

⊃ 1000000000

･l

Jt2a ^ [ S

l E u n

1983 1984 1986 19881983 1984 1986 1988

Extending帥eBassMode一 Asnotedabove,theBassmodelassumesthetotalsizeofthemarket(totalpopula-

tion,N)isconstantJngeneral,thepopulationofacommunityorthenumberof

householdsinamarketgrowsovertimethroughbirths,deaths,andmlgration.In

thecontextofinnovationswithveryshortlifecycles(e.g.,thelatestgenerationof

videogames)oracutediseasessuchasmeasles,theassumptionofconstantpopu-

lationisreasonable.Butforinnovationsordiseaseswhoselifecyclesextendover

manyyears(e.g.,thediffusionofcabletelevisionortheAIDSepidemic),popula-

tiongrowthcanbesignificant･

336 PartIIITheDynamicsofGrowth

A.RevisetheBassmodeltoincorporategrowthinthesizeofthe totalmarket.

AssumethetotalpopulationsizeisastockincreasedbyaNetPopulation IncreaseRatethataggregatesbirths,deaths,andnetmigration(itiseasy,but notnecessary,torepresentexplicitbirth,death,andnetmigrationrates

separately;Seechapter12).TheNetPopulationIncreaseRateisgivenbythe

totalpopulationandtheFractionalNetlncreaseRate,whichcanbeassumed constant.Nowyoumustdecidehowtheincreaseinpopulationispartitioned

betweenpotentialadoptersandadopters.ThesimplestassumptlOnisthatall increasesinpopulationsizeaddtothepoolofpotentialadopters･Recalling

thatallpeopleorhouseholdsinthepopulationareeitherpotentialoractual adopters,reformulatethepotentialadopterpopulationasP-NIA･Even

thoughthepotentialadopterpopulationisastock,itisfullydeteminedby thetotalpopulationandadopterpopulationandsocanberepresentedasan auxiliaryvariable.

Applyyourextendedmodeltothecabletelevisionindustry.Theunit

ofadoptionforcabletelevisionisnottheindividual,buthouseholds(and possiblybusinesses).ThecabletelevisionindustryintheUSbeganinthe

early1950S.Atthattimethenumberofhouseholdswasabout40million. Bythelate1990S,therewerenearly100millionhouseholds,anaverage householdformationgrowthrateofabout1.9%/year.Selectparametersfor

advertislngeffectivenessandwordofmouththatapproximatelyreplicatethe patternofcableadoption(Figure9-16).Itisnotnecessarytomatchthedata

exactly;anapproximatefitissufficient･ExplorethesensitivityOfthemodel todifferentpopulationgrowthrates.Whatistheimpactofvariable populationsizeonthedynamics?

B.Responseoftotalmarketsizetopmee. Inmostmarkets,Onlyafractionofthetotalpopulationwilleveradoptanew

innovation.The丘'actionofthepopulationthatmighteveradopttyplCally dependsonthebenefitsoftheinnovationrelativetoitscost(itspriceandany otherassociatedcosts,e.g.,switchingcosts,costsofcomplementaryassets, trainingcosts,etc.;seeRogers1995).Innovationsarenotstatic:their benefitso洗enincreaseovertimeasresearchandproductdevelopmentlead

toimprovementsinfeatures,functionality,quality,andotherattributesof productattractiveness.Similarly,theprlCeOfnewproductsoftenfalls slgnificantlyovertimethroughlearnlngCurves,scaleeconomies,andother

feedbacks(Seechapter10)･ModifythemodelyoudevelopedinpartAto includetheeffectofproductprlCeOnf-hesizeofthepotentialadopterpooh Assumethepotentialadopterpopulationisafractionofthetotalpopulation, lessthecurrentnumberofadopters:

P=FractionWillingtoAdopt*N-A (9-40)

where,ingeneral,theFractionWillingtoAdoptdependsontheoverall attractivenessoftheinnovationorproduct(itsbenefitsrelativetocosts):

FractionWillingtoAdopt-i(InnovationAttractiveness) (9-41)

Chapter9 S-ShapedGrowth:Epidemics,ⅠnnovationDi軌lSion,andtheGrowthofNewProducts337

Tokeepthemodelsimple,assumethattheonlyfeatureoftheinnovationthat

variesistheprlCe.AsimpleassumptlOnisthatthedemandcurveforthe

productlslinear.Forthecaseofcabletelevision,assumethatdemandisa

linearfunctionofthemonthlycost(ignoreinstallationcharges)･Sincenearly allUShouseholdshavetelevision,assumetheFractionWillingtoAdopt wouldbe100%whencableisfreeandwouldfalltozeroifthecostwere

$200/month.

Tbtestthemodel,assumeprlCeisexogenous.First,runthemodelwith

priceconstantataninitialvalueof$100/month.Tofocusonthedynamicsof

thepriceeffectalone,assumetheFractionalNetIncreaseRateforthetotal

populationiszero.SinceprlCeisconstant,thetotalpopulationshouldbe

constant,andthemodelreducestotheorlglnalBassformulation.Simulate

yourmodeltocheckthatitbehavesapproprlatelywhenthepnceisconstant.

NowtesttheimpactofvaryingPricesbyassumingthepriceOfcable fallsovertime.First,testtheeffectofasuddendroplnPrlCe,tO,Say,

$25/month.Trythepricedropatdifferentpointsinthediffusionlifecycle.

C.Isyourmodelrobust?

Typically,pncesfalloverthelifecycleofasuccessfulnewproductor innovation.Butmodelsmustberobustandbehaveapproprlatelyunder

allpotentialcircumstances,notonlythehistoricalorexpectedbehavior.

Acommonandimportantwaytotestforrobustnessistheextremecondi- tionstest(chapter21).Inanextremeconditionstest,aninputtoamodelis

assumedtosuddenlytakeonextremevalues･Themodelmustcontinueto

behaveapproprlatelyevenifthatextremevaluewillneverariseinreality.

Forexample,suddenlydestroylngallinventorylnamodelofamanu-

facturlngfirm mustforcetheshipmentrateimmediatelytozero.Ifshipments

donotfalltozero,themodeler(andclient)immediatelyknowthereisabasic

flawinthemodel.Asanextremeconditionstestinyourmodel,suddenly

raisethepricetoaverylargenumber(suchas$1millionpermonth)･If

prlCeSWeretOrisethatmuch,whatmusthappentothepotentialadopter

population?Tbthepopulationofsubscribers?implementtheprlCeriseat variouspolntSinthelifTecycle.Doesyourmodelbehaveapproprlately?What

problemorproblemsarerevealedbythetest?Propose,implement,andtest

revlsionsthatcorrectanyproblemsyouidentify.

D｡InteractionofdiffusionandthelearningCurve.

ThepricesOfmanynewproductsandservicesfallovertimeaslearnlng, scaleeconomies,andothereffectslowercostsandascompetitionintensifies.

Maketheproductpricearter.doger10-tisPartOfthemodelstrlLiCtureby

incorporatlngalearnlngCurve.LeamlngOrexperiencecurvescapturethe

waylnWhichproducers,distributors,andothersinthevaluechainlearnto

produceatlowercostsastheygalnexperience.Usuallycostsareassumed

tofallascumulativeexperiencewiththeproductorservicegrows･In

amanufacturlngSettlng,Cumulativeexperienceisusuallyproxiedby

cumulativeproduction.Inaserviceindustry,cumulativeexperiencemight

betterberepresentedasdependingonthecumulativenumberoftransactions

338 PartHITheDynamicsofGrowth

andwilldependontheadopterpopulationandthenumberoftransactions

eachadoptergeneratespertimeperiod.Typically,unitcostsfallbyafixed

percentagewitheverydoublingofexperience.Costreductionsoflo啄to

30%perdoublingofcumulativeexperiencehavebeendocumentedinawide

rangeofindustries(see,e･g"Teplitz1991;Gruber1992;ArgoteandEpple

1990)･Toincorporatealearningcurveintoyourinnovationdiffusionmodel,

firstassumethatanycostreductionsarefullypassedintoprice:

Price-InitialPrice*EffectofLearnlngOnPrice

EffectofLearnlngOnPrice- CumulativeExperience

CumulativeExperience-INTEGRAL(AdoptionRate, InitialCumulativeExperience)

TheexponentcdetermineshowstrongthelearningCurveisandshould

benegative(costsfallascumulativeexperiencegrows).Tbrepresenta

leamlngCurveinwhichcostsfall30%foreachdoublingofexperience,

setc-log2(0.7)--0.51.12

Testyourmodelforahypotheticalmanufacturingfirmthatintroducesa

newconsumerdurableproductintheyear2000.Theproducthashighmarket

potential.Setthefollowlngparameters:Assumethatloo鞄ofthetotal

populationof100millionhouseholdswillpurchasetheproductifitisfree

butthatdemandfallstozeroifthepriceis$2500perunit.Settheinitial

priceto$2000/unit,andsetinitialexperienceto10millionunits(reflecting

leaninggainedonpriorproductsandprototypes).Researchonconsumer

durablesshowstypicalproductlifecycleslastfromaboutayeartoaslong

as20yearsormore(Parker1994),dependingonthecost,benefits,size,

trialability,novelty,andotherattributesoftheproduct,alongwiththeroleof

complementaryassetsandotherinfrastructure(computersaren'tvaluable

withoutsoftware;atelevisionisuselesswithoutprogrammlngpeoplewantto

watchandnetworksorcableoperatorstodistributeit)ATocapturetherange,

definethefollowingtwoscenariosforthediffusionoftheproduct:aSlow

scenario,inwhichtheproductofthecontactrateandadoptionfraction(ci)

is1.0/year,andaFastscenario,inwhichtheproductofthecontactrateand

adoptionfractionciis3.0/year.Assumeforbothscenariosthat1%ofthe

potentialadopterpoolwillpurchaseastheresultofadvertisingperyear.

12ForalearningCurveWherecostsCfallbyafixedfractionperdoublingofexperienceE,costs areglVenby

C-Co(E/Eo)C.

WhenEhasdoubled,costshavefanenbyafractionf,so

(1-f)Co-Co(2Eo侶 o)c

c-ln(1-f)/ln(2)-1og2(1-f)A ForalearningCurVewithf-0.30,C-0.5146.Sincef,thefractionalcostreductionperdoubling ofexperience,hasamoreintuitivemeanlngthantheexponentc,itisconvenienttoformulatecin themodelasacomputedconstant,C -ln(1If)nn(2)andthenspecifythecostreductionfractionf asaconstant.

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts339

Befbrerunnlngyourmodel,drawacausaldiagramshowingthefeedback

structurecreatedbythelearningCurveandhowitinteractswiththestructure ofdiffusion.Withoutsimulation,sketchthedynamicsyouexpectforthe

fractionofthemarketwillingtoadopt,thepotentialadopterpopulation,

adoptionrate,andadopterpopulation.Alsosketchthepathofrevenuesyou

expect.Assumetheproductispurchased,notleased,andignorerevenues

thatmayderivefromsaleofservicesoraftermarketproductstotheadopters

(revenuedependsonlyontheadoptionrateandprice)･

Aftersketchingthedynamicsyouexpect,runthemodelforboththeFast

andSlowcases.Describethedynamics,andcomparetoyourintuitiveesti-

mates.ExperimentwithdifferentstrengthsforthelearningCurverelativetothe

diffusionprocess.HowdodiffusionprocessesandlearningCurvesinteractto

determlnethegrowthofanewproduct?Whataretheimplicationsofvery

rapiddi仇lSionforrevenues,capacityplanning,andnewproductdevelop-

ment?Whatimplicationsforstrategy(pricing,capacityacquisition,andmar-

keting)doyoudraw?

9.3.5 FadandFashion:

Mode軸g竜heAbamd⑳mmem昔o菅anEFW⑳Va竜iom

TheBassdiffusionmodelisanalogoustotheSImodelofchronicinfection.Every-

oneeventuallyadoptstheproductandadoptersneverabandontheinnovationor

discontinueuseoftheproduct.Theseassumpt10nSareappropriateforsomeinno-

vationsbutdonotapplytothehugecategoryoffashionsandfads･

Afad,bydefinition,involvesthetemporaryadoptionofanewideaorproduct,

followedbyitsabandonment.Inafad,thosewhoadoptsoonerorlater(usually

sooner)discontinuetheiruseoftheproductandnolongergeneratewordofmouth

thatmightleadtofurtheradoption.ThoughmanybabyboomersworeNehrujack-

etsorgrannydressesinthe1960S,polyesterleisuresuitsorrainbow-coloredplat-

formshoesinthe1970S,andpowersuitswithyellowtiesorshoulderpadsinthe

1980S,fewareseenwearlngthemtoday･13Fadandfashionareofcoursecomm on

intheapparelindustrybutalsoariseinnearlyeveryotherdomain,fromhomefur-

nishings,vacationdestinations,cuisines,automobiles,andinvestmentstostylesin theartsandmusic,academictheoriesinthesciencesandhumanities,andhotnew

buzzwordsandgurusincorporatestrategy,organizationaltheory,andmanagement

consulting.

TheBassmodelcannotcapturethedynamicsoffadsinpartbecauseadopters neverdiscontinuetheiruseoftheinnovation.Further,becausethecontactrateand

adoptionfractionareconstant,theearliestadoptersareJustaSlikelytoinfectpo-

tentialadoptersasthosewhojustpurchasedtheproduct･FormanyInnovations

(notonlyfads),however,people'spropensitytogeneratewordofmouth,andtheir

enthusiasmandpersuasiveness,varyovertime.Usually,wordofmouthdecaysas

peoplebecomehabituatedtotheinnovation･Thosewhohaverecentlyembraceda

13ThefashionindustryfrequentlyreintroducesoldfashionsIThefashionsofthe70swere recycledinthelate90S,includingplatformshoesandbellbottoms,butthankfullynotpolyester leisuresuits.

340 PartIIITheDynamicsofGrowth

newideaorpurchasedanewitemaremuchmorelikelytotalkaboutitthanthose

whohavelongsinceadoptedtheinnovationeveniftheycontinuetouseit.Indoor

plumbingcanhardlybeconsideredapasslngfad,yetpeopledonotrushouttotell theirfriendshowwonderfulflushtoiletsare.

Inthe1980sSelchowandRightersoldtensofmillionsofcopleSOfthegame

TrivialPursuit.SalesboomedasTrivialPursuitbecameoneofthehottestproducts

inthetoyandgamemarket.Theboomwasfedlargelybywordofmouthandso-

cialexposureaspeopleplayeditatthehomesoftheirfriends.Afterafewyears,

however,salesslumped.Muchofthedeclinecanbeattributedtothefamiliarmar-

ketsaturationloop:thegamewassosuccessfulthecompanydepletedthepoolof

peoplewhohadnotyetpurchasedacopy.Butthefadingnoveltyofthegamewas

alsoafactor.Thepopulationofadoptersisstilllargeinthesensethatmanypeople

stillownacopyofTrivialPursuit.However,mostofthesecopleSareinatticsand

closets.Thepopulationofactiveadopters,thosewhostillplaythegameandgen-

eratewordofmouthcontactswithothers,issmall.

Discontinuationofuseandthedecayofwordofmouthcaneasilybeincorpo-

ratedintheinnovationdiffusionframeworkbydisaggregatlngtheadopterpopula-

tionintodifferentcategories,eachrepresentlngdifferentdegreesofuseand

propensitiestogeneratewordofmouth.Thesimplestextensionofthemodelisto

dividethetotaladopterpopulationintotwocategories,ActiveAdoptersandFor-

merAdopters.Thediscontinuationrate(therateatwhichactiveadoptersbecome

formeradopters)dependsontheaveragedurationofusefortheinnovation(the

simplestassumptionisthatthediscontinuationrateisafirst-orderprocess).Word

ofmouthandhencetheadoptionratewouldbegeneratedonlybythepopulation

ofactiveadopters.

TherevisedmodelisanalogoustotheSIRepidemicmodel.Nowonlyactive

adopters(analogoustotheinfectiouspopulation)generatewordofmouththat

mightinduceadditionaladoption.Formeradoptersareanalogoustothepopulation

ofrecoveredindividuals.Havingpurchasedtheproductbutnolongeractivelyus-

1ngit,theformeradoptersarenolongerinfectioustoothersandarealsoimmune

toreinfection-exposuretoadvertlSlngOrWOrdofmouthfromactiveadopters

won'tinduceagingbabyboomerstobuyanotherleisuresuit･14

ThekeyinsightfromtheSIRepidemicmodelistheconceptofthetlPPlng

polnt:exposuretOinfectiousindividualswillnotproduceanepidemicifpeoplere-

coveranddevelopImmunityfasterthantheycaninfectothers.Similarly,newin-

novationsmightfailtotakeholdeveniftheygeneratepositivewordofmouth

becauseactiveadoptersdiscontinueusagefasterthantheypersuadeothersto

adopt.Thoughadistresslnglylargenumberofbizarrefashionsanduselessprod-

uctsareembracedbyeagerconsumerswhomindlesslyallowmarketerstomanlp-

ulatetheirtastes,manymorefailtotakehold.

IntheSIRmodel,thetipplngpointisdefinedbyareproductionrateofone.

Thereproductionrateisthenumberofnewcasesgeneratedbyeachinfectiveprior

14AsintheextendedSIRmodelsdevelopedinsectlOn9･2,thepopulationofadopterscouldbe disaggregatedfurther,forexample,intocohortsofpeoplewhoadoptedtheinnovation1,2,...,n timeperiodsago,tocapturesituationswherethecontactrateandadopt10nfractiondecaygradually ratherthaninafirst-orderpattern(chapter12).

Chapter9 S-ShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts341

torecoveryandisdefinedbytheproductofthecontactnumber(thenumberofin- fectiouscontactsgeneratedbyeachinfectivepriortorecovery)andtheprobability ofcontactingasusceptibleindividual(equation(9-26)).Usingtheterminologyof theinnovationdi軌sionframework,thereproductionrateistheproductofthe

numberofpersuasivewordofmouthcontactsgeneratedbyeachactiveadopter

prlOrtOdiscontinuationandtheprobabilityofencounterlngapotentialadopter:

cid(;),1 (9-45,

wherecisthecontactrate,iistheadoptionfraction,distheaveragedurationof

activeusefortheinnovation,Pisthepopulationofpotentialadopters,andNisthe

totalpopulation･ Ifthereproductionrateisgreaterthanone,thepositivewordofmouthfeed-

backdominatesthesystemandafadisborn･Thefadendswhenthepoolofpo- tentialadoptersfallsenoughtobringthereproductionratebelowone･Ifthe reproductionrateislessthanone,thepositivewordofmouthloopisdominatedby thenegativefeedbacksandtherewillbenoepidemicofadoption.

However,unliketheSIRmodel,adoptionintheBassinnovationdiffusion

frameworkalsoarisesfromadvertlSlngandotherexternalinfluences.Inthesim-

pleBassmodeltheeffectivenessofadvertlSlnglSaconstant,implyingthatthead- vertlSlngbudgetisconstantthroughtime.Evenwhenthesystemisbelowthe tippingpoint,everyonewilleventuallyadopttheinnovation(thoughitmaytakea

verylongtime)i Intherealworld,advertislnglSexpensiveanddoesnotpersistinde丘nitely.

Themarketingplanformostnewproductsincludesacertainamountforakickoff

adcampaignandotherinitialmarketingefforts･Iftheproductissuccessful,further

advertlSlngCanbesupportedoutoftherevenuestheproductgenerates･If,how- ever,theproductdoesnottakeoff,themarketingbudgetissoonexhaustedandex-

ternalsourcesofadoptlOnfall.AdvertlSlnglSnoteXOgenOuS,aSintheBassmodel, butispartofthefeedbackstructureofthesystem.ThereisatlPPlngPOlntforideas andnewproductsnolessthanfordiseases.

ModehgF:ads

A.ModifytheBassmodel(Oryourextensionsofitdevelopedinsection9･3･4)by

disaggregatlngtheadopterpopulationintoactiveadoptersandformeradopters･ Assumewordofmouthisonlygeneratedbyactiveadopters.Calibrateyourmodel

torepresentafad.Assumethetotalpopulationis100millionhouseholds,thatthe averagedurationofactiveuseis1year,andthat1%ofthepotentialadopterswill

adoptastheresultofadvertlSlngeachyear･Assumeacontactrateof100perper- sonperyear.Runthemodelforthreecases:astrongwordofmouthcasewherethe adoptionfractionis0.025,anintermediatecasewheretheadoptionfractionis0.01,

andaweakcasewheretheadoptionfractionisO･001.Contrastthebehaviorofthe modelinthethreecases,Howdoestheinclusionofadoptionfromadvertising

causethebehaviorofthemodeltodifferfromthepureSIRmodel?Canafirm

compensateforweakwordofmouthbyamassiveadvertisingCampaign?

342 PartIH TheDynamicsofGrowth

B.Howdomostorganizationssettheiradvertisingbudgets?Drawacausaldial gramthatcapturesyourunderstandingofthewaylnWhichadvertislngisdeter mined.Whatfeedbackloopsarecreatedbythetypicalbudgetingprocess?How mighttheyaffectthedynamicsofadoption?HowmightsuchanadvertlSlngPOlicy affectthenatureofthetippingPOintforadoptionofanewproduct?

C･Whatotherprocessesandinformationsourcesmightcontributetothedynam- icsofafad?Developacausaldiagramcapturingyourideas･Whatadditionalfeed- backloopsarecreated?Howmighttheyaffectthedynamics?Giveexamples.

9.3.6 ReplacemeniPurehaseも

TheBassdiffusionmodelisoftendescribedasafirst-purchasemodelbecauseit doesnotcapturesituationswheretheproductisconsumed,discarded,orupgraded, allofwhichleadtorepeatpurchases.

Onepopularwaytomodelrepeatpurchasebehavioristoassumethatadopters movebackintothepopulationofpotentialadopterswhentheir丘rstunitisdis- cardedorconsumed.Therateatwhichtheproductisdiscardedandtherefore血e rateatwhichpeoplemovefromtheadopterpopulationtothepoolofpotential adoptersdependsonthenumberofadoptersandtheaveragelifeoftheproduct (Figure9-20).Modelingreplacementdemandinthisfashionisanalogoustothe lossofimmunltytOadisease･Now,insteadoffallingtozero,thepotentialadopter populationisconstantlyreplenishedasadoptersdiscardtheproductandreenterthe market(Figure9-21).Theadoptionrate(salesrateforaproduct)rises,peaks,and fallstoaratethatdependsontheaveragelifeoftheproductandtheparametersde- terminingtheadoptionrate.Discardsmeanthereisalwayssomefractionofthe populationinthepotentialcustomerpool.Byvarylngtheproductlifeandstrength ofthewordofmouthfeedback,therateofdiffusion,includingtheheightofthe salespeakandthedepthofthebustwhenthemarketsaturates,canbevaried.The modelshowninFigure9120assumesafirst10rderdiscardprocessbutcaneasilybe modifiedtorepresentanydistributionofdiscardsaroundtheaverageproductlife usinghigher-orderdelays(chapter11).

Becausethosediscardingtheproductreenterthepotentialcustomerpool,they aretreatedexactlylike丘rst-timebuyersandmustgothroughanotherprocessof becomlngawareOfandbeingpersuadedtobuytheproductthroughadvertlSlngOr wordofmouth.Insomecasesthelifetimeoftheproductissolongandtheattri- butesoftheproductchangesomuchoverthisspanthatprlOrexperienceislargely irrelevantandrepeatpurchasedecisionsarereasonablysimilartoinitialpur- chasedecisions.BuHbrmostproducts,thecustomerhasalreadymadethedecision tocontinueuslngtheproductandsimplypurchasesanewone･Insuchcasesthe initialandrepeatpurchasedecisionsmustberepresentedseparately,asshownin Figure9122.Heretheadoptionprocessisseparatedfromthenowofpurchases. Thetotalsalesrateisthesumofinitialpurchasesandrepeatpurchases.Therepeat purchaserateistheproductofthenumberofadoptersandtheaveragenumberof unitspurchasedbyeachadopterpertimeperiod.Figure9-23showstyplCalmodel behavior.

Chapter9 S-ShapedGrowth:Epidemics,InnovationDi軌lSion,al-dtheGrowthofNewProducts343

FIGURE9-20

Modelingproduct discardand

replacement

purchases

Customersdiscard

theproductwitha timeconstant

glvenbythe

AverageProduct

Life,thenretum tothePotential

AdopterPool･

FIGURE9-21 Behaviorofthe

Bassmodelwith

discardsand

repurchases

Showsthebehav-

iorofthemodel

inFigure9-20 withanAverage ProductLife

l-5years, a-0.01,C-100, andi-0,025.

(% )

u o !Ie 一n

d o d 一t210 1 -O u O !10t2 J

( ) ｡ a

r̂u O !tt?lnd o d lt=70〓 0 % )

s a l t 2∝ PJt=3 S !CB P ue uO !td o pv

4 5 6

3 Years

4 5 6

344

FIGURE9･22

Modelingrepeat purchases

Totalsafesconsist

ofinitialand

repeatpurchases･

Eachpotentia一

adopterbuysInitial

SalesperAdopter

unitswhenthey

firstadoptthe productand continuesto

purchaseatthe

rateofAverage

Consumptionper

Adopterthereafter.

FIGURE9-23 Behaviorofthe

repeatpurchase model

Behaviorofmodel

inFigure9-22, Withthesame

parametersasin

Figure9-21anda

totalpopulationof 100million,initial

purchasesof

1unitperperson, andreplacement purchasesof

0.2unitsper

PersonPeryea｢･

PartIII TheDynamicsofGrowth

[nilialSalesi fniti'al R;peatL he竺讐 : 一軒.-.~Consumption

perAdopter

'7 sadesRate雪

perAdopter Purchase Purchase

Rate Rate

.pか卯言dOi;It,tirai J c♂ ＼ AdFoy.I,eps★■†十It★+

++ +,AdoptionRate .プ汐

2 3 4 5 6 Years

T t23

ĴSt!u n u O !H

u )

a lt2正 S a ltZS

0 1 2

3 Years

4 5 6

Chapter9 SIShapedGrowth:Epidemics,InnovationDiffusion,andtheGrowthofNewProducts345

Model声ngtheLifeCycleofDurabieProducts

ThemodelinFigure9-22doesnotexplicitlyrepresentthestockofproductheldby

theadopterpopulation.Repeatpurchasesaremodeledasdependingonthecurrent

adopterpopulation.Thisformulationisapproprlatefornondurableconsumables suchasfood,wherethelifetimeoftheproductisveryshortrelativetothediffu-

sionprocessandtheacqulSltlOnandconsumptlOnOrdiscardoftheproductdonot

needtoberepresentedseparately･Fordurableproducts,however,itisusuallyIm-

portanttorepresentthestockofproductandthediscardrateexplicitly･

ModifythemodelshowninFigure9-22torepresenttheadoptionandinstalled baseofaconsumerdurablesuchasvideocassetterecorders(VCRs).Youmayuse

eitherthesimpleBassformulationortheextendedmodelyoudevelopedinsection

9.3.4includingtheeffectofprlCeOnthesizeofthemarketandthelearningCurve

(whenVCRswereintroduced,theaveragepricewasabout$2000/unit,butbythe

1990stheaveragepricehadfallento$200/unit)･

Thediscardratefordurableproductsisoftenstronglyagedependentandisnot

wellapproximatedbyafirst10rderprocess･TomodeltheinstalledbaseofVCRs, createtwostocks,NewVCRsandOldVCRs.ThestockofnewVCRsisincreased

bythePurchaseRate.AsVCRsage,theymoveintothestockofoldVCRs･As-

sumetheaverageVCRremainsnewfor3yearsandthattheagingrateisafirst-

orderprocess.ThoughsomenewVCRsdobreakdownandarediscarded,for

simplicityassumethediscardrateofnewVCRsiszero･Assumetheaveragelife-

timeofoldVCRsis5years,glVlngatotalaveragelifeof8years･

Whatdeterminesthepurchaserate?First,householdsthathaveadoptedthe

VCRwillseektoreplacethosethatbreakdownandarediscarded(ordiscardaus-

ableunittobuyanewonewithbetterfeatures)･Second,thosehouseholdswillbuy morethanthediscardratewhenthenumberofVCRstheycollectivelydesireex一

ccedsthenumbertheyactuallyhave(andwillbuylessthanthediscardrateshould

theyfindtheyhavemorethantheydesire).Thepurchaserateisthenthesumofthe

discardrateandanadjustmentforinstalledbase.Theadjustmentfortheinstalled

baseismostsimplyfomulatedasasimplefirst-ordernegativefeedbackprocess:

AdjustmentforInstalledBase

(DesiredVCRs-TotalVCRs)

StockAdjustmentTime

(9-46)

wherethetotalnumberofVCRsisthesumofthenewandoldVCRstocks,andthe

StockAdjustmentTimerepresentstheaveragetimerequiredforpeopletoshopfor

andpurchaseaVCR･DefinethedesiredstockofVCRsasdependingonthenum- berofhouseholdsthathaveadoptedtheVCRandtheaveragenumberofVCRsde-

siredperhousehold.ThechallengetoextendtheBassmodelinsection9･3･4 introducedthenotionthatthefractionofthepopulationwillingtoadopttheprod-

uctdependsonitsoverallattractiveness,includingprlCe･Thegrowthofmarkets

formanyimportantProductsinvolvesbothaprocessofadoptionbyanincreaslng

fractionofthepopulationandagradualincreaseinthenumberofunitsownedby

eachhouseholdasrealprlCeSfallandashouseholdincomerises･Whentheywere firstintroduced,households"madedo"withjustonecar,phone,TV,andcomputer･

AsprlCeSfell,qualityrose,andtheimportanceoftheseproductsindailylifegrew,

346 PartHI TheDynamicsofGrowth

thenumberperhouseholdgrew.Byexplicitlyrepresentlngthenumberofunitsde- siredperadopterthemodelcanrepresentsituationswhereadoptersincrease山e numberofunitstheydesireastheirincomegrows,asprlCedeclines,orasotherat-

tributesofproductattractivenessimprove.Fornow,assumethenumberofVCRs desiredbyeachadopterhouseholdisone.

NotethatifthedesiredstockofVCRsincreasesabovetheactualstock(say

becausepricesfallsomoreadoptinghouseholdsdecidetobuyasecondVCR),the purchaseratewillriseabovethediscardrateandthestockwillincreaseuntil thegaplSClosed.ShouldthedesiredstockofVCRsfall,thepurchaseratewillfall

belowthediscardrateandthestockofVCRswillgraduallyfall. Testtherobustnessofyourformulationforthepurchaserate.Implementan

extremeconditionstestinwhichthedesiredstockofVCRssuddenlyfallstozero

fromaninitialsituationinwhichthedesiredandactualstocksareequalandlarge.

Modifyyourformulationforthepurchaseratetoensurethatitbehavesappropr1- atelyeveniftherearemanymoreVCRsthandesired.

VCRsforthehomemarketwereintroducedbySonyln1975.Bytheearly

1990sapproximately80%ofUShouseholdshadatleastoneVCR.Selectparame- tersforyourmodelthatareroughlyconsistentwiththesedata.Useyourjudgment

toestimatetheotherparameterssuchasthestockadjustmenttime･Forsimplicity, assumethetotalnumberofhouseholdsintheUSis100millionandconstant.Sim-

ulatethemodelanddiscusstheresults.Inparticular,whatisthepatternofadop-

tion?Whatisthepatternofsales? SincetheintroductionoftheVCRtheaveragedurationofproductlifecycles

forconsumerelectronics,Computers,andmanyotherproductshasshrunk.Lifecy-

clesofjustafewyearsorevenlessarecommon.Simulatethemodelassumingthe wordofmouthfeedbackisthreetimesasstrongasthevalueyouselectedforthe VCRcase_Howlongdoesitnowtakefor80%ofhouseholdstoadopttheproduct?

Whataretheimplicationsforsales?Why?Whatdifficultiesdoshortproductlife cyclesposeforfirms?

9.4 SuMMAPY

S-Shapedgrowtharisesthroughthenonlinearinteractionofpositiveandnegative feedbackloops.Anygrowlngquantltycanbethoughtofasapopulationgrowlng inanecologlCalnichewithacertaincarrylngCapaClty.S-Shapedgrowtharises

whenthecarryingCaPaCltyisfixedandwhentherearenoslgnificantdelaysinthe reactionofthepopulation'sgrowthrateasthecarrylngCapaCltylSapproached.

ThestructureunderlylngS-shapedgrowthapplleStOaWiderangeolgrowth

processes,notonlypopulationgrowth.TheseincludetheadoptlOnandd肝usionof newideas,thegrowthofdemandfornewproducts,thespreadofinformationina

communlty,andthespreadofdiseases,includingbiologlCalpathogensandcom- puterviruses.

Chapter9 S-ShapedGrowth:Epidemics,InnovationDi軌sion,andtheGrowthofNewProdtlCtS347

AnumberofanalytlCallytractablemodelsofS-shapedgrowthwereintro-

duced,includingtheloglSticgrowthmodel,theSIRepidemicmodel,andtheliass diffusionmodel.Importantextensionstothebasicepidemicandinnovationdiffu-

sionmodelsweredevelopedtoillustratehowmodelerscanidentifytherestrictive assumptlOnSOfamodel,bothexplicitandimplicit,andreformulatethemodelto bemorerealistic.

Thelogistic,epidemic,andinnovationdiffusionmodelscanbefittohistorical data,andthefitisoftenexcellent.However,thoughnonlineargrowthmodelssuch

astheloglSticandBassmodelsarewidelyusedandoftenfitcertaindatasetsquite well,youshouldnotusethese(orany)modelsasblackboxesforforecasting.

¶)Createrealisticandusefulmodelsofproductdi軌Sionandinnovationadop- tionyoumustexplicitlyportraythefeedbackstructureofadoptionandgrowth,in-

cludingthesourcesofattractivenessforthenewideaorproduct,thecompetition, technicalinnovation,changlngCriteriaofuse,andotherfactorsthatinfluence adoptlOnandgrowth.Manyrichandinsightfulsystemdynamicsmodelsofinno- vationdiffusionhavebeendevelopedandareusedsuccessfullytoanticipate growthanddesignpoliciesforsuccess(see,e.g.,Homer(1987)foramodelof emergingmedicaltechnologiesandUrban,HauserandRoberts(1990)forfeed-

backmodelsforprelaunchforecastingofnewautomobilemodels). Thehistoricalfitofamodeldoesnotshowthatthemodelis"valid."Many

models,eachwithdifferentassumptlOnSaboutthefeedbackstructureandeach generatlngdifferentdynamics,Canfitanysetofdataequallywell.Groundyour modelsincarefullnvestlgationofthephysicalandinstitutionalstructuresandde-

cision-makingprocessesoftheactorsinthesystemanddon'tforce-fitdataintothe assumptionsOfanypreselectedfunctionalformormodel.Modelsshouldnotbe

usedasexercisesincurvefittingusingtheaggregatedata･Onlymodelsthatcap- turethecausalstructureofthesystemwillrespondaccuratelyasconditionschange andpoliciesareimplemented.

EI冨

P護良f;ie皇軍!_?i達e盲?iee孟書で遠 P¢S畳t,量ve二Feed~bae.k

Foruntoeveyyonethathathshallbegiven,andheshallhaveabundance;but fromhimthathathnotshallbetakenawayeventhatwhichhehath.

-MatthewXXV:29

Thischapterexplorespathdependence,apattemofbehaviorinwhichsmall,ran- domeventsearlyinthehistoryofasystemdeterminetheultimateendstate,even

whenallendstatesareequallylikelyatthebeginnlng.Pathdependencearisesin

systemswhosedynamicsaredominatedbypositivefeedbackprocesses･Thechap- terexploresthecircumstancesinwhichpositivefeedbackcancreatepathdepen-

dence,theroleofrandomeventsearlylnthehistoryofapath-dependentsystem,

andthewaysinwhichapath-dependentsystemcanlockintoaparticularequilib-

rium.Feedbacktheoriesofpathdependenceandlockinaredevelopedforanum- berofimportantexamplesirTAb71Si王IeSS,technology,andeconomics,

10.1 PATHDEPENDENCE

Whydoclocksgoclockwise?Whydopeopleinmostnationsdriveontheright? WhyisthediamondbusinessinNewYorkconcentratedintotheareaaroundwest

47thStreet?WhydonearlyalltypistsleantheinefficientQWERTYkeyboardlayl out?HowdidMicrosoft'sWindowsandlntel'sprocessorscometodominatethe

marketforpersonalcomputers?Whyaretheresomanywinner-take-allmarkets-

349

350 PartIIITheDynamicsofGrowth

situationswheresuccessaccruestothesuccessful,wheretherichgetricherandthe

poorgetpoorer?Andwhatdothesequestionshavetodowitheachother?Allare

examplesofsystemsexhibitingpathdependence.Pathdependenceisapatternof

behaviorinwhichtheultimateequilibriumdependsontheinitialconditionsand

randomshocksasthesystemevolves.Inapath-dependentsystem,small,unpre-

dictableeventsearlylnthehistoryofthesystemcandecisivelydetermineitsultト matefate.

Theeventualendstateofapath-dependentsystemdependsonthestartlng

polntandonsmall,unpredictableperturbationsearlyinitshistory.Evenwhenall

pathsareinitiallyequallyattractive,thesymmetryisbrokenbymicroscoplCnoise

andexternalperturbations.Positivefeedbackprocessesthenamplifythesesmall

initialdifferencesuntiltheyreachmacroscopICSignificance.Onceadominantde-

signOrStandardhasemerged,thecostsofswitchingbecomeprohibitive,sothe

equilibriumisself-enforclng:thesystemhaslockedin暮

Theexactgaugeofarailroadisoflittleconsequence(withinbroadlimits).At

thestartoftherailage,noonegaugewasabetterchoicethananyother.Yetthe

standardgaugeusedintheUSandmostoftheworldis1.44meters(4feet8.5

inches).Howdidthisconvergencearise?Earlyrailroads,eachunconnectedtothe

others,utilizedawiderangeofdifferentgauges(oneearlylineuseda7foot

gauge!).Rollingstockwasspecifictoeachnetworkandcouldnotbeusedonlines

withadifferentgauge･Butasrailnetworksgrew,compatibilitybecamemoreand

moreimportant(whengaugesdiffered,goodstransshippedfromonelinetoan-

otherhadtobeunloaded血.omonetrainandreloadedonanother,greatlyraislng

costsandslowingdelivery),Railroadsofferingcompatibilityenjoyedahugecost

advantagesincethesamerollingstockcoulduseanypartofthenetwork.Gradu-

ally,thesmallerrailroadsadoptedthegaugeusedbythelargestnetworks.Theat-

tractivenessofthatgaugewasthenincreasedstillfurther,formlngapositive

feedback.SmallerrailroadsuslngIncompatiblegaugeslostbusinessorconverted

theirroadandrollingstocktobecompatible.Soonaslnglegauge-withtheun-

likelydimensionsof1.44meters-emergedasthedominantstandard.Bythe

1860S,thecostsofswitchingtoanothergauge(AbrahamLincolnisreportedto

havearguedfor5feet)wereprohibitive:thesystemhadlockedintothestandard.1

Similarpositivefeedbacksareresponsibleforotherexamplesofpathdepen-

dence:Themoretypewriterswiththe(〕WERTYkeyboardweresold,themore

peoplelea川edtotypewiththatlayout,andthemoresuccessfulQWERTYma-

chinesbecame,whilemakersofalternativekeyboardslostbusiness.Asthemarket

shareofWintelcomputersgrew,moresoftwarewaswrittenforthatplatformand

lessdevelopedforotherplatformsandoperatlngSyStemS･Themoresoftware

availableforaparticularoperatingSystem,thegreaterthedemandforcomputers

compatiblewiththatsystem,increasingWintelmarketsharestillfurther.

1someclaimthatthestandardgallgeemergedbecauseitwasthewidthofjigsdesignedorigト nallyforwagons,whichinturnhadthosedimensionstofittherutsontheroads,whichinturnwere determinedbytherutsinRomanroads,whichweresetbythewidthofRomanchariotsandwag- ons,whichinturnweresizedtoaccommodatethewidthoftwoRomanhorses.Iftrue,itillustrates thewaylnWhichpositivefeedbackcancauseastandardtopersistlongaftertheinitialrationalefor itsselectionhasvanished.

Chapter10 PathDependenceandPositiveFeedback 351

Whatcausessomesystemstoexhibitpathdependencebutnotothers?Pathde-

pendencearisesinsystemsdominatedbypositivefeedback.Figure10-1illustrates

thedifferencebetweenasystemdominatedbynegativefeedbackandapath-de-

pendentsystemdominatedbypositivefeedback.First,imaglneaSmooth-sided

bowl.ThelowestpolntOfthebowlisanequilibrium-amarbleplacedtherewill

remainthere･Theequilibriumisstable:pushingthemarbleofftheequilibriumcre-

atesaforceopposlngthedisplacement.Amarbledroppedanywhereinthebowl

willeventuallycometorestatthebottom(thoughitmayrollaroundawhilefirst).

Theequilibriumisnotpathdependent:themarblecomestorestatthesamespot

nomatterwhereitisdroppedandnomatteritsinitialvelocity(aslongasitstays

withinthebowl-theequilibriumisonlylocallystable)･Astableequilibriumis

alsocalledanattractorbecauseallpointsareattractedtoit.Technically,because

theequilibriumislocallyandnotgloballystableitisanattractoronlyforpolntS withinitsbasinofattraction.Thebasinofattractionisthebowl.Insideit,all

polntSleadtotheattractoratthebottom.Outsidethebowl,thedynamicsaredif-

ferenLTheDeadSeaandGreatSaltLakeareexamples:Rainfallinganywhere

overthesewatershedsendsupintheirsaltybrine.Rainfallingoverotherwater- shedsflowstothesea.

FIGURE10-1 PathdependencearisesinsystemswithlocaHyunstableequiFibria.

Left:AlocallystableequiFibrium･Thesystemisgovernedbynegativefeedback:thegreater thedjspracementoftheba川fromtheequilibriumP*,thegreatertheforcepushingitbacktowardthe centerandequilibrium.Aballplacedanywhereinthebowleventuallycomestorestatthebottom; perturbationsdon'taffecttheequilibriumreached.

R/'ght:Alocallyunstableequ‖ibriumlThesystemisgovernedbypositivefeedback:thegreater thedisplacementoftheball,thesteeperthehiHandthegreatertheforcepu"ingitawayfromthe equilibriumatP'.Theslightestdisturbancecausestheballtofanoffthepeak.Theinitialperturbation determinesthepathtakenbytheba"andperhapstheultimatedestination-thesystemispath dependent･

Positionof F

Forceon Ba-I

BaJJ(P) 皇室 !_. _,+'3r'-".

Discrepancy

1呼､ー___一一 (P- P★ )

EquilibriumPositionPositionof FForceonBaJl Ban(P) 主_R:㌔+ju'5g三;Discrepancy巧守しー______一･一十(P-P★)

EquilibriumPosition

352 PartIIITheDynamicsofGrowth

Nowturnthebowlupsidedown.Thetopofthebowlisstillanequilibrium- ifthemarbleisbalancedexactlyatthetopltWillremainthere･However,theequl- 1ibriumisnowunstable.Theslightestperturbationwillcausethemarbletomove slightlydownhill.Astheslopeincreases,thedownwardforceonthemarblein- creasesanditmovesstillfurtherdownhill,inapositivefeedback.(Anunstable equilibriumisalsotermedarepellorbecausenearbytrajectoriesareforcedaway fromit.)Thesystemispathdependentbecausethedirectiontakenbytheballde- pendsontheinitialperturbation:Asmallnudgetotheleftandthemarblerollsto theleft;anequallysmallshocktotherightanditmovesfartherright･Ofcourse,

thoughtheequilibriumatthetopofthebowlislocallyunstable,thesystemasa wholemustbegloballystable.Themarbleeventuallycomestorest･Butthepath- dependentnatureoftheball'smotionneartheequilibriumpointmeansitcancome torestanywhereonthefloor,andtheparticularspotitreachesdependsonthat small,initialdisturbance.

ImaglnerainfallingnearthecontinentaldivideofNorthAmerica･Tworain- dropsfallafewinchesapart,OneJusttOtheeastofthedivideandoneJusttOthe west.Thedifferenceinlandingspotmightbeduetosmall,unobservablediffer- encesinthewindasthetwodropsfallfromtheclouds･Thoughtheybeginonly inchesapart,oneendsupinthePacific;theother,thousandsofmilesawaylnthe GulfofMexico.MicroscopicdifferencesininitialconditionsleadtomacroscopIC differencesinoutcomes.

Theinvertedbowlillustratesanotherimportantfeatureofpath-dependentsys- tems:lockin.Whentheballisbalancedatthetopofthebowl,allequilibriumPOI

sitionsareequallylikely.Youcaninfluencewherethemarblecomestorestwith theslightesteffort:Blowgentlytotheleftandthemarbleendsupononesideof theroom;blowtheotherwayandthemarblerollstotheotherside･Oncetheball hasstartedtomovedowntheslopeabit,however,ittakesagreatdealmoreenergy topushitbacktothetopandovertheotherway･Thefarthertheballhasmoved andthefasteritisgoing,theharderitistoalteritscourse･

Atthedawnoftheautomobileageitdidn'tmatterwhichsideoftheroadpeo- pledroveon.ButastrafficdensitylnCreaSed,theimportanceofaconsistentstan- dardgrew.Themorepeopledroveononeside,themorelikelyltWasnewdrivers inadjacentreglOnSwoulddriveonthesameside,increasingtheattractivenessof thatsidestillfurther,inapositiveloop.Mostnationsrapidlyconvergedtooneof thetwostandards,WithGreatBritainandhercolonies,alongwithJapanandafew

othernations,electlngleft-handdrivewhilemostoftherestoftheworldcon- vergedtoright-handdrive.Initially,theSwedeselectedtodriveontheleft,asin GreatBritain.AstrafficandtradewiththerestofEuropegrew,andastheSwedish

autoindustrysoughttoincreasesalesinthelargerrightlhanddrivemarket,itbe- cameincreasinglyinconvenientandcostlyfortheSwedishsystemtobeatodds withtheprevailingstandardinEuropeandNorthAmerica･SeeingthattheSwedish roadandautosystemwasrapidlylockingin,theSwedesenglneeredaremarkable change.At5AMOnSeptember3,1967,theentirenationbegantodriveonthe right.Sweden'sabilitytoeffecttheswitchsmoothlywaspartlyduetomassive prioreducationandahugepublicworksefforttochangeroadsignage･Butthesuc- cessoftheswitchalsodependedonthesmallsizeandlowdensityofthepopula- tion,bothhumanandautomobile.In1967thetotalpopulationofSwedenwasless

Chapter10 PathDependenceandPositiveFeedback 353

than8million,andtherewereonlyabout2millioncars,or46peopleand12cars

persquaremile･MostofthegrowthinSweden'sautopopulationandhighwaynet-

worklayahead;thedisruptlOnandcostsoftheswitchweresmallcomparedtothe

benefits･ImagineWhatitwouldcosttodaytoswitchfromlef tJoright-handdrive

inJapan.ThoughJapanisonlyabout80%aslargeasSweden,inthemid1990sit

washometoabout126millionpeopleand40millioncars,morethan870people

and275carspersquaremile.ThedisruptlOnandcostwouldfaroutweighany

benefits｡Japanhaslongsincelockedintoleft-handdrive.

Path-dependentsystemsaremorecommonthanmanyofusimagine.The

choiceofstandardssuchastheshapeofelectricalplugs,thelocationoftheprlme

meridian,andthelengthofthestandardmeterinParisareallarbitrary,butoncea

glVenChoicebecomesaccepted,thesystemlocksintothatchoice,eventhough

otheralternativeswereJustasattractiveearlyon.Pathdependenceandlockinare

notrestrictedtoeconomic,technical,orhumansystems.Complexorganicmole-

culessuchasaminoacidsandthesugarsinDNAcanexistintwodifferentforms,

identicalexcepteachisthemirrorimageoftheother.Theseenantiomersare

knownastheL(levo,orleft-handed)andD(dextro,orright-handed)forms.The

chirality(handedness)oftheenantiomersdoesnotmatterinisolation-thephysi-

calpropertiesofLandDmoleculesarethesame.Yettheproteinsinessentiallyall

lifeonearthhavelevochirality.Positivefeedbackandlock-inareresponsible.Just

asyoucannotputarighthandedgloveonyourlefthand,thedifferentthree-di-

mensionalstructuresofthetwotypesmeantheD-aminoacidsarephysicallyin-

compatiblewithproteinsbuiltoftheleft-handedform.Mostchemicalreactions

tendtoproducedifferentenantiomersinequalproportions,leadingmanyscientists

toconjecturethatbothleftandrightaminoandnucleicacidswereequallycom-

monintheprlmOrdialsoupoftheearlyoceans.Bychance,theproteinsthatbe- camethebasisforlifeonearthwereformedfromleft-handedaminoacids.Asnew

organismsevolvedfromtheirleft-handedancestors,thewebofleft-handedlife

grewinmagnitudeandcomplexlty,Whileanyright-handedfわrmsbecameextinct. Lifeonearthhasremainedlockedintothelefトhandedform seversince.2

EdentifyingPathDependerミC昏

Identifyasmanyexamplesofpath-dependentsystemsasyoucan.Considereco-

nomic,technical,social,scientific,physical,biological,andotherexamples.For

eachcase,identifyatleastonepositivefeedbackprocessthatmightberesponsible

forthepath-dependentbehaviorandsketchitintheformofacausaldiagram.

2RNAandDNAarealsochiral(oneformtwistsleft,one,right).Butonlytherighトhanded formsarestereoscoplCallycompatiblewiththeL-aminoacids,soessentiallyallnaturalterrestrial nucleicacidshavethesameright-twistingChirality.Somephysicistsconjecturethattheinitialpush favoringtheleft-handedaminoacidsderivedfromparltyViolationsoftheweaknuclearforce,in whichcertainradioactivedecayreactionsfavoronechiralform.However,amechanismforprefer- entialselectionoftheL-formbytheweakforceorotherphysicalprocessessuchaspolarizedlight hasnotyetbeendemonstrated.

354 PartIIITheDynamicsofGrowth

10t2 ASIMPLEitF!oDELOFPATHDEPENDENCE:

THEPoLYAPROCESS

Youcaneasilyconstructasimpleandcompellingexampleofpathdependence.

ImaglneaJarfilledwithsmallstones.Thereareblackstonesandwhitestones.

Stonesareaddedtothejaroneatatime.Thecolorofthestoneaddedeachperiod

isdeterminedbychance.Theprobabilityofselectlngablackstoneisequaltothe

proportionofblackstonesalreadyinthejar｡ItisthislastassumptlOnthatglVeSthe

systemitsuniqueCharacterandcreatespathdependence.Supposethejarinitially

containsoneblackandonewhitestone.Theprobabilitythenextstoneyouchoose

willbeblackisthen1/2.Supposeitturnsouttobeblack.Nowtherearetwoblack

andonewhitestonesinthejar.Theprobabilityofpickingblackonthenextdraw

isnow2/3.Supposeitisblack.Now3/40fthestonesareblack.Thepreponder-

anceofblackstonesmeansitismorelikelythannotthatstillmoreblackstones

willbeadded,andthejarislikelytoendupwithmoreblackthanwhitestones.But

supposeonthefirstdrawawhitestonehadbeenchosen.Thelikelihoodofdrawl

lngablackstoneonthesecondroundwouldthenhavebeen1/3insteadof2/3.The

Jaristhenlikelytoendupwithmorewhitethanblackstones･ThetrajectoryOfthe

system,andtheultimatemixofstonesinthejar,dependsonitshistory,onthepar-

ticularsequenceofrandomevents.Figure10-2showsacausaldiagramofthissys-

tem,knownasaPolyaprocessafteritsinventor,themathematicianGeorgePoly乱 (1887-1985).

ThePolyasystemcontainstwofeedbackloops,onepositiveandonenegative,

foreachtypeofstone.3Thegreaterthenumberofblackstones,thegreaterthe

chanceofaddinganotherblackstone(apositiveloop).Atthesametime,the

greaterthenumberofblackstones,thegreaterthetotalnumberofstonesandso

thesmallertheimpactofanynewblackstoneaddedtothejarontheproportionof

blackstones(anegativeloop).

Figure10-3Shows10simulationsofthePolyaprocess･Eachis200periods

long.Atfirst,eachstoneaddedtothejarhasalargeinfluenceontheprobabilityof

choosingthenextstone(thefirststoneaddeddetermineswhethertheprobability

ofchoosingablackstoneis2/3or1/3).Thepositiveloopdominates.Butasthe

numberofstonesgrows,eachnewstonehasasmallerandsmallereffectonthe

proportions.Thepositiveloopweakensrelativetothenegativeloop･Eventually,

thenumberofstonesissolargethatthenextstoneaddedhasanegligibleeffecton

theproportionofeachcolorinthejar.Thepositiveandnegativeloopsareexactly

balancedatthatpoint.Theproportionofeachcolorwillthenstabilize,sinceon

averagestoneswillbeaddedinthefutureinthesameproportionasthosealready

inthejar.

Theratioofblacktowhitestoneseventuallyreachesequilibrium,butthatratio

dependsonthehistoryofthecolorsselected.Smallrandom eventsearlylnthe

3Theprocesscaneasilybegeneralizedtoanynumberofcolors･Theprobabilitythenextstone addedisanycolorClthenequalstheproportionofthatcolorintheJar,Cl/∑JCj(onlyonecolorlS addedperperiod).

Chapter10 PathDependenceandPositlVeFeedback

F【GURE10-2 ThePolyaprocess

Everyperiodonestoneisaddedtothetotal.TheprobabilityofchooslngaStoneOfaglvencolor equalstheproportionofthatcolorinthetotalpopulation.

TheruleforaddingstonesofaglVenCOlor.JS

BlackStonesAddedperPeriod-

WhiteStonesAddedperPeriod-

(

1ifRandomDraw<ProportionofBlackStones 0otherwise

1if(1-RandomDraw)<ProportionofWhiteStones 0otherwise

355

wheretheRandomDrawisanumberdrawnatrandomfromauniformdistributionontheinterval[0,1].

historyofthesystemtlplttowardonepathratherthananother.Theequilibrium

ispathdependent.Theaccumulationofstoneseventuallylocksthesysteminto

equilibriumataparticularproportionofeachcolor.Toreversetheproportionof

blackstones血･om2:1to1:2whentherearethreestonesinthejarrequlreSdrawing

threewhitestonesinarow,aneventwithaprobabilityoflo啄 [P(ThreeWhite

stonesl2Black,1White)-(1/3)(2/4)(3/5)]･Butto誓ovefromaratioof2:1to1:2 whenthereare200blackand100whitestonesrequlreSdrawing300whitestones

inarow,aneventwithavanishinglysmallprobability(8.3×10~84tobeprecise).

356

FIGURE10-3 Tenrealizationsof

thePolyaprocess

FIGURE10-4

Equilibrium distributionofthe

Polyaprocess

Histogramshows

theproportionof

b一ackstonesby decHeafter500

periodsin10,000 simu一ations.The

distributionis

quiteuniform:

A一lproportions

areequallylikely

inequilibrium.

PartIIITheDynamicsofGrowth

s a

uo tsと Ot2Ig 10 u O !Ij Odo J d

O芯 e H q

Lu ]S -0 u O

] 1

0 t= Jl比

50 100 150 200 Time(periods)

0.12

0.10

0.08

0.06

0.04

0.02

0.00

)

ProportionofBlackStonesafter500periods

Themorestones,thelesslikelytherewillbeanymovementawayfromthecurrent

proportion:thesystemlocksintowhateverbalanceemergesfromitsearlyhistory･

Polyaprovedthattheprocesswillalwaysconvergetoafixedproportionof

blackstones,andthattheparticularproportiondependsonthehistoryofthe

randomeventsalongtheway.Polyaalsoprovedtheremarkableresultthatthedis-

tributionoffinalproportionsisuniform,thatis,thefinalfractionofblackstonesis

equallylikelytobeanywherebetween0and1･4Figure10-4showsthedistribution

oftheproportionofblackstonesafter500periodsinasetof10,000simulations･

Thedistributionisnearlyuniform:Allproportionsofblackstonesareequally

likelylnthel10ngrun(seeArthur1994IrOrfurtherexamples)･ 1●11

4Thedistributionisuniformonlyforthespecialcasewherethenumberofstonesaddedper periodisoneandthejarinitiallycontainsonewhiteandoneblackstone･Otherinitialconditions orrulesforselectlngthenumberandtypeofthestonesaddedleadtodifferentequilibriumdistri- butions.JohnsonandKotz(1977)provideacomprehensivetreatmentofummodelsofthistype･

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-5 Phaseplot forthelinear

Polyaprocess Thelineshows

theprobabilityof addingablack stoneasafunction

oHheproportion ofblackstones.

Everypointonthe Fineisanequi‖b- rium;everyequl- 1ibriumpointhas neutralstability.

auo IS ¥ U t2I t) e B u!p p v

- o ^ )!J!q E2q O J d

0 ProportionofBlackStones

357

10.2.1 Genera他ingtheMode!:

NonlinearPo!yaProcesses

ThePolyaprocessillustrateshowpathdependencecomesabout,butitisavery specialmodelwithanumberofrestrictiveandunrealisticassumptions.First,the

dynamicsdependonthefactthattheflowsarequantized:Thoughstonesareadded withprobabilitiesinproportiontotheirprevalenceinthejar,eachstoneiseitherall

blackorallwhite.Eachperiodtheproportionofeachcolormustchange.Ⅰnstead

ofajarofstones,imaginefillingthejarwithblackandwhitepalntmixedinpr o -

portiontothecurrentshadeofgrayinthejar.Theshadeofgraywouldnever

change,nomatterwhatitwasinitially(youcanapproximatethecontinuoustime, continuousflOwsituationinthemodelshowninFigure10-2byallowingfractional stonestobeaddedperperiodorreducingthetimestepbetweenperiods).Second, theprobabilityofaddingaparticularcolorislinearintheproportionofthatcolor

(Figure10-5).Thefunctiondefiningtheprobabilityofaddingaballofagiven colorliesexactlyonthe45oline,SoeverypolntOnthelineisanequilibrium.In

general,however,thedecisionrulesdeterminlngtheflowsinpath-dependentsys- temsarenonlinearfunctionsofthestatevariables.

IftheprobabilityofaddingastoneofaglVenCOlorisanonlinearfunctionof

theproportionwiththatcolor,thenumber,locationandstabilityofequilibria,and thedynamicsallchange.

Supposetheprobabilityofchooslngablackstoneischaracterizedbythenon-

1inearfunctioninFigure10-6･Thesystemnowhasonlythreeequilibria(points

358

FIGURE10-6 NonHnearPolya Process

Theprobabilityof choos】ngablack stoneisnowa nonlinearfunction

oftheproportion ofblackstones

inthejar.The systemhasthree equilibria.

PartIIITheDynamicsofGrowth

a u o IS q 3 e lg

e 6 u !p p v

1 0 )̂

!l!q e q O J d

ProportionofB一ackStones

wheretheproportionofblackstonesandtheprobabilityofaddingablackstone areequal):0,0.50,and1.Thepointszeroandloo鞄∬eequilibria:Ifthejarisall blackorallwhite,itwillremainso.Likewise,whentheproportionofblackstones

isone-half,theprobabilityofchoosingablackstoneisone-half,so(onaverage)

theproportionofstonesremainsconstant.Whentheproportionofblackstones risesabovehalf,however,theprobabilityofchoosingblackincreasesmorethan proportionately,andwhenitislessthanone-half,itfallsmorethanproportionately.

Theequilibriumat0.50isunstable:Ifthefirststoneaddedisblack,theprobabil- ityofaddingmoreblackstonesincreasesdramatically,movingthesystem(onav- erage)towardthestableequilibriumat100%blackstones.Similarly,ifthefirst

stoneiswhite,theprobabilityofdrawlngmoreWhitestonesincreasessharply,and thesystemwilltendtowardthestableequilibriumofallwhitestones.Ofcourse, sincethesystemisstochastic,Sometimesarunofonecolorwillmovethestateof

thesystembackacrosstheratio1:1. Figure10-7shows10realizationsofthenonlinearPolva1)rOCeSSShowninFig-

ure10-6.Alltrajectoriesmoverapidlyawayfromtheinitialratioof1:1,andafter

200periods,thejarisnearlyallonecolorortheother･WherethelinearPolya processhasaninfinitenumberofequilibria,thisnonlinearprocesshasonlythree; ofthese,onlytwoarestable.Yetthesystemisstillstronglypathdependent:which

ofthetwostableequilibriadominatesdependsentirelyonthehistoryoftheran- domeventsasthesystemevolves.Likethelinearprocess,thesystemlocksinto

whicheverequilibriumthepositiveloopreinforces,asdeterminedbythechance

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-7

Dynamicsofthe non=nearPolya Process

Thesystemtends towardaHone co一ororaIHhe

other,depending ontheearlyhis- toryofrandom events.Notethe

trajectoryShown withaheavylHle wheretheear一y leadofwhite stonesisreversed

byarunofblack, leadingthesystem toJockintothe

predominantly blackequilibrium. Therearizationsof therandomdraw inthesesimula- tionsarethesame

asinFigure108

s Q u

OtS q3 t21 g

1 0 u

O菅Od o左

50 100

Time(periods) 150 200

359

eventsearlyon.NotethetrajectoryinFigure10-7(shownasaboldline)wherethe

Jarismostlywhiteinthebeginnlng,butduetoarunofblackstones,theratiore-

versesafterabout30periods.Thepositivefeedbacksthenfavorblackstones,and

thejarsoonlocksintothepredominantlyblackequilibrium.

Lockinismuchswi氏erandstrongerinthenonlinearsystem.Inthelinear

case,thesystemhasneutralstability:Everypointisanequilibrium,andnoneof

thepointsisbetterthananyother.Inthenonlinearexamplehere,thetwostable

equilibriaarestrongattractors.Thepositivefeedbackcontinuestodominatethe

dynamicsevenastheproportionofaglVenco一orincreases･Likethetworaindrops

fallingoneithersideofthecontinentaldivide,trajectoriesoneithersideofthe

50%pointareattractedonaveragetowardoneofthestableequilibriumpoints･

Thejarendsupnearlyallonecolor-winnertakeall･

riO.3 PATHDEPENDENCELNTHEEcoNOrtJIY:VHSvERSuSBETAMAX

Ⅵdeocassetterecorders(VCRs)areubiquitousinhomes,businesses,andschools.5

Youcanbuyorrentvideosatnearlyeverymallandmainstreet.Thefilmindustry

earnssignificantrevenuefrom salesofvideorights,andmanyfilmsaremade

directlyforthehomevideomarket,neverenjoyingtheatricalrelease･Muchofthis

successdependsonthecommonformatusedbythevastmaJOrltyOfVCRs,known

asVHS,whichensuresmachinesmadebydifferentcompaniesarecompatible

withoneanotherandwiththetapesavailableinthemarket･6How didVHS becomethestandard?

5TheVCRindustrydataandhistorypresentedherearebasedinpartondatacollectedanda modeldevelopedbyEdAnderson(personalcommunication,1996)･Ⅰ'mgratefultoEdforpermis- siontousehisdataandmaterials.

6whileVHSisnowthestandardfor1/2inchVCRsaroundtheworld,differentreglOnSdo useincompatibleslgnalformats.NorthAmericausestheNTSCformatwhileEuropeusesthe PALformat.

360 PartIIITheDynamicsofGrowth

VHSwasactuallyalatecomertothehomevideorecordermarket.Homevideo recordingtechnologycameofagein1975whenSonyIntroducedtheBetamaxsys- tem.Offeringordinarypeoplethechancetorecordtelevisionbroadcastsandplay moviesinthecomfortoftheirownhomes,VCRssoonbecamethehothomeelec-

tronicsproductofthelate1970sandearlySOS(Figure10-8).Asiscommonincon- sumerelectronics,largerproductionvolumes,learnlngeffects,andincreasing competitionledtohugepricedropsforVCRsevenastheirfeaturesandfunction- alityIncreased.Demandsoared.By1994,about85%ofUShouseholdsownedat leastoneVCR,andsaleshadreached13millionunitsperyearintheUSalone. VCRadoptioninEuropeandtherestoftheworldfollowedsimilardynamics.

WhenVCRsfirstbecameavailable,aprlmeuseWas"timeshifting"-the recordingofbroadcaststobeplayedbackatamoreconvenienttime.Timeshi氏ing alsomadeitpossibletofast-forwardthroughcommercials.Withinafewyears,

however,theprlnClpaluseofVCRsbecametheplaylngOfprerecordedtapes-

films,musicvideos,exercisetapes,andsoon･SalesofprerecordedtapesintheUS explodedtomorethan80millionperyearby1994,andthevideorentalindustry tookoff(FigurelO18).

ThedatafortheaggregateVCRmarketconcealthefightfordominance amongdifferentVCRformats.Sony'SproprietaryBetamaxtechnologywasthe firstcassette-basedhomevideotechnologytoreachthemarket,some18months aheadofitsprlnClpalrival,theVHSstandardlaunchedbyaconsortiumofMat- sushita,JVC,andRCA(Cusumano,Mylonadis,andRosenbloom1992).Though BetamaxandVHStechnologiescostaboutthesame,thetapesandmachineswere notcompatible.Consumershadtochoosewhichstandardtoadopt.Theattractive- nessofeachformatdependsonvariousfactors,includingprlCe,Picturequality, playtime,andmachinefTeaturessuchasprogrammability,easeofuse,size,andre- motecontrol,amongothers.

Themostimportantdeterminantofproductattractivenessiscompatibility.To swaptapeswiththeirfriendsandfamiliespeoplehadtohavecompatiblema- chines.AstheinstalledbaseofmachinesofaglVenformatincreased,theattrac-

tivenessofthatfo-attopotentialnewbuyersincreased,whichinturnincreased themarketshareofthatformatandboostedtheinstalledbaseevenfurther.Even

moreimportantly,peopletendedtobuymachinescompatiblewiththebroadestse- lectionofprerecordedtapes.Videorentalshopschosetostocktapesinthemost commonformatsincethesewouldrentmoreoftenandyieldmoreprofit.Movie studios,inturn,chosetooffertheirfilmsintheformatcompatiblewiththemost populartechnologyandtheordersplacedbythevideostores･

Thesepositivefeedbacksmeanthattheformatwiththelargestinstalledbase ofmachines,allelseequal,willbethemostattractivetoconsumersandcontent providers.Uncheckedbyotherloopsoroutsideevents,thesepositivefeedbacks confergreaterandgreatermarketshareadvantagetotheleader,untiloneformat completelydominatesthemarketandtheotherdisappears.AsshowninFigure 10-9,thisispreciselywhathappened.Bythelate1970sVHShadgainedamar- ketshareadvantageoverBetamax.SoonthemajorityOfprerecordedtapeswere alsocomlngOutintheVHSformat.VHSmarketshareandsalescontinuedto growwhiletheBetamaxsharesteadilyshrank･By1988thetriumphofVHSwas

FIGURE10-8 DiffusionofVCRs intheUS

Chapter10 PathDependenceandPositiveFeedback

SalesofVCRsandPrerecordedTapesintheUS

(Lt2

0̂Ju O!lJ!∈ ) S a l t2

S ∝ 3 ^

1975 1980 1985 1990 1995

FractionofUSHouseho一dswithatLeastOneVCR

SP I0 LJa S n O H I0

1 u a 3 Jla d

2500

2000

_ 1500 ⊂ =〉i::I 坊 1000

500

1980 1985 1990 1995

AveragePriceofVCRs

1975 1980 1985 1990 1995

Source:Anderson(1996).

T a p e S a l e s

(m iHio nJy ea

r )

361

complete.SonywasforcedtoabandonBetamaxtechnologyforthehomemarket andin1988announcedthatitwasswitchingitsProductlinetotheVHSformat.

ThestrongeffectofcompatibilityonproductattractivenessexplainshowVHS rapidlyachieveddominanceoverBetamax-onceitachievedaleadinmarket

362

F】GURE10-9 Betamaxvs. VHSformats inthehome VCRmarket

PartIII TheDynam icsofGrowth

USSa一esofVCRsbyFormat

2aN S l!u n uO ≡ !≡

√+㌔

㌢ Tota川CRSales

i?'＼ vHS /

㌢

y# '〆.,〆′....ノ Beta

1975 1980 1985 1990 1995

USSa一esofPrerecordedTapesbyFormat

人U

( L t2a Ĵ

uO ! l l E

u l)

S a 】 e s

a d t2 ト

PaPJO OaJ a J d

1975 1980 1985 1990 1995

MarketShareofVHSFormatVCRsandTapes

( %

)

巴

LIS laqj t2 m

vHSsSaTea:eミ /'〈＼ vTHaSpeShsaarEesofや-＼ vHSShareof

1975 1980 1985 1990 1995

Source:Anderson(1996).

shareandintheshareoftheinstalledbase.Buttheexistenceofstrongpositivenet- workandcompatibilityeffectsdoesnotexplainhowVHSfirstachievedthatlead. AcloselookatthedatainFigurelO19showsthatfromitsintroductionthrough 1980,aperiodof5years,Betamaxwasthemarketshareleader.Asthefirstprod- ucttomarket,Betamaxshouldhavebeenabletousethepositivenetworkand compatibilityfeedbacks,alongwithlearnlngCurves,SCaleeconomies,andother

Chapter10 PathDependenceandPositiveFeedback 363

PositivefTeedbacksfavorlngtheearlyleader,togalnaCOmmandingadvantageand preventlaterentrantsfromsucceeding.Whathappened?

InthePoly乱modelofpathdependence,randomeventsearlyinthehistoryof

asystemcantipthesystemtowardoneoutcome.AsseeninFigure10-7,theseran- domeventscansometimesreversetheratioofcoloredstonesinthejar.Perhaps Beta'sfailurewasjustbadluck;perhapschanceledtoarunofeventsfavoring

VHS,destroylngSony'Searlylead.Suchanexplanationisunsatisfying.Unlikethe randomselectionofstonesinthePolyaprocess,electronicsmakersdidnotflip

coinstodete-inewhichtypeofVCRtomakeandcustomersdidnotspinaWheel offわrtunetodecidewhichfbmattobuy.Therandomshocksinapath-dependent systemstandforeventsoutsidetheboundaryof血emodel-thatis,thoseevents

forwhichwehavenocausaltheory.AgoalofmodelinglStOexpandtheboundary ofourmodelssothatmoreandmoreoftheunexplainedvariationinthebehavior ofasystemisresolvedintothetheory.

TherearemanytheoriestoexplainhowBetamaxlostitsearlylead.Klopfen-

stein(1989)notesthatVHSofferedlongerplayandrecordtime(originallythe VHSplaytlmeWas2hourstolhourforBetamax;by1988theratiowas8hours

forVHSto5.5hoursforBetamax).Longerplaytime,Klopfensteinargues,gave VHStheearlyedge.Ⅰncontrast,Arthur(1994)arguesthatBetamaxhadasharper plCturethanVHSandwasactuallythesuperiortechnology.

AnearlyVHSpriceadvantageisanothertheorybutdatasupportlngltare weak.Pricedataarehardtoget,butsuggestthatwhileVHSmachineswereabout

7%cheaperthanBetamaxmachinesin1978,theywereactuallymoreexpensive thanBetamachinesthefollowlng3years.Pricedoesnotseemtobeadecisivefac- torinexplainlnghowVHSovertookBetamax.

Cusumano,Mylonadis,andRosenbloom(1992)pointtothedifferentbusiness

strategiesemployedbySonyandMatsushita.Sony,Seekingtoprofitfromtheir proprletarytechnology,wasreluctanttolicenseBetamaxtootherfirms.Incon-

trast,JVCanditsparentMatsushitaaggressivelysoughtpartnersamongother manufacturers,setlowerlicensingfeesthanSony,andevendelayedtheintroduc- tionofVHSuntiltheyandtheiralliescouldagreeoncommontechnicalstandards.

MatsushitaalsobuiltVCRssoldunderthelabelofotherfirms,speedingproduc- tionrampup.Matsushitathusgainedaccesstothedistributionchannelsofthese firms,andalsogainedlargerproductionvolumethaniftheyhadkepttheirtech- nologyproprietary.Consequently,Matsushitaenjoyedgreaterscaleeconomiesin

distributionandproductionandgainedexperiencethatmoveditdowntheleamlng curvemorerapidly.

Thedevelol)mentOftheprerecordedtape industryplayedakeyrole,Priorto

1977,themaJOrltyofprerecordedtapeswereaimedattheadultentertainmentsec-

tor(similartotheearlydaysoftheworldwideweb)IRCA,Matsushita'slargest customerintheUS,soughttoJump-Startthemarketforgeneralaudiencevideos

andthusVCRsalesbyofferingtwofreeVHStapeswitheachVCRitsold.RCA alsoencouragedfirmssuchasMagneticVideotoinvestinVHSequlPmenttOSup-

plyprerecordedtapesfortheUSmarket.Largescaleproductionofprerecorded Betamaxtapeslaggedbehindbyaboutayear(Cusumano,Mylonadis,andRosen-

bloom1992)･NotefromFigure10-9thattheVHSshareofprerecordedtapepro- ductionactuallyexceedsVHS'sshareoftheinstalledbaseuntil1983,which furtherincreasedtheattractivenessofVHStovideorentalstoresandcustomers.

364 PartIIITheDynamicsofGrowth

Formu5atingI-aDyr!amicHypo紬esisfor

theVCFHn･justry

1.Usingtheinformationabove(andanyadditionalsourcesyouwish)develop acausalloopdiagramtoexplainthedominanceofVHSinthehomeVCR market.Yourdiagramshouldbesimplebutshouldcapturetheimportant feedbacksdescribedabove,bothpositiveandnegative.

2.Useyourdiagramtoexplainwhythemarketconvergedtoasingleformat, andwhyVHSwonthefomatbattle.

3.HowmightSonyhavealtereditsstrategytopreventVHSfrombecoming dominant?

4.Sony'SBetamaxformatlosttoVHSintheI/2inchhomeVCRmarketbut remainsthemarketleaderinthemarketforprofessionalquality3/4inch

equlPmentusedbytelevisionandnewsorganizations･Howdothefeedback structureandstrengthofthevariousloopsdifferintheprofessionalmarket

comparedtothehomemarket?Whatimpactdothesedifferenceshaveon effectivestrategy?

5.SinceVHSbecamethedominantstandard,othertapeformatsandvideo

technologieshavebeenintroducedforthehomemarket,especially

inexpensivecamcorders.Avarietyofcamcordertapeandcassetteformats coexist,including8mm,SuperOrhi8mm,Panasonic'scassettetechnology, andothers.Noneofthesehasbecomedominant.Howdotheusesof

camcordersandthedeterminantsofcamcorderattractivenessdiffer

comparedtothehomeVCRmarket?Howdothesedifferencesaffectthe strengthofthefeedbackloopsinyourmodel?Whatisthelikelyimpactof thesedifferencesonthedynamicsandonstrategiesforsuccessinthe camcordermarket?

10.堵 PosmvEFEEDBAeK:TMEENGENEOFCORPORATEGROWTH

Thenetworkandcomplementarygoodseffectsthatdominatedtheevolutionofthe VCRmarketarebuttwoofmanypositivefeedbacksthatcandrivethegrowthofa

business.Thissectionsurveyssomeoftheimportantpositivefeedbacksthatcan causeafirmtogrow.Sincepathdependenceariseswhenpositivefeedbacksdom-

inateasystem,theprevalenceofpositiveloopsincorporategrowthmeansthatthe potentialforpathde†)endenceintheevolutionofcorporations,industries.andthe

economyasawholeisgreat, Thediagramsbelowpresenttheloopsinahighlysimplifiedformat,focuslng

onthesalesofasinglefirminanindustry.Thediagramsdonotexplicitlyshowthe

competitors,butallfirmsinaparticularmarketarelinkedthrough competitionfor marketshareandthroughmaterialsandlabormarkets,financialmarkets,distribu-

tionnetworks,themedia,andthesocialfabricingeneral.Thediagramsalsoomit

themanynegativefeedbacksthatcanhaltthegrowthofthefirm･

Chapter10 PathDependenceandPositiveFeedback

〟/謡 .sf l.es. ASdS ;

365

10.4.1 ProductAwareness

Howdopotentialcustomersbecomeawareofafirm'sproducts?Therearefour prlnClpalchannels:advertlSlng,directsalese批)rt,wordofmouth,andmedia

attention.Eachofthesechannelscreatespositivefeedbacks(Figures10-10and l0-ll).

Inmostfirmstheadvertisingbudget(supportingads,tradeshows,andthelike)

growsroughlyasthecompanyandrevenuegrow.Largeradvertisingbudgetshave

twoeffects:(1)morepotentialcustomersaremadeawareoftheproductand choosetoenterthemarket(loopRl);(2)totheextenttheadvertisingiseffective, moreofthosewhoareawareandinthemarketarelikelytobuytheproductof-

feredbythecompany(R2)ASimilarly,thelargertherevenueofthefirm,thegreater thesalesbudget.Themoresalesrepresentatives,andthegreatertheirskillandex- perience,themorecallstheycanmake,themoretimetheycanspendwithcus-

tomers,andthemoreeffectivetheircallswillbe,increaslngbothtotalindustry demand(R3)andtheshareofthetotaldemandwonbythefirm(R4).

Whileafin controlsitsadvertlSlngandsalesbudgets,wordofmouthandme- diaattentionarelargelyoutsidethefirm'sdirectcontrol(Figure10-ll).As sales

boosttheinstalledbaseandthenumberofcustomerswhohaveexperiencewiththe product,favorablewordofmouthincreasesawareness,increasingtotaldemand

(R5)andalsopersuadingmorepeopletopurchasetheproductsofthefirm(R6). Ahotproductorcompanywillalsoattractmediaattention,which,iffavorable, Stimulatesadditionalawarenessandboostsmarketsharestillmore(R7-9).There

aremanyprocessesbywhichafirmorproductcanbecomehot(popular)and attractunsolicitedmediaattention.Stronglyfavorablewordofmouthcanstimu-

1atemediacoverage,especiallyforhighlyinnovativenewproductsandproducts

FIGURE10-10 Advertisinganddirectsaleseffondriveawarenessoftheproduct.

J) sales///ー~､､＼＼素 Revenue

.;;

Sharefrom Advertismg

Market Share

4..＼㌣-｣ dve蜘 g/ 鯉 ,i Sharefrom SaJesEffort

Industry AwaXness Demand fromAds

㌍･号も+

Attractiveness

366 PartIIITheDynamicsofGrowth

FlGURE10-11 Howwordofmouthandmediareportscreateahotproduct

thatshowwellontelevision.Rapidgrowthofsales,revenue,pro恥 Orstockprice canalsoattractmediaattentionandturntheproductintoasocialphenomenon.

Amazon.Comprovidesaprominentexamplefromthelate1990S.

Productshortages-andtheprlCegOuglng,prOfiteerlng,andnearriotstheycan create…alsoattractmediaattention.ShortagesareespeciallyImportantincreating

theimpressionaproductishotforconsumergoodssuchastoys(recentexamples includeBeanieBabiesandFurbies).Footageoffrenziedshopperstramplingeach

othertogetthelastTickleMeElmotheweekbeforeChristmascanmultiplythe crowdsatthemallexponentially.

Thestrengthoftheseloopsdependsofcourseontheattractivenessoftheprod- uct;anexcellentproductofferedatagoodpriceWillbeeasiertosellandwill generatemorefavorablewordofmouththananoverpriced,poorqualityproduct･ Whichofthesechannelsofawarenessdominatesdependsonthepartictllarprod- uctandmarket,andnotallfirmsutilizeallthreechannels.Fastfoodchainsdonot

haveadirectsalesforceandrelyinsteadonadvertising(andwordofmouth);

specialtytoolmakersfocustheirresourcesondirectsaleseffortandadvertise muchless.

ThetimedelaysandstockandflOwstructureofthesefourchannelsofaware-

nessalsodiffer.ThedelaysinstartlngandstopplngadvertisingCampaignsare shortrelativetobuildingacompetentandskilledsalesforce.Wordofmouthis weakwhenanewproductisfirstlaunchedbutcangrowrapidlyanddominatethe

Chapter10 PathDependenceandPositiveFeedback 367

FIGURE10-12 SpreadingfixedcostsoveralargervolumelowerspriceandIeadstolargervolumesl

6 玩 lndustry Demand 主=:I‥DemandfromSpreadingFixedCosts

Market Share

㌔ Product

+ Sales~一一一一

主=:I-

Share from

Spreading FixedCo sts

Attr.activeness

Expected Mar.ketSize

FixedCostsof

Developmentand

unkixed( Costs

UnitCosts

L __priceオ /

Production

1L UnitVariable + costs

Sourcesofinfomationavailabletothemarketastheinstalledbasegrows.Theme-

diaspotlighttendstoburnverybrightforashortwhile,thenfadesastheattention ofeditorsandaudiencemovesontothenextobjectofdesire.

Further,whilethestrengthoftheadvertlSlnganddirectsalesloopsareunder thedirectcontrolofthefirm,thewordofmouthandmedialoopsarenot.Wordof mouth(favorableandunfavorable)isdifficultforafirmtocontrol,thoughfirms

canstimulatecommunicationamongcurrentandpotentialcustomersbysponsor- 1nguSerS'groupsandconferencesandbyhiringopinionleadersasspokespeople.

Similarly,thoughmanyfirmstodayarehighlyskilledinmediarelations,thereis nosure-firewaytogetyourproductfeaturedonanetworkmagazineshoworalist ofhotwebsites.

■沌 4.2 IJnitDeveiopmenモCosts Manyproductsandservicesinvolveconsiderableup-frontdevelopmentandca-

pacityaCqulSltlOncosts.Thegreatertheexpectedlifetimesalesoftheproduct,the

lowerthefixedpricePerunit,andthelowerprlCeCanbewhilestillachievingthe requiredreturnoninvestment(Figure10-12).Lowerpricesstimulateindustryde-

mand(RIO)andleadtoagreatershareofthattotal(Rll),boostingsalesandcut- tingfixedcostsperunitstillmore.

Thelargertheup-frontcostsofproductdevelopmentandproductioncapaclty,

thestrongertheseloopswillbe･Inalabor-andmaterials-intensiveindustrysuch assubsistenceagrlCulture,fixedcostsaresmall.Intechnology-andknowledge-in-

tensiveindustriesinvolvingsignificantproductdevelopmenteffort,nearlyallthe costsareincurredpriortoproductionofthefirstunit.Developlnganewautomo- bileorcommercialaircraftcostsseveralbilliondollars;allthedesignanddevell

opmentcostsandallthecostsforcapaclty,tOOling,trainlng,andmarketingmust bebornebeforejobonerollsofftheline.There'sasaylnginthesemiconductor

368 PartIII TheDynamicsofGrowth

industrythatitcostsafewbilliontomakethefirstchip,butthenalltherestare free.Softwaredevelopmentistheparadigmcase:Astheintemetexpands,themar- ginalcostofdistributionisrapidlyapproachingzero,whileup-frontdevelopment costsarerlSlng･

Theindustriespowerlngtheworldeconomyareincreaslnglyknowledge based,andupjrontcostscaptureagrowingShareofthetotalcostsofproduction･ Inaworlddominatedbythesepositiveloops,traditionalru1esofthumbforprlClng nolongerapply.Notehowfixedcostperunitdependsonexpectedvolume.When theseloopsdominatethedynamics,expectationsabouthowlargelifetimevolume willbecanbestronglyself-fulfilling.Imaginetwofirmswithidenticalcosts launchingidenticalproductsatthesametime.Oneexpectstowinabouthalfthe marketandestimatesmarketpotentialconservatively,believlngltCanlowerpnces asvolumeexpands.Theotherexpectstowinthedominantshareofthemarketand believeslowerprlCeSWillgreatlyexpandtotaldemandforthecategory･Theag- gressivefirmthereforesetspricesmuchlowerthantheconservativefirmand mighteveninitiallysellataloss.Theaggressivefirmwinsthelargestshareofthe market,whichallowsittolowerpricesStillfurther,whiletheconservativefirm findssalesofitsproductaredisappointing.Theexpectationsofbothfirmsareful- filledandtheirmentalmodelsarereinforced･.Theaggressivefirmlearnsthatprl C -

1nglow,evenbelowcurrentunitcosts,Canleadtomarketdominanceandhuge profits,whilemanagersattheconservativefirmlearntobeevenmorecautious aboutprojectingsales;aclassicexampleofaself-fulfillingprophecy(Merton 1948/1968).

Thoughnotshowninthediagram,expectationsoflifetimevolumecandepend notonlyoncurrentsales,butalsoonforecastsofpotentialindustrydemand,mar- ketresearch,andknowledgeaboutthedevelopmentofcomplementarygoods･ ManyoftheseotherpossibleInputstOa丘rm'sbeliefaboutmarketpotentialalso closepositiveloops.Softwaresalesforecastsriseastechnicalprogressincomputer hardwareleadstofasterandcheapercomputers;lowersoftwareprlCeS,inturn, stimulatethedemandforhardwarethathelpsmakethatbeliefareality.

10.4.3 PriceandProductionCost

Spreadingup-frontdevelopmentcostsoveralargervolumeisnottheonlywayto lowerunitcosts.Figure10-13showsthepositiveloopscreatedbyeconomiesof scaleinproduction,economiesofscope,1earnlngCurves,andprocessinnovation･

Economiesofscaledifferfromthedevelopmentcostloopsdiscussedabove.In manyindustries,unitcostsfallasthescaleofproductionrises(atleastuptoa point).Largerpapermills,oilrefineries,andthermalpowerplantsareo鮎nmore efficientthansmallerones.Thereareboththermodynamicandorganizationalrea-

sons.Largerboilers(e.g･,inacoal-firedpowerplant)havealargerratioofvolume tosurfaceareaandthereforehigherthermalefficiency.Inaddition,everypaper

mill,oilrefinery,andpowerplantrequiresinstrumentation,safetysystems,loglS- ticscapacitytOhandleincomingandoutgolngmaterials,andotherfacilities;sim- ilarlyeverybusinessmusthaveacertainminimalamountofadministrativestaff andoverhead.Thecostoftheseactivitiesusuallydoesnotriseasquicklyaspro- ductionvolume,sofirmscanlowerprlCeSaStheygrow,whichcreatesopportuni- tiestoincreasethescaleofoperationsfurther(R12)･Theopportunitytorealize

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-13 Scaleandscopeeconomies,learningcurves,andprocessimprovement

Eacheffectcreatestwopositiveloops:OneincreasessalesthroughmarketsharegalnS,andone increasessa一esthroughexpansionofthetotalsizeofthemarket.

i.柚子IndustryDemandShare

:㌧ +1Product

saResく√-宣 Breadthof

ProductLine

う

ScaieofOperations ▲R13･EconomleSofScopeARi2:.EconomiesofScale

Attractiveness

＼＼ price璽電i 十

UnitCosts

Investmentin Process

Improvement

Cumulative

Experience

369

Process

lmprovement

sucheconomiesofscalebyconsolidatinggeneral,administrative,andoverhead

functionsisapowerfuldriverofmergersandacquisitions(Seesection10.4.8).An-

otherpowerfulsourceofscaleeconomiesarisesfromdivisionoflabor.Largeror-

ganizationscanaffordtodividetheworkintoincreaslnglyspecializedtasks.Ithas

longbeenobserved(atleastsinceAdamSmith'sfamousdiscussionofapinfac-

toryinTheTVealthofNations)thatdivisionoflaborboostsindividualproductivity andleadstolowerunitcosts(Seesection10.5).

Economiesofscope(R13)arisewhenafirmisabletosharecapacity,labor,

technicalknow-how,andotherresourcesacrossmultipleproductlinesandbusi-

nessunits･Cabletelevisioncompaniescanofferhigh-speedinternetaccessuslng

thesamecablenetworkwithlowincrementalcapitalcosts.Shoppingmallsandso-

calledcategorykillersinofficesupplies,toys,hardware,andotherretailmarkets

reducedunitcostsdramaticallybyofferingahugerangeofproductsunderone

verylargeroof.TheseHbigbox"retailersalsoreducedsearchcostsfortheir

customersbyprovidingone-StopshoppingjustOffthefreeway,whichboosted

productattractivenessandmarketshareattheexpenseofthesmallerstoreson MainStreet.7

LearnlngCurvesalsocreatepositiveloopsfavorlngtheleadingfirm.Learnlng

(orexperience)curveshavebeendocumentedinawiderangeofindustries,from

commercialaircrafttobroilerchickens(Teplitz1991).Theleamingcurvearisesas

workersandfirmslearnfromexperience.Asexperiencegrows,workersfindways

toworkfasterandreduceerrors.Typically,theunitcostsofproductionfallbya

7Thecostsofmalls,intermsoftrafficcongestion,decayofthecentralbusinessdistrict,andso onareallexternalized,lowerlngtheirapparentcostsbelowtheirtruecoststothecommunlty･

370 PartIIITheDynamicsofGrowth

fixedpercentageeverytimeCumulativeproductionexperiencedoubles･8Forex-

ample,costsmightfall30%Witheachdoublingofcumulativeoutput.Learnlng

curveswith10-30%improvementperdoublingofexperiencearetyplCalinmany industries.LowerunitcostsenablelowerprlCeS,increasingbothmarketshareand industrydemand(R14)andboostingsalesstillmore.

Finally,thelargerthefirm,thegreateritsinvestmentinresearchanddevelop-

mentleadingtoprocessinnovationsthatlowercosts(R15).Suchresearchcanin-

cludethedevelopmentofmorehighlyautomatedtooling,morereliablemachines,

andmoreefficientplantlayout･ItcanalsoincludetraininglnProcessimprovement techniquessuchastotalqualitymanagementwhichenhancetheabilityofworkers todetectandcorrectthesourcesofdefects,thusboostingPrOductivltyandlower-

1ngCOStS･

ThedelaysandstockandflOwstructureofscaleandscopeeconomiesdiffer fromlearningCurvesandprocessimprovement.Scaleandscopeeconomiesde-

pendonthecurrentvolumeofsalesandbreadthofthefirm'sactivities･Anacqui- sition,forexample,canquicklyboostscaleandscope.Similarly,ifthefirm shrinks,itsscaleandscopeeconomiesarequicklylostandthepositivefeedbacks

reverse,speedingthedeclineinthefirm'sattractiveness･Leamingbydoing,R&D,

andtheresultsofprocessimprovementareembeddedintheorganization'scapltal stock,workerknowledge,androutines.Theyareslowertodevelop.Andifsales turndown,cumulativeexperienceandprocessproductivltytendtopersist,decay- ingmuchmoreslowly(thoughtobesure,know-howandexperienceareoftenlost, dependingonhowthefirm downsizes).

10･4A･ NetworkEffeclsさndComp!ementaryGoくさds

AsillustratedbytheVCRindustry,theutilityofaproductoftendependsonhow manyothersarealsousingit(thenetworkeffect;R16inFigure10-14)andon

theavailabilityofcompatibleproductstousewithit(thecomplementarygood effect;R17).

Compatibilityandnetworkeffectsboostproductattractivenessandthusex-

pandthetotalsizeofthemarket(justasthegrowthoftheinternetmadecomputer ownershipmoreattractive,leadingmorepeopletousetheinternet).Theseloops

tendtofavorthemarketshareleaderwithinanindustry,assumingCOmPetlngProd- uctsareincompatible.BesidesVCRs,theclassicexampleoftheseloopsinthe 1980sand90SwasthebattleforcontrolofpersonalcomputeroperatingSystems,

particularlytheeclipseofthetechnicallysuperiorMacintosharchitectureby血e Wintelplatform.

Justasinthecaseoffixedcosts(section10.4.2),t-1edecisionbythirdparties

toproducecomplementarygoodsforaparticularproductdependsontheirexpec- tationofthemarketpotential,andhencetheexpectedprofitability,ofthatplatform.

Firmscanshapethoseexpectationsinavarietyofways,includingearlysharingof technicalspecificationswithpotentialthirdpartydevelopersandsubsidiesfor adoptionOftheplatform.OtherstrategiesincludeconsortiaandjointVenturesWith

BsometimesthelearnlngCurveisformulatedasdependingoncumulativeinvestmentratherthan cllmtllativeproduction,asinArrow(1962).

Chapter10 PathDependenceandPositlVeFeedback

FIGURE10-14 NetworkandcompatibHityeffects

Eacheffectcreatestwopositiveloops:OneincreasessalesthroughmarketsharegalnS,andone increasessalesthroughexpansionofthetotalsizeofthemarket,

Jndustry MarketShare

De･ml pip:duct Attractiveness

㌣＼ i,ttrSchiev.ewn.erskS Size

Attractivenessfr10m

Availabilityof Complementary

Products

ARj_7I.

E xpected M arketSize

と.

complementary Attractivenessof Goods MarkettoThird

Parties

Complementary Goods

371

thirdparties(e.g.,theformationbyMatsushitaoftheVHSconsortium),horizontal andverticalexpansionintothemarketsforcomplementaryproducts(e.g.,Sony'S

purchaseoffilmstudiostocontrolcontentandmediafTortheirhardwareproducts, orIBM'spurchaseofLotus),andfreedistributionofcomplementarygoods(e･g･,

Netscape'sdecisiontoglVeawayItsWebbrowsertostimulatesalesofitsserver software,astrategysoonimitatedbyMicrosoft).Inthesoftwareindustry,Some firmsstrateglCallytimetheannouncementofnewproductstopreempttheirrivals

andinfluencethirdpartydevelopers,sometimesevenannounclngthenearavail- abilityofvaporware(productsthatdon'tyetexisteveninprototypefわrm).When

thenetworkandcornplementarygoodsloopsarestrong,expectationsaboutwhich platformwillultimatelytriumphcanbestronglyselfjulfilling.

10.4.5 ProductDifferentiation

Anothersetofpositivefeedbacksarisesfromtheabilityoffirmstoinvestinprod- uctdifferentiation(Figure10-15).Asfirmsgrow,theycaninvestmoreinactivities

thatimprovetheattractivenessoftheirproductstocustomers･Mostproductscan bedifferentiatedfromthoseofcompetitorsthroughenhancedfeatures,function-

ality,design,quality,reliability,andsuitabilitytothecurrentandlatentneedsof

372 PartIH TheDynamicsofGrowth

FIGURE10-15 Productdifferentiation

lndustry Demand

PricePremium

forSuperior Technology

-'=i; ProductDjfferentiatjon(TotalDemandEffect)

Markr Share

て+

Product Attractiveness

Sales

三重ミ Product

Differentiation (ShareEffect)

告＼ー_ノE聖t

lnvestmentin Product Features

/ Features:

aFunctionality 'SuitabilitytoCustomerNeeds 'QualityandReliability 8ServiceandSupport IOtherAttributes

customers.Firmscanalsoinvestinsuperiorserviceandcustomersupportinfra-

structure･Totheextenttheseinvestmentsincreasetheattractivenessoftheprod- uctsintheeyesofcustomersthefirmcangalれmarketshare,boostingrevenueand enablingstillmoreinvestmentindifferentiation(R18).Morecapableanduseful

productsalsoincreasetotaldemand(R19).Finally,companiesofferingclearlysu- periorproductscanoftenchargeaprlCePremiumwithoutchokingoffgrowth.The highermarglnSenabledbysuchapricePremiumenablethefirmtoincreaseitsin- vestmentindifferentiationstillfurther(R20).

Manyhigh-techfirmsareengagedinatechnologyraceinwhichcompetition isprimarilyfocusedontheearliestintroductionofthefastest,mostpowerfulprod- uctwiththemostfeatures.Butdifferentiationdoesnothavetofocusontechnoll

ogyandproductfeatures.IBMsuccessfullypursuedthedifferentiationstrategyfor

decadesanddominatedthecomputerindustryfromitsinceptionthroughtheper- sonalcomputerrevolutioninthe1980S.IBM'sdifferentiationinvestments,how-

ever,focusedonproductreliabilityandespeciallyoncustomerserviceand support.TomWatson,Jr.,likehisfather,understoodthatthemostimportantdeter-

minantofproductattractivenessfortheircoremarket-middlemanagersinlarge corporations-waspeaceofmind.Especiallywhencomputersanddataprocessing werenovel,inthe1950sand60S,theseorganizationswerereluctanttoinvestin

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-16

Newproduct deve一opment createsnew

demand,boosting development resources.

Price

孟_≡ PricePremium forUniqueness

PricePremiumfor

UniqueNew Products

′ 二二童Sales

'F hdustry Demand

Venue

主王NewUses,NewNeeds

373

㌔ .ProductDevelopmentCapabilityandEf書or.t 二㌧＼ー New 〆

Products

computlngunlesstheyweresureitwouldbehighlyreliableandthatwhensome-

thingwentwrongtheycouldgetitfixedquickly. IBM focuseditsdifferentiationstrategyonproductqualityandreliability,

buildingthelargestandmostresponsivesalesandserviceorganizationinthebusi- ness.Itssuccessnotonlyenabledittogainmarketshareandincreasethesizeof

thedataprocesslngmarketbutalsotochargethehighestprlCeSintheindustry.

Otherfirmsenteredthemainframebusiness,somecreatedbyformerIBMpeople (e･g･,Amdahl),butcouldnevergainmuchmarketshare,eventhoughtheyoffered lowerprlCeSformachinesofcomparableperformance.IBMmaintaineditsdomi- nanceofthemainframeindustrybycontinuouslyinvestinghugesumsinfurther developmentandarticulationofitsserviceandsupportin丘.astructure,evenwhile

generatingCOnSistentlystrongprofitgrowthforitsshareholders.Ofcourse,while

IBM'sdifferentiationstrategywasspectacularlysuccessfulfordecades,allposi- tiveloopseventuallyencounterlimits,andthecompanystumbledbadlylnthe

1980swhenitfailedtoantlCIPatethefundamentalchangesinthecomputerindus- trycausedbythemicroprocessorandpersonalcomputerrevolution.

10.4.6 NewProductDeve!opment

ThedevelopmentofentirelynewproductsisacoreenglneOfgrowthformany firms(FigurelO116).Thegreatertherevenueofafirm,thelargerandmoreeffec- tivethenewproductdevelopmenteffortcanbe.Newproductscreatenewdemand,

boostlngrevenueandincreaslnglnVeStmentinnewproductdevelopmentstillmore

(R21)･Andjustasdifferentiationenablesfirmstochargehigherprices,firmsthat bringnovelandimportantproductstomarketcanoftencommandaprlCePremium untilimitatorsarrive.HigherprlCeSfurtherincreasetheresourcesavailabletofund

thedevelopmentofstillmorenewproducts(R22),sothe丘rmcanstayaheadof competitors.

374 PartIII TheDynamicsofGrowth

Intelhassuccessfullyusedthesenewproductdevelopmentloopstofendoff competitionfromclonemakerssuchasAMDandCyrixwhodevelopchipscom-

patiblewithbutcheaperthanlntel'S.Intelinvestsaboutlo啄ofitsrevenueinR&D (morethan$2.3billionin1997),whichenablesittoofferthefastestandbestPC-

CompatiblechipatanytlmeandleadstomoresalesgrowthandmoreR良D.Power hungrycomputerusersarewillingtopayasubstantialprlCepremiumforthelat- est,fastest,mostpowerfulchip.

Thefirmsprofitingmostfromthenewuses,newneedsandpricePremium loopsarethosebestabletoidentifythelatentneedsofpotentialcustomers.They understandwhatpeopledon'tyetknowtheywantorcreateaneedpeopledidnot havebefore-andthenbringproductsaddressingthoseneedstomarketquickly, effectively,andatlowcost.Thecapabilitytodosoisnotsimplyamatterofthe R&Dbudgetbutdependsonthesizeoftheinstalledbaseofusersandthefirm's abilitytocollectandactontheirsuggestionsJtisacompetencebuiltupovertime throughexperienceandthroughinvestmentinproductdevelopmentprocessim- provement･

Thestrengthoftheseloopsalsodependsontheabilitytoprotectinnovative newproductsfromimitationbycompetitors.Patentsofferanobviousmethodto protectsuchinnovationsandarecriticaltothesuccessofthenewproductdevel- opmentloopsinthepharmaceuticalindustry,amongothers.Moreimportant,how- ever,istheabilitytoweakencompetitors'abilitytousethesameloops.Intelnot onlychargesaprlCepremiumforitslatest,fastestchipbutalsousesthemarglnS fromthesetopofthelinechipstolowerprlCeSOnOlderprocessorsas,orevenbe- fore,theclonemakersbringtheirchipstomarket.BycuttlngPricesforolderchips, htellimitsthemarglnSOftheclonemakers,Weakeningtheirabilitytousethe positivedifferentiationloopstoerodeIntel'slead.

10.4.7 MarketPower

Thelargerafirm,themorecloutithaswithitssuppliers,workers,andcustomers. Suchold-fashionedmonopolypowerenablesfirmstolowertheirunitcostsand prlCeS,leadingtolargermarketshareandsalesandstillmorebargalnlngpower (R23-25inFigure10-17).

Thebenefitsofmonopolypowerdonotshowuponlyinthefirm'sunitcosts. Supplierswillgive-orbeforcedtoglVe-Preferentialtreatmenttotheirlargecus- tomersondeliverytermsandpaymentschedules,tosharetechnicalknowledge,to respondtocustomerchangerequests,andtomakeotheraccommodationsthatglVe thefirmanadvantageoveritssmallerrivalswhogettheshortendofthestickin termsofsupplierattentionandresources.Forthesmaiierfirms,thepositiveloops actasviciouscycles.Largefirmscanoftenreceivepreferentialtreatmentfrom theirdistributionchannelsandcustomers,asforexample,whenthelargeconsumer productsfirmsdemandthebestshelfspaceinretailoutlets.

Similarly,thelargerafirm'sshareoftotaljobsinacommunity,thefewerop- portunitiesforalternativeemploymentthereare,sojobturnovermayfall,reduc- 1ngtrainlngcosts.Firmswhoseworkershavenoalternativesourcesof employmentnotonlycanpaylowerwagesandbenefitsbutcanalsosavemoney byscrimpingOninvestmentsinworkerhealthandsafety.Sweatshopsarealltoo

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-17 Monopolypowerovercustomers,suppliers,andworkersisself-reinforcing.

Eacheffectcreatestwoloops:Oneincreasesmarketshareandoneincreasestotaldemand.

MarketPoweroverSuppliers u去･.

lndustryMarket Demand share

+㍗ ptr｡d u ct

l竺･PoweroverSuppliers Attractiv eness

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PoweroverLabor 阜垂5･ Powerover Customers

375

Market Powerover Customers

commoninmanyindustries,includingtheapparelindustry,andnotonlyinIn-

donesiansneakerplants.Thecompanytownofthe19thcenturywastheultimate

expressionofthisprocess,where,forexample,asteelorminingcompanynotOnly paidlowwagesbutalsoownedallthehouslngandstoresandchargedexorbitant rentsandprlCeS.Workersoftenfelldeeplyindebt,trapplngthem inwhat

amountedtodefactoslavery.Thesedominantfirmsalsousedtheextraprofitgen- erated丘.omtheirpoweroverworkerstohirePinkertonsandotherpnvatesecurity forcestoputdowneffortstoorganizeorstrike(astrategyAndrewCarnegieem-

ployedeffectivelyinhisPittsburghsteelmills).Suchpracticesstillexisttoday,in thesugarcaneindustry,forexample.Largefirmsalsohavetheresourcestoimport workers丘.omotherreglOnStOensurethebalanceofsupplyanddemandinthe

labormarketcontinuestofavortheemployer,evenasthefirmgrows.Inthe19th century,therobberbaronsbroughtChineselaborerstotheAmericanWesttokeep wageslowwhiletheybuilttherailroads;todaylargeagribusinessesimportwork-

erstoharvestcropsatlowwages.

10,4t8 MergersandAcquisi!ionS Growthcanbepoweredbyacquisitionsofrivalfirms(horizontalexpansion)and ofsuppliersandcustomers(verticalintegration).Thelargerafirm,themorecapi-

tallitcanraisetofinancemergersandacqulSltions.IfacqulSltlOnSCOnSOiidatethe firm'sdominantposition,profitsmayrlSethroughtheexerciseofmonopolypower overlabor,Suppliers,andcustomers,enablingthefirmtobuystillmoreofitsrivals

(R26inFigure10-18).Ifverticalintegrationenablesthefirmtoloweritscosts,it cangainfurthermarketshareandstimulateindustrydemandandgrowstillmore (R27).Acquisitionscanalsoenhanceeconomiesofscaleandscopeorpemit丘rms

toguaranteeasteadyflowofcomplementaryproducts(seesectionslO･4･3and 10.4.4),aprocessimportantintheconvergenceofthefilm,television,entertain- ment,andnewsindustries.Disney'spurchaseofCapitalCities/ABCinthemid

376 PartIIITheDynamicsofGrowth

FFGURE10-18 Self-rejnforclnggrowththroughacquisition

Eacheffectcreatestwoloops:Oneincreasesmarketshareandoneincreasestotaldemand.+ ･---辛

IndustryMarketDemandshare へpr｡dfuc･tAttracl:iveness

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pricey - cUonsi.tsL Customers

1990sprovidedABCwithaccesstocontentforitsentertainmentprogrammlng whileatthesametimeglVingDisneyaccesstoABC'snewsandmagazineshows

tomarkettheirproducts,alongwithanetworkoftelevisionstationstobroadcast theirfilms,videos,andpromotionalspecialS.

Ofcourse,thesynergyoftentoutedastherationaleformergerscanbeelusive.

ManyacqulSitionsfailtolowerunitcosts,stimulateeconomiesofscope,orbuild monopolypower.Negativeloopsarislngfromincompatiblecorporatecultures, overcentralization,orlossoffocuscandilutetheearningsOfthecombinedfirm u1-

timatelyleadingtothedivestitureofthedisparatebusinessunits. TheconsolidationofmarketdominancethroughtheacqulSitionofweakerri-

valshaslongbeenacommonstrategy,mostfamouslyusedinthelatelワthand

early20thcenturiesbythegreattrustssuchasUSSteel,ConsolidatedTわbacco, AmalgamatedCopper,AmericanSmeltingandRefining,NorthernSecurities,and

ofcourse,StandardOiHn1909,accordingtotheCensusBureau,44%ofallgoods intheUSweremadebyjustl%oftheindustrialfirms.Manyofthesecontrolled

morethanhalfthetotalmarketintheirindustries.Thepaceofmerger,acqulSition, andconsolidationinthelatelワthcenturyhasbeensurpassedonlylnthe1980sand

1990S.Theriseofthetrustsinthelatelワthcenturyledtoabacklashintheformof theShermanantitruStactandtrustbusterslikeTeddyRoosevelt(see,e.g.,Mowry 1958).Itremainstobeseenwhetherthesesamenegativefeedbackswillariseonce

agalninresponsetothegrowlngCOnSOlidationofmarketpowerintheglobalecon- omytoday.

10.4.9 WorkforceOuaZityandLoyaはy Theabilityofafirmtooffersuperiorproductsandservicedependsonthecom-

mitment,skill,experience,andqualityofitsemployees･Themoreprofitablea firm,thehigherthewagesandbenefitsitcanpaytorecruitandretainthebestand

Chapter10 PathDependenceandPositiveFeedback

F】GURE10-19 Profitablegrowthleadstorecruitmentandretentionofthebestpeople.

Eacheffectcreatestwoloops:oneincreasesmarketshareandoneincreasestotaldemand.

//ザ sTl evenLT .

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PerceivedCareer

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377

thebrightest(R28inFigure10119).Andthefasteracompanygrows,thegreater thecareeropportunitiesandjobsecurityforemployees(R29).

Thestrengthofthewagepremiumloophasincreasedgreatlyinrecentyearsas firms,especiallyfirmswithbrightgrowthprospects,haveincreaslnglyturnedto stockoptionsaSaformofcompensation.Employeeswhosecompensationistied

toprofitsharingorthecompany'sstockoftenworkharderandlongerthanthose onstraightsalary.Stockoptions,bonuses,andprofitsharingallowfirmstorecruit highlyqualifiedpeoplewhilereducingbasesalaries,freeingadditionalresources

thatcanbeinvestedinstrengtheningotherfeedbacksdrivinggrowth,suchasnew productdevelopment,differentiation,oracqulSltlOnS.Asgrowthacceleratesand thestockprlCesoarsthecompanycanpaypeopleevenlessup-front.

ThepositivefeedbacksinFigure10-19arehighlynonlinear.Ittakesmany yearstobuildupaloyal,skilled,high-qualityworkforce,butafirmcandestroy

thatcapabilityveryquickly.Whengrowthstallsorthefirmdownsizes,opportuni- tiesforadvancementandpromotionquicklydisappear.Thebestandmostcapable arethefirsttoleaveastheyhavethebrightestprospectsandbestoutsideopportu-

nities･Thelossoftheseabove-averageemployeesfurthererodesthefirm'scapa- bilitytodeliverattractiveproductsorservices,leadingtostillmoredownsIZlng andattritioninaviciouscycle.FirirlSthatrelyheavilyonstockoptlOriSareespe-

ciallyvulnerabletoaslowdown.Ifthegrowthprospectsofthecompanydimand theprice/eamlngSmultiplefalls,people'soptlOnSmaybecomeworthless,leading todemandsfわrhighercashcompensationthatstealresourcesneededtopromote

growthjustwhentheyareneededmost.Thesepositiveloopscanspeedtheimplo- sionofadecliningorganization.

IBMagalnProvidesanexample.FordecadesIBM'ssuccessenabledittooffer

excellentsalariesandbenefits,defactolifetimeemployment,andexcellentoppor- tunitiesforpromotion.Consequently,thefirmwasabletorecruitthecreamofthe

378 PartIIITheDynamicsofGrowth

cropanditsemployeeswererenownedfわrtheirloyaltyandcommitment,qualities

thatgreatlystrengthenedIBM'sabilitytoprovide仙eserviceandsupportitscus-

tomersrequired.Whentheriseofthepersonalcomputerevisceratedthemain-

frameindustryandgrowthstalled,opportunitiesforpromotiondriedup.Hiring

plummeted.ThecompanywasmuchlesssuccessfulinattractlngtopCandidatesfor

thefewnewjobstheydidoffer,Inanattempttopreservethedecades-oldno-1ay-

ofFpractice,therewereseveralearlyretirementprograms,duringwhichmanytop

peopleleftforgreenerpastures;theirdeparturesfurthererodedthecapabilitiesof

theorganization.Eventhesegenerousprogramsprovedinadequate,andsoonlay-

ofFsandmassivereorganizationsbegan.MoralesankfurtherandproductivltySuf-

feredasemployeesandmanagersworkedtoprotecttheirjoborfindanewone,

1eavlnglesstimeandenergyforthebusiness･9Thelossofloyalty,experience,and

skilldeepenedandprolongedthecrisis.

10.4.10 Thee⑳S官⑳甘eap直音aL首

Profitablegrowthleadstohigherexpectationsoffutureearningsandahighermar-

ketvalueforthefirm.Thehigherthemarketvalueandstockprice,thelowerthe

costofraisingnewcapitalthroughtheequitymarket(Figure10-20).Similarly,

thoughnotshowninthefigure,thegreaterafirm'sprofitsandcashflOwandthe

highermarketvaluerelativetobookvalue,thelowertheriskofdefault,so血e

lowerthecostofdebtasthepremiumovertheprimeinterestratefalls.Thelower

thecostofcapital,thelowerthefirm'Scostsofdevelopmentandproduction.

Lowercostsincreaseprofitsandcashflowstillfurther,leadingtoevenhighermar-

ketvalueandastilllowercostofcapital(R30).Aslowerunitcostspemitlower

prlCeSWhilemaintaininghealthyprofitmarglnS,marketshareandindustrydemand

rise,leadingtoevengreatermarketvalueandfurthercuttlngthecostofcapital

(R31).Alowercostofcapitalalsoallowsthefirmtoincreaseitsinvestmentinca-

pacity,R&Dandnewproductdevelopment,serviceandsupportinfrastructure,hu-

manresources,acquisitions,andotherresourcesthatstrengthenthepositive

feedbacksdrivinggrowth(R32).Finally,asthecapitalmarketsrespondtothe

greatergrowthrateofthefirmbyraisingexpectationsoffutureearn1ngS,themar-

ketvaluewillriseevenhigher,furtherloweringthecostofcapital(R33).

Theseloopsareoftenquitepowerfulforrapidlygrowinghigh-techfirm s.Ini-

tialpublicofferings(IPOs)ofinternetcompaniesinthemid1990sprovidean

example.Manyofthesefirmswereabletoraisesubstantialcapitalatrelatively

lowcost(i.e"bysellingonlyasmallfractionoftheirequity)relativetotherisk,

9Therearemanyexamplesoffirmsexperiencingthisdeathspiral.Sastry(1997)developsasys-

temdynamicsmodeladdresslngtheseissuesandshowshowanotherdeathspiralcanbecreatedby

too-frequentreorganizations.inre.sponsetopoPrbusinessperformance･Masuch(1985)describesa feedbackmodeloforganizatlOnSlnWhichpositiveloopscanleadtodownsizlnganddecline･Case

studiesofthesedynamicsincludeDomPn,Glucksman,andMass(1995),whoshowhowpositive feedbacksledtodifferentfatesfortwolmitiallysimilarUKinsurancecompanies;Risch,Troyano-

Bermudez,andSterman(1995),whoshowhowthesepositiveloopsdefeatedan?wstrategyfora makerofspecialtypaper;andSteman,Repenning,,andKofman'S(1997)simulat10nmodelofa high-techcompanywherepathdependenceandpositivefeedbackledtounanticIPatedsideeffects inthefirm'squalitylmprOVementprogram.

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-20 Profitablegrowthlowersthecostofcapital,stimulatingfurthergrowth.

Eacheffectcreatestwoloops:Oneincreasesmarketshareandoneincreasestotaldemand. ComparableloopsfordebtfinanclngarenotShown.

RecentRevenue

379

∴ ~吾Industry Demand Market

stareProductAttr.activeness

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{wthGrowthRate

ExpectedFuture Eamings

StockPrice

eventhoughmanyhadnevermadeanymoney.Amongthemoreestablishedfirms enjoyingrapidgrowth,manyareabletopaynodividendsasinvestorsprefertolet

thefirmreinvestitsearningsinadditionalgrowth. BecausethemarketvalueofafirmisqulteSensitivetorecentprofitsandes-

peciallygrowthrates,thestrengthoftheseloopscanchangequickly.Adropln growthexpectationsforanyreason(asalesslowdown,theentryofastrongcom- petitortothemarket)canswiftlyreducemarketvalue,effectivelylockingthefirm outoftheequitymarketfornewcapital.AsmarketvalueandcashflOwfallrela-

tivetocurrentobligations,theperceivedriskofdebtincreases,andthebondmar- ketwillrequlreahigherriskpremiumonanynewborrowlng.Whiletheseloops

canglVeahealthy,growlngfirmstillgreateradvantageoveritsslowergrowlng, lessprofitablerivals,theycanswiftlybecomeadeathspiralforanorganizationin financialdistress.

380

FIGURE10-21 T hegoldenrule: Whoever hasthegold makestherules.

PartHI TheDynamicsofGrowth

10.4.11 TheRulesottheGame

Thelargerandmoresuccessfulanorganization,themoreitcaninnuencethein- stitutionalandpoliticalcontextinwhichitoperates.Largeorganizationscan changetherulesofthegameintheirfavor,leadingtostillmoresuccess-and morepower.Figure10-21showstheresultinggoldenruleloopR34.Thegolden ruleloopmanifestsinmanyforms.ThroughcampaignCOntributionsandlobbying, largefirmsandtheirtradeassociationscanshapelegislationandpublicpolicyto givethemfavorabletaxtreatment,subsidiesfortheiractivities,protectionfortheir markets,priceguarantees,andexemptionsfromliability.Throughoverlapping boards,therevolvingdoorbetweenindustryandgovernment,andcontrolofme- diaoutlets,influentialandpowerfulorganizationsgainevenmoreinfluenceand power.Innationswithoutatraditionofdemocraticgovernment,theseloopslead toself-perpetuatingOligarchieswhereatightlyknitelitecontrolsahugeshareof thenation'swealthandincomewhilethevastmaJOrltyOfpeopleremainimpover- ished(e｡g.,thePhilippinesunderMarcos,ⅠndonesiaunderSuharto,andcountless others).Theelitefurtherconsolidatesitscontrolbysubsidizingthemilitaryandse- cretpoliceandbuyinghigh-techweaponryandtechnicalassistancefromthede- velopedworldtokeeptherestivemassesincheck.Eveninnationswithstrong democratictraditionsthesepositiveloopscanoverwhelmthechecksandbalances designedtoensuregovernmentof,by,andforthepeople.

10.乱12 Amb重電旨omandAspira竜ioms Anotherpowerfulpositivefeedbackarisesfromtheasplrationsandambitionsofa firm'sfoundersandleaders(Figure10-22).Allorganizationsmustchoosewhether toeattheirseedcomorplantittoseekanevenlargercropnextseason:Firmscan payouttheirprofitstoshareholdersintheformofdividends,Ortheycaninvestin thefurthergrowthoftheenterprise.Whichcoursetheytakedependsontheirasp1- rationsforgrowth.Growthasplrationsthemselvesarefrequentlyflexibleandadapt

Favorab一e Ru一esofthe

Game

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Chapter10 PathDependenceandPositiveFeedback 381

toactualaccomplishment(seechapter13;CyertandMarch1963/1992;Forrester 1975b;Lant1992).

Byconstantlyrevislngaspirationsupward,theleadershipofanorganization cancreateperpetualpressureforgreaterachievement･Manytopmanagersbelieve theproperwaytomotivatetheirtroopsisbysettingaggressivestretchobjectives-

goalsthatarefarabovecu汀entachievement(see,e･g･,HamelandPrahalad'S1993 conceptofstrategyasstretch).Astheorganizationrespondsandactualachieve- mentrises,thebarisraisedfu一血er.ThusbusinessunitsareoftenglVenaggressive

salesandprofitgrowthgoalsforthecomingfiscalyear.Thesehigh-levelgoalsare

thentranslatedintospecifictargetsfortheindividualactivitieswithineachunit,

eachbasedonrecentperformancebutadjustedbyastretchfactor.Forexample,

eachfunctioninthebusinessunitmightberequiredtocutcostsby15%nextquar-

terwhileraislngthequotaforeachsalesrepresentative20%. Theuseoffloatlnggoalsbasedonrecentperformanceplusastretchfactorcan

behighlyeffective.Settinggoalsoutinfrontofactualaccomplishmentoftenhelps

peoplereachtheirultimatepotential.Athletesseektoexceedtheirpersonalbestor breakthemostrecentrecord;whentherecordfalls,thegoalshiftsaswell.Asstu-

dentsmasterasubjectorconcept,theyareglVenmoredifficulttasks･Managersset theirsightsonthenextpromotion.PoliticiansaspiretOthenexthighestoffice.

Buttherearedangers･Liftinggoalsasaccomplishmentrisesmeanstherewill alwaysbetensionanddissatisfaction-ahungerformore.Thathungercanbea

powerfulmotivatorbutitcanalsoleadtoburnout,frustration,andfeelingsofin- adequacy(see,e.g.,Homer1985formodelsofworkerburnoutunderstretchob-

jectives;alsoseeSimon1982)･A王Iditcanleadtomonomaniacalbehavior,in whichpeoplesacrificetheirfriends,family,andethicsinendlesspursuitofthe nextlevel.

Theabilityofleaderstoarticulatetheirvisionandspurthebesteffortsoftheir

employeesdependsnotonlyontheirpersonalcharisma,butalsoonthesizeofthe

FIGURE10-22 Floatinggoalsandstretchobjectives

Levelof ノAehievementヽ隻ドMotivation,Effort,Jnvestment ;eahenon:t∑/ //

Stretch を-/′~Factor

O い a':ectt?vhes Aタ ieeSvb:emQentPerformance(GapbetweenAspirationand.L Achievement'+

382 PartHITheDynamicsofGrowth

organizationandtheintegrltyOfitsculture,traditions,andfolklore･Thelargerthe organizationandthelesscohesiveitsculture,theharderitisforleaderstoproject

theirgoalsandmotivateemployees,Creatlngnegativefeedbacksthatcanlimitthe abilityofstretchobjectivestogenerategrowth.10

10.4.13 Creat岳ngSynergy青orCorporal(モGrow的

Theprecedingsectionsidentifiedmorethanthreedozenpositiveloopsthatcan drivethegrowthofabusinessenterprise.Howimportantarethey?Iftheseloops aresignificant,thefirms(orindustrygroups)mostsuccessfulinexploitingthem shouldexhibitgrowthrates,Profitability,andmarketsharessignificantlyhigher thanaverageoverextendedperiodsoftime.Firmswherethepositiveloopsoper- ateasviciouscyclesshouldyieldpersistentlylowerreturns･However,traditional economictheorysuggeststhatmarketsaredominatedbynegativefeedbacks:If profitsinanindustryweresignificantlyhigherthanaverage,existingfirmswould expandandnewfirmswouldenterthemarket,expandingproductionandpushing pricesdownuntilprofitswerenohigher,onaverage,thaninanyotherindustryor foranyotherfirm(onarisk-adjustedbasis).

Theexistenceofpersistentdifferencesinprofitabilityacrossfirmsandindus- trieshasbeenstudiedintensively.Mueller(1977,1986)examinedalargesample ofthebiggestUSindustrialfirmsandfoundsignificantlydifferentratesofprofit acrossfimlS,evenforfirmswithinthesameindustrygroup,andthatthesediffer-

encespersistoververylongtimeperiods(atleastseveraldecades)･Cubbinand Geroski(1987)documentsimilarresultsforUKfirmsandconcludedthat"Whilst

two-thirdsofoursampleconvergedtowardsacommonprofitabilitylevel,asolid coreoffirmsappearabletomaintainsomeindependencefrommarketforcesmore orlessindefinitely."Muelleralsoexaminedthedynamicsofprofitability･Presum- ablyifthenegativefeedbacksoftraditionaleconomicsdominate,firmswhose profitsarefarfromaverageatanytime(duetotransientshocks)wouldtendtoI wardtheaverage,whilethosenearaveragewouldtendtoremainthere･Mueller foundjusttheopposite:Firmswithaverageprofitabilitywere,overtime,more likelytomlgratetOStatesOfeithersignificantlyhigherorslgnificantlylower

profits.Firmswithhighprofitshadhigherthanexpectedprobabilitiesofcontinul lngtOgeneratehighprofits;theperformanceoffirmswithlowprofitswasmore

likelythanexpectedtoremaindisappolntlng･Thesedynamicsareconsistentwith thedifferentiating,disequilibriumeffectsofthemanypositivefeedbacksdiscussed above.

Whatdetermineswhetherthepositiveloopswilloperateasvirtuouscycles leadingtogrowthandhighprofitabilityorvicioljSCyclestrappingafirmin-aself- reinforcingcycleofdeclineandlowprofit?Inthemostsuccessfulfirmsmanyof

theseloopsactinconcert,generatingsubstantialsynergies･Achュetal･(1995)ex- aminedtheperformanceofthefastestgrowingandmostprofitablefirmsinthe U S- so-Calledgrowthtigers-toseeifthefeedbacksdrivlngtheirgrowthcouldbe

identified.Theydefinedagrowthtigerasafirmwhosesalesgrowthrateoverthe

10Forrester(1975b)developsamodelexploringthedynamicsofgoalformationinorganizations addresslngtheseissuesofleadershipandgrowth･

Chapter10 PathDependenceandPositiveFeedback 383

prlOr10yearswasthreetimesgreaterthantheaverageoftheS&P500andwhich

outperformedtheS&P500intotalreturntoshareholdersoverthepr10r5years.In

asampleofmorethan1200firms,97metthesecriteria･Thegrowthtigerswere notallsmallstartups:1994Salesrangedfrom$130millionto$12.5billion.Nor

weretheyallhigh-techfirms:though28%ofthetlgerSWereinthecomputersec-

tor(includingIntel,Microsoft,Compaq,3Com,andSun),theremainderincluded firmsinsuchlow-tech,matureindustriesasindustrialequlPment,businessandfi-

nancialservices,retail,distributionandwholesaling,apparel,fashionandsports, andhealthcare(e% ,Nike,TheHomeDepot,USHealthcare,WilliamsISonoma,

UnitedAssetManagement,WernerEnterprises,andNautica).Sustainedgrowth andprofitabilityarenotmerelyafunctionofbeinginahotindustry(ofcoursehot

industriesarehotbecausethepositiveloopsdrivingtheirgrowtharestrong). Thegrowthtigersgenerateadisproportionateshareofthegrowthintheecon-

omyasawhole･WhilecomprlSlngjust8%ofthefirmsinthesample,theycreated

15% ofthetotalsalesgrowth,28% ofthejobgrowth,and47% oftheprofit growth.CloseexaminationshowedthatthetlgerSdidnotrelyonanysingleposi- tivelooptodrivetheirgrowthbutsuccessfullyusedmanyofthepositivefeed- backsdiscussedabovetocreatesynergy.Microsoftistheparadigmcase.Thecosts ofproducingsoftwarearealmostentirelyup-frontdevelopmentcosts,sothere-

ductioninunitcostsasthesoftwaremarketexplodedisaverypowerfulgrowth driver.Similarly,Microsoft'SexpansionfromoperatlngSystemstOapplications, theinternet,newsnetworks,publishing,automotivecomputing,andothermarkets

createspowerfulscaleandscopeeconomies.Microsoftalsobenefitsfromlearnlng curvesandfromsubstantialinvestmentinprocessimprovementfocusedonim-

provingCustomerneedsassessmentandspeedingso氏waredevelopment.Itinvests heavilylnProductdifferentiationandnewproductdevelopment.Microsoft'sfi-

nancialcloutenablesittopreemptcompetitionbyacqulrlngrivalsandpotentialri-

vals,oftenbuyingsoftwarestart-upsandincorporatingtheirproductsinto Microso打SownapplicationsandoperatlngSystems.Microso打smarketpoweren-

ablesittonegotiatefavorabledistributionagreementsandpriceswithcomputer makers･Itsgrowthallowsittorecruit血ebestprogrammersandmanagersand compensatethemwithstockoptlOnS,Whichbuildsadedicatedandproductive workforceandfreesupresourcesforotherinvestments.Microsoft'spositivecash

flowandhighprlCe/earningsmultiplecutitscostofcapitalfarbelowthatof

weakerrivalsandriskystartups.Andgrowthispowerfullydrivenbytheexpansive aspirationsofBillGates,avisionhehas,through awell-fundedpublicrelations e批)rt,successfullyarticulatednotonlywithinMicrosoftbutinsocietyatlarge throughghost-writtenbooksandmediaappearances.

Mostofall,Microsoft'ssuccessstems血.ompowerfulnetworkandcomple- mentarygoodseffects.Thesefeedbacksoperatethroughmanychannels,linking hardwarearchitectureandoperatlngSystems,OperatlngSystemsandapplications,

applicationsandusers,andsoftwareandprogrammers.Thelargertheinstalled baseofMicrosoftproducts,themoreattractivearecomputerscompatiblewith thoseproducts(poweredbylntelandlntel-compatiblechips).Themorepersonal

computerssoldwithlntellnside,thelargerMicroso氏'sinstalledbase,Thelarger theinstalledbaseofMicrosoftoperatlngSystems,themoresoftwarewillbede- velopedforthosesystemsbythird-partydevelopers,andthemorethird-party

384 PartIIITheDynamicsofGrowth

softwarethereisthegreatertheattractivenessoftheWintelplatform.Thelarger

thenumberofpeopleuslngMicrosoft'sapplications,themoreimportantitisfor

otherstohavecompatiblesoftwaretoexchangedocumentswithcolleaguesand

friends,sothegreatertheattractivenessofMicrosoft'sapplications･Andthelarger

Microsoft'sshareoftheinstalledbase,thegreaterthenumberandhigherthequal-

ityOfprogrammers,supportpersonnel,andITmanagerstrainedinthosesystems andthescarcerarethosefamiliarwithotheroperatingSystemsandapplications.

Poweredbythesepositivefeedbacks,Microsoftgrewfromits1975founding

toafirmwith1997revenuesof$11.3billion.ByAugust1999itsmarketcapi-

talizationwasnearly$500billion;bycomparison,GeneralElectric,withabout

7timesmorerevenueand9timesmoreemployeesthanMicrosoft,wasworthless than$400billion.

BillGatesisqulteawareOfthesepositivefeedbacksandtheirroleinhissucI cess(Table1 0-1).

Ofcourse,growthcannotcontinueforever.Ultimately,asthelimitstogrowth

areapproached,Variousnegativefeedbacksmustgrowstrongeruntiltheyover-

whelmthepositiveloops.IfMicrosoftcontinuestogrowatitshistoricalrate,its

saleswouldexceedthegrossdomesticproductoftheUnitedStatesby2018,when

BillGateswillbeonly63yearsold,eveniftheUSeconomykeepsgrowlngatits historicalrate.ll

Someofthenegativefeedbackswerealreadyapparentbythemid1990S･Con-

cernoverMicrosoft'sabilitytousethepositivefeedbacksdrivinggrowthtodom-

inatethesoftwaremarketprompteditscompetitorstoJOlntogethertopromote

Sun'sJava.Microsofthasproventobeadeptatbluntlngthesemovesthroughwhat

BillGatescallsHembraclngandextending"theinnovationsofitscompetitorsJt

waspreciselyconcernoverMicrosoft'sabilitytoembraceandextend,tousethe

positiveloopstodominatetheemerglngdigitaleconomy,thatpromptedtheUS

JusticeDepartment's1998antitrustsuitoverthebundlingofMicroso打slnternet

ExplorerwiththeWindowsoperatlngSystem.

Notallthepositivefeedbacksthatcandrivecorporategrowtharecompatible

withoneanother.Pursuingthedifferentiationstrategybycharginghigherprices

basedonthesuperiorityOfyourproductsandsupportcapabilitiesconflictswith

uslnglowinitialprlCeStOdrivethescaleeconomy,learnlngCurve,andnetwork/

complementarygoodseffects.Manylong-successfulfirmsstumbledwhenthepos-

itiveloopsdrivinggrowthintheirindustrychangedwhiletheirstrategydidnot.

Forexample,thefailureofSony'SBetamaxcanbetracedtoamismatchbetween

theirstrategyandthedominantloopsinthehomeVCRmarket･Sonyhadlongpur-

suedastrategyeml)hasizlngProductdifferentiationandinnovation,andSony

productstypicallycommandedasignificantpricePremium relative tothoseof

competitors.Sony'sstrategyworkedverywellinmarketswherestandardswere

alreadyestablished(suchastelevision,stereoamplifiers,andcassettetapeplayers) butwasineffectiveinamarketwherenetworkeffectsandcomplementaryassets

llFrom1985through1997Microsoftsalesgrewfrom$140millionto$11.36biuion/year,a compoundgrowthrateof37%/year.Overthesameperiod,nominalUSGDPgrewfrom$4181bill lionto$8079billion,acompoundgrowthrateof5.5%/year･Atthesegrowthrates,thetwocurves intersectafter21.1years.

Chapter10 PathDependenceandPositiveFeedback

TABLE10-1 BHGatesuses

positivefeedback

conceptstoguide Microsoft's

Strategy.

385

PositiveFeedbaeks

CommentsofB‖Gates Referenced

"Thenetworkhasenoughusersnowthatitis

benefitingfromthepositivefeedbackloop;the

moreusersitgets,themorecontentitgets, themoreusersitgets.Wewitnessedthissame

Phenomeヮa(sic)withapplicationavailability･The moreapprlCationsareoutthere,themoreattractive thedevicebecomes,andthebetterthesoftware

businessbecomes"(Interview,RedHerring,Oct. 1995).

"Thisisatimeperiodwherenowthere'sabroad

awarenessthatWindowsNTisbyfarthehighest-

Volumegeneralpurposeserverplatform.The

growththerecontinuestoamazeus,andit'sa

positivefeedbackloop.Aswegotmore

appllcations,NTseⅣersgotmorepopular.Asit's

gottenmorepopular,we'vegotmoreapplications"

(ComputerResellerNews,23Septi996)

"lt'saHaboutsca一eeconomiesandmarketshare.

Whenyou'reshipplngami"ionunitsofWindows

softwareamonth,youcanaffordtospend$300

miMonayearimprovlngitandstillse"atalow

price"(Fortune,14June1993).

"Thebiggestadvantagewehaveisthatgood

developersliketoworkwithgooddevelopers"

(CusumanoandSelbyi995,MicrosoftSecrets).

"Mostpeopledon'tgetmiHionsofpeopleglvlng themfeedbackabouttheirproducts"Wehavethis

wholegroupoftwothousandpeopleintheUS

alonethattakesphonecallsaboutourproducts

andlogseverythingthat'sdone.Sowehave

abetterfeedbackloop,lnCludingthemarket"

(CusumanoandSelby1995,MI'crosoftSecrets).

Networkand

ComplementaryGoods

Effects(R16-17)

UnitDevelopmentCosts andScaleEconomies

Loops(R10-12)

LoyaltyandQualityof

Workforce(R28-29)

LearnlngCu rveand Processlmprovement Loops(R14 andR 15)

(theinstalledbaseandavailabilityoftapes),ratherthanfeatures,quality,orrepu-

tation,Werethemostimportantdeterminantsofproductattractiveness.Managers

andentrepreneursmustdesigntheirgrowthstrategybyidentifvinEthosepositive

loopslikelytobemostimportantintheirmarkets,mostcompatiblewithonean-

other,andmostconsistentwiththecapabilitiesandresourcesthefirmeitherhasor

candevelop.

10.5 Pos汀IVEFEEDBACK,tNCREASINGRETURNS, ANDEcoNOMeCGROWTH

ThemanypositivefeedbacksdiscussedinsectionlO･4notonlydrivethegrowth

ofindividualcorporationsbutpowerthegrowthofentireindustriesandofthe

386 PartIIITheDynamicsofGrowth

economyasawhole.TherecognltionthatpositivefeedbackistheenglneOfeco- nomicgrowthcanbetracedbackatleasttoAdamSmith'sTVealthofNations.

Smithandtheotherclassicaleconomistsdidnotdrawcausaldiagrams,butthe variousfeedbacksareclearlyseenintheirwritings.Smithfocusedondivisionof laborastheprlnClpalsourceofproductivltygrowth.Asaprocessisdividedintoa largernumberofroutinizedoperations,productivltygrowsbecausespecialization enablespeopletolearnfaster,tocustomizetheirtoolsandcapitaltothespecific task,andtoeliminatethewastedeffortthatcomesfrommovingfromoneopera- tiontoanother.Smithnotedthat"thedivisionoflaborislimitedbytheextentof themarket,''recognlZlngthepositivefeedbackbywhicheconomicgrowthenables greaterspecialization,whichinモumleadstogreaterproductivltyandstillmore economicgrowth.

Economistsgenerallyrefertothesepositiveloopsasincreasingreturns.The termdenotesasituationinwhichtheoutputofaprocessincreasesmorethanpro- portionatelyasitsInputsgrow,incontrasttotheusualsituationofdiminishingre- tums,whereoutputsaturatesasinputsgrow(asinagriculture,whereharvestsare limitedbytheextentandfertilityofthelandnomatterhowmuchfertilizerorla- borareapplied).BesidesAdamSmithotherearlytheoriesofincreasingreturns weredevelopedbyAl血.edMarshall(in1890)andAllynYoung(in1928;see BuchananandYoon1994foranexcellentcollectionofkeyworksintheeconom- icsofincreasingreturns).Formalmodelsembodyingpositivefeedbacksinclude PaulKrugman'S(1979)modelsofinternationaltradeandPaulRomer'S(1990) modelsofendogenouseconomicgrowth.

Krugman,forexample,notedthatinthetraditionaleconomictheoryoftrade, dominatedbydiminishingreturns(negativefeedbacks),twoidenticaleconomies wouldhavenoincentivetotrade,sincethegreatertransportationcostsoftrade wouldmakeitmoreefficientforeachtoproducethegoodstheyneedlocally. However,inthepresenceofpositivefeedbackitbecomesadvantageousforthetwo economiestotradeeventhoughtheyhaveidenticalresources,technologleS,and consumerpreferences.Theapparentlyparadoxicalresultarisesbecauseboth economiescanproducemoreifeachspecializesintheproductionofoneclassof goodsandtradeswiththeotherfTortheresttheydesire-specializationboostspro- ductivity,hencetotaloutputincreases.Ⅰnterestlngly,inthecaseofinitiallyidenti- caleconomies,itdoesn'tm atterwhichsubsetofgoodseachchoosestoproduceas longastheyspecialize;in practicethechoicewouldbedeterminedbychance eventsearlyinthehistoryoftradingrelations,leadingtotheclassicalpathdepen- denceanalyzedabove.

TheimplicationsofPositivefeedbacka13plvnotonlvtonationsenEaEedinin-

ternationaltradebutalsotoanydistincteconomicentitiesthatcanexchangegoods withothers,includingreglOnSWithinaslnglenation,citiesandtownswithinare- glOn,neighborhoodswithinaclty,Oreventhemembersofafamily.Whenthepos- itivefeedbackscreatedbydivisionoflabor,scaleandscopeeconomies,learnlng bydoing,andsoonarestrong,Specializationandtradecanquicklytransforman initiallyidenticalgeography into ahighlyvarlegatedlandscapewithspecialized centersofindustrysuchassiliconvalleyortheNewYorkdiamonddistrict.

Romershowedhowgrowthforaneconomyasawholecouldarisefromsome ofthepositiveloopsdescribedabove,particularlythoserelatingtoresearchand

Chapter10 PathDependenceandPositiveFeedback 387

development,learningbydoing,andotherinvestmentsinhumancapital.Increas- 1ngreturnsarisebecausetheknowledgecreatedbyR&Doremployeetrainlng,for example,cannotbekeptfullyprlVate.Whileamachinetoolcanonlybeusedin oneplaceatatime,knowledgeofhowtodesignamachinetoolcanbeusedby morethanone丘rmatatime;knowledgeisnotconsumedbyusagethewaymate- rialgoodsare.Consequently,afirm'sinvestmentsinR&Dandtrainlng,forexam- ple,notonlybenefitthefirmbutalsospillovertobenefitotherfirms.Inthe languageofeconomics,thesespilloverscreateexternalities,thatis,benefitsexter- naltothefirm.Theseexternalitiesspeedeconomicgrowthbecausetheybenefit manybesidesthefirmundertakingtheinvestment,increaslngthetotalsizeofthe marketandfurtherstrengtheningthemanypositiveloopsthatdependonthescale ofactivltylnanindustryorreglOn.Romeralsoshowedthatbecauseindividual firmsgenerallydon'tunderstandandcan'ttakeadvantageofthebenefitstheir knowledgeinvestmentscreatefortheeconomyasawhole,thereisatendencyfor firmstounderinvestinhumancapitalandR&D.

10.6 DoESTHEEcoNOMYLocKINTOINFER10RTECHNOLOGIES?

Oneconsequenceofpathdependenceisthatrandomeventsearlylntheevolution ofasystemcanpushitdownonepathoranother.Theserandomshockscanbe smallandmightgounnoticedatthetime,oreveninhindsight.Theycaninvolve chanceeventswithinthefirmsintheindustryorspilloversfromunrelatedpoliti- cal,technical,orsocialeventsintheworldatlarge･Thepositivefeedbacksamplify thedifferencesamongthecontendersuntiloneemergesasthestandardanddomi- natestheindustry.Successbegetssuccess.Asthewinneremerges,thecostsof switchingfromonestandardtoanotherbecomegreaterandgreateruntilthesys- temlocksintothatequilibrium.ThePolyaprocessdescribedinsection10.2shows

howpathdependenceandlockincanoccurwhenallequilibriaareinitiallyequally attractive.Itdoesn'tmatterwhetherwedriveontherightorleftorwhetherclocks goclockwiseorcounterclockwise,Solongasweallchoosethesamedirection. Morecontroversialisthenotionthatpathdependencecanleadtheeconomyto lockintoequilibria-toproducts,technologleS,andwaysoflife-thatareinferior toothersthatmighthavebeenchosen(see,e.蛋.,Arthur1994).

Ifthedominantdeteminantofproductattractivenessiscompatibilityandthe availabilityofcomplementarygoods(e･g･,VCRs,personalcomputers,keyboard layouts),thenafirmmightbecomethemarketleadereventhoughitstechnology isinferior.ManyarguethattheVCRindustryprovidesanexampleoflockintoan infbriortechnology,polntlngOutthatBetamaxofferedsuperiorpICturequalityand istodaythestandardforprofessionalvideoequipment(othersfocusonVHS'S longerplaytimetoarguethatitwasafterallthesuperiortechnology).TheMacin- toshoperatingSystemWasClearlysuperiortoMicroso打sDOSandearlyversions ofWindows,yetMicroso打ssystemsbecamethestandardwhiletheMacintosh steadilylostmarketshare.TheQWERTYkeyboardinventedbyChristopher Sholesinthe1870siswidelyconsideredtobeinferiortothe1936Dvorakkey- boardintermsoftrainingtime,tyPlngspeed,errorrates,balancebetweentheleft andrighthands,andcomfort,yetnearlyeveryonecontinuestolearntheQWERTY

388 PartIIITheDynamicsofGrowth

layout･12TheirrationalEnglishsystem ofmeasurement,withitsfeet,yards,

pounds,gallons,andacres,isclearlyinferiortothemetricsystemyetcontinuesto beusedintheUS.

ThelikelihoodoflockinglntOaninferiortechnologyincreasesWiththe

strengthofthepositiveloopsthatconferadvantagetothemarketleaderindepen-

dentoftheattributesofthetechnologyltSelf,Thestrongerthenetwork,compati-

bility,developmentcost,marketpower,andgoldenruleloops,themorelikelyitis

theultimatewinnerwillbedeterminedbyfactorsunrelatedtoproductquality,

functionality,andfeatures.ContinuedlockintotheQWERTYkeyboardisdue

tothegreatimportanceofcomplementaryassets,specifically,typiststrained

inQWERTYTheswitchingcostsofretrainingthehugeinstalledbaseoftypistsin

theDvoraksystemoutweightheadvantageofDvorak,perpetuatingthedominance

ofQWERTY.13

Theprevalenceofpositivefeedbacksintheeconomydoesoccasionallycause

lockintoinferiortechnologies.Buttheissueisconsiderablymorecomplex.Tech-

nologiesevolve.Aninitiallyinferiortechnologymightwinthebattleformarket

shareandemergeasanewstandard,butlaterimprovementsmightovercomeits

initialdeficiencies.MicrosoftagalnProvidesanexample･TheDOSoperatlngSys-

temwasunquestionablyinferiortotheMacintosh,yetMicrosoftbecamethein-

dustrystandardwhiletheMacwithered.Microsoftwasthenabletoimitatethe

graphicalinterfaceoftheMac,incorporatingmanyOfitsfeaturesintheWindows

operatlngSystem.ThefirstversionsofWindows,throughWindows3.1,werestill

clearlyinferiortotheMacintosh.ButMicrosoft'sdominanceallowedittoinvest

heavilyinfurtherimprovements.Windows95and98,inthejudgmentofmany,

closedmostofthegap,andfurtherinnovationwillnodoubtleadtostillgreater

functionality.Wh ilethenetworkandcomplementarygoodsloopsdidleadthesoft-

wareindustrytolockintoatechnologythatwasinferioratthetime,thenewprod-

uctdevelopmentanddifferentiationloopsgraduallyerasedthedeficit.Ofcourse,

theMacintoshoperatlngSystemWOuldpresumablyhaveevolvedatahigherrate

haditwonthebattleandbecomethestandardJtisentirelypossiblethatcomputer

userswouldhavebeenbetteroffiftheinitiallysuperiortechnologyhadwon.Itis

notpossibletoanswersuchquestionsdefinitivelybecausewecanneverknOwhow

muchbetterthelosersmighthavebecome.

Amoresubtleissueconcernsthecoevolutionofpeople'stasteswithtechnol-

ogy.People'spreferencesarenotstatic;theyevolveandchangewithexperience･

Yourlikesanddislikesadapttoyourcircumstances.Theamountofsaltorhot

pepperpeopleconsiderpalatable,theamountofpersonalspacepeoplerequlre,the

12TherelativemeritsofQWERTYandDvorakarestilldebated.LiebowitzandMargolis(1990) arguethatmanyofthestudiesshowingthesuperiorltyOftheDvoraklayoutareflawed.Thepre-

ponderanceoftheevidence,however,suggestsDvorak'slayoutismoreefficientthanQWERTY.

13Asanotherexample,Moxnes(1992)developsamodelshowinghowaneconomycanlock

intoaninferiorenergysupplysystem;seealsoFiddaTan(1997)･StermanandWittenberg(1999) developamodelofscientificrevolutionwhosedynamicsexhibitstrongpathdependenceandfind thattheprobabilityaglVentheoryrisestOdominanceinitsdisciplineisonlyweaklyrelatedtoits intrinsicexplanatorypowerwhilestronglydeterminedbyenvironmentalconditionsatthetimeof itsfounding.

Chapter10 PathDependenceandPositiveFeedback 389

amountofleisuretimeandaccesstoopenspacepeopledesireallv∬ywidely acrosscultures.Habituationisapowerfulprocess.

Similarly,people'Sevaluationofatechnologycandifferovertimeeventhough thetechnologyItselfmaynotchange.Manycitydwellerslivemoreorlesshappily inenvironmentsnoisier,morecrowded,andmorepollutedthananytheirancestors

couldhaveimaginedortolerated.Ourevaluationsoftheattractivenessanddesir- abilityoftheensembleoftechnologleSandsocialstructuresmodemsocietyhas

beenlockedintoforthepast50yearsdifferfromthewaywewouldhaveevaluated themin1950.Becausepeople'spreferences,tastes,andstandardsaremalleable, technologyandourassessmentsandreactionstoitcoevolve･GarudandRappa (1994)Showhowsuchcoevolutionshapedtheemergenceofcochlearimplants,a

technologytoprovidehearingfortheprofoundlydeaf･RivaltechnologleSledto competlngnotionsofwhatsuccesswouldmeanforpatientsreceivlngthetechno1-

ogy(e.蛋.,theabilitytodecodespeechatalowercostortohearawiderspectrum ofsoundatahighercost),ultimatelyaffectinggovernmentregulationsandstan- dardsforthetechnology.

10.7 LIM!TSTOLtocK【N ThePolyamodelandexamplesofpathdependencesuggestthatpathdependent systemsrapidlylockintoastableequilibrium,whichthenpersistsindefinitely. Theclockwiseconventionwasestablishedbythe1500S.Theprlmemeridiancon- tinuestobelocatedinGreenwichthoughthesunhaslongsincesetontheBritish

empire.AndtheQWERTYkeyboardhasbeenthebaneoftypingstudentsforover

acentury.Areallpath-dependentsystemsperpetuallytrappedintheequilibriato whichchanceeventsleadthem?Istherenoescape?

Therearemanyexamplesinwhichadominantstandardwasoverthrown.Such

revolutionsusuallyoccurwhenthesysteminwhichthestandardisdominantbe-

Comesobsoleteorisitselfoverthrown.Thedinosaursruledtheearthformillions

ofyears,butafteracatastrophicasteroidimpactcausedmassextinctionsthrough-

outtheplantandanimalkingdoms,dinosaursdidnotreemerge･Theimpactde- Stroyedtheecosysteminwhichthedinosaurshadbecomethedominantstandard･ IntermsofthePolyaprocess,themassextinctioneventremovedmostofthe

stones(species)fromthejar(availableecologicalniches),Sothattheselectionof newstones(theevolutionofnewspecies)wasonceagainstronglyinfluencedby randomevents.Lifefilledthejaronceagain,butdifferentformsoflifebecame dominant.14

InaprocessSchumpeterfamouslydubbedcreativedestruction,economicde-

pressionscanunfreezeaneconomythathaslockedintocertaintechnologleS･ Everyeconomyneedsbasictechnologiesforenergy,transportation,andcommu- nications.AnensembleoftechnologleSandinfrastructurebuiltaroundcoal,steam,

rail,andthetelegraphdominatedtheindustrializedworldinthelatelワthandearly

20thcenturies.Populationsandindustrywereconcentratedinlargecitiessur- roundedbyfarmandforest.ThesetechnologleSandsettlementpatternswereself- reinforclng.Coalhasafairlylowenergydensltyandisdifficulttohandle,which

14seeGould(1990)fordiscussionofpathdependenceinevolution.

390 PartIIITheDynamicsofGrowth

favorscentralizedsettlementpatternsandtransportmodeslikerailandsteamship･ Telegraphlineswereoftenstrungalongtherailroadrightofway,lowerlngthecost ofinfrastructureandmaintenance･Thecoal-steam-rail-telegraphensemblere- maineddominantuntiltheGreatDepressionofthe1930S.Thedepression bankruptedmanyofthefirmsintheseindustries,theirphysicalinfrastructurede- teriorated,andthepoweroftheirleaderswaned.

Whentheeconomybegantorecoverfromthedepressioninearnestafter WWII,newinvestmentdidnotrecreateandrefurbishtheoldnetworksandtech-

nologiesbutfocusedinsteadonanewensembleofbasictechnologleS｡Thenew economyofthepostwarerawasbuiltaroundoil,naturalgas,andelectricltyfor energy;intemalcombustionandelectricmotorsformechanicalpower;auto-

mobilesandaircraftfortransportation;andtelephone,radio,andtelevisionfor colnmunication.Thesuburbsemergedandindustriallocationpattemsbecameless centralized･ThesetechnologiesWerealsomutuallyreinforclng:Catalyticcracking enabledcrudeoiltoberefinedintogasolineatlowcost;gasolineisanenergy- dense,easilyhandledfuelsuitableforalargefleetofsmallvehiclesanddecentral- izedsettlementpatterms;internalcombustionenglneSareSmallandpowerful enoughtouseinaircraft;andsoon.AllthesetechnologleSWereinventedwellbe- forethe1930S,butthecostsofswitchingwereprohibitivebecausetheywerein-

compatiblewiththeexistingensembleoftechnologleSandsocialstructures.

Despitetheirgreatpotential,thenewinventionscouldnotachievewidespreaduse untiltheoldinfrastructure-physical,social,andpolitical-wassweptawaybythe GreatDepressionandSecondWorldWar.Thedepressionandwarfunctionedas amassextinctioneventthaterasedthebasisfortheoldtechnologleSandthe firmsthatdominatedthem･Justasnewformsoflifeevolveaftereverymass extinction,anewanddifferenteconomyemergeswiththerecoveryfromevery majordepression.15

Greatupheavalssuchasdepressionsorwarsarenotneededtounfreezeasys- temthathaslockedintoaparticularequilibrium｡Shiftsintechnologicalarchi- tectureoftenunderminethebasisfわrthedominanceofaparticulartechnology, standard,orfirm.Thetransistormadevacuumtubesobsolete,andnoneofthe

leadersinthevacuumtubeindustrywereabletotranslatetheirdominanceinthe oldtechnologyIntoaleadershiproleinthesolid-Stateworld.HendersonandClark (1990)showthatdominantfirms(atleastinsomeindustries)rarelymaintaintheir leadershippositions,orevensurvive,aftersuchchangesinproductarchitecture. Thesamepositiveloopsthatconfercumulativeadvantagetoafirmbybuildingup networksofskills,relationships,andknow-howspecifictothefirm'Stechnology andmarketalsocreateinertiaandrigiditythatmakeitdifficulttoadoptaradical andincompatiblenewtechnology(seeSastry1997).

Thearchitecturalshiftsthatundermine thedom inantdesignanddominant firmsinanindustryoftenarisefrominnovationscreated bythoseveryfirms.The computerindustryprovidesanotherexample･Firm s suchasIBM andDigital Equipmentbecamehugelysuccessfulthroughexploitationofmanyofthepositive

15Forfurtherdiscussionoftheinteractionbetweeneconomiccyclesandtheevolutionofbasic technologies,seeGrahamandSenge(1980)andSterman(1986).

Chapter10 PathDependenceandPositiveFeedback 391

feedbacksdescribedabove,especiallythedifferentiationandinnovationloops (SectionslO･4･5andlO･4･6)･Byprovidingsuperiorserviceandsupport(IBM)and

technicallyexcellentproducts(Digital),thesefirmswereabletochargecompara- tivelyhighprices;intum,highmarglnSProvidedtheresourcesforfurtherinvest-

mentindifferentiationandinnovation.ThesedifferentiationstrategleSworkedvery

wellduringtheearlyyearsofthecomputerindustrywhenthecostsofcomputers wereveryhigh,volumesweresmall,developmentandcapacltycostsWereamod-

estfractionoftotalcosts,andcomputerswereusedforalimitedsetofspecialized functionsincentraldataprocessingCenters.

Ascomputersbecamecheaper,morewidelyavailable,andeasiertouse,ser-

viceandsupportbecamelessimportant.WhenpeoplebuyanewPCevery2years

tokeepupwithtechnicalprogress,warrantytermsandservicecapabilityareless important;whenapplicationsuseapolntandclickinterface,trainlngandsupport arelessimportantasemployeesteachthemselvesandeachother.Asthecostof

manufacturingfellwhilethecomplexityofdesignsincreased,upjrontdevelop- mentcostsbecamemoreandmoreimportant.Ascomputlngcostsfell,computing

becamedecentralized･Insteadofamultimilliondollarmainframesequesteredina cold,cleanroom,theemployeesnowhadacomputerontheirdesk.Networking andcompatibilitybecamemuchmoreimportant.Theexplodingnumberofcom-

putersinusecreatedlucrativemarketsforapplicationsthatinducedthirdpartiesto enterthesoftwaremarket,bothgreatlystrengtheningthecomplementarygoods

feedbackandreducingthehardwaremakers'controloverthesecomplementary goods.

TheverysuccessofthecomputerindustrylneXploiting血epositiveinnovation

andproductdifferentiationloopscausedthesefeedbackstoweaken,destroylngthe effectivenessofthestrategiesthathadcreatedthatsuccess.Differentiationbecame

lessandlessimportant,whilecompatibilityandsoftwareavailabilitybecamemore

andmoreimportant･Successinamarketdominatedbycompatibility,software availability,andeconomiesofscalerequiredaggressivelylowerprlCeStOgenerate thevolumerequiredtooffsethighdevelopmentcostsandwinthebattleformarket

share･MainframeandminicomputermakerslikeIBM,DigitalEquipment,Wang Laboratories,DataGeneral,andPrimeComputerfailedtorecognizetheshiftin

loopdominancetheythemselveshelpedtobringabout･Thesefirmssuddenly foundthemselveswithcapabilities,resources,Strategies,andcoststructures

grosslyoutofalignmentwiththerequlrementSforsuccess･Whereoncetheyrode thepositivedifferentiationfeedbackstogreaterandgreatersuccess,nowthese loopsbecamedeathSpiralsleadingtofasterandfastercollapse.Someofthesefor- merindustrygiantssurviveasmereshadowswhilemanyvanishedaltogether,

10.8 MoDEuNGPATHDEPENDENCEANDSTANDARDSFoRMAT10N

ThelinearandnonlinearPolyaprocessesaboveprovidesimpleillustrationsof path-dependentsystemsbuttheydonotproviderealisticmodelsofpathdepen- denceineconomicorsocialsystemssuchasthecompetitionbetweenBetamaxand VHSorthetriumphoftheWintelarchitectureovertheMacintosh.Thissection

392 PartIIITheDynamicsofGrowth

developsasimplemodelofpathdependenceintheeconomy,amodelwithmore realisticformulationsforthedecisionrulesandwhichcanbeelaboratedtoinclude

themanypositivefeedbacksdescribedabove.

10.8.1 ModelStructure

ThebattlefordominancebetweenBetamaxandVHSistypicalofstandardsfor- mationfornewproductsinmarketswheretheutilityoftheproductdependsonthe sizeoftheinstalledbaseandthenetworkofusers.Onefaxmachineisnotusefu1-

faxmachinesonlybecomeusefulwhenthereisanetworkofothercompatiblema- chines.Manyproductsdependontheavailabilityofcomplementaryresources: personalcomputersarenotusefulwithoutcompatiblesoftware;automobilesare notusefulwithoutnetworksofroads,gasolinestations,andotherauto-friendlyIn- frastructure.Insuchmarkets,theattractivenessofaproductbasedonagivenStan- darddependsonitsinstalledbase,andmarketsharewilldependontherelative attractivenessofthedifferentcompetlngStandards.Figure10-23showsthestruc- tureofasimplemodeltocapturethesefeedbacks.Thediagramrepresentstwo productscompetlngtObethestandardinamarket.Theproductsareassumedtobe incompatible.Tokeepthemodelassimpleaspossible,onlythemostbasicposi- tivefeedback,throughtheinstalledbase,isrepresentedexplicitly.Pricesandother determinantsofproductattractivenessaredeliberatelyexcluded.Thechallengeat theendofthissectioninvitesyoutoextendthemodeltoincludethesevariables andotherimportantloopssuchastheprocessbywhichdevelopersofcomplemen- taryproductschoosewhichformattoadopt.

Theinstalledbaseofeachfirmisincreasedbythesalesofeachfirm'sproduct (twofirmsi-1,2areassumedinthesimulationsbelow,butthemodelcan

accommodateanynumberoffirms).Forsimplicity,assumenodiscardsandno repeatpurchases,sothereisnooutflowfromtheinstalledbase･

ⅠnstalledBaseProducti-INTEGRAL(SalesofProducti, InitialInstalledBaseofProducti)

(10-1)

Thesalesrateofeachfirmistheproductofindustrydemandanditsmarketshare:

SalesofProducti-TotalDemand*MarketShareProducti (1012)

Fornow,assumeindustrydemandisexogenousandconstant.Inrealityofcourse therearemanyfeedbackstoindustrydemand(section10.4).

Marketshareisdeterminedbytheattractivenessofeachfirm'sproductsrela- tivetOtheattractivenessOftheotherfirlTrlS'products.TheformulationforlTrlarket sharemustmeetseveralcriteria.First,marketshareshouldbeincreaslngaSthe attractivenessofthefirm'sproductrisesanddecreasingaStheattractivenessof competitors'productsrises.Second,marketsharemustbeboundedbetween0and

lO0%.Finally,thesumofthemarketsharesofallfirmsmustequal100%atall times.Ausefulformulationthatmeetstheserequirementsis

MarketShareProducti AttractivenessofProducti

TotalAttractivenessofAllProducts

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393

394 PartIIITheDynamicsofGrowth

wherenisthetotalnumberoffirms.Totalattractivenessisthesumoftheattrac-

tivenesslevelsofallproductsinthemarketplace.

Howshouldattractivenessbespecified?Attractivenessdependsonawide

rangeofvariables,includingprice,availability,quality,service,features,andso

on.Inthissimplemodel,Overallattractivenessistheproductoftwoterms:theef-

fectofcompatibilityonattractiveness(thenetworkeffect)andtheeffectofall

otherfactorsofattractiveness･Theformulationaggregatestheeffectsofprice,fea-

tures,availability,andsoonintoaslnglefactor,whichinthissimplemodelisas-

sumedtobeexogenous｡

Attractivenessof EffectofCompatibilityonAttractivenessofProducti Producti *E脆ctofOtherFactorsonAttractivenessofProducti(1 0-5)

Theeffectofcompatibilityonattractivenesscapturesthenetworkandcompatibill

ltyeffects:thelargertheinstalledbase,thegreatertheattractivenessofthatprod-

uct･Thereareanumberofplausibleshapesfortherelationshipbetweeninstalled

baseandattractiveness･OnecommonlyusedrelationshiplSglVenbytheexponen- tialfunction

EffectofCompatibility onAttractiveness -EXP

ofProducti [

SensitivltyOf Attractiveness* oInstalledBase

InstalledBase

ofProducti Thresholdfor

ompatibilityEffects)]

(10-6)

Inthisequation,attractivenessrisesexponentiallyastheinstalledbasegrowsrela-

tivetotheThresholdforCompatibilityEffects.TheparameterSensitivityOfAt-

tractivenesstoInstalledBasecontrolsthestrengthoftheeffect.Thethresholdisa

scalingfactorthatrepresentsthesizeoftheinstalledbaseabovewhichnetworkef-

fectsbecomeimportant･16Theexponentialcurveforattractivenessisplausible:

WhentherewereonlytwotelephonesintheUnitedStates,theutilityofthephone

wasnotverygreattothethirdpotentialbuyer,butwhentherewere100million,

theutilityofthetelephonetothenextbuyerwasmuch,muchgreater.Theexpo-

nentialfunctionmeansattractivenessrisesatanincreasingrateaStheinstalledbase

grows･17Thelargerthethresholdforcompatibilityeffects,thelargertheinstalled

basemustbebeforeitseffectonattractivenessbeginstooutweightheeffectsof otherfactorsofattractiveness.

Forexample,Betamax,asthefirsthomeVCRformattoreachthemar-

ket,hadalargerelativeadvantageininstalledbaseintheearlyyears.Buteven

thoughthereweremanymoreBetamaxmachinesthanVHSmachinesearlyon,the

effectofthisrelativeadvantagewasslight:sofewpeoplehadmachinesthat

I6Mathematically,onlytheratioofthesensitivltytOthethresholdmatters･Nevertheless,也cyare conceptuallydistinct.ApplyingthesensitivltytOthenormalizedratioofinstalledbasemakesit mucheasiertointerpretthemodelandparameters.

17TheexponentialfunctionissimpleandconvenientanalytlCallybutisnotrobust･Withthe exponentialfunctionforattractivenesstheincreaseinattractiveness血.omaddinganotherunitto theinstalledbaseisalwaysgreaterthanthatoftheunitbefore.Amorerealisticfunctionwould saturateforhighlevelsoftheinstalledbase,representingtheeventualdominanceofdiminishing returnsastheinstalledbasebecomesverylarge･Chapter14discussesth econstructionofsuch nonlinearfunctions.

Chapter10 PathDependenceandPositiveFeedback 395

compatibilitywasnotyetanissueformostpotentialpurchasers.Astheinstalled

basegrew,however,compatibilitybegantoloomlargeinpeople'sassessmentsof

productattractiveness.

Inthissimplemodeltheotherfactorsofattractivenessareexogenousandas-

sumedtovaryrandomlyaroundtheneutralvalueofone:

EffectofOtherFactors

onAttractiveness -NORMAL

ofProducti (

StandardDeviation NoiseSeedfor

ofRandomEffects, RandomEffectson onAttractivenes AttractivenessofProduct

(10-7)

wheretheNORMAL(mean,standarddeviation,noiseseed)functionsamplesfrom

anomaldistributionwithameanandstandarddeviationsetbythemodeler.The

noiseseedisdifferentforeachproducttoensurethattherandomeffectsforeach

productareindependent･18

Theformulationformarketsharemeetsallthreecriteriaforagoodformula-

tion.Thegreatertheattractivenessoffirmi,thegreateritsmarketsharewillbe,

Marketshareiszeroiftheattractivenessofthefirm'sproductsiszeroandloo鞄if

thecompetitors'productsarecompletelyunattractive.Thesum ofthemarket

sharesforallfirmswillalwaysequalloo鞄foranynumberoffirms.Theseprop-

ertiesholdforanyfunctionsrelatingProductattributestoattractiveness･Many

shapesfortheindividualattractivenessfunctionsareplausible.Theexponential

functionusedhereisespeciallyconvenientbecauseitcanbetransformedintoa

forminwhichmarketsharescanbeexpressedasalinearfunctionoftheattributes

ofproductattractiveness,allowlngtheattractivenessfunctionstobeestimatedby

standardregressiontechniques.Whenproductattractivenessisspecifiedasthe

productofexponentialfunctionsofeachattribute,theformulationformarketshare

isknownasalogitfunction,becausemarketshareasafunctionofproductattrib-

utesfollowsalogisticcurve･19

Figure10-24illustratesthelogltmodelforvariousvaluesoftheparameters.

Thegraphshowsthemarketshareoffirm 1inatwojirmmarketasitsinstalled

basevaries.Theinstalledbaseoffirm2isassumedtobeconstantandequaltothe

thresholdforcompatibilityeffects.Thegraphshowstheresultingmarketshareof

firm1fordifferentvaluesofthesensitivltyOfattractivenesstoinstalledbase.Inall

cases,whentheinstalledbasesofthetwoproductsareequal(alongwithallother

factorsofattractiveness),eachfirmreceiveshalfthemarket.Marketsharefollows

theloglSticcurveasinstalledbasevaries･Notethatthemarglnalimpactofan increaseininstalledbaseonmarketsharediminishesasinstalledbasebecomes

verylarge:oncemarketshareapproaches100%,furtherincreasesinattractiveness

18Theformulationfortherandomeffectsonattractivenessusedhereselectsanewrandomdraw everytlmeStepin血esimulation.Thisistechllicallynotcorrect,sincechanglngthetimestepfor updatingth estatesofthemodelwilldramaticallyaltertherandomshocksaffectingthesystem. "Random"shocksinrealsystemsarecorrelated,especiallyovershorttimeframes,sincerealsys- temshaveinertiathatpreventsverylargechangesinthevaluesofvariablesfromonemomentto thenext.Amoreapproprlatemodelofthenoiseprocesswouldbeso-calledpinknoise,thatis, noisethatisseriallycorrelated.SeeappendixBformodelsofpinknoisesuitableforusein continuoustimesimulations.

19Thepropertiesandestimationissuesforlogltmodelsandothermodelsofchoicearediscussed inmanystatisticstexts,e.g.,AldrichalldNelson(1984).

396

FIGURE10-24 Behaviorofthe

logitmodelfor marketshare

Twofirmsare assumed.The

9raPhshowsmar- ketshareoffirm1 asafunctionof itsinsta"edbase relativetothe thresholdforcom-

patibilityeffects, forvariousvalues

ofthesensitivityof attractivenessto instaHedbases. Theinstalledbase offirm2isas- sumedtobe constantand

equa一tothe thresho一din allcases.

PartIII TheDynamicsofGrowth

(

s s

aru o !s ua ∈ !p ) a J

t? L JS la嘗

0.0 0.5 1.0 1.5 LnstaHedBaseofProducti

ThresholdforCompatibilnyEffects (dimensionless)

haveasmallerandsmallereffectsincethereissimplylessadditionalmarketshare

togain.ThegreaterthesensitivltyOfattractivenesstotheinstalledbase,the

sharperandsteeperthelogisticcurve,andthemorerapidlyshareapproachesits extremevaluesasinstalledbasevaries.

10.8.2 ModeJBehavior

TosimulatethemodeltheparametersweresetasshowninTable1012.Inparticu-

lar,thesensitivltyOfattractivenesstoinstalledbaseissetto2,representlngamod-

estnetworkeffect.If,earlyinthehistoryofthemarket,theinstalledbaseof

product1is20%ofthethresholdwhilethatofthecompetitorislo啄 ,themarket

shareoffirm 1Willbeonly55%,eventhoughitenjoysa2:1advantageininstalled

base.IfthecompetitorhadlO0%ofthethresholdwhilefirm1had200%asmuch

(stilla2:ladvantage),themarketshareoffirm lwouldthenbe88%,reflectingthe

greaterimpactofalargeinstalledbaseonattractiveness･

Thesimulationbeginswithalevelplayingfield:theparametersforbothfirms

areidentical,Theonlydifferencebetweenthefirmsarisesthroughtherandom

variationsintheattractivenessofeachproductfromotherfactors.Theserandom

effectsareassumedtohaveaverysmallstandarddeviation,just1%.

Figure10-25shows20simulationsofthemodel.Priortotheintroductionof

anyrandomvariationsinproductattractivenessthetwofirmshavethesameover-

allattractiveness,andmarketshareremainsattheinitialequilibrium of50%.

Whentherandomeffectsbegin,attimezero,thenetworkeffectisweak,somar-

ketsharefluctuatesrandomlyintheneighborhoodof50%.Astheinstalledbaseof

eachfirm grows,however,thepositivenetworkfeedbackgainsinstrengthandam-

plifiesanysmalladvantageininstalledbasecreatedbytherandomshocksinprod-

uctattractiveness.Astheinstalledbaseadvantageofonefirmgrows,thepositive

networkfeedbackgainsevenmorestrength,furtherboostlngthemarketshareof

theleaderuntilshareapproacheslO0%.Thereareonlytwostableequilibria:com-

pletemarketdominanceorextinction.Giventheparametersinthesimulation,the

systemlocksintooneoftheseequilibriaquiterapidly.

Figure10-26showsthedistributionofmarketsharesforfirm 1atvarious

timesinasampleof5000simulations.Priortoyear0,therearenorandomeffects

Chapter10 PathDependenceandPositiveFeedback

TABLE10-2 Parametersfor simulationof instaHedbase model

FIGURE10-25 Simulationsof theinstaHed basemode一

Twentysimula- tionsareshown. Attimezerothe standarddeviation oftherandomeト

fectsonproduct attractiveness risesfrom OtoO.01.

397

TotalDemand

SensitivityofAttractivenessfromlnstaHedBase

ThresholdforCompatibilityEffects StandardDeviationofRandomEffects

onAttractiveness

fnitiallnsta=edBaseProducti

InitialTime

TimeStepforsimulation

lmi"ionunits/year

2(dimensionless) lmi"ionunits

0.Ol(dimensionless) 1unit

-1years

0,25years

tL)

LL)

L ∈ Lに

ha Je LJS

芯空 e M

-101 2 3 4 5 6 7 8 9 10 Years

andthesystemisbalancedontheunstableequilibriumof50%marketshare.At timezero,the丘rstrandomshocksbegintoperturbthesystem,butthepositive

feedbackshavenotyetbeguntooperate.Marketshareistightlyclusteredbetween about49%and51%,andthedistributionofmarketsharesisnomal(bellshaped).

Thedistributionchangesonlyslightlyforthefirstfewyears,evenafterthefeed- backsinthesystembegintooperate.Byyear4thevarianceofthedistributionof marketshareshasgrownsubstantially,butthedistributionstillappearstobe

roughlynormal,withaslnglepeakat50%marketshare.Byyear6,thedistribu- tionhasspreadstillfurtherandhasbeguntobifurcateintotwomodes.Theposi-

tivenetworkfeedbacknowrapidlydifferentiatesthetwofirmsfromoneanother, untilonegalnSIOO%ofthemarketandtheotheriswipedout.Byyear10,the

marketshareofthewinningfirminnearlyallsimulationsisgreaterthan95%. ThebehaviorofthemodelissimilartothenonlinearPolyaprocessinsection

lO壬2=HoweverラーhemodelrelaxestherestrictiveassumptionsofthePolvamodel.

First,themodelisformulatedincontinuoustime.Second,wherethePolyaprocess

selectsonlyonestoneperperiod,eitherblackorwhite,heretotalsalesaredivided intosimultaneousandcontinuousflowsofsalesforeachproduct.WherethePolya processchooseswhichcolortoaddbasedonaslnglerandomevent,themodelhere includesmultiplesourcesofrandomvariationinconsumerchoices.

Mostimportantly,theattractivenessofeachproductdependsnotonthesizeof theinstalledbaserelativetothatofotherproductsbutontheabsolutesizeofeach

product'sinstalledbase.InthePoly乱process,theprobabilityofselectlngaglVen colordependsonlyontheproportionofstoneswiththatcoloralreadyinthejar.

398 PartIII TheDynamicsofGrowth

FIGURE10-26 Evolutionofthedistributionofmarketshare

ThedistributionofmarketshareforFirm1in5000simulations,Shownevery2years.Verticalaxisis

theproportionofsimulationsfaHlngWithineach5%incrementofmarketshare.

MarketShare, Firm1

Chapter10 PathDependenceandPositiveFeedback 399

ThisassumptlOnisnotrealisticforproductswithcompatibilityandnetwork effects･First,consumersarenotlikelytoknowtheinstalledbaseofeachproduct, andthedecisionrulesinmodelsshouldnotuseinformationtherealdecisionmak-

ersdonothave･Second,thePolyaassumpt10nmeanstheeffectofcompatibilityon marketshareisthesameforagivenratiooftheinstalledbasesofthedifferent products,nomatterhowlargetheinstalledbase.A2:linstalledbaseadvantagefor

VHSwouldyieldthesamemarketshareadvantagewhethertheinstalledbasewas 20VHSto10Betamaxmachinesor20millionto10million.

People'sdecisionsareinfluencedbycompatibilitywiththemachinesowned byothersintheirsocialnetwork.Thelargertheinstalledbaseofeachproduct,the greaterthechancethatanypotentialbuyerwillhavefriendsandfamilywhoal-

readyownthatformat,Clearly,whentheinstalledbaseofproductsisverylow,

compatibilitylSnotyetafactorforprospectivepurchasers.Asthetotalinstalled

basegrowsandmoreofthepeopleapotentialbuyerinteractswithhavetheprod- uct,compatibilitybecomesprogressivelymoreimportant.Theformulationfor productattractivenessmeetsthiscriterionbecauseitdependsonthesizeofthein-

stalledbaseofeachproduct(scaledbytheThresholdfわrCompatibilityE恥cts). Theexponentialfunctionforattractivenessreducestheeffectofdifferencesinin-

stalledbasewhenthetotalinstalledbaseisverysmallandamplifiesthedifference asthetotalinstalledbasegrows.

Asaresult,thestrengthofthepositivenetworkfeedbackincreasesasthemar-

ketgrows･Theseshiftsinloopdominancecanbeillustratedbyconstructlngthe phaseplotforthemodel･ThephaseplotshowshowmarketshareforaglVenProd- uctdependsonthatproduct'sshareofthetotalinstalledbase.Thephaseplotis analogoustothephaseplotforthenonlinearPolyaprocessshowninFigurelO16.

ThefractionoftheinstalledbaseofaglVenProductisanalogoustotheproportion

ofstonesofagivencoloralreadyinthejar･Marketshareisanalogoustotheprob-

abilityofaddingastoneofaglVenCOlortothejar.

Asinthepriorphaseplots,thefixedpoints(Pointswherethephaseplot crossesthe45oline)areequilibriaformarketshare(FigurelO127).Wheneverthe curvedefiningmarketshareliesabovethe45oline,marketshareforfirm1exI

ceedsfirml'sshareoftheinstalledbase,causlngfirm l'sshareoftheinstalled basetorise.ThetrajectoryOfthesystemmowsalongthemarketsharecurvetothe

right,towardahighershareoftheinstalledbase,untilsharereachesequilibriumat afixedpointwhereitmeetsthe45oline.Conversely,whenthephaseplotliesbel lowthe45oline,firml'smarketshareislessthanitscurrentshareoftheinstalled

base,soitsshareoftheinstalledbasewillfall･ThetrajectoryOfthesystemflows alongthephaseplottothele氏untilitcomestoanotherequilibriumwhereitmeets the45oline.

Becausetheshareofinstalledbaseriseswhenevermarketshareisabovethe

450lineandfallswhenevermarketshareisbelowit,thestabilityofanyequilib-

riumpointiseasilydeterminedfromthephaseplot.Iftheslopeofthephaseplot atanequilibriumpointisgreaterthan1,thatequilibriumpointisunstable.Aslight increaseintheproduct'sshareofinstalledbasecausesanevengreaterincreasein

marketshare,furtherboostlngtheproduct'sshareoftheinstalledbaseandpro- gressivelymovingthesystemawayfromtheequilibrium･Aslightdecreaseinthe product'sshareofinstalledbasecausesalargerdroplnmarketshare,furtherre- ducingtheshareofinstalledbaseandmovlngthesystemfarthertotheleft,away

400

FIGURE10-27

Hypotheticaf phaseplot showlnglocation andstabilityof equ‖ibria

Fixedpoints (wherethephase p一otcrossesthe 45oline)are theequilibria ofthesystem. Fixedpoints wherethephase plothasaslope greaterthan1are unstable;those withslopeJess than1arestable. Arrowsindicate

theflowalong thephaseplot.

PartIIITheDynamicsofGrowth

(ssa luO! S uau !P )

〓

np o J d

.aJ e

LJS la

qJe≡

hstalfedBaseofProduct1 TotallnstalledBase

(dimensionless)

fromtheequilibriumpolnt･Wh entheslopeofthephaseplotisgreaterthanunity, thesystem'sdynamicsaredominatedbythepositivefeedbacks.When,however, theslopeofthephaseplotatanequilibriumpolntislessthan1,thenaslightdrop inproductl'sshareoftheinstalledbasecausesasmallerdroplnmarketshare. Sincemarketshareexceedsthecurrentshareoftheinstalledbase,theshareof血e

installedbasewillincrease,raisingmarketshareandmovlngthesystembackto- wardtheequilibriumpoint･Anincreaseininstalledbasehasasimilarcompen-

satoryeffectbecausethemarketsharerisesbylessthantheinstalledbase,diluting theinstalledbaseuntilthesystemretumstotheorlglnalequilibrium.

Whentheslopeofthephaseplotislessthanunlty,thesystem'sdynamicsare dominatedbynegativefeedback.Becauseingeneralthephaseplotisnonlinear,its slopevaries,andasitdoes,Sotoodoestherelativeimportanceofthepositiveand negativeloopsinthesystem.Pointswheretheslopeofthephaseplotshiftsfrom lessthan1togreaterthanlmarkshiftsinloopdominancefromnetnegativetonet positivefeedback.

1 1.r- Figtife10-28Showsthepnaseplotforthemarketsharemodei･Thephaseplot

showsthemarketshareoffirm1asafunctionoftheproportionofproduct1inthe totalinstalledbase.However,unlikethenonlinearPolyaprocess(Figure10-6),the strengthofthepositivenetworkeffectloopgrowsasthetotalinstalledbasegrows. Thereforetheshapeofthephaseplotrelatingfirm1'smarketsharetoitsfraction ofthetotalinstalledbasechangesasthetotalinstalledbasegrows.Thefigure showsfourofthesecurves,forsituationswherethecompetitor'sinstalledbaseis 0.10,0.50,1,and2timesthesizeofthethresholdforcompatibilityeffects.The systemalwayshasanequilibriumwherethemarketshareandshareofthetotal

Chapter10 PathDependenceandPositiveFeedback

FIGURE10-28 Phaseplotfornetworkeffects model

Thephaseplotshowsthemarket shareoffirm1asafunctl'Onofllts shareofthetotalinsta‖edbase.

Thefunctiondependsonthesizeof theinstalledbaseofthecompetitor andisshownforfourvaluesoHhe

competitor'sinsta‖edbaserelative tothethresholdforcompatibility effects(B2-Jnsta"edBase Product2/Thresho一dfor

CompatibilityEHects).Thearrows showthedirectionofflowforeach Curve.

Toderivethephaseplot,notethat marketshareforfirmlisglVenby thelogitmodel

MS1-Al/(Al+A2)

whereMSismarketshareandAis

theattractivenessofeachproduct. Assumlngtheothereffectson attractivenesshaveaneutraleffect, attractivenessisdeterminedonlyby thenetworkeffect:

A.-exp(sB.)

wheres-Sensitivityof AttractivenessfromCompatib冊y andBEistheinstaHedbaseof productirelativetothethreshold forcompatibilityeffectsITheratio oftheinstaHedbaseofproduct1to thetotaHnstaHedbase,R,is

R-Bl/(Bl+B2).

ExpressingBlaSB2R/(1-R)and substitutingintotheequationfor attractivenessyie!dsma.rketshare forproductlasafunctionof productl'sshareoHhetota一 installedbase:

MS1-eXP【S(R/(1-R))B2】/ (expls(R/(1-R))B2]+explsB2]).

Thefourcurvesinthefigure assumeB2-0.1,0.5,1,and2.

(ssa luO!S u a ∈ !P )

IU nPO Jd. aJt2LJS laU

e LN

0.50

401

0.00 0.25 0.50 0.75 1.00

日nstaHedBaseofProduct1 Tota日nstalledBase

(dimensionless)

installedbaseare50%.However,theshapeofthecurves,andthe

numberandstabilityofequilibria,changedramaticauyasthe

marketgrows. Wh enthetotalinstalledbaseoftheindustryissmall,thenet-

workeffectisweak.ThecurveinFigure10-28labeledB2-0.l

showshowmarketshareevolveswhen也ecompetltOr'shstaued baseisjustlO%ofthethresholdforcompatibilityeffects.When theinstalledbaseisverysmall,thenetworkeffectissoweakthat

theequilibriumat50%oftheinstalledbaseisstable(thephase plotcrossesthe45oheat50%sharewithaslope lessthan1).

Overawiderange,randomshocksaffectingmarketshareare self-correcting:tOtheextentashockmovesthesystemaway from50%,marketshareadjuststocompensate,graduallyretum- ingtheinstalledbasetoaratioof1:1.Notethattherearetwoad-

ditionalequilibria:anunstablepointWhentheshareofinstalled baseisabout90% andastablepolntWhentheshareofin- stalledbaseislO0%.Todominatethemarketwhenthetotal

installedbaseissmall,firm1wouldhavetohaveatleast90%of theinstauedbase.

Asthetotalinstalledbaserises,thepositivenetworkeffect

loopgrowsstronger.Theslopeofthephaseplotatthe50%point rises,andtheunstableequilibriumpolntat90%sharemovesto theleft.Wh enthecompetltOr'sinstalledbaseishalfthethreshold

(thecurvelabeledB2-0.5),theslope ofthephaseplotatthe 50%equilibriumlSJustaboutequalto1.Atthispoint,theinitial

402 PartIIITheDynamicsofGrowth

50%equilibriumisbistable:marketsharenowalwaysliesabovethe45oline.If theshareofinstalledbaseforfirm1drops,marketsharerises,compensatingfor thedisturbanceandreturnlngtheshareofinstalledbaseto50%,butanincreasein

installedbasecausesanevengreaterriseinshare,movlngthesystemaway丘.om the50%equilibrium.Ifrandomshocksinitiallygive丘rm1asmalladvantagein installedbase,marketsharewilltendtoriSefurtheruntilfirm1dominatesthemar-

ketandreachesthestableequilibriumatloo鞄oftheinstalledbase.

Furthergrowthinthetotalinstalledbasecontinuestoincreasethestrengthof

thepositivenetworkeffectloopuntilitdominatesthedynamicsofthesystem. Whenthecompetitor'sinstalledbaseisequaltothethreshold(thecurvelabeled

B2-1),theslopeofthephaseplotatthe50%equilibriumisgreaterthan1,and theequilibriumat50%isunstable.Therearenowtwostableequilibria:oneat loo鞄oftheinstalledbaseandoneatabout20%.Thepositiveloopsdominatethe system.ThefirmthatgalnSthelargestshareoftheinstalledbasewinsaneven largershareofthemarketandbeginstoconsolidateitsdominanceoftheindustry whilethosefindingthemselveswiththesmallestsharesoftheinstalledbasefall fartherandfartherbehind.

Asgrowthcontinues,thestrengthofthepositivenetworklooprisesStillmore, furtheracceleratlngtheleader'Srisetodominance.Bythetimethecompetitor'sin- stalledbasehasreachedtwicethethreshold(thecurvelabeledB2-2),thephase plotisqulteSteeparoundthe50%equilibriumandthetwostableequilibriahave movedcloserto0andlOO%･Thepositiveloopsarenowsostrongthatlockintoa singlestandardisqulterapidandthechancethatanyrandomshocksorpolicies mightreversetheoutcomeisvanishinglysmall.

10.8.3 PoEicy萱mp批ati｡ns

Themodelresultshaveclearimplicationsforfirmsseekingtousepositivefeed- backssuchasnetworkeffectstogalnadecisivemarketshareadvantageandelim- inatetheircompetitors.Whenanewproductisfirstintroducedtoamarketwhere nopriorStandardshavebeenestablished,thenetworkeffectislikelytobequite weak.Marketsharewillbedeterminedprimarilybyotherproductattributessuch

asquality,price,features,andsoon.Duringthisperiod,alateentrantmight,byof- feringasuperiorproduct,aggressiveprlClng,JOlntVenturesWithprovidersofcom- plementaryassets,andothermeans,overcomethefirstmover'sadvantagein

installedbaseandtakeleadershipoftheindustry.Thewindowofopportunityfor suchactionislimited,however.Asthemarketgrows,networkeffectsandthe availabilityofcomplementaryproducts(e.蛋.,Compatibleprerecordedtapesfor

VCRs,Compatiblesoftwareforcomputers)growinimportance.Afirmthatestabl lishesaleadininstalledbase,intheavailabilityofcomplementaryassets,andin

theperceptlOnthatitisthemarketleaderislikelytogalれanedgeinmarketshare thatleadstofurthergainsinaself-fulfillingprophecy.Astheinstalledbasegrows andthenetworkeffectsbecomeevenstronger,thechancethatalateentrantcan overcometheadvantageofthefirstmoverdeclinesrapidly,bothbecausethetotal installedbaseisgrowing(requiringtheupstarttosellmoreunits)andbecause

compatibilitybecomesamoreandmoreimportantdete-inantofcustomerpur- chasedecisions(givingthecu汀entleadermoreofanedge).

Chapter10 PathDependenceandPositiveFeedback 403

ThesedynamicsdescribewhathappenedintheVCRindustryandhelpexplain

whySony,asthefirstmover,wasunabletoconvertitsearlyleadintomarketdom-

inancedespitethelargenumberofpositivefeedbacksconferringCumulativead- vantagetotheleader.WhenVHSwasintroduced,theinstalledbaseofVCRswas

sosmallthatcompatibilitywasnotyetanissuefわrmostcustomers.Otherattributes

ofproductattractivenessdominatedinthepurchasedecision･WhereasSony,hop-

1ngtOmonopolizetheformattheybelievedwouldbecometheindustrystandard,

kepttightcontrolofthetechnology,thusrestrictlngItsavailabilityandkeeplngthe

prlCerelativelyhigh,MatsushitadecidedtolicenseVHSwidelyandcheaply･The

VHSconsortium,thoughthelaterentranttothemarket,wasabletogainthelargest

shareofthemarketjustatthepolntWheretotalsalesgrowthexplodedandrapidly overcametheinitialinstalledbaseadvantageofBetamax.VHSbecametheleader

aroundthetimefilmstudiosbegantoissuefilmsforthehomevideomarkeLOnce

thefilm studiosdecidedtoproducetapesforthehomemarket,compatibility becamethedominantattributeofattractivenessinthepurchasedecisionofmost

customers,andfilm studioschosetoissuetapesinthemostprevalentformat.

Matsushita'sstrategygavethemtheleadinshareofVHStapesJustatthetime

compatibilitybecamecritical.ThoughSonytriedtofightbackbylowerlngPrlCeS

andencouragingProductionofBetamaxformattapes,thewindowofopportunity

hadshut.Thegrowthoftheinstalledbasehadstrengthenedthenetworkeffectsso muchthatVHS'sleadcouldnotbeovercome.ThefateofBetamaxwassealed.

Po!EcyAnaSys;ls

Usethemodeldevelopedinsection10.8toexplorethepoliciessuggestedbelow. Inthesetests,Startyoursimulationsattimezero,Withtheparametersdescribedin

Table10-2.However,youshouldeliminatetherandomshocksbysettingthestan- darddeviationofrandomeffectsonattractivenesstozero.

1･Suppose丘rm1attemptstogalれinitialadvantagebyseedingthe

marketplacewithsomefreeunits,Sothatatthestartofthesimulationthe installedbaseoffirm1is10,000units,whilefirm2'sinitialinstalledbase remainslunit.Runthemodel.Whatistheinitialmarketshareoffirm1?

Whathappenstomarketshareovertime,andwhy?

2･Supposefirm2attemptstocounterfirml'sefforttowinthemarketby

dolingout10,000freeunitsofitsownproduct.However,ittakestimefor

firm2toreact,sothefreeunitsoffirm 2'sproductdon'tbegintoreachthe

lTTlarketu壬Iti16王r.Onthshavepassed.Supposefurtherthatittakes1yearto distributeall10,000units.

Toimplementthispolicy,modifytheequationforSalesofProduct2as follows:

SalesofProduct2-TotalDemand*MarketShareProduct2+ExtraSalesof

Product2*PULSE(ExtraSalesStartTime,DurationofExtraSales)

ExtraSalesStartTime-0.5

DurationofExtraSales- 1 (10-2a)

404 PartIIITheDynamicsofGrowth

where

PULSE(SBauhraIiTne,ロムtthS::i≡me≦Time≦StartTime'Duration (10-2a)

ThePULSEfunctioniszerountiltheStartTime,thentakesavalueof1for

Durationtimeunits,andreturnstozerothereafter.

Themodifiedequationthereforeincreasessalesofproduct2atarateof

lO,000unitsperyearfor1yearstartlngattime0,5years,increaslngthein-

stalledbaseofproduct2exactly10,000units,allelseequal･

Doesfirm2'Spolicyofseedingthemarketwith10,000extraunitsto

counterfirm1'sinitial10,000unitadvantagework?Why/whynot?

3.Howmanyunitsmustfirm 2addtoitssalesrateoverthecourseofayear

startlngattime0.5toovercomefirm l'sinitialadvantageandwinthemar-

ket?EstimatlngthisquantltytOthenearest1000units/yearissufficientpre- CISIOn.

41Supposefirm2waitsuntilyear5tocounterfirml'sadvantage(again, firm1startswithaninitialinstalledbaseof10,000unitsandfirm2starts

with1unit).Howmanyunitsmustfirm2nowaddtoitsinstalledbaseover

thecourseof1yeartoovercometheleadoffirm1andcapturethemarket?

Why?EstimatingthisquantitytOthenearest10,000unitsperyearissuffi-

cientprecision.

5.Whatdoyouconcludeabouttheoptlmalstrategyforafirminmarketschar-

acterizedbystrongpositivenetworkeffects?Howwouldyouimplement

thewinnlngStrategy?Whatconsiderationsmighttemperorreversethis conclusion?

6.Whatotherstrategiesbesidesfreedistributionofproductmightafirmuseto

countertheinitialadvantageofarival?Giveexamples.

Extending帥eModel

Thischallengeinvitesyoutorelaxsomeofthemodel'ssimplifyingassumptionstO

explorethesensitivltyOftheresultstoalternativerepresentationsofindustryand firmstructure.

1.Turnoveroftheinstalledbase:Inthesimplemodelthereisnooutflow

fromtheinstalledbaseofproduct.Inreality,productssuchasVCRsand

computerswearoutorarereplacedbylmprOVedproducts.Revisethemodei

toincludeproductdiscardsandtumoveroftheinstalledbase.Assumethe

averagelifetimeofbothproductsisthesameandequalto5years.Also

assumethediscardprocessis丘rst-order,thatis,thatthediscardrateequals

theinstalledbaseofeachproductdividedbytheaveragelifetime.

Assumeeverypersonorhouseholddiscardingtheproductpurchasesa

replacement･Youwillthereforeneedtomodifytheequationfortotal demandtoincludethereplacementdemand,consistingOf仙esumofthe individualdiscardrates.

Chapter10 PathDependenceandPositiveFeedback 405

Explorethebehavioroftherevisedmodelfordifferentvaluesofthe productlifetime(settingtheaveragelifetimeoftheproducttoaverylarge number[suchasonetrillion]givesyouthebasecaseoftheoriginalmodel). Whatistheeffectofdiscardsontherateatwhichthesystemlocksintoa standard?Explainintermsofthefeedbackstructure. Hint.l Plotthemarket

shareandshareofinstalledbaseforfirm1. Howdoestheirrelationship changeastheaveragelifetimeoftheproductchanges?

2 ･ Thesimplemodelaggregatesmanypositivefeedbacksintoaslngleeffect

ofinstalledbaseonproductattractiveness･ However, thenetworkeffect isonlyoneofmanyimportantpositiveloops. Theavailabilityofcomple一 mentaryresourcesisoftenevenmoreimportant. VCRswithoutcompatible tapesandcomputerswithoutcompatiblesoftwareareuseless;theDvorak

typewriterkeyboardisfasterthantheQWERTYkeyboardbutisuseless withoutDvorak-trainedtypists. Aggregatlngtheeffectofcomplementary productsintothenetworke恥ctisnotgenerallyapproprlatebecausethese twoloopsoperatewithdifferenttimedelaysandinvolvedecisionsmade bydifferentgroups(complementaryproductscanbeproducedbythird

parties). Modifythemodeltoincludetheavailabilityofcomplementaryproducts explicitly. Todoso,ma kethefollowingaSSumPtlOnS:

a. Thetotalproductionofcomplementaryproductsisdividedintop

ductionofgoodscompatiblewithproduct1andproductionofgoods compatiblewithproduct2.

b ･ Thetotalproductionofcomplementarygoodsshouldbeproportionalto

thetotalinstalledbaseofproduct1andproduct2･ Thebiggerthesize ofthemarket,t hegreatertheoutputofcomplementaryproducts(e.g., videotapes,so ftware, typists)willbe.

C. Usethelogitformulationtodeterminetheshareoftotalcomplemen-

tarygoodproductiongoingtOeachproduct. Theshareofcomplemen- tarygoodsproducedforeachformatisglVenbytheattractivenessof

thatformatrelativetotheattractivenessofallformatopt10nS. Theat- tractivenessofaglVenformattoaproducerofcomplementarygoods dependsonthesizeoftheinstalledbaseofproductsuslngthatformat. Aggregatetheeffectsofallotherconsiderationsintoanexogenous term, "attractivenessofproductitothirdpartiesfromotherfactors. "

d . Productionofeachtypeofcomplementarygoodaccumulatesina

stock. Assumecomplementarygoodshaveanaverageusefullifeof

⊃yearsLaSSumeafirst-orderdiscardprocess). TuTrliikepartiabove, dis- Cardsofcomplementarygoodsarenotautomaticallyreplaced(thatis, thetotalproductionofcomplementarygoodsdoesnotincludethetotal discardrate). Assumetheinitialinstalledbaseofeachtypeofcomple一 mentarygoodiszero(youmayvarythisasapolicylater).

e. Modifytheformulationfortheattractivenessofeachproduct(equation

(1015))toincludeaneffectoftheavailabilityofcomplementarygoods. Theeffectshouldbeformulatedanalogouslytothenetworkeffect. Se1 1ectparametersyouthinkarereasonable(usetheVCRcaseasaguide,

406 PartIIITheDynamicsofGrowth

butdon'ttrytoreplicatethehistoryoftheVCRindustryexactly-you aretryingtobuildageneralmodel).Inparticular,Setparameterssothat boththenetworkandcomplementarygoodseffectsareimportantand sotherelativeimportanceofthenetworkeffectandavailabilityof complementarygoodsarereasonableinyourjudgment.Document yourmodel(Seechapter21);includebriefjustificationforyourselec-

tionofparameters.

f. Testyourmodel,refiningtheparametersifnecessary.Whatistheim- pactofanexplicitrepresentationofcomplementarygoodsonthedy- namicsofstandardformation?Explainintermsofthefeedback structure.ExplorethesensitivltyOfthesystemtoparameters･Explore theresponseofthesystemtopolicies,including

i. Seedingthemarketwithfreeunits,asinthepreviousChallenge･

ii. Seedingthemarketforcomplementarygoodsbyensurlngthereis aninstalledbaseofcomplementarygoodscompatiblewithyour formatwhenyourproductislaunched･

iii.EnterlngIntoJOlntVenturesOrOtheragreementsthatincreasethe attractivenessofyourlbmattoproducersofcomplementary goods.

iv. Otherpoliciesyoumightentertain.

10.9 SuMMARY

Pathdependenceisacommonphenomenoninnaturalandhumansystems,Path dependencearisesinsystemsdominatedbypositivefeedbackEvenwhenallpaths areinitiallyequallyattractive,thesymmetryisbrokenbymicroscoplCnoiseand externalperturbations.Thepositivefeedbacksthenamplifythesesmallinitialdif-

ferencestomacroscopICSlgnificance1Onceadominantdesignorstandardhas emerged,thecostsofswitchingbecomeprohibitive,sotheequilibriumisself-en- forclng:thesystemhaslockedin.Lockinpersistsuntilanarchitecturalshiftor largeextemalshockrendersthedominantdesignobsolete･Awiderangeofposi- tivefeedbacksdrivesthegrowthofbusinesses.Theevidencesuggeststhatthe profitabilityofindividualfirmsandtheevolutionoftheeconomyasawholeis stronglyinfluencedbythesepositiveloopsandexhibitspath-dependentbehavior･ Successfulfirmsareabletostrengthenseveralofthepositiveloopsthatcandrive growthtocreatesynergleSthatleadstocumulativesuccess･

ratn(lependenceintheeconomylSCOmmOnbecausethegrowthofbusiness enterprlSeSisdrivenbyahostofpositivefeedbacks.Thesefeedbacksinvolvescale economies,learning,networkeffects,marketpower,andmanyotherprocesses. Themostsuccessfulfirmsareabletocreatesynergybyusingensemblesofthese feedbackstocreateamutuallyconsistentstrategy.However,successwithoneset ofthesepositiveloopscanleadtoinertiaandrigiditythatpreventafirmthatdom- inatesinonereglmefrommaintainlngitsdominanceasthetechnical,economic, political,orsocialenvironmentchanges.

呈呈

T3聖星野S

Delayalwaysbreedsdangey:

-MigueldeCervantes(DonQuixote,Bookiv,Chap.ii.)

NeverdotodaywhatyoucanputoHtilltomorrow.Delaymaygiveclearer lightastowhatisbesttobedone.

-A乱ronBurr

Delaysareacriticalsourceofdynamicsinnearlyallsystems.Somedelaysbreed dangerbycreatlngInstabilityandoscillation.Othersprovideaclearerlightby filterlngOutunWantedvariabilityandenablingmanagerstoseparateslgnalsfrom noise･Inthischapteryouwillexplorethestructureandbehaviorofdelays,develop variousmodelsofdelays,andtesttheirresponsetoarangeofinputs,Thechapter willhelpyouunderstandthedynamicsofdelayssothatyoucanusethem approprlatelyinmorecomplexmodels.Thechapteralsopresentscasestudies highlightingtheuseofdelaysinvariouscontexts,includingcapitalinvest- mentinthemacroeconomyandforecastingdemandatasuccessfulsemiconductor rnap.ufacturer.

ll.1 DELAYS:ANINTRODUCT10N

DurationandDyrlamicsof【)cbys

Beforeconsideringhowtomodeldelays,reflectonsomedelaysincommon processes･AnswerthefollowingquestionswithoutusingOutsidereferencesorany

409

410 PartIV ToolsforModelingDynamicSystems

computersimulations;glVeyourbestintuitiveestimate.Don'tspendmorethana fewminutesonthischallenge.

1.ManufacturlngfirmsdeterminetheamountofplantandequlPmentthey needbasedonthedemandtheyexpectfortheirproductsaswellasthe expectedprofitabilityofthenewequlPment.Supposethereisasudden, unantlClpatedlo啄increaseinordersforthefirm'sproduct,Howlongdoes ittake,onaverage,beforethefirm'SproductioncapacityIncreasestOthe newlevel?Assumeinvestmentsinnewcapacltyareexpectedtoyieldthe firm'srequiredretumoninvestment.

2.Suppose血ereisasudden,unanticlpatedincreaseoflo瑞inthetotal demandformanufacturedgoodsthroughouttheeconomy.Howlongdoesit takefortheeconomyasawholetoincreasetotalmanufacturlngCapacitytO thenewrateofaggregateorders?

3.ConsiderthemarketforagrlCulturalcommoditiessuchaspork.Whatisthe averagedelaybetweenariseintheprlCeOfporkandtheresultingIncrease inporksupply?

4.Howlongdoesittakeeconomicforecasterstorevisetheirestimatesof inflation?Thatis,ifthereisanunanticIPatedincreaseintheinflationrate, howlongwillittakefortheforecastsoftheexpertstoadjusttothenew rate?

5.HowlongdoesittakeanationliketheUnitedStatestorespondtoan environmentalchallengesuchasairorwaterpollution?Thatis,whatis thetimerequiredtorecognlZehighlevelsofpollutants,suchascarbon monoxideemittedbyautomobiles,andreducethemwithinsafelimits?

6.Considerthepostoffice.Supposeyoudepositamassmailingof1000 letters-allsentfirstclass-tovariousdestinationsaroundthecountry. Sketchthepattemofdeliveriesyouexpect,assumlngnOlettersgetlost.

7.Considerafirm'sforecastoftheorderrateforitsproductSupposethe actualorderrateandtheforecasthavebeenequalfわralongtlme.Now supposetheactualorderratesuddenlyandunexpectedlyincreasesby50% andremainsatthenewrate.Sketchtheresponseoftheforecast.

8.Supposeittakes5daysforamanufacturertoreceivepartsfromasupplier. Ifthefirmorders10,000unitsperday,howmanyunitsareinthestockof partsonorder?Supposethepartsorderratesuddenlyandunexpectedly increasesto20,000perdayandremainsatthehigherrate,Sketchthe responseJOfthedeliveryrateandoftileStockofpartsonorder.

9.Supposethepartorderrateforthefirminquestion8remainsconstantat lO,000units/day.Suddenlythetimerequiredtodeliverthepartsperma- nentlyincreasesfrom5to10days.Sketchtheresponseofthedeliveryrate andthestockofpartsonorder･

ChapterllDelays 411

FIGUREll -1

Delaysalways containstocks.

11･1rl DefiningDelays DelaysarepervasiveJttakestimetomeasureandreportinfomationJttakestime

tomakedecisions.Andittakestimefordecisionstoaffectthestateofasystem.

Modelersneedtounderstandhowdelaysbehave,howtorepresentthem,howto

chooseamongvarioustypesofdelaysinanymodelingsituation,andhowtoesti- matetheirduration.

Adelayisaprocesswhoseoutputlagsbehinditsinputinsomefashion(see

thetoppanelinFigurell-1).Considerwhat'sinsidetheboxmarkedDelay:Alit-

tlereflectionshowstheremustbeatleastonestockwithineverydelay.Sincethe

outputgenerallydiffersfromtheinput(itlagsbehind),theremustbeastockinside

theprocesstoaccumulatethedifferencebetweenInputandoutput.Considerthe

processofmailingletters.Theinputtothedelayistherateatwhichyoumaillet-

ters･Theoutptltistherateatwhichyourlettersaredelivered.Wherearetheletters

betweenthetimeyoumailthemandthetimetheyaredelivered?Theyresideina

stockofLettersinTransitwithinthepostofficesystem(Figurel111Showsthe

structureforthepostofficeandthegeneralstructurefわrmaterialdelays).

ThetypeofdelayshowninFigurell-1isknownasamaterialdelay,sinceit

capturesthephysicalflowofmaterial(inthiscaseletters)throughadelayprocess.

OtherexamplesofmaterialdelaysincludetheflOwofproductthroughasupply

chain,theconstructionofbuildings,Ortheprogressionofdesigntasksthrougha

productdevelopmentprocess.Ineachtherearephysicalunits(casesofbeer,

squarefeetofspace,orengineeringdrawings)movingthroughtheprocess.Notice

thattheonlyoutflowfromthestockoflettersintransitinthediagramisthedeliv-

eryrate;inthemodel,lettersareneverlostormisdirected(unlikeintherealpost Office).Theflowoflettersthroughthedelayisconserved.

TheoutputofadelaytagsbeMndtheinput:

Generalstructureofamaterialdelay:

Materialin Transit!n官!owRate

Thepostof朋ceasadelay:

Letters in Trans it

Mailing

Rate Delivery

Rate

412 PartIV ToolsforModelingDynamicSystems

ManydelaysrepresentthegradualadjustmentofperceptlOnSOrbeliefs;these

areinformationdelays･Thedelaybetweenachangeintheorderrateforyourcom-

pany'sproductsandyourbeliefaboutthelikelyfutureorderrateisanexampleof aninformationdelay.Supposeordersforyourproducthavebeensteadyat1000

unitsperday,andyouexpectthemtocontinueatthatrate･SuddenlyordersJump to2000units/day.Youareunlikelytoimmediatelyincreaseyourbeliefaboutt0-

morrow'sordersto2000units･Butiftheorderrateremainsat2000units/day,day afterday,youwillgraduallyincreaseyourexpectationoffutureordersuntilit eventuallyreachesthenewrate.ThereisadelaybetweentherecelptOfnewinfor一

mationandtheupdatingofyourbeliefs･Thoughthereisnophysicalflowofmate-

rial,informationdelaysstillinvolvestocks.Intheexample,thestockinthedelay isyourbeliefaboutfutureorders,apsychologicalstateresidinglnyourmental

model.Ingeneral,anybelieforpercept10ninvolvesaninformationdelaybecause wecannotinstantaneouslyupdateourmentalmodelsasnewinformationisre- ceived.Otherexamplesofinformationdelaysincludeaveragessuchastheaverage

productionrateofaproduct.Asshownbelow,informationdelaysdonotinvolve conservedflowsandcannotbemodeledwiththesamestructuresusedformaterial

delays.

ll.2 MATERIALDELAYS:STRUCTUREANDBEHAVSOR

Havingdefinedthestockandflowstructureforamaterialdelay(Figurellll),itis

necessarytoformulateadecisionrule(equation)fortheoutflowrate･Inmanysit- uationstheoutflowsfromstocksareconstrainedbyvariousresourcesandyou

mustexplicitlymodelthewaytheseresourcesdeterminetheoutflow(seechapters 13and14).Productioncannotoccurwithoutlabor,materials,capital,andotherre-

sources.ThecapacityOfthedelaylSsometimeshighenoughrelativetotheinflow ratesthatyoucanassumetheoutflowdependsonlyonthepastinflows.Inmodell

lngthecommercialrealestatemarketofacltyyoumightconcludethatthecapac- 1tyOftheconstructionindustryintheregionisample,orsufficientlyflexible,and

modeltheconstructiondelayfornewbuildingsasaconstant.Youmightmodelthe

dimlSionofdioxinthroughatowll'sgroulldwatersupplyasapuredelaywi血a constantdelaytlmebasedonthecharacteristicsofthesoilandsubsurfacemor-

phology･Insuchpuredelaystheprocessgovernlngtheoutflowfromthestockof

materialintransitdependsonlyonhowmuchmaterialisintransitandhowlong it'sbeenthere,notonanyexternalresources.Thedelaytlmeisindependentofthe

lnPutOrStockintransit,andtheprocessislinear.Suchpuredelaysaremodeledas

uncapacitatedqueulngprocesses. TheassumptionthatadelaylSnotCapaCltyCOnStrainedisalwaysanapprox1-

mationandholdsonlyoveracertainrangeofinputsJftherealestatemarketinthe

citybooms,ordersfornewbuildingsmayoutstrlPthecapacityOftheconstruction industry,andtheaveragedelaybetweencommisslonlnganewbuildingandits completionwillincrease.InthesecasestheresourcesconstrainlngthecapacltyOf theprocessmustbemodeledexplicitly.

YoumustanswertwoprlnClpalquestionsforeverydelay.First,whatistheav- eragelengthofthedelay?Second,whatisthedistributionoftheoutputaroundthe averagedelaytlme?

Chapterll Delays

FIGUREll-2 Somedistributions oHheoutflowfrom

adelay

Theinputllnalf casesisaunit

pulseattimezero. OutflowAisa

pIPeFinede一ayIn whichaHitems

arrivetogether

exact一y1de一ay timeafterthey enter.Outflow

distributLlonsB-D

exhibitdifferent

degreesof variationin

processlngtimes forindl'vllduaHtems

SOsomearrlVe beforeandsome

aftertheaverage delaytimeLlnall casestheaverage

delaytimeisthe sameandthe areasundereach distributionare

equal(100%OHhe quantityaddedby thepulseinput). Eachcurve

representsthe probability distribution

describingthe

chancethatany panicularitemwill exitthede一ayata pa什iculartime.

■l

O !Ja d

u lgJJ a S 一n

d l!u⊃ -0 %

1 2

Time(multiplesofaveragedelaytime)

413

1lr2､l WhatlstheAverageLengthoftheDelay?

Howlong,onaverage,doesittakeitemstoflowthroughthedelay?Equivalently,

whatistheaverageresidencetimeforaunitinthedelay(howlongonaverage

doesaunitstayinthestockofmaterialintransit)?

FortheUSpostoffice,theaveragedelayfordomesticfirstclassmailmightbe

ontheorderof2days.Foremail,theaveragedelaybetweensendingandreceiv-

ingmessagesviatheinternetmightbeontheorderofafewseconds.(Inwhat

stock(S)doyouremailsresidebetweenthetimeyousendthemandthetimethey

arereceived?)Inanyapplication,thelengthofthedelayisanempiricalissuetobe

investigatedbydatacollectionandfieldstudy(Seesectionll.5).

ll.2,2 WhaMs軸eDis的buti⑳no骨油eOutpu竜

around帥eAverageDelayTime?

Whathappensonceitemsenterthedelay?Aretheyprocessedfirst-come,first-

servedoristheresomemixingandreshufning?Doallunitsspendthesametime

inthedelay,oristheresomevariationaroundtheaverage,withsomeunitsflow1

1ngthroughthedelayfasterandsomeslowerthanaverage?Figurell-2shows

somepossibilitiesfortheoutnowfromadelay.

ThefigureshowstheresponseofseveraldifferentdelaystoapulselnPut. ApulseInputisanalogoustoamassmailingofalargenumberofletters:acertain

quantityOfmaterialisInjectedintothedelayatasingleinstant･1Thefigureshows

tThepulsefunction,alsoknownastheDiracdeltafunction8(t),isthelimitofarectangular pulsestartingattimeT,withduration(width)Wandheight1/W,asthedurationofthepulsegoes tozero:

8(t,T)-lima(t,T,W)-Wう0 {

Ofort≦T

/WforTく t≦T十W Ofort>T+W

Thepulsefunctionhas.anareaofunity;thusanarbitrarypulseinputofQunitsattimeTisgiven byQS(t,T)AⅠnsimulatlOnmodels,QB(t,T)isapproximatedbyarectangularpulsewithaduratlOn equaltothesimulationtimestepDTandaheightofQ/DT.

414 PartIV TbolsforModelingDynamicSystems

theoutputofthedelayasapercentpertimeperiodofthetotalquantltylnputtOthe delayattimezero.Inallfourcasestheaverageprocesslngtimeisthesame.One

possibility(OutflowA)isthattheitemsenteringthedelayallproceedthroughthe delaylnexactlythesameorderandexitafterexactlythesametime.Inthiscase,

theoutputofthedelaylSalsoapulseexitlngthedelayexactly1delaytlmeafter

thepulselnput･Anautomobileassemblylineapproximatesaplpelinedelay.The

carsmovedownthelineinsequence,eachexitinginthesameordertheyentered･ WhenthelineisrunnlngSmoothlythedelaytlmeOrresidencetimeinthedelaylS

thesameforallandtheorderofentrydeterminestheorderofexit.Inthelanguage

ofqueuingtheory,theservicedisciplineoftheassemblylineisFIFO(firstin, firstout).

Thetermsen,icedisciplinereferstothedecisionruleforchooslngWhichof theunitsinthestockofmaterialintransitwillbeprocessedandexitfirst.Other

typesofservicedisciplineincludeLIFO(lastin,firstout),acommonsituationin

mykitchenpantry,wherethemostrecentlypurchaseditemsareoftenplacedatthe frontoftheshelvesandarethenusedfirstbecausetheyblocktheolderitemsbe-

hindthem･Whenyourotateyourstocktoreducespoilageyouareshiftingfrom

LIFOtoFIFOdiscipline･Manyotherrulesarepossible,includingrandomselec-

tionorselectionbasedonsomeotherattribute,aswhencandidatesfororgantrans- plantsareselectedbasedonhowsicktheyareorthechancesofsuccessratherthan

onhowlongthey'vebeenonthewaitlnglist･2

Whenlargenumbersofitemsormultipleserversareaggregatedtogether,ser-

vicedisciplineiso枕enneitherstrictlyFIFOnorLIFOJfyoumailalargenumber oflettersallatonce,theywillnotallbedeliveredatonce.Therewillbeadistrib-

utionaroundtheaveragedeliverytime,WithsomelettersarrivingSOOnerthanav-

erageandsomearrivlnglater.Thevariationarisesbecausethelettersaredestined

fordifferentrecIPlentS,andthetraveltimestoeachdestinationdiffer.Moreim-

portant,unlikecarbodiesontheassemblyline,lettersarenotprocessedinthe

sameordertheyaremailed･Duringthevariousstagesofprocesslng,thelettersare

血Ⅹedwithothers･Sortingthelettersbydestinationsotheycanberoutedproperly causessomeofthemixlng.Someisinadvertentaswhenthecontentsofacorner

mailboxaredumpedintoabinfortransporttothelocalbranch.

TheconsequenceofmixinglSSOmerandomizationoftheprocesslngOrder･

Anothersourceofdispersionintheoutflowdistributioniscausedbyrandomvari-

ationsintheprocesslngtlmeitself･Considerthecheckoutdelayatasupermarket.

Youmightchoosetomodelthecheckoutprocessasaslnglematerialdelaywhere theinnowrateistherateatwhichshoppersjoinaCheckoutlineandtheoutflow

rateistherateatwhichtheyleavethemarket.Variationsintheamountoffoodin

eachshopper'sbasketandinthespeedoftheclerksmeantheprocessingtimefor

eachcustomerandeachcheckoutlanecandiffer.CustomersjOlnlngthecheckout linenexttoyoursafteryoudosometimesleavebeforeyoudo,sotheorderofexit

isnotthesameastheorderinwhichpeoplequeue(aseveryoneknows,theline

youareinisalwaystheslowest)｡

2zenios,Chertow,andWein(forthcoming)developadynamicmodeltoevaluatevarious policiesforallocatlngkidneystotransplantcandidates.

ChapterllDelays 415

Thesesourcesofdispersionmeanthatingeneral,whenmanyItemsareintro- ducedintoadelayatonetime,Someitemswillexitearlierthanothers,spreading outthedistributionofthedeliveryrate･Theresponseofadelaytoapulseinput suchasshowninFigurell-2canbethoughtofastheprobabilitydistributionde- scribingthelikelihoodthatanyglVenitemisdeliveredataparticulartime.Distri- butionAhasnovariabilityindeliverytimes.DistributionsBIDhavedifferent degreesofmixing;Ofthese,distributionBhasthemostvariabilityindelivery times,whiledistributionDhastheleast.AllfわurdistributionsA-Dhavethesame

averagedelaytime,andal1conservetheinflow,Sotheareaundereachdistribution isthesam e(100%oftheinfloweventuallyexitsfromthestockofmaterialintran- sit,or,equlValently,theprobabilitythatanyglVenletteriseventuallydelivered islOO%).

Inspecifyingdelays,youmustconsidernotonlytheaveragelengthofthede- laybutalsothedistributionofdeliveriesarou王Idthemeandelay.Sometimesyou canestimatetheoutputdistributionfromthedata.Othertimesyoumustestimate itbydirectinspectionofthedelayprocesstoseewhetherthereismixlngOrStrict FIFOdisciplineandwhethertheprocesslngtlmeOfindividualitemsisconstantor variesrandomlyfromitemtoitem.

ll.2.3 PipeHneDeはy

Asintheexampleoftheautoassemblyline,yousometimesneedtomodeladelay inwhichthedelaytlmeisconstantandinwhichtheorderofexitfromthedelaylS preciselythesameastheorderofentry.TodosorequiresaPipelinedelay,also knownastransportationlag(themetaphorisanassemblylineinwhichitemsare transportedinorderandataconstantrate;Figurell13).

Inthepresentationbelowtheinflowtothedelayswillbeexogenous.Explor1 1ngtheresponseofdifferentdelaystoidealizedexogenousInputsSuchasapulse, step,ramp,andfluctuationhelpsdevelopyourintuitionfortheirbehaviorso youcanselecttheapproprlatetypeinanymodelingsituation.Ofcourse,inyour modelstheinputstodelayswillingeneralbeanendogenouspartofthefeedback structure.

ThestockofmaterialintransitforanymaterialdelaylSglVenby

MaterialinTransit-INTEGRAL(Inflow(t)-Outflow(t),MaterialinTransit(0)) (ll-1)

Forthepipelinedelay,theoutflowissimplytheinflowlaggedbytheaveragedel laytlmeD:

Outflow(t)-Inflow(t-D) (1112)

DistributionAinFigure1112isapipelinedelay:Whentheinflowisapulse,the outflowisapulseexactlyDtimeunitslater.Thereisnomixingintheprocesslng order,noranyvariationinindividualprocesslngtimes;thedelaytlmeforeachitem equalstheaveragedelaytlme.

ll.2.4 First10rderMaterialDelay

Manydelaysdonotapproximateapipelinedelay;thereismixlngandvariation intheindividualprocessingtimes,causlngSomeVarianceinthedistributionof

416 PartIV TわolsforModelingDynamicSystems

FdGUREll -3 Pipelinedelay:Structure

lnapIPelinedelayindividuaHtemsexitthedelaylnthesameorderandafterexactlythesametime, likewidgetsmovlngdownanassemblyllneataconstantspeed.

MaterialinTransit(I)=INTEGRAL(Inflow(I)IOutflow(I),MaterialinTransit(0))

Outflow(t)=lnflow(t-AverageDelavTimel

deliveries･Consideranexampleattheoppositeextremefromaplpelinedelay,say, waterdrainlngfromasink.Furtherimaginethatthewaterinthesinkisthoroughly mixedatalltimes(Figure11-4).

InthecaseofperfTectmixlng,theprobabilitythatanyparticularwatermole- culeisthenexttoflowoutofthesinkisthesameforallthemoleculesinthesink,

independentofhowlongthatmoleculehasbeeninthesink･Perfectmixlngmeans theorderofentrylSirrelevanttotheorderofexit.Putanotherway,perfectmixing destroysallinfomationabouttheorderofentry.

Theoutflowfromafirst-ordermaterialdelaylSalwaysproportionaltothe stockofmaterialintransit:

Outflow-MaterialinTransit/D (11-3)

whereDisagaintheaveragedelaytlme.NotethattheonlyinputstOtheoutflow ratearethestockofmaterialintransitandthedelaytime;infわrmationabout theorderofentryofindividualitemstothestockisnotusedtodeteminetheouト flowrate.

Equation(11-3)isthefamiliarlinearfirst-ordernegativefeedbacksystem (chapter8).Theoutflowrateformsanegativefeedbackloopsincethegreaterthe stockofmaterialintransit,thegreatertheoutflow,lowerlngthestock.Distribu-

tionBinFigurell-2showstheresponseofafirst-ordermaterialdelaytoapulse input.Theresponseisthefamiliarpatternofexponentialdecay(Figurell-5):

Chapterll Delays

FIGUREll-4 First10rder

materialdelay: Structure

Theoutflowis

proportionaltothe stockofmateriaf intransit.The contentsofthe

stockareperfectly mixedata"times, soa"itemsin thestockhavethe

sameprobabi一ityof exiいndependent oftheirarrival time.

417

Outflow=MaterialinTransit/AverageDelayTime

Immediatelyafterthepulse,thestockofmaterialintransltJumpsuPtOIOO%of

thequantltyaddedbythepulseinput.Theoutflowrateimmediatelyrisesto

lO0%の unitspertimeperiod.Sincetheoutflownowexceedstheinflow,thestock ofmaterialintransitstartstofall.Asitfalls,sotoodoestheoutflowrate,sothe

stockofmaterialintransitandoutflowratefallatdiminishingrates.Theinitial

outflowratewoulddepletethestockintransitin1delaytlme,butasthestockin

transitfalls,sodoestheoutflowrate.Afterldelaytimehaspassedthestockin

transithasfallenby63%;after2Dperiods,86%oftheitemshavebeendelivered;

andafter3Dperiods,95%havebeendelivered･3

ll.2.5 Higher-OrderMateria一De?ays

Pipelinedelays,WiththeirrigidFIFOservicediscipline,aregoodmodelsforsome

processessuchasassemblylines.First-orderdelays,withtheirassumptlOnOfper-

fectmixing,arereasonablemodelsofotherdelayprocesses,suchaschemicaland

heatdi軌lSioninphysicalandbiologicalsystems,andsomeanalogousdimISion

processesinsocialsystems.BetweentheseextremesliemanyIntermediatecases

wherethereissomemixlnglntheprocesslngOrder.Inthesecasestheoutflow

3Recallthatexponentialdec?y.isgivenbyS-Soexp(-tD)sowhent-D,thestockShas fallentoexp(-1)-0.370fitslnltiallevel.Seechapter8.

418

FIGUREll-5 Pu一seresponseof first10rdermaterial

de一ay

Theinputtothe delayISaunit pulseattimezero･ Thestockof materialintransit

instantlyJumpstO 100%,then

decays exponentiaHywith atimeconstant

equa一tothe averagedelay time.Theinitiaf rateofoutflow

woulddep一etethe stockJLntransitinl

delaytime(note thetangenttothe trajectoryofthe stockintransitat

timezero),butas thestockintransit

falls,sodoesthe outflowrate,

yieldingthe fami‖arpattemof exponentialdecay･

PartIV ToolsforModelingDynamicSystems

( A )!lu t2n b a S ln d -0 % )

l JS u e J1 u

〓 t2!JIa lt2≡

1 2

Time(multiplesofaveragede一aytime)

StockofMaterialinTransit

1 2

Time(multiplesofaveragedelaytime)

graduallyrises,reachesapeak,andthentailsofftozero,Similartodistributions

CandDinFigurell12･Consideragainthepostoffice･Lettersdonotallarriveat

onetime,asinaplpelinedelay,butneitheristhedeliveryrategreatestimmediately

afteryourlettersaremailed･Though 1ettersarenotprocessedinlockstep,neither

istheorderofdeliveryindependentoftheorderofmailing.Thereispartialmix-

1ng.PartialmixingCanarisewhenadelayconsistsofmultiplestagesofprocesslng

inwhichitemsflowsequentiallyfromonestagetothenext,butwhereeachstage

introducessomemixing.

ForthecaseofthepostofficeラyOllCaneasilyidentifymanystagesofprocess-

1ng.Lettersfirstgointothecornermailbox;thenontothetruckthatcollectsthe

mail;thenintobinsatthelocalpostoffice;then,aftersortlng,Ontotrucksforde-

liverytothecentralpostoffice;thenthroughmorestagesofsortlngandprocessl

1ng;thenontotrucks,trains,orplanesfortransporttothedestinationcities;血ento

thelocalpostofficesinthedestinationcommunities;andsoonuntiltheyarriveat

themailboxesofthereclplentS.Eachstageintroducessomemixlngandvariability

inindividualprocesslngtlmeS.Ifthepurposeofyourmodelwastoreenglneerthe

postofficeworkflowsystemyoumighthavetorepresentallthesestagesseparately

andexplicitlyaccountforthedifferentdelaytlmeSandcapacitiesofeachstage.

ChapterllDelays

FIGUREll -6 Higher-orderde一aysareformedbycascadingfirst-Orderdelaystogether

419

Stage1ExitRate=Stage1StockinTransiVStage1AverageDe一ayTime

OutflowRate=Stage2StockinTransitIStage2_AverageDelayTime

Youwouldhaveaverydetailedmodelindeed.Forotherpurposes,suchdetail wouldnotbenecessaryandapuredelaymightbeapproprlate･

InmanysettlngSthestagesofprocesslnglnSuchasystemcanbeapproxi- matedwellbycascadingseveralfirst10rdermaterialdelaystogetherinseries.For example,asecond10rdermaterialdelayconsistsoftwofirstl0rderdelaysinwhich theinputtothesecondstageistheoutputofthefirststage(Figure11-6).

420 PartIV ToolsforModelingDynamicSystems

Thetotalstockintransitisthesumofthestockintransitateachstage･Theav-

eragetotaldelayfrominflowtooutflowisthesumoftheaveragedelaysofthein-

dividualstages･Inthisfashionyoucanconstructdelayswithanarbitrarynumber

ofstagesIDelaytimesfortheindividualstagescandiffer,ifthedataandmodel

purposewarrantit,thoughoftenitisfinetoassumeeachstagehasthesamedelay

time･Adelaywithnstages,eachwith1/nofthetotaldelaytlme,isknownasan

nth-ordermaterialdelay･Theequationsforthenth-ordermaterialdelay,denoted bythefunctionDELAYn,∬e

Outflow-DELAYn(Inflow,D): ∩

TotalMaterialinTransit-∑ MaterialinTransit.1-1 MaterialinTransitl-INTEGRAL(NetInnowi,MaterialinTransit-(0))

MaterialinTransitl(0)-Inflow*D/n

NetInflowrate.- (

Inflow-ExitRateStage- forュ-1

ExitRateStagelrl 1ExitRateStagelfori∈ (2,‥.,n-i)

ExitRateStagen】1- Outflow fori-n

ExitRateStagel-MaterialinTransit./(D/n)fori∈(1,.‥,n-1)

Outflow-MaterialinTransitn/(D/n) (ll-4)

TheinitialconditionMaterialinTransltl-Inflow*D/ninitializesthedelayln

equilibriumsothattheinitialoutflowequalstheinitialinflow.

DistributionsCandDinFigurell-2Showtheresponsetoaunltpulsefora

third-andtwelfth-orderdelay,respectively･Thehighertheorderofthedelay,the

lessmixlngandthesmallerthevarianceoftheoutput.Inthelimit,aninfinite-or-

derdelayconsistsofaninfinitenumberofstageseachwithaninfinitesimaldelay

time.Suchadelayprovidesonebinorstockofmaterialintransitforallitemsen-

terlngataglVeninstantandmovesthemfromonestagetothenextbeforethenext

setofitems,enterlnginthenextinstant,areadded･Thusaninfinite-orderdelay

preservestheorderofentryandpermitsnomixlng:itisequlValenttoaplpeline delay.

Figurell-7Showsthepulseresponseofathird-orderdelay;Figure11-8shows

thestocksandmowsfortheintermediatestagesofprocesslng.Immediatelyafter

thepulse,thestockofmaterialinstage1jumpstolOO%ofthequantltyadded.

EachstageofthedelaylSa丘rst-orderdelay;1nathird-orderdelaytheaveragede-

layforeachstageisone-thirdofthetotaldelay･Thusthestagelexitrateisexpo-

nentialdecaywithatimeconstantofD/3･Theexitratefromstage1istheinputto

stage2･Thestockofmaterialintransitinstage2risesaslongasitsInputexceeds

itsoutput･Atabouttime-0･34D,thestockinstage2hasrisenenoughfortheexit

rateofstage2toequalitsinflowfromstagel.Thestockinstage2peaks.From

thenonthestage2exitrateexceedstheinflowtostage2,Sothestage2stockin

transitfallsandwithit,thestage2exitrate.Similarly,thestage2exitrateisthe

inputtOStage31Thestage3Stockintransitrisesuntilitsoutflowequalstheinflow,

Chapterll Delays

FlGUREll-7

Pulseresponseof athird-orderdelay

( A

)

!l u e n

b a S I n d -0 %

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l!S ut巴 r

Lu 〓 t!!Ja le ≡

0 1 2

Time(multiplesofaveragedelaytime)

StockofMateriaHnTransit

0 1 2 3

Time(multiplesofaveragedelaytime)

421

whichoccursataboutt=0.67D,thengraduallyfallsoffastheoutflowfromthe delayexceedstheinnowtostage3.

Similardynamicsapplytodelayswithorderhigherthan3.RefTerringbackto Figurell12,notethat,exceptforthepipelinedelay,thepeakresponseofmaterial delaysofordernprecedesthemeandelayandthereisalongtailinthedistribution ofdeliveries:manyltemSaredeliveredearlierthanaverage,butsomearedelivered

muchlater･NotealsothatastheorderofthedelayIncreases,andhenceasthede一 greeofmixlngdecreases,thedeliverydistributiontightensup:feweritemsaredel liveredearlierthanaverage,morearedeliveredneartheaveragedelaytime,and

feweraredeliveredmuchlaterthanaverage.Thehighertheorderofthedelay,the smallerthevarianceinthedeliverydistribution.

ll .2.6 HowMuchis岳ntheDelay?Little'sLaw Thestockofmaterialintransitaccumulatesthedifferencebetweentheinflowand

outflowtothedelay.It'simportanttoknowhowbigthestockintransitwillbefor

422

FIGUREll-8

Pu一seresponseof

third-orderde一ay

bystageof

PrOCeSSlng

PartIV ToolsforModelingDynamicSystems

P O !J a d a

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Ja S Ind l g u n

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StockofMaterialinTransit

l＼

r otalstockinTransit

㌔ Stage1

0 1 2 3

Time(multiplesofaveragedelaytime)

anyglVendelayandinflow.Supposetheinflowhasbeenconstantlongenoughfor

thedelaytoreachequilibrium.How biglSthestockintransit?Considerthe

pipelinedelaywithinputI,output0,anddelaytimeD:0(t)-Ⅰ(t-D).Suppose

theinflowandstockintransitareinitiallyzero.Attimezerotheinflowsuddenly

increasestoaconstantlevelI.TheoutflowwillcontinuetobezerountilDperiods

havepassed.Duringthistime,thestockintransitSisincreasedbylunitseach

period･AfterDperiods,0-Iandthestockofmaterialintransitreachesequilib-

rium･TheequilibriumquantltylntransitisthereforeDIunits･4

4ThestockintransitforanydelaywithinputIandoutput0is

S(t)-lot[Ⅰ(S)-0(S)]ds+S(0)

ForapipelinedelaywithS(0)-0andastepincreaseintheillputfrom0toIunits/periodattime

zero,0(t)-0fort<DandIfort≧D,SotheequilibriumvalueofthestockintransitS∞is

s--I.DlI-0]dsII,mlI-.,ds-DI

ChapterllDelays 423

Nowconsiderafirst10rderdelay(equation(1113)).Theoutflowofafirst10rder delayis0-S/D.Sinceinequilibriumtheinflowandoutflowareequal,the equilibriumstockintransitisDIunits,thesameasthatforthepipelinedelay･In fact,theequilibriumstockintransitforadelayisalwaysDIunits,rega71dlessof theprobabilitydistributionoftheou研ow.Thisremarkablepropertyisknownas Little'sLaw,afterJohnLittle,anMITprofessorofoperationsresearchwhofirst provedit.Little'sLawmeansthatinequilibrium,thestockintransitisfully characterizedbytheaveragedelaytimeandinflowrate･ByLittle'sLaw,afirm ordering10,000Widgetsperdayfrom asupplierrequlrlng5daystodeliver will,inequilibrium,have50,000widgetsonorder,independentofthedelivery distribution.

Little'sLawhelpsexplainhowdelaysglVeSystemsinertia･Ifbusinessgoes sourandthecompanycutspartorderstozero,itswidgetinventorywillstillswell byanadditional50,000unitsbeforedeliveriesfromthesuppliercanbecutoff(as- sumingnoordercancellationsarepossible).

Little'sLawcanalsobeusedtoestimatetheaveragelengthofadelayfrom knowledgeofthestockintransitandflowsthroughthedelay.Inequilibrium,the averageresidencetimeofitemsinthedelaylSglVenbytheratioofthestockin transittotheoutflowrate,D-S/0 -S/I.Thusifaninsurancecompanyhasa

pendingpoolof50,000unresolvedclaimsandsettlesanaverageof25,000per month,theaveragetimeclaimantswaittoreceivepaymentis2months･Again,this measureofdeliverytimeholdsstrictlyonlylnequilibrium.

Example:ConstructionDelaysI'ntheE/ectricUti/I'tyIndustry

Little'SLawhasdramaticimplicationsforthecashflowandfinanclngrequire- mentsofabusiness.Considertheelectricpowerindustry.Upthroughtheearly 1970Stypicalleadtimesfわrnewplantswereabout5yearsandtheaverageservice lifeofplantswasabout20years.Ifthedemandforpowerwasconstant,anin- vestor-ownedutilitywith10gigawatts(gw,billionwatts)ofcapacitywouldthere- foreneedtoaddanaverageof0.5gwofcapacltyperyeartoreplaceretirementsof oldplants.Witha5-yearconstructiondelay,theutilitywouldhavetohave-and finance12.5gwofcapacityunderconstructionatalltimes,one-quarterofits existlngCapaClty.Inthe1970S,leadtimesforlargeplantsincreasedasutilities builtlargerandlargerplantsinasearchforreturnstoscaleandasenvironmental andregulatoryconstraintslengthenedpemittlngdelays･Leadtimesrosetoabout 10yearsforlargecoalplantsandevenlongerfornuclearplants.Tooffsetthere- tirementofoldplantswhentheleadtimeis10years,constructionworkinprogress mustdoubleto5gw,halfofcapaclty,

Inreality,thesituationwasfarworse,sincethedemandforpowerwasgrow- 1ngatabout7%/yearthroughtheearly1970S.Tooffsettheretirementofoldplants andincreasecapacity7%/year,a10gwutilitywouldneedtocompleteconstruc- tionof1･2gwthatyear･Witha5-yearconstructiondelay,theutilitywouldneedto startconstructionof1.8gwofcapacityandwouldhavetofinancetheconstruction ofabout7･2gwofcapacltyunderconstruction･

Whentheconstructiontimedoublesto10years,therequiredcompletionrate ofl.2gwforcestheutilitytostartconstructionof2･4gwofnewcapacltyand

424 PartIV ToolsforModelingDynamicSystems

financemorethan17.4gwofcapacltyunderconstruction-a240%increaseand

aninvestmentgreatlyexceedingthebookvalueofexistlngCapaClty･5Ordersfor

powerplantssurgedinthemid1970S,asutilitiestriedtorespondtotherisinglead

times.Hugedebtsweretakenontofinancetheever-greaterstockofconstruction

workinprogress.Ⅰnmanycases,electricpowerrateswereraisedtoenableutilities

toservicethesedebts.However,ashigherrates(andlowerthanexpectedeco-

nomicgrowth)causedpowerdemandtofall,theutilitiessuddenlyfoundthem-

selvescarryingdebtforpowerplantstheydidn'tneed･Ordersfornewplants

plummeted,andmanywerecanceled,butasthehugestockofplantsundercon-

Stmctioncontinuedtocomeonline,theindustryfounditselfwithexcesscapacity.

ProfitsfTellandratesrosestillmore.Insomeregions,thehigherratesledtoeven

lowergrowthinpowerdemand,forclngratesevenhigher,inwhatmanyanalysts

calledthe"spiralofimpossibility."Anumberofmajorutilitieswentbankruptdurl

lngthisperiod,especiallythosebuildinglarge,longlead-timeplants･Theexcess

capacltylastedthroughmostofthe1980S.Manyforward-thinkingutilitiesrealized

thatpowerplantswithshortplannlng,permittlng,andconstructiontimeswerea

betterinvestmenteventhoughtheircostsperkilowattofcapacityWerehigher:In

anenvironmentofuncertaindemandgrowth,thevalueofimprovedcashflOwand

lowerrisksofhavingthewrongcapacityexceedthegenerationcostsavlngSOf-

feredbylarger,longleadtimeplants(Ford1997)A

5ThisexampleisadaptedfromFord(1997).NotethatLittle'SLawholdsonlyinequilibrium. WhentheinflowtoadelaylSgrOWlngthesteadystatesizeofthestockintransitisnotindepen- dentoftheoutflowdistribution.Thecalculationsinthetextassumetheconstructionprocessfor powerplantsischaracterizedbyaplpelinedelay･Inthiscase,theconstructioncompletionrate C(t)-S(t-D),whereSistheconstructionstartrateandDistheconstructiondelayJnthesteady stateofexponentialgrowthatfractionalrateg/year,thestartratemustthereforebeCexp(gD)･ Givena5-yearconstructiondelayand7%/yeardemandgrowthrate,completionof1･2gw/year requiresthestartratetobel･2exp(0･07*5)-1･70gw/year;anda10-yearcompletiontinleyields S-1.2exp(0.07*10)-2.42gw/year.AtanytimetthestockofcapacityunderconstructlOn CUCis

CUC- 上

[S(S)-C(S)】ds

Withoutlossofgenerality,assumetheconstructioncompletionrateisCogw/yearattimezero･ln thesteadystateofexponentialgrowth,thestockofcapacltyunderconstructionattimezeroisthen

cUc(o)-仁 [C(t)exp(gD,-C(t)]dt-[exp(gD,-1]lMOmc(t)dt-[exp(gD)-1,I_omcoexp(gt)dt-幣

WithCn-1.2gw/yearand2-0.07,a5-yearconstructiondelavrequiresconstructionworkin

p,rogresstobell2[exp(0･07*5)-1]/0･07-7･18gw;witha10-ye,ardelayconstructioninprogress rlSeStO112lexp(0･07*10)I1]/0･07-17･38gw･TotestthesensitivityofthiscalculationtotheFsI sumeddistributionofpowerplantdeliveries,considertheextremeassumptionthattheconstructlOn

delayforpo㌣erplantsisfirst-order(theactualdistributionofthedelayoutflowmustbemuch closertoaplpelinedelay).ThenaconstructioncompletionrateofCogw/yearrequiresCoDgw underconstruction,or6gwfora5-yeardelayand12gwfora10-yeardelay･Forthestockof capacltyunderconstructiontogrowatfractionalrategrequires

等 -S-C｡-gcUc ラ S-C.-gcoDラ S-C｡(1･gD)

implyingS-1.62gw/yearfora5-yeardelayandS-2･04gw/yearfora10-yeardelay･

ChapterllDelays 425

Example:AccumulationofToxicCompoundsintheFoodChain Little'sLawalsohelpsexplainwhytoxinssuchasdioxinaccumulateinthefood

chainandinhumansandmaycausesignificanthealthproblemseventhoughtheir

concentrationintheenvironmentisverylow.Thedioxinfamily(includingsome

furansandPCBslpolychlorinatedbiphenyls])arewidelyconsideredtobeamong

themostpotentcarcinogensknown.Theyarealsoestrogenmimicsthatmaydis-

ruptendocrineandreproductivefunctionandhavebeenassociatedwithlearning

disabilities･Dioxinsandotherchlorinatedhydrocarbonscommonlyusedinpes-

ticidesandherbicidesaresolubleinfatandpersistinthebodyforyears.The

halfllifeofdioxinandrelatedtoxinsinfattytlSSuehasbeenestimatedtobe7to

llyears,Correspondingtoaverageresidencetimesof10to16years･6ByLittle's

Law,theequilibriumconcentrationofdioxininanylevelofthefoodchainwould

be10to16years'worthofaverageintake.Predatorsconsumlngthoseorganisms

wouldtheningestmuchhigherconcentrationsthantheirprey.Ateachlevelofthe

foodchain,theaccumulationoftoxinscausedbythelongdegradationdelayam-

plifiestheconcentrationoftoxins.Somespeciesoffishhavedioxinconcentrations

100,000timesthatofthesurroundingwater.

Whiletypicalhumanintakeratesofdioxinareverysmall,concentrationscan

builduptohigherlevelsoveralifetime.Averagedailyexposureisestimatedat

3to6picogramsofdioxintoxicequlValentperkilogramofbodyweightperday

(3I6pgTEQnig/day),mostofwhichweingestinourdiet.7Howcansuchsmall

intakerateshaveanyeffectonhumanhealth?BesidestheextremetoxicityOf

dioxin,theansweristhelongresidencetimefordioxininthebody.Assuminga

16-yearhalfllife,theequilibriumconcentrationofdioxininhumansIngesting6pg

TEQ/kg/daywouldbe35,000pgTEQperkilogramofbodymass.Thisvalueis

roughlyconsistentwith,thoughsomewhatsmallerthan,estimatesofaverageloads

of40,000to100,000pgTEQ/kgbodymass,suggestingeitherthehalf-livesare

longerortheintakeratesarehigherthancurrentlythought･NotethatLittle'sLaw

appliesonlylnequilibrium Inthedioxinexample,itwouldtake40to64yearsto

reachtheequilibritlmlevelassumingaconstantintakerate(afirsトorderdelayad-

justs98%ofthewaytoequilibriumafter4timeconstants),furthersuggestingthat

estimatesofdioxinlngeStionratesoritshalf-lifeinthehumanbodyaretoolow.

ResponseofMater弓aEE)e室ays一考OS始ps,Ramps, andCycles

Thediscussionsofardescribedtheresponseofmaterialde一aystoapulselnptlt,

analogoustoaslnglemassmailingofletters.OthercommonlnputSusedtotest

systemsarethestep(asudden,permanentincreaseintheinputfromonerateto

6Recallfromchapter8thatthehalf-lifeofanexponentialdecayprocesswithtimeconstantDis ln(2)D=苛0.7D.

7Apicogram.isatrillionthofagram(Onepartin1012)AAtoxicequivalentconvertsthetoxicity ofdifferentdioxln-likecompoundsintotheequlValentquantityoftheparentcompoundinthe dioxinfamily,2,3,7,8-tetrachlorinateddibenzo-p-dioxin(2,3,7,8-TCDD)･Sourcesfordioxininfor- mation:USEPA(1994);seealso<www.epa.gov/futures/risk/nccr/dioxin.txt.html>.

426 PartIV TbolsforModelingDynamicSystems

another),theramp(asuddentransitionfromaconstantleveltolineargrowth),ex-

ponentialgrowth,andcycles.Totestyourunderstandingofdelays,dothefollow- 1ngChallengebeforeproceeding.

I.Wl'thoutusingcomputerSimulation,sketchtheresponseofafirst-order

materialdelaywithanaveragedelaytlmeOf5daystotheinputsshownin Figurell-9.InallcasesassumethatprlOrtOtimezerothedelaylSin

equilibriumwiththeoutflowandinflowbothequalto100units/day.

a. Stepinput.Attimezerotheinflowstepsupt0200units/dayand

remainsatthehigherrate.

b. Rampmput.Attimezerotheinflowstartstoriselinearlyatarateof5

units/day.

C. Exponentialgrowth.Attimezerotheinputstartstogrow

exponentiallyat5%/day.

d. Oscillation｡Attimezerotheinputbeginstonuctuatewithan

amplitudeof±100units/dayandaperiodof10days･

2.Afteryouhavesketchedyourintuitiveestimateoftheresponseofthedelay

totheseinputs,testyourunderstandingbybuildingamodelofafirst-order delayandsimulatingltSresponsetOtheseInputs.Wereyoucorrect?

3.Repeatsteps1and2forathird-orderdelayandfわrapIPelinedelay.How doestheorderofthedelayaffecttheresponsetothedifferenttypesof

lnPutS?Doesthesteadystateresponseofthedifferentdelaysdiffer?The steadystateresponseisthebehaviorafteralongtlmehaspassedandthe

relationshipofinputandoutputisnolongerchanglng･Howdoesthe transient(shortrun)responseofthedi触rentdelaysvary?

4.Explorehowtheresponseofthedifferentdelaystothedifferentinputsis affectedbychangesinthedelaytlme.Inparticular,exploretheresponseof thedifferentdelaystothefluctuatlngInputfordifferentdelaytlmeS.

ll .3 lNFORMAT10NDELAYS:STRUCTUREANDBEHAV10R

ThediscussionsofarexaminesmaterialdelaysinwhichtheinputtothedelaylSa

physicalinflowofitemstoastockofunitsintransitandtheoutflowisthephysi-

calflowofitemsexltlngthestock.However,manydelaysexistinchannelsofin- formationfeedback,forexampleinthemeasurementorperceptionofavariable, orintheupdatingofbeliefsandforecasts,suchastheperceivedorderratefora firm'sproductormanagement'sbeliefaboutfutureinflationrates･

WhydoperceptlOnSandforecastsinevitablyInvolvedelays?Allbeliefs,ex-

pectations,forecasts,andprojectionsarebasedoninformationavailabletothede- cisionmakeratthetime,whichmeansinformationaboutthepast.Ittakestimeto

gathertheinformationneededtoformjudgments,andpeopledon'tchangetheir mindsimmediatelyonthereceiptOfnewinformation.Reflectionanddeliberation oftentakeconsiderabletime.Weoftenneedstillmoretimetoadjustemotionally toanewsituationbeforeourbeliefsandbehaviorcanchange.

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FIGUREll -10 Feedback structureof

adaptive expectations

Theperceived valueoftheinput adjuststothe actuallnPutin proportiontothe sizeoftheerror

inyourbelief. Theadjustment timedetermines

howrapidlybe一iefs respondtoerror.

PartIV ToolsforModelingDynamicSystems

Informationdelayscannotbemodeledwiththesamestructureusedformate-

rialdelaysbecausethereisnophysicalinflowtoastockofmaterialintransit.The

Inputsandoutputsofmaterialdelaysareconserved;forexample,astrikeatthe postofficelengthensthedelayindeliveringmail,reducingthedeliveryrateand

causlngthestockofmailintransittobuildup.Incontrast,informationsuchasper- ceptlOnSandbeliefsisnotconserved.Considerafirm'sforecastoftheorderrate

foritsproducts.Theexpectedorderraterespondswithadelaytochangesinactual marketconditions.Thephysicalorderratedoesnotflowintothedelay;ratherin-

formationabouttheorderrateentersthedelay.Becauseinformation,unlikemate-

rialflows,isnotconserved,adifferentstructureisneededtocaptureinformation delays.

ll .3.1 ModeljngPeFCePtions:AdaptiveExpectations andExpoplentialSmoo的ing

Thesimplestinformationdelayandoneofthemostwidelyusedmodelsofbelief adjustmentandforecastinglSCalledexponentialsmoothingoradaptlVeexpecta- tions.AdaptlVeexpectationsmeanthebeliefgraduallyadjuststotheactualvalue

ofthevariable.Ifyourbeliefispersistentlywrong,youarelikelytoreviseituntil theerroriseliminated.Figurelト10showsthefeedbackstructureofadaptlVe expectations.

InadaptlVeexpectationsthebelieforperceivedvalueoftheinp叫 Ⅹ,isa stock:

丈 -INTEGRAL(ChangeinPerceivedValue,X(0))

Input: Reported Vaneof V-ariabie

(X)

(ll-5)

′ヽ支=INTEGRAL(ChangeinPerceivedValue,X(0))

′ヽ ChangeinPerceivedVa一ue=Error/D≡(X-X)/D

Chapterll Delays 429

FIGUREll-ll

Responseof adaptive expectationsto astepchar唱e intheinput

Theresponse toapermanent changeinthe Inputvariable isexponential adjustmentto thenewlevel.

Therateofchangeinthebeliefisproportionaltothegapbetweenthecurrentvalue

oftheinput,X,andtheperceivedvalue:

ChangeinPerceivedValue-(X-X)の (ll-6)

InamaterialdelaythestockisthequantltyOfmaterialintransitandtheoutputof

thedelaylSaflow.Ininformationdelaysthebeliefitself,X,isastock.Why?A

perceptlOnOrbeliefisastateofthesystem,inthiscaseastateofmind･Yourbelief

aboutthevalueofsomequantltytendstoremainatitscurrentvalueuntilthereis

somereasontochangeit.Inadaptiveexpectations,abeliefchangeswhenitisin

error,thatis,whentheactualstateofaffairsdiffersfromtheperceivedstateofaf-

fairs.Thelargertheerror,thegreatertherateofadjustmentinyourbelief.You shouldrecognizethisstructureasanotherexampleofthefamiliarfirst-orderlinear

negativefeedbacksystem(chapter8).Thestateofthesystemadjustsinresponse

tothegapbetweenyourcurrentbeliefandtheactualvalueofthevariable.This

structureisknownasafirst10Yderinformationdelay,Orasfirst10Yderexponential smoothing.

Figurel111lshowstheresponseoffirst10rdersmoothingtoapermanent

changeintheinput,startingfromaninitialequilibriuminwhichtheperceivedand

actualvaluesofthevariableareequal.Theresponseisclassicexponentialgoal-

seekingbehavior.TherateofbeliefupdatinglSgreatestimmediatelyafterthe

PerceivedandActualValues

P O

!Jla d

u J!1 lSl!un

1 2

Time(multiplesofaveragedelaytime)

430 PartIV ToolsforModelingDynamicSystems

changeintheactualvalueofthevariable,whentheerrorinthebeliefisgreatest.

Asthebeliefisupdated,theerrorfalls,andsubsequentadjustmentsdiminish,until,

afteraboutfourtimeconstantshavepassed,thebeliefisonceagainCOrreCt.

Afirm'sforecastsofincomingOrdersillustrate･Firmsmustforecastdemand

becauseitiscostlyandtimeconsumlngtOalterproductionrates.Inventoriesand

backlogsshouldbuffershort-termdifferencesbetweenordersandproduction.A

goodforecastlngProcedureshouldfilteroutshort-termrandomchangesinincom-

ingorderstoavoidcostlychangesinoutput(setups,changeovers,hiringandfir-

ing,overtime,etc.)whilestillrespondingquicklytochangesintrendstoavoid

costlystockoutsorexcessinventories.Thechallengeistoberesponsivewithout

overreactingtOnoise,thatis,totellwhichchangeindemandisthebeginnlngOfa

newtrendandwhichisamererandomblip.

ExponentialsmoothinglSWidelyusedinforecastingduetoitssimplicityand

lowcostofcomputation.Additionally,exponentialsmoothinghasthedesirable

propertythatitautomaticallyattemptstoeliminateforecasterrors.Figurell-12

showstheresponseofadaptiveexpectationstoasimulatedorderstreamforaprod-

uct.Thesimulatedorderrateinthisexamplefollowsarandom walk,varying

widelyfromdaytoday,Weektoweek,andmonthtomonth･Theexpectedorder

rateisformedbyadaptlVeexpectationswitha7-daytimeconstant.Exponential

smoothingdoesagoodjobofsmoothingouttheshort-term,high-frequencynoise

whilestillfollowlngtheslowermovementsinorderssuchastherisefromabout

600units/dayaroundday50toabout1300units/dayaroundday120.Notethatthe

peaksandtroughsintheexpectedorderratelagthetum1ngPOlntSintheactualor-

derrate:theprocessofsmoothinglneVitablyIntroducesadelay･

TbseewhyexponentialsmoothingIntroducesadelay,noticetheroleofthead-

justmenttimeconstantDinthenegativefeedbackstructureofadaptiveexpecta-

tions.Thenegativeloopfunctionstoeliminatetheerrorintheforecastbutdoesso

gradually,soasnottooverreacttotemporarychangesintheinput.Yourbeliefisa

weightedaverageofthecurrentvalueofthevariableandyourpastbelief,whichin

turnrenectsthepriorhistoryofthevariable･8

Theanalogywithaweightedaveragecanbemadeexact.Consideragainthe

problemofforecastingafirm'Sorderrate.Acommonwaytofilterouthigh-fre-

quencynoiseiswithamovingaverage.Forexample,a7-daymovlngaverageOf

dailysaleswouldbei/70fthesumofthedailysalesforthepastweek.Everyday,

theaveragewouldbeupdated.Ingeneralamovlngaverage,Ⅹ,Canberepresented

asaweightedsum ofallpastvaluesofthevariableX:■ 史(t)-∑ WIX(卜 i) (ll-7)⊥-U

8Recalltheanalyticsolutionofthefir st-orderlinearnegativefeedbackloopsyŝtem(chapter8)I WhentheinputisaconstantX*,thecurrentvalueofthestateofthesystem,hereX,isglVenby

wheretheweightw-exp(-tの)･Thatis,thecurrentvalueoftheperceptionisaweightedaverage oftheinitialvalueofthebeliefX(0)andtheactualvalueofthevariableXl.Theweightonthe initialvalueofthebeliefdeclinesexponentiallyataratedeterminedbythetimeconstantD.

Chapterll Delays

FIGUREll-12

Adaptive expectations smoothoutshort- termnolLse.

Responseof exponential smoothingto hypotheticalorder rateforaproduct. Theexpected orderrateis

formedby exponential smoothI-ngwLrtha 7-dayadjustment time.Theorder ratefollowsa

randomwa一k(the changeindaily ordersisnormally distributedwitha standarddeviation

of50units/day).

1500

1250

>､ tq⊂】i;=I 望1000 1= =I

750

500

OrderRate L_.ら

Expected

0 50 100 150 200 250 300

Days

431

wheretheweightswimustSumtOlJnthecaseofa7-daymovlngaverageOf

dailyvalues,theweightsare1/7forthesevenmostrecentvaluesandzeroforall

prlOrValues.Supposesaleshadbeenconstantforatleastaweekatarateof

X *units/day･Thesalesforecastwouldequaltheactualsalesrate:X-XO･Now

supposesalessuddenlydoubledandremainedatthehigherlevel･Onthenextday

themov享ngaverageforecastwouldonlyriseby14%‥文-(x*+x*'x*'x*+ X*+X等十 2X¥)/7-(8/7)X*.Eachdaytheaveragewouldincreasebyanother%

untilafteraweektheforecastXwouldfinallyequalthenewsalesrate2X*･The

processofaveraglngnecessarilyIntroducesadelaybecausenew valuesare weightedinwiththeoldvalues.

Theweightsinamovlngaverageindicatetherelativeimportanceofeachpast

observationinformingthecurrentperceptlOnOrbelief.Inthecaseofa7-daymov-

1ngaverage,yeSterday'ssalesareglVenJustaSmuchweightastheweek-oldsales

rate,whileallsalesdatapriortOlastweekareignored.Thereisusuallynostrong

reasontoassumeasuddendiscontinultyintheimportanceofthepast.Amorerea-

sonablemodelistoassumetheimportanceofthedatadeclinewithage.First-or-

dersmoothinglSamOVlngaverageWheretheweightswldeclineexponentially.

Themostrecentvaluegetsthemostweight,Witholdervaluesgettlngprogres-

sivelyless.

Adaptiveexpectationsareaverysimplemodelofexpectationformation.

SmoothingusesJustaSingleinput,ratherthandrawlngOnmanysourcesOfdata.

Thatslnglecueisthenprocessedinasimplefashion.Cansuchasimpleprocedure

actuallybeusedtomodelthewayfirmsformforecastsorthewaypeopleadjust

theirbeliefsandexpectations?SurprlSlngly,theanswerisoftenyes｡Surveysof forecastingmethodsshowexponentialsmoothingisoneofthemostcommonfore-

castingtoolsused･SmoothinglSespeciallypopularwhenafirmmustforecastthe

demandforthousandsofdistinctitems.Inthesecasesthesimplicity,lowcost,and

error-Correctlngpropertiesofsmoothingmakeitanexcellentchoice.

Manystudiesshowthatfirst-orderadaptiveexpectationsareoftenanexcellent

modelofthewaypeopleforecastandupdatebeliefs.ⅠnaJustlyfamousstudy,

Makridakisetal.(1982,1984)ranacompetitiontoidentifythebesttime-series

forecastingmethods･TheycomparedtheforecastingPerformanceof21forecast-

ingtechniques,fromnaiveforecasts(tomorrowwillbeliketoday)tosophisticated

432 PartIV ToolsforModelingDynamicSystems

methodssuchasARIMAmodels.Themethodswerecomparedacross1001data

series,encompasslngaWiderangeofsystems,timehorizons,samplingfrequen-

cies,andpatternsofbehavior.Ingeneral,firsトorderexponentialsmoothingper- formedextremelywell.Asecondcompetition(Makridakisetal.1993)examined

judgmentalforecastlngmethods,findingmanyjudgmentalforecastsarewellap-

proximatedbysimplesmoothing.Armstrong(1985)providesacomprehensivere- viewofforecastlngmethodsanddocumentstheextensiveliteratureshowing仙e

wideuseandcomparativeaccuracyofexponentialsmoothinglnmanyCOnteXtS (seealsochapter16).

ll .3.2 hlighe卜Order…nformat岳QnDelays Justastherearecaseswherefirst10rdermaterialdelaysarenotapproprlate,SOtoo therearesituationswhereexponentialsmoothinglSnotthebestmodelofaninfor- mationdelay.Inafirst10rderinformationdelay,likethefirst10rdermaterialdelay,

theoutputrespondsimmediatelytoachangeintheinput･Inmanycases,however, beliefsbegintorespondonlyaftersometimehaspassed･

Inthesecases,theweightsonpastinformationareinitiallylow,thenbuildup

toapeakbeforedeclinlng･Recentvaluesoftheinputmightreceivelowweightfor severalreasons.OftenthedelayInterveningbetweentheactualstateofasystem

andthedecisionsthatalteritinvolvesmultiplestages･Thecurrentvaluesofthein-

putmaysimplybeunavailableduetomeasurementandreportlngdelays･Once dataarereportedtheremaybeadministrativedelays(reportedinfTormationmaynot betakenupforconsiderationimmediately).Finally,theremaybecognitiveand

decision-makingdelays-ittakestimefordecisionmakerstorevisetheirbeliefs andfurthertimetofinalizeajudgmentandactonit･Informationdelaysinwhich therearemultiplestagesareanalogoustothemultiplestagesinmaterialdelaysand

requlreanalogoushigher-orderdelays･ Onewaytomodelahigher-orderinformationdelaylSWiththepipelinedelay

structureinwhichtheoutputissimplytheinputlaggedbyaconstanttimeperiod･

Suchadelaymightbeusedtomodelthemeasurementandreportlngprocesses, wherethereportedvalueavailabletodecisionmakersistheactualvaluesomepe-

riodoftimeinthepast:

ReportedValue(t)-ActualValue(t-D) (ll-8)

whereDisthereportingdelay.SuchadelaylSanalogoustotheinfinite10rderma-

terialdelayorplpelinedelaydiscussedabove･Theoutputofthedelaytracksthe lnPutexactlybutisshiftedDunitsintime･

Moreoften,themeasurementandreportlngOfinformationinvolvesmultiple

stages,andeachstageinvolvessomeaveraglngOrSmOOthing･Firmscannotreport theinstantaneousvalueofflows,suchastherateatwhichordersarebeingplaced

thisinstant,butmustaverage(sumup,oraccumulate)salesoversomefinitetime

periodtofilteroutshort-termvariationsandprovideameaningfulestimate･Gen- eratlngaforecastmightactuallyinvolveseveralstagesofinfわrmationprocesslng･ First,orderratesforarecentperiodsuchasadayorweekarereportedbyindi- vidualsalesrepresentatives,introducingareportingdelay.Then血eweeklysales

figuresareaggregatedandreportedtomanagement,introducinganotherdelay･

Chapterll Delays 433

Managementperiodicallyreviewsthesalesfiguresandthenappliesaforecastlng

proceduresuchassmoothing(eitherformallyorjudgmentally).Theseestimates

canthenbeusedtosetproductionschedules･Furtherdelaysareintroducedasthe

informationisprocessedforuseinotherdecisions,suchasbudgetsorearnlngSes-

timatespreparedbymarketanalysts.

InsomecasesthepurposeofthemodelmightrequlreyoutOportrayeachof

thesestepsexplicitly.Usuallyltissufficienttoaggregatethemtogetherintoasin-

gleinformationdelay.Justasfirst10rdermaterialdelayscanbecascadedinseries

togeneratehigher-orderdelayswithmorerealisticresponserates,sotooyoucan

cascadefirst-ordersmoothingstructurestogenerateafamilyofhigher-orderin-

formationdelays(FigurelI-13).

Annth-orderinformationdelay,denotedbytheSMOOTHnfunction,consists

ofnfirst10rderinformationdelayscascadedinseries.Theperceivedvalueofeach

stageistheinputtothenextstage,andtheoutputofthedelayistheperceived

valueofthefinalstage.Eachstagehasthesamedelaytime,equalto1/nofthe

totaldelayD:

Output-SMOOTHn(Input,D):

Output-Sn

Sl-INTEGRAL(ChangeinStagel,Sl(0))

Sl(0)-Input

ChangeinStagel- (

(Input-Sl)/(D/n) fori-1

(Sl_1-Sl)/(D/n) fori∈(2,‥.,n)

FIGUREll-13 Structureofthethird10rderinformationdelay

(ll-9)

Output-SMOOTH3(lnput,D)

Output-S3

S3-INTEGRAL(Changein

ChangeinStage3-(S2I

S2-INTEGRAL(Changein

ChangeinStage2-(Sl-

S1-lNTEGRAL(Changein

ChangeinStagel-(Enput

Stage3,S3(0))

S3)/(D/3)

Stage2,S2(0))

S2)/(D/3)

Stage1,Sl(0))

-Sl)/(D/3)

434 PartIV TわolsforModelingDynamicSystems

Figurell-14comparestheresponseofthefirsト,third-,andtwelfth-orderin- formationdelaystoastepIncreaseintheinput.Aswiththematerialdelays,the highertheorder,thesmallertheinitialresponseandthesteeperandfastertheeven- tualrisetothefinalvalue.Inthelimitofaninfinite-orderdelay,theoutputwould exactlytracktheinputt-Dperiodsinthepast:aplpelinedelay.

ll .4 RESPONSETOVARIABLEDELAYTJMES

Anotherimportantissueinmodelingdelaysiswhetherthedelaytlmeisconstant orchanging.Relativeto也epurposeofyourmodel,Canyouconsidertheduration ofthedelaytobeconstant,ormightitvary?Ifitvaries,doesitvaryexogenously orendogenously?WhathappenswhenthedelaytlmeChanges?

ThedelaytlmeSforbothmaterialandinformationdelayscanchange.Raising thespeedlimitonUSinterstatehighwaysfrom55to65reducedthedelaylnthe transportofrawmaterialsfromsuppliertocustomer(assuminganytruckerswere actuallyobeyingthe55mphspeedlimitinthefirstplace).Replacingamainframe- basedaccountlngSystemandmanualdataentrywithagloballyintegrated,real timeclient-servernetworkandpoint-of-salescannerdatacanreducethedelayln themeasurementandreportingOfthesalesrateforafirm'sproducts.

DelaytlmeSCanV∬ybothexogenouslyandendogenously.Forexample,acrit- icalparameterinamodelofafirm'ssupplychainistheaveragedelaybetween placlngandreceivingOrders氏)rpartsandmaterials.Canyouconsiderthistimeto befixed?Inmanyindustriestheresupplytimeisavariable,andbothexogenous andendogenousfactorsinfluenceit.Forexample,theresupplytlmeOftendepends ontheseasonoftheyear(anexogenousfactor).Thetimerequiredtodeliverfresh strawbe汀iestomarketinBostonisshorterinsummerwhenlocalberriesare

inseasonandlongerinwinterwhenthesupplylinestretchestoCaliforniaand Mexico.

Thelengthofadelayoftendependsonthestateofthesystemitself.Howlong willyouwaittowithdrawcashfromanATM?Iftherearenopeopleaheadofyou inline,thedelayistheminimumtimerequiredforyoutoinsertyourcard,enter yourcode,collectyourcash,andgetyourcardback-aboutaminute.However,

FIGUREll-14

Responseof

higher-order cielayStOa stepInput

｣ }:{,!r.r percelIVedValue

1e+ //,.Iorder///:;:∫.′/3rd ..:,/ Order.; ;12th

0 1 2 3

Time(multiplesofaveragedelaytime)

ChapterllDelays 435

thelengthoftimeyoumustwaitincreasesiftherearepeopleaheadofyouinline･ Inturn,therateatwhichpeoplejolnthelinedependsonhowmanypeopleareal- readyinline:whenthelineislong,peoplewillwalkbyandwaituntilthecrowd isn'tasbig(abehaviorknownasbalking).Theaveragewaitingtime(thedelayin

gettingserved)thereforedependsendogenouslyonthenumberofpeopleinthe delay(thelengthofthequeueofpeopleawaitingservice)･

Similarly,thedelaylnreceivingPartsfromsuppliersdependsonboththenor- malorderprocesslngt1meandonthesuppliers'backlogofordersrelativetotheir

capacity･Whensuppliershaveamplecapaclty,theycandeliverrapidly･Whenca- pacltyisfullyutilized,backordersaccumulate,andcustomersareputonallocation (theyreceivea丘.actionoftheirorderandareforcedtowaitlongerthanexpected)･

Inthelongrun,customerswillseekalternativesuppliers,forminganegativeloop thatreducesthedeliverydelay.Butintheshortrun,beforenewsupplierscanbe foundandqualified,customersmayactuallyordermoreinanattempttogetwhat

theyreallydesire.Ifyoursuppliertellsyouitcanonlyshippartofyourorderthis week,youmayordermorethanneededinthehopeofreceivlngWhatyouactually

require･Placingsuchphantomorderscreatesapositivefeedbackthatfurtherin- creasesthesupplier'sbacklogandlengthensthedeliverydelaystillmore,often leadingtoinstabilityinorders,production,andinventory(Seechapter18)･

Resp⑳閃Se⑳菅De日ays竜OehamgmgDe日aLyTimes

Todevelopyourunderstandingofhowthedifferenttypesofdelaysrespondto variationsinthedelaytlme,answerthefollowlngqueStions･

1. Consideramodelofthepostofficeasathird10rdermaterialdelay(equation (11-4))｡Assumethatthemailingrateisconstantandthatthesystemisinequi-

librium-themailingrateanddeliveryrateareequal･WithoutuslngSimulation, SketchthebehavioryouexpectlfthedelaytlmeSuddenlyandpermanentlyin-

creasesfrom5daysto10daysonday5.Maketwographs-Oneshowingthe mailingrateanddeliveryrateandtheothershowlngWhatyouexpecttohappen tothestockoflettersintransit.Sketchtheresponseyouwouldexpectifthedelay

timesuddenlydroppedfrom5to2.5days･

2.Nowconsiderafirm'sforecastoforders.AssumethefirmusesadaptlVeeXI

pectationstoforecastorders,equation(11-6).Assumethattheorderrateiscon- stantandthattheexpectedorderrateisequaltotheorderrate(thesystemisin

equilibrium).Withoutusingsimulation,Sketchthebehavioryouexpectifthe timetoadjusttheforecastsuddenlyandpermanentlydecreasesfrom6monthsto 3months.

3.Afteryou'vesketchedyourintuitiveestimates,buildthemodelsandsimu-

latetheirresponsetochangesinthedelaytlme.Wasyourintuitioncorrect?If

therearedifferencesintheresponseofthematerialandinformationdelaysto changesinthedelaytlmeS,explainwhy.

436 PartIV TわolsforModelingDynamicSystems

ll.4.1 Nonぎine即AdjustmenモT套mes:

ModeHngRatchetE軸 cts

Oftenthetimeconstantforaninformationdelaydependsnonlinearlyontheinput. Thedelayinadaptingourselvestoanewsituationmaybelongerthanthedelayln

reactlngtOfurtherinstancesofthestimulusoncewehavecometoexpectit.Peo-

plegetusedtohigherincomefasterthantheyadapttoadropintheirincome.We

sometimeslearnmorerapidlythanweforget.Becausefirsトordersmoothing(and

allthedelaysdiscusseduptonow)islinear,itrespondssymmetricallytoinputsof

anymagnitudeandtoincreasesaswellasdecreases･Onewaytomodelasymmet-

ricaladjustmentsiswithanonlineardelaylnWhichthetimeconstantforthedelay dependsonthestateofthesystem.

Inthe1940S,theeconomistJamesDuesenberrynoticedthataggregatecon- sumptioneXPendituresseemedtorisefasterthantheyfellasincomefluctuated

overthebusinesscycle･Hehypothesizedthatpeoplerapidlyraisedtheirexpec-

tationsoffutureincomewhenincomeincreased,boostlngtheirconsumptlOn

quickly,butwereslowtoglVeuPtheirdesiredstandardoflivinglnthefaceofhard

luck,leadingthemtospendneartheoldrateseventhoughincomehadfallen.

Such"ratcheteffects"CanbemodeledbyassumlngthetimeconstantDtakes

ononevaluewhentheinputtothedelayXexceedstheoutputXandanotherwhen

theinputfallsbelowtheoutput:

D-(DD華 ≡登 (ll-10, whereDIisthetlmeCOnStantthatcharacterizestheadjustmentwhentheoutputis

increasing(whenX≧X)andD,isthetireconstantgoverningtheadjustment whentheoutputisdecreasing(whenXくⅩ).Inthecaseofincomeexpectations,

thehypothesissuggestsdownwardrigidityofexpectations,thatis,DIくDD･9

Sterman,Repenning,andKofman(1997)usedthenonlinearsmoothingstruc-

turetocapturetheresponseofworkerstonewsoflayofFsinamodelofprocessim-

provement.Improvementprogramshavethepotentialtocreateexcesslaborif

productivityrisesfasterthanthedemandfortheproduct.Thewillingnessofwork-

erstoparticlpateinimprovementprogramswashypothesizedtodependonper-

ceivedjobsecurity.Perceivedjobsecuritydependedonworkers'memoryofpast

layoffs(alongwithotherfactorssuchasexcesscapacity):perceivedjobsecurityis

likelytobehigherinafirmthathasn'tlaidoffanyworkersforyearsthaninone

wherelayoffsarecommon.Thememoryofpastlayoffswasmodeledusingthe

nonlineardelayinequation(11110).Theinputwasthefractionoftheworkforce

llaidoffintherecentpastandtheoutputwasthememoryoflayoffs.Setting

DIiDDCapturedtheresultsofourfieldstudiesshowingthatperceptlOnSOfjob

securityfallswiftlyonnewsofalayoffandtakeyearstorecover,evenifthereis

nosubsequentdownsizing(Figure11-15).Thenonlinearsmoothing structurealso

workswithhigher-orderinformationdelays.

9ThougheconomistsdatingbacktoKeyneshavesuggestedthatwagesandpricesmightalso exhibitratcheteffects,rislngmorerapidlythantheyfall,empiricalstudiesarescarce;Somedonot supportthehypothesis(e.g.,RassekhandWilbratte1990).

ChapterllDelays

FIGUREll-15 Nonlineartime constants: structureand behavior

Simu一ationof

responseof perceivedjob securitytopurse inlayoffslThe timeconstantfor

increaslngthe memoryoflayoffs Dl-1week; forforgetting thehistoryof pastlayoffs DD-50weeks.

500

(

葛

â P 3) 0IU O JVLg

O u O JI U t

ぶ)

tt=tj l

10̂ e 1

40 60 Weeks

80 100

437

ll .5 EsTIMATINGTHEDURATIONANDDrsTRIBUTl0NOFDELAYS

Theaveragelengthofadelayandtheshapeoftheresponsedistributioncanbees-

timatedbytwoprlnCIPalmethods:statisticaltechniquesandfirsthandinvestigation oftheprocessinthefield.

11.511 EstimatingDelaysWherlNumerict3IData AreAvailable

Awiderangeofeconometricandstatisticaltoolscanhelpyouestimatethedura- tionanddistributionoflagsfromtimeseriesdata,whensuchdataareavailable (seeHamilton1980forareview;furtherdetailsareprovidedinanygoodecon0- metricstext).

Thoughyoucanwritetheoutputofalagastheweightedsumofpastvaluesof theinput(seeequation(ll-7)),itisusuallyinfeasibletoestimatetheweightsdi- rectlyduetomulticollineantyandlackofdata.Themaineconometrictechniques availableforestimatinglagsfromtimeseriesdataincludetheKoyckorgeometric

lag,polynomialdistributedlags,rationaldistributedlags,andARIMAmodels(See section11.7).Manyeconometricandtimeseriesstatisticalpackagesareavailable toestimatethesemodelsfromtimeseriesdata.

Inchoosinganestimationmethodyoumusttradeofftheflexibilityofthefor- mulationagalnStthenumberofparameterstobeestimated.Somemethodsassume

theshapeoftheresponse(equivalenttoassumingtheorderof山edelay)andesti一 matethemeandelaytlme.TheKoyckorgeometriclag,forexample,iseasilyes- timatedbutassumesthedelayisfirst10rder(seesection11.7).Othertechniques, suchasthepolynomiallagmethod,imposefeweraprlOrirestrictionsontheshape

ofthelagdistributionbutrequlremoredata.Youshouldnotconstraintheshapeof thedelaylnadvanceunlessthereisstrongindependentevidencetosupporta

438 PartIV TわolsforModelingDynamicSystems

particularlagshapeorifsensitivltyanalysュsSuggeststheresultsofinterestarenot contlngentOntheshapeofthedelaydistribution.

WhileyoumayestimatethelengthanddistributionofadelayusingeCOnO -

metrictechniques,youshouldnotusetheestimatedregressionequationinyour simulationmodel.Instead,youshouldreplacetheestimateddistributedlagwith

thematerialorinformationdelaythatbestmatchestheestimatedlag･Thereare severalreasons.First,econometrictechniquesaredesignedfわrdiscretetimesince

mosteconomicandbusinessdataarereportedatregular,discreteintervalssuchas

amonth,quarter,oryear.Systemdynamicsmodelsareusuallydevelopedfわrcon- tinuoustime.Thetimestepforupdatingthestatevariablesisoftendiftbrentfrom

andusuallyshorterthanthedatareportlngperiodusedtoestimateadelay･Using thecontinuoustimedelaythatbestmatchestheestimateddiscretedelayensures

thatyourmodelwillberobusttochangesinthesimulationtimestep.Second,re一 gressionequationsforlagshavefixedlagweights,implyingafixeddelaytime.In

manysituations,however,thelengthofadelaylSactuallyavariable･Evenifthe delaytlmeisthoughttobeconstantinthecurrentversionofyourmodel,further workmayrevealthatthedelaytlmemustbeincorporatedasanendogenousvari- able.Thematerialandinformationdelaystructuresusedinsystemdynamicsre-

spondapproprlatelytochangesinthedelaytimes,Whilearegressionequationfor adistributedlagdoesnotenabledelaytlmeStOVary･Regressionequationsfordis-

tributedlagsalsodonotdistinguishbetweenmaterialandinformationdelays.Ma- terialandinformationdelaysresponddifferentlytochangesindelaytlmeS.Your

modelmustproperlydistinguishbetweenthetwotypesofdelaytorespondappro- prlatelytochangesindelaytimesandtoensureconservationofmaterialmows.

Example:TheLaggedResponseofEnergySupplytoPn'ce

DelaysplayedanimportantroleinRogerNaill'S(1973)modelofthenaturalgas industry.ExplorationeffortrespondstochangesinprlCe,butonlyafteraconsider-

abledelay･Fortunately,Khazzoom(1971)hadcarefullyestimatedthedistributed lagresponseofgassupplytochangesinprlCe･Ratherthanuslngthediscretetime formulation,however,Naillfoundthattheestimateddelaywasapproximatedwell

byathird-orderdelaywitha4･5-yeardelaytime(Figurell-16)･WhereasKhazI zoomtreatedthedelaybetweenprlCeandsupplyasaslngle,aggregateprocess, Naill'smodelexplicitlyportrayedtheexplorationanddiscoveryprocess.Explic-

itlymodelingInvestmentinexplorationcapltalwi血amaterialdelaymeantNaill

couldsimulatetheresponseofnaturalgassupplytochangesinthedelaybetween theinitiationofexplorationactivityanditsresults,Changesthatmightarisefrom

changesinexplorationtechnologyラgOVernme王nlregulationsラーhelocationanddepth ofgasresources,orthecapacityOftheindustrysupplyingdrillrlgS･

Example:CapitalInvestmentintheMacroeconomyI

Capitalinvestmentisamajordecisionforanybusiness,andunderstandingthere- sponseofinvestmenttochangesineconomicconditionsiscriticalintheformation

offiscalandmonetarypolicy.Sinceinvestmenttakestime,policymakerssuchas centralbankersandgovemmentsmustunderstandthelengthanddistributionofthe lagsintheresponseofinvestmenttochangesinpolicyleverssuchasinterestrates,

FIGUREll -16

Approximating adiscretetime

distributedlagwith acontinuousdelay

Khazzoom(1971) estimatedthe

laggedresponse ofnaturalgas supplytochanges inpnce.The graphshowshis estimatesofthe

responsetoa 1¢/MCF(thousand cubicfeet)impulse inthepnceofgas, Naill(1973)found a4.5-year,third一 Orderdelay matchedthe

estimatedlagwell･

ChapterllDelays

j U M N Oコ 1 rM

2 4 6 8 10 12

439

TlMEELAPSEDINYEARSAFTERTHEIMPULSE

Source:Naill(1973,p.229)Reproducedwithpermission･

taxes,andthelevelofdemandintheeconomy.Howlongdoesittaketobuildnew

capitalplant?

Figurell-17showsdataforonepartofthecapitalinvestmentprocess:the

constructiondelay.Thefigureshowsthedistributionofconstructioncompletions

forprivatenonresidentialinvestmentprojectsderivedbyMontgomery(1995)from

USDepartmentofCommercesurveydata･Thesurveyscover52,000construction

projectsfromallsectorsoftheeconomy.Themeandelaybetweenthestartofcon-

structionandcompletionis16.7months(1.4years)･Thedatadescribeonlythe

physicalconstructionprocessanddonotincludeplannlngandadministrativede-

laysintheinvestmentprocess.

Theconstructiondelaydistributionisapproximatedextremelywellbyasec-

ond-ordermaterialdelaywitha16.7-monthaveragedelaytlme,thesamemeande-

layasthedata.Theloworderofthedelay,consistentwiththelargevariancein

completionrates,isduetotheaggregationofmanytypesofcapitalplantinthe

surveydata,dataspannlngallsectorsoftheeconomy･Delaydistributionsforcap-

italplantatthelevelofparticularindustriesortypesofstructures(e･g･,semicon-

ductorwaferfabs,powerplants,officebuildings)wouldhavelowervarianceand

wouldrequirehigher-orderdelays.

Interestlngly,Montgomeryfoundonlysmallvariationsintheaveragedelay acrossthedecades,andhisestimateof16.7monthsisveryclosetothe15-month

meanconstructiontimeestimatedbyMayer(1960)froma1954surveyofUScon-

structionprojects.ThemeananddistrilDutionofconstructiontimesappearstobe

quiteStableoverthepast40yearsdesplteSlgnificanttechnicalchangeandshiftsin

thecompositionoftheeconomy.Therelativelysmallrangeofvariationsuggests

thattheconstructiondelayanddistributioncanbemodeledwiththesamestructure

andparametersoverlongtlmehorizons･

Example:CapitalInvestmentintheMacroeconomyll

Theroughly17-monthaverageconstructiondelaylSOnlypartofthetotallagln

theresponseofcapltalinvestmenttochangesinbusinessconditions｡Estimatesof

440

FIGUREll-17 Theconstruction

lagforcapital plant:datavs. mode一

Data:Distribution ofconstruction

completiontimes forUSprJVate nonresidentjar structures, 1961-1991,as estimatedby Montgomery (1995)from USDept･of CommercesuⅣey data.Themean

faglS16.7months. Mode/:Secondl ordermateria一

delayw-Fth averagedelay timeof 16.7months.

PartIV ToolsforModelingDynamicSystems

u l u

O ≡ P

S I n d

l !

u n

I O

./ o

36 48

thetotaldelaybetweenachangein,say,demandforafirm'sproductsandthecom- pletionofnewcapacltyaremuchlonger,typlCally2to3years,astheyIncludethe administrative,decisionmaking,appropriations,permittlng,design,andotherde-

laysaswellasthephysicalconstructionprocess.Businessesandorganizations suchastheFederalReservemustaccountfortheentiredelaywhensettlngPOlicy.

Thelagsincapitalinvestmenthavebeenintensivelyexploredinmacro- economicsformorethan50years.AcommonformulationknownastheneoI classicalinvestmentfunction(see,e.g.,Jorgenson,Hunter,andNadiri1970)

presumesfirmsfirstcalculatetheoptimallevelofcapltalstocktheydesire,K*, basedontraditionalstaticprofitmaximizationconsiderations,thenadjustthe actualstockKtowardthedesiredlevel:

K(t)-L(K*,D) (ll-l l)

ThelagoperatorLdenotesadistributedlagwithmeandelaytlmeD.Theoptlmal

capitalstockK*iscalculatedbyassumingfirmssetthedesiredcapltalstockatthe levelthatmaximizesprofits,whichinturnisafunctionofindustrydemand,inter- estrates,taxes,themarglnalproductivltyOfthecapitalstock,andpossiblyother variables.ThedistributedlagLisestimatedfromdataongrossinvestmentorcap-

italexpendituresbynotlngthat血erateofchangeofthecapitalstockKisnetin-

vestment,thatnetinvestmentisgrossinvestmentlesscapitaldiscards,andby

assumlngthatdiscardsdependonthecurrentcapitalstock.Discardsareusuallyas-

sumedtobeafirst-orderdecayprocesswithaconstantaveragelifeofcapital･The resultinglagestimatessubsumetheconstructiondelaytoyieldameananddistri- butionforthetotaldelaybetweenchangesinbusinessconditionsandtheresponse ofcapltalinvestment.

AmajorProblemwiththeneoclassicalinvestmentfunctionisthatthemeande- layandlagdistributionareassumedtobefixed･ThetimebetweenplaclnganOr- derfornewplantandequipmentandreceivingthatcapitalfromthesupplieris assumedtobeindependentofthesupplier'scapacityutilization.Yetwhensuppli- ershaveexcesscapaclty,thedeliverytlmeWillbeshort,whileduringbooms,when

suppliercapacityisfullyutilized,thedeliverydelaywillincrease･Senge(1978) foundthatdeliverydelaysforcapitalgoodsvariedby±50-75%overthebusiness

ChapterllDelays 441

cycle･10Modelswherethelagdistributionisfixedaremisspecifiedbecausethey

implicitlyassumesuppliersofplantandequlpmenthaveunlimitedorperfectly

flexibleproductioncapacity,aPhysicalimpossibility.Ingeneral,modelsinwhich

delaysarespecifiedasdistributedlagsratherthanconservedstockandnowstruc-

turesarenotrobustandfrequentlyviolatebasiclawsofphysics.

Thesystemdynamicsnationalmodel(SDNM),amacroeconomicmodelde-

velopedbytheMITsystemdynamicsgroup(Forrester1977,1979;Forresteretal.

1976;Mass1975),addressedthisandotherdefectsoftheneoclassicalfunctionby

explicitlyrepresentlngtheinvestmentprocessattheoperationallevel.Themodel

distinguishesbetweenperceptlOndelaysandmaterialde一aysandcapturesthecon-

servedflowsoforders,acquisitions,anddiscardsofplantandequlPment･Theac-

qulSltlOndelayvarieswiththecapacltyutilizationofthecapltalproducing

industries.Figure1i-i8Showsasimplifiedrepresentationoftheinvestmentfunc-

tion.InsteadofrepresentlnglnVeStmentaSaSlngledistributedlag,themodelrep-

resentsthestagesofinvestmentseparately,distinguishingbetweentheplannlng

processandthecapitalorderingandconstructionprocess･Capitalstockisin-

creasedbyacqulSltionsanddecreasedbydiscards.Discardsareassumed,asinthe

neoclassicalmodel,tobeafirst-orderexponentialdecayprocess.Theacquisition

ratedependsonthebacklogofordersforcapitalandthecurrentdeliverydelayfor

capital.Thebacklogofcapitalonorderisincreasedbyorders.Orderslagtherate

oforderstarts,capturingapproprlationandadministrativedelaysininvestment.

Theorderstartraterespondstofourfactors:(1)replacementofcapitaldiscards;

(2)adjustmentfortheexpectedgrowthindemand,basedonpastgrowthinship-

ments;(3)thegapbetweenthedesiredandactualstockofcapital,and(4)thegap

betweenthedesiredandactualsupplylineofcapitalonorder(Seechapter17).

Thedesiredsupplylinedependsontheperceiveddeliverydelayforcapitaland

therequiredreplacementofdiscardedcapltal･Thedesiredstockofcapitalispro-

portionaltodesiredproductionbutismodifiedbytheperceivedmarginalreturnon

newcapital.Firmsareassumedtorespondtotheprofitabilityofanewinvestment,

butwithadelaycausedbythedifficultyofassesslngChangesinthemarglnalp ro -

ductivltyandmarglnalcostofcapital.Desiredproductiondependsonexpected d e -

mand,andisthenadjustedtocorrectdiscrepanciesbetweenthedesiredandactu a l

levelsofinventoryandbacklog.Expecteddemandismodeledasaninformatio n

delayofshipmentdata.ThemodelprovidesanoperationaldescrlptlOnOfthe c a p -

italinvestmentprocess,allowlngthedelaysinthedifferentpartsoftheproc e s s to

beseparatelyspecifiedandestimated.

Senge(1978,1980)Showedthatthedisequilibriuminvestmentfunctionused

intheSDNMincludestheneoclassicalinvestmentfunctionasaspecialcase.The SDNM investmentfunctionreducestotheneoclassicalfunctionwhenanumber

ofequilibriumandperfectinformationassumptionsaremade.Theseincludethe

assumpt10nSthatinventories,backlogs,andthestockofcapitalonorderalways

10ThelargevariationincapitaldeliverydelaysSengefounddoesnotconflictwiththerelatively stabledistributionofconstructiontimesMontgomery(1995)documented.Thetotaldeliverydelay includestheconstructiontimeplusanyadditionaltimeanorderspendsinqueueawaitlngthestart ofconstruction･Duringboomperiods,thispreconstructionwaitlngperiodincreasesasthebacklog ofprojectsWaitingforconstructioncrewsandequipmenttObecomeavailablebuildsup･

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ChapterllDelays 443

equaltheirdesiredlevels;thatfirmsinstantlyandperfectlyperceivedemandand themarginalproductivltyOfcapital;thatthedeliverydelayforcapitalisconstant; andthatcapacityutilizationisalwaysconstantatthedesiredlevel･Sengeused econometrictechniquestoestimatetheparametersoftheSDNMinvestmentfunc-

tion.WhilethesystemdynamicsmodelrelaxedtheunrealisticassumptlOnSOfthe neoclassicaltheory,theaddedcomplexltyOfthemodelmadeeconometricestima- tionofthevariousdelaysmuchmoredifficult,bothstatisticallyandinthecreation ofconsistentdatasets.Tbensuretherobustnessoftheresults,Sengetestedeight

differentspecifications,eachprogressivelyrelaxingmoreOftherestrictiveasI sumptlOnSOftheneoclassicalformulation.

Sengetestedthemodelwithquarterlydataforfourindustries:durableand nondurablemanufacturlng,electricalmachinery,andtextileproducts･Thesein- dustriesspannedtwomajorlevelsofaggregation:durableandnondurablemanu- facturlngtogetheraccountfortheentiremanufacturlngSectorOftheeconomy, whiletheothertwoindustriestestedthemodel'sabilitytoexplaininvestmentata moredisaggregatelevel.

Theregressionresultssupportedthedisequilibriumsystemdynamicsfunction･ Forallfourindustrygroups,theSDNMinvestmentfunctionexplainsmoreofthe varianceinthedata,withlessautocorrelationintheresidualsthantheneoclassical

function,whileyieldingstatisticallysignificant,plausibleestimatesforthemodel parameters･Themodelalsogeneratesmorerealisticbehaviorwhensimulatedthan theneoclassicalfunction.Table11-1reportstheestimationresultsfornondurable manufacturlng.TheestimateddistributionsforthreekeylagsareshowninFigure lト19.Thesedelayswereestimatedbythepolynomialdistributedlagmethod, allowlngthelagshape,aswellasthemeandelay,tobeestimatedratherthan assumed.

ThelaglnaVeraglngShipmentstoformdemandforecastswashypothesizedto befirst-order,andindeed,theestimateddistributionoflagweightsforaverage

shipmentsisapproximatedwellbyfirst-orderexponentialsmoothingwithadelay timeofabouttwoquarters･Theresponseofinvestmenttochangesintheperceived deliverydelayforcapitalwasalsoexpectedtobefirsトorder,andtheestimated weightsarewellapproximatedbyfirst-ordersmoothing,thoughwithamuch longeraveragedelayofabout13years･Alongerdelayintheresponsetochanges incapitalavailabilitylSexpected.Deliveryquotesforplantandequlpmentareun- certainandunreliable;managersmustwaitasubstantialfractionofthenormalde- liverydelaybeforetheycangleanreliableinformationontheprogressof equlpmentOrdersortherateofconstructionofnewplant･Moretimeisrequiredto determinehowtoalterinvestmentplanstocompensateforchangesinleadtime･ flllnally,theresponseofgrowthexpectationstochangesinthegrowthrateolshlP一 mentswashypothesizedtobeahigher-orderdelay･Theregressionssupportthis hypothesis.Theestimatedlagdistributionisbellshaped:Growthexpectationsdo notrespondsignificantlytoshort-termchangesinactualdemandgrowthrates･The estimateddistributionisapproximatedreasonablywellbyathird-orderdelayof therateofchangeinaverageshipments(averageshipmentsaregivenbyfirst-order smoothingofactualshipmentswiththeestimated2･13quarterdelay)･

SengealsocomparedtheestimateddelaystotheaprlOrljudgmentalestimates developedbythemodelingteam(TableIレl),Insomecasestheaprioriestimates

444

FIGUREll -19 Estimatedlag distributions forinvestment

comparedto continuous

timeFags

Estimated

lagsfound bypolynomial distributedlag methodwith

thirddegree polynomial; COnSumer nondurables. Errorbarsshow ±1estimated standarderror.

PartIV ToolsforModelingDynamicSystems

AverageShipments

EstimatedLag Distribution

1 2 3 4

Quarters

PerceivedDeliveryDelayforCapital

Quarters

12 16

ExpectedGrowthinShipments

0 Ì

Source:Senge(i978).

弓2 i6

arenotstatisticallydifferentfromtheestimatedvalues.Forotherparametersthere isalargedifferencebetweenthetwo.Thesediscrepanciesledtoreconsiderationof

thelogicbehindthejudgmentalestimatesandtheapproprlateneSSOfthedata sourcesandestimationmethods.Insomecasesthejudgmentalestimateswere

revisedinlightoftheestimationresultsorimprovedmodelformulationswere

Chapterll Delays

TABLEll-1 Comparisonofestimatedandjudgmentalestimatesofinvestmentdelays

445

Estimated APriori EstimatedStandard

Value Estimate DeviationofEstimate

Parameter (quarters) (quarters) (quarters)

TimetoAverageShipments

TimetoPerceiveMarglnal ReturntoCapital

TimetoPerceivetheDeHvery DelayforCapital

TimetoFormGrowth

Expectations

SupplyLineCorrectionTime

CapitalStockCorrectionTime

TimetoCorrectInventoryand Back】og

DesiredlnventoryCoverage

DesiredBacklogCoverage

FractionalDiscardRate

(AverageLifeofCapital)

2.13 2.00

4.12 8.00★

5.36 8.00★

7.25 6.10

3.02 10.00★

12.10 10.00

1.73 3.00★

0.47 1.33★

1.65 1.33

0･0384/quarter 0.0156/quarter★ (6.5years) (16years)

1.88

0.32

0.96

1.17

0.86

2.18

0.37

0.033

0.34

0.00043/quarter

Estimatesfortheconsumernondurablessector.

'indicatesestimatedandjudgmentalvaluesdlfferbymorethan2estlmatedstandarddeviations,indicatingaslgnlfECantdiffer- encebetweenthetwoestimates

Source:Senge(1978,pplilo).

developed.Inothercases,thediscrepancywastracedtolimitationsoftheestima-

tionprotocoloranimperfectmatchbetweentheconceptintheinvestmentfunction

andthedataseriesusedtoproxylt,andtheaprlOriestimatewasretainedforsim-

ulationpurposes.

11.5.2 Est…matingDelaysWhenNumericaiData AreNotAvailable

lnmanysituations,datafromwhichtoestimatethedurationandshapeofdelays

arenotavailable.Inthesecasesyoumustestimatetheseparametersfromdirectin-

spectionofthedelayprocess,experiencewithanalogousdelaysinrelatedsystems,

orjudgment.

Judgmentalestimatesofaggregatedelayscanbequlteunreliableandusually

underestimatetheirduration.Recallthechallengesatthestartofthischapter.What

wasyourestimateoftheinvestmentdelayforthemanufacturlngeconomy?How

aboutthetimerequiredforporksuppliestorespondtoprlCeChangesorforecon-

omiststoupdatetheirinflationforecasts?Mostpeopledramaticallyunderestimate

theseandotherdelays.Theactualdelaysareroughly3years,2years,and1year,

respectively(Senge1978;Meadows1970;Sterman1987).Thelongerthedelay,

446

TABLEll -2

DelaysinsocietaF

responsetoair

poHutioninthe UnitedStates

PartIV ¶)OlsfわrModelingDynamicSystems

thegreaterthedegreeofunderestimation.Whatwasyourestimateofthedelay

inrecognlZlngandreactlngtOairpollution?AsshowninTablell-2,morethan

50yearshavepassedfromthefirstundeniableevidencethatairpollutioncauses

significanthealthproblems,suchasdeath,yetmostmajormetropolitanareasinthe

USarestillnotlncompliancewiththeprovisionsoftheCleanAirAct.

Decompositionisausefulstrategytominimizetheunderestimationofdelays.

Insteadofestimatlngthetotallengthofthedelay,decomposetheprocessintoits

variousstages,thenestimatethelengthoftimerequiredforeach･Senge'scapltal

investmentmodeldecomposedthetotalresponselagIntoadisaggregate,opera-

tionalmodelwhoseindividuallagscouldbeestimatedjudgmentallyfromdirect

1800S:Widespreaduseofcoalforindustryandhearlngreadstogrowlngair pollutioninurbanareasofEuropeandtheUnitedStates.

1948:SmoginDonora,Pennsylvaniakills20peopleandsickens6000.

Soonafter,coa一fumeski=nearly800inLondon.

1955:FirstUSFederalAirPoHutionControlActraidpnmaryresponsibilityfor limitingairpo"utionuponstatesandcities,buta"ocated$5millionfor research.

1963:FederalCLeanAirActrecogmzesalrPO"utiondoesnotrespectstate

boundaries;setsupregulationsforcontrolofinterstateabatement;provides

moreassistanceforstateandJocalgovernments･

1970:CleanAirActstrengthenedbydefinlng"safe"standardsforSO2,CO, particulates,VOCs(VolatileOrganicCompounds),NOx,ozone,andlead.

Stateplanstomeetstandardsrequiredby1975.

1977:DeadlinepostponeduntiH982as78Citieswereinviolationofthe ozonestandard.

1988:Ninetyurbanareaswith150mi"ioninhabitantsexceedozone standard;40violateCOstandard.

1990:ComprehensiveamendmentstoCleanAirActrequlrea"citiestomeet

ozonestandardby2007(exceptLosAngeleswhichhasuntil2010).Stricter

regulationsforautoemissions,gasoline,SO2,andmanynewlyregulated pollutants.

1997:AmbientconcentrationsofaHsevenregulatedpo"utantsdropplngVery

slowly(exceptlead,whichplummetedassoonasleadedgasolinewas

banned,thoughmuchleadfromprioremissionsre〔ainsinsoils)IMedical evidenceshowshealthproblemsanddeathsfromalrpollutiongrowlng. 1ククmiIlinninH.qlivLqin月rl与力_qVinlFl1linn†hLln7nnl∋くIFlnrbrrlFPAqLILBkqI∩■-~="■Y= ■ーVL‥TH'~~■ーY-〉T■〉r-""'ミプ■"〉〉'-〉一■ーー■ー■HW"■､~■■~▲∫t､~))■…~L､′

Stiffenozoneandparticulatestandards.IndustryaHocatesmi"ionstofight

thestrengthenlngOfstandards,

Timefromclearsignalofproblemtofirstmeaningfullaw:22years.

TlmefromfirstJawtomeasurable.steadyimprovementsinairquarlty: 20years.

TimefromfirstlawtofuncompHancewithlaw:27yearsandcounting.

TotaqdelayfromfirstclearslgnaHofuncomp日iance:>50years.

Sou/℃e:ParaphrasedandcondensedwithpermlSSionfromD.MeadowsandA.AtKisson,The Ba/atonBullet/'n,1997,pp.16-17.

ChapterllDelays 447

Observationofbusinessdecisionmaking;subsequentstatisticalestimationshowed

thejudgmentalestimateswereoftenreasonable.

TodecomposeadelayforthepulPOSeSOfjudgmentalestimation,mapthestock

andflowstructureoftheprocessattheoperationallevel･Forexample,considerthe

delayintheresponseofaggregateporksupplytopricechanges(Figurell-20).

DecompositionrevealsthefollowingSequence.First,hogfarmersmustdecide

thatariseinprlCeislikelytopersistlongenoughtoJustifyinvestlnglnincreaslng

production･Thentheymustincreasetheirbreedingstock(bywithholdingsome

maturesowsfrommarket),thenbreedthesows.Afterthegestationdelay,thelit-

tersareborn.Thepigletsrequlrefurthertimetomature,thenspendadditionaltime

inafeedlotuntiltheyreachtheoptimalweightwherethegalninmarketvalue

fromgreaterweightisbalancedbythecostofadditionalfeed.Onlythenarethey

senttoslaughter,increasingthesupplyofpork.Mostofthesedelaysarebiolog1-

callydetermined,easilyestimated,andquitestable.Thegestation,maturation,and

feedlotdelaysareabout3･8,5,and2months,respectively,atotalmaterialdelayof

about11months(Meadows1970).Howlongisthedelayinadjustingproducers'

expectationsaboutthefutureprlCeandinbuildingupthebreedingstock?Because

ittakesaboutayearbetweenbreedingandtheresultingIncreaseinhogsupply,

producerscannotaffordtoreacttooquicklytoprlCeChangesbutmustwaitlong

enoughtobeconfidenthigherpricesWillpersist.Studiesshowforecastsoffuture

hogpricesareStronglyinfluencedbyrecentprlCeS,WithlittleweightonprlCeS

morethanayearinthepast(BesslerandBrandt1992).Meadows(1970)estimated

theexpectationformationdelaytobeabout6monthsandthebreedingstockad-

justmentdelayatabout5months.Thusthetotaldelaybetweenachangeinthe

prlCeOfhogsandtheresultingchangeinhogproductionisabout22months.Not

surprlSlngly,suchalongdelayinthemarketfeedbackregulatlngPrlCeSleadstoin-

stability:hogprlCeStendtooscillatewithanaverageperiodicityofabout4years

(Seechapter20).

DecompositionalsoglVeSinsightintotheshapeoftheoutflowdistributionfor

eachdelay.Themorestagesinadelay,thetightertheoutputdistributionwillbe

andthesmallertheinitialresponse.Thevarianceinthegestationprocessissmall;

Meadows(1970)reports90%offarrowingstakeplace111to119daysafterbreed-

1ng,indicatingaVeryhigh10rderdelay.Thevarianceinthematurationandfeedlot

delaysisgreaterthanthatofthegestationdelay,buttheshortrunresponsetoa

pulseInputissmall.Thesedelayscouldprobablybemodeledadequatelywitha

third-orsixth-orderdelay.Priceexpectationsandthedelayinadjustlngthebreed-

ingStock,however,canprobablybemodeledasfirst-orderprocesses:Bothpri c e

expectationsandthebreedingStockarelikelytorespondcluickestw hentheg a p

betw eenthedesiredandactualstatesisgreatest.Becausethetotaldelaycascad e s

m any distinctstages,manyofwhichhavelowvariance,theshort-run response o f

hog productiontohigherprlCeSisnegligible･ll

llActuauy,theshort-runeffectofprlCeincreasesonsupplylSnegative.Fortheaggregateindus-

try,thebreedingstockcanonlybeincreasedbywithholdingsomesowsfromslaughter.Thefirst responseoftheslaughterratetoariseinexpectedpriceisthereforeareductioninsupply,creating apositivefeedbackloop:HigherprlCeSleadtolowershort-runsupplyandstillhigherprlCeSaSPro- ducerssendfewersowstoslaughtertoincreasetheirbreedingstock･Agoodmodelofthehogpro- ductionsystemmustincludethisdestabilizlngloop,aprocessthatcannotbecapturedinmodels, suchascobwebmodels,thattreatthesupplyresponseasanaggregatedelay.Seechapter20.

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Chapterll Delays 449

ll.5.3 ProcessPoint:WalktheLine

Evenwhennumericaldataareavailable,directinspectionisimportant.Youshould

besuspiciousofdatainafirm'sinformationsystems,andtakethetimetoinvesti一

gatetheprocessfirsthand.InmodelingamanufacturingProcessyouShouldgoto

theactualplantandwalktheline.Followafewpartsthroughtheentireprocess,

fromthetimetheyarriveatthereceivlngdockuntiltheyareshippedtoacustomer･

Inaserviceoperation,followthecustomerandpaperworkfromstarttofinish.

Finan(1993)studiedthecycletimesforfabricationofvariouspartsatamajor

commercialaircraftmanufacturer.Thefirm'SorderplannlngSystemWasSupposed

totrackpartsandsubassembliesastheyflowedthroughthemanufacturlng

process.Downloadingthedataforarepresentativesampleofpartsrevealedthat

therecordedcycletimesforeachlotwerealwaysexactlyequaltothetimealloト

ted.TbtakeatyplCalexample,thescheduledcompletiontimeforaparticularpart

was10days.Datain也einformationsystemshowedeverylotwasdeliveredex-

actly10daysaftertheorderwasreceived.However,cross-checkingotherrecords,

walkingtheline,andinterviewlngtheworkersshowedtheactualdelayaveraged

22days,withastandarddeviationof9days.Only2of20lotsexaminedwere

completedin10daysorless.Obviouslythestarttimesrecordedintheinformation

systemhadbeenback-Calculatedbysubtractlngthescheduledcycletimefromthe

completiondateofthelots.

Firsthandinvestigationoftheprocessonthefactoryfloornotonlyyieldeda

betterestimateofthedelaybutrevealedsignificanterrorsandwastedeffortinthe

informationandcontrolsystemsgovernlngtheoperation･NotsurprlSlngly,the

poorqualityofsystemsandprocedureskeptthecompanyfromincreaslngproduc-

tionsmoothlyandrapidlywhenorderssurged･Theresultingproductionbottle-

necks,extracosts,anddelaysindeliveriestocustomersledtomorethan$1billion

inextraordinarychargesandasignificantdeclineinprofitsjustasdemandreached

anall-timehigh.

ll .6 SystemDynamicsinAction:

Forecas軸 gSemieondue昔orDemam812

Understandingandmodelingdelayscanoftenyieldsignificantvalue,evenwithout

thecomplexityOfafullsimulationmodelofthefeedbackstructureofthebusiness･

ChipmakerSymbioslnc.usedsimplemodelsofdelaystodramaticallyimproveits

abilitytoforecastdemandforitsintegratedcircuits,stabilizingproductionsched-

ules,improvlngCapacityutilization,andlowerlngproductionandcapacltyaCqul- sitioncosts.

Symbioslnc.isasuccessfulsemiconductorandcomponentmanufacturerwith

headquartersinFortCollins,Colorado･Symbiosmakesafullspectrumofhard-

wareandsoftwareforstoragemanagementandperipheralsincludingstandardand

12IamindebtedtoSymbiosandtoLyleWallis,KarlBraitberg,KevinGearhardt,Michael Haynes,andMarkPaichforper血ssiontopresentthiscase,theirwillingnesstosharetheirdataand experiences,andtheirassistanceinitspreparation･In1998SymbioswassoldtoLSILogicCorp,a chipmakerlnMilpltas,Califbrnia･

450 PartIV ToolsforModelingDynamicSystems

applicationspecificintegratedcircuits(ASICs),hostadapters,I/0technologies,

andstoragehardwareforhigh-performanceworkstationsandservers.Theircus-

tomersareoriginalequipmentmanufacturers(OEMs)inthecomputerandelec-

tronicsindustry.Throughoutthe1990sSymbiosenjoyedrevenuegrowthofabout

20%/year,reachingabout$600millioninrevenuein1996with2300Employees worldwide.

Likeallchipmakers,Symbiosiscaughtbetweentherapidgrowth,technical

change,andvolatilityofthesemiconductormarketontheonehandandthehigh

costsandlongdelaysofadjustingmanufacturingCapacityOntheother.Semi-

conductorwaferfabsareamongthemosttechnicallysophisticatedandexpensive

factorieseverbuilt.TypicalfabsforASICscostabout$1billion;fabsforhighper-

formancemicroprocessorscostabilliondollarsmore.Giventhehighfixedcosts

ofsemiconductormanufacturlng,COnSistentlyhighutilizationofachipmaker's

fabsisessentialforprofitability.However,capacityCanOnlybeadjustedwithlong

delays･Thedelaybetweenthedecisiontobuildafabandthefirstuseableoutputis

severalyears.Longcapacityadjustmentdelaysmeanchipmakersmustbeableto

forecastdemandreliablyoverqultelonghorizons･13

AsDirectorofBusinessPlanningandModelingforSymbios,LyleWallis

struggledwiththisdilemma.Thereislittleroomforerror.Theintegratedcircuit

marketisverycompetitive.ManyofSymbios'customersareverylargeandwield

considerablemarketpoweroversuppliers.Rapidtechnicalchangeputsapremium

onthequalityandresponsivenessofthefirm'sdesignandenglneerlngStaff.The

qualitystandardsOEMsrequlretheirsupplierstomeetareamongthemoststrin-

gentinanyindustry.Pricecompetitionisintense.And,perhapsmostimportant,de-

liverytimeisacriticalcompetitivebattleground.Becausethelifecycleofthe

productsuslngthesechipsisoftenveryshort,chipmakersmustdeliverontime.As Walliscommented,

WhenyouunderestimatedemandyourdeliverytimeCanStretchoutfrom12weeks to24weeks-whichseemslikeinfinitytoyourcustomers.Butatthesametime youcan'taffordtoholdexcesscapacitythatislikelytogounutilized.

Symbios,likemostchipmakers,continuouslydevelopedandrevisedbottoms-up

forecastsofproductionrequirementsandrevenues.Thesecustomerdemandfore-

casts(CDFs)weredevelopedbycollectingthecustomers'ownprojectionsofde-

liveryrequlrementSbylineitemforthenextfourquarters.ASymbiosmanager

describedtheprocess:

The[CDF]processbeginswithaSymbiossalesrepresentativevisiting-.acus- tomertoobtainthecustomer'sdemand13rOjections.Afterobtainingthecustom er's

forecast,thesalesrepresentativereviewstheforecastwithaSymbiossalesm an-

ager.Tわgether,thesalesmanagerandsalesrepresentativedeterminethelikelihood

13symbiosmakesabout80%ofitschipsinitsownfab･Llkemanyfirmsintheindustry, Symbiosusesoutsidefoundriestohandledemandpeaksandtoproducesomesmallvolume,older products.WhileoutsourclngtOeXternalfoundriesprovidessomeflexibility,therearestillsubstan- tialdelaysbetweenthedecisiontooutsourceandthedeliveryofproduct,andthelesspredictable theneedforoutsourclng,themoreexpensiveitistolocate,qualify,andcontractwithexternal fわundries.

ChapterllDelays

FIGUREll-21

ActualbiHings comparedto 6-and12-month customerdemand forecasts

Thegraphshows theCDFs

preparedinmonth t-hpJotted agalnStactua一 billingsformontht (wherehisthe forecasthorizonof

6or12months).lf theforecastswere

accuratethey wou一dcorrespond exacuytoactua一 biHngs･Allthree seriesare31mOnth

centeredmovlng averagestofilter outmon州y fluctuations.

(oo L

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0 12 24 36 48 Month

60 72

thatthecustomerwillhittheirprq】ections.Iftheyhaveconcernsthatthecustomer maybeover-orunderforecastlng,theyenteraconfidencefactorintotheforecast oradjusttheprojection.TheforecastisthensubmittedtoSymbiosmarketingman- agersandproductmarketingengineers.Afterreviewlngtheforecasts,themarketing managersandenglneerSalsohavetheopportunitytOadjusttheconfidencefactor andalterthecustomer'sforecast‥.Oncereviewedbymarketing,theforecastbe- comesavailableforusecompany-wide.

Therationaleforthebottoms-upforecastswasformanyyearsunquestioned

throughouttheorganization･Thedemandforecastinformationcamedirectlyfrom

thecustomers,whoshouldknowtheirownrequlrementSbest･Usingcustomerre-

qulrementSforecastscreatesastrongchannelofcommunicationbetweenthe

OEMsandchipmakersanddemonstratestothecustomersthatthesuppliersarelis-

tenlngandrespondingtotheirneeds.YetthemoreWallisexaminedtheaccuracy

ofthebottoms-upCDFs,themoreconcernedhebecame･

Figurell-21showsthe6-and12-monthrevenueforecastsbasedonthecus-

tomerdemandfわrecastsagalnStactualbillings.Thefわrecastsoffuturesalespre-

paredinmontht…hareplottedattimetagainstactualbillingsfb∫montht(也isthe

forecasthorizonof6or12months;thedataare3-monthcenteredmovingaverages

tofilterouthigh-frequencynoise).Iftheforecastswereaccuratetheforecastand

actualbillingscurveswouldbeidentical.Wallisimmediatelynoticedseveralfea-

turesoftheforecasts･First,thebottoms-upforecastsarenotveryaccurate.The

meanabsolutepercenterroris40%forthe61mOnthforecastsand46%forthe

121mOnthforecasts･14second,theforecastscorrelatepoorlywithactualbillings･

Thelbrecaststendtomoveoutofphasewithactualbillings;thatis,theytendtobe

highwherT.biliingsarelowandviceversa.Third,fullleforecastsareconsistentlytoo

highSomeofthebiasreflectsoveroptlmisticforecastsofconsumerdemandbythe

OEMs.SomereflectseachOEM'SefforttoensurereceiptOfsufficientoutput

bypaddingorderstothesupplier(andthencancelinglaterifnecessary).Fourth,

theforecastsareextremelyvolatile.Theforecastsfluctuatesignificantlyaroundthe

14Themeanabsolutepercenterror(MAPE)isdefinedas

MAPE- 100*三1! .(lcD巨 Billin gs.I/Billin gs.)

452

FIGUREll -22 Sixand12-month customerdemand forecasts

comparedto actua一bookings

Theforecastsare

plottedatthetime theyweremade. Forecastsoffuture

demandarehigMy correlatedwith currentorders. AHthreeseriesare 3-monthcente｢ed

mOVJngaverages tofilterout

monthly fluctuations.

PartIV TわolsforModelingDynamicSystems

(o o L

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がofもろ～○Aq12-MOnthCDF十㌔も rdmQも仇Jが㌦★★★.㌶ 6-MonthC-F

0 12 24 36 48 60 Month

growthtrend,withmuchgreatervariancethanactualproduction.Chasingthefluc- tuationsinforecastscausedcostlyerrorsinproductionplannlngandcapaclty aCqulSltlOn･

Figure11-22comparesthe6-and12-monthforecastsagalnStCurrentbookings (theorderrate)AHere,theforecastsoffuturesaleshavebeenplottedatthedatethe forecastsweremadetoshowtherelationshipbetweencurrentbookingsandthe currentbeliefsofcustomersaboutfuturedemand.Boththe6-and12-monthcus-

tomerforecastsarehighlycorrelatedwithcurrentcustomerorders(thecorrelation betweenbookingsandthecustomerdemandforecastsisabout0.70forbothfore-

casthorizons;thecorrelationbetweenthetwoforecastsis0.96).Lookingclosely, youcanseealagofseveralmonthsbetweenthepeakinactualbookingsandthe

peaksintheforecast･CustomersappeartoprojecttheirfuturerequlrementSbyex- trapolatingtheirrecentactualorders.Thelagarisesfromshort-termsmoothingof recentordersandadministrativedelaysinpreparlngtheforecasts.

Wallisconcludedthatthecustomerdemandforecastsrespondedstronglytore- centevents,particularlythecurrentdemandrequlrementSOfthecustomers,and containedlittleusefulinformationonfuturerequlrementS.Whencustomersneed

moreproductrightnow,their6-and12-monthforecastsincreasesharply;when theyneedlessrightnow,theirforecastsoffutureneedsdrop.Consequently,short-

terminventoryandsupplylineadjustmentsfindtheirwayintoforecastsoffuture

demandeventhoughthesetemporaryinfluencesonordersusuallyhavelittlebearl lngOndemand6or12monthsout｡Theerrorsandvolatilityofthebottoms-up

forecastscausedSymbiostomakefrequentandcostlychangesinproduction schedulesandcapacity,eatlnguPProfitsandcrimpingthecompetitivenessofthe btlSi_rleSS,

Further,becausethecustomers'MRPandproductionplannlngSystemsreacted

totheavailabilityoftheproducts丘.om suppliers,forecastvolatilitywasself- reinforcing･Fluctuatlngdemandmeantproductswouldsometimesbeplacedon allocation,stretchingoutdeliveryschedules.Duringperiodsofallocation,cus-

tomers'MRPsystemsandproductionplannersrespondedbyseekingtohold greatersafetystocksandorderingfartherahead,forecastingStillgreaterfuturere- quirementsandleadingSymbiostoaddcapaclty.OnceadequatecapacltyCameOn-

lineandtheproductwentoffallocation,ordersfellascustomersrespondedtothe

Chapterll Delays 453

readyavailabilityoftheproductbycancelingtheirdefensiveorders,leadingtoex-

cesscapacity.Asordersfell,Sotoodidforecastsoffuturerequirements,Causing

SymbiostocutproductionplansandcapacltyaCqulSitionandsettingupthenext

cycleofinadequatecapacity,allocations,andsurglngOrders･

Finally,producingandupdatingthebottoms-upforecaststooktoolongand

costtoomuchIttooktoolongtogetthedatafromthecustomersandateupalot

ofSymbios'salesandmanagementtime.Thedatafrequentlycontainederrorsand

inconsistenciesthattookfurthertimetoworkout.Wallisruefullyconcluded,

"Usinga'bottoms-up'forecastisworsethannothingforsizlngthebusiness."

Thepoorperformanceofthebottoms-upforecastswaswellknownthroughout

theorganizationWallisnotedthepastreactiontoeachforecastingfailure:

Ineachcasewewouldfindsomethingtoblame.Usually,weblamedthesalesforce fornotbeingabletoforecast,Sowewouldhavethemarketinggroupsdothework. Thenwewouldswitchbacktosalesaftersometime.Or,weblamedthesoftware

systemandchangedthat.

Heconcludedthatthereweredeeperstructuralreasonsfortherepeatedfailureof

thebottoms-upforecasts:

Mypositionisthatstructurallyeachofthesesystemswassimilarandthateachpro- ducedsimilarresults.Theyalwaystakethecurrentsituationandprojectitintothe forecasthorizon.Insuchasituationevennormalseasonalfluctuationcausesreal

problems.Wehavelookedatthedataproducedbysalesversusmarketingversus differentbusinessunitsandcanfindnorealdifferenceinbehavior.

Andherecognizedthathehadnotbeenimmunetotheseproblemshimself:

Infact,Iwentbackandlookedatmylforecasting]dataforwhenIwasasalesman- agerandwhenlwasabusinessunitdirector-samebehavior.

Despitethestrongevidenceofthefailuresofthebottoms-upforecasts,manyinthe

organization-nottomentionthecustomers-werestronglycommittedtothecur-

rentforecastlngprocessanddidn'tbelievetheanalysis･

Asaverycustomer-orientedcompany,thecustomers'forecastisaverycompelling Input,evenifintellectuallyoneknowsthatthecustomers'forecastlngProcessis flawed.First,ltmakessomesensethatthecustomersshouldknowtheirbusiness.

Second,theyareINYOURFACEdemandingwhateveritisthattheythinkthey want,whetherltmakessenseornot.And,selectivememorylSpervasive.Ifthey fallshortoftheirforecast,itisforgotten.ButmisstheirforecastJustOnceandthere

ishelltopay.Customersappeartobelievethattheirforecastsareprettygoodin splteOfevidencetothecontrary.

Wallisknewthatyoucan'tbeatsomethingwithnothing;polntlngOuttheproblems

causedbythecurrentsystemwithoutproposlngabetteraltemativewouldonlycre-

ateangerandfrustration.

Butwhatwerethealternatives?Onepossibilitywastousesimpletrendpro-

jectionbasedonactualaggregatebillings.Simpleextrapolationisfastandcheap

andyieldedreasonableresultsattheaggregatelevel.However,extrapolative

methodsdidn'tprovideenoughdetailtoplanproductionorcapacltyatthelevelof

particularproductionlinesorproductfamilies,andmanylnthecompanydidn't

454 PartIV ToolsforModelingDynamicSystems

believetrendprqJectionscouldbetrustedbecausetheydidn'ttakethecustomers'

ownrequlrementSforecastsintoaccount. Anotherpossibilitywastouseeconometricforecastsofsemiconductorindus-

trydemandbysegment･Manymarketresearchandconsultingorganizationssell

suchforecasts･However,theindustryforecastso洗en,evenusually,misstheturn- 1ngpOlntSintheindustry･Further,theturningpointsinthedemandforSymbios'

productsdidn'talwayscoincidewiththesegmentturnlngpOlntS.Finally,econo一 metricmodelshadpoorforecastlngaccuracyatthelongertimehorizonsneededto plancapaclty.

HavingplayedthelieerDistributionGame(Sterman1989b,chap.17),Wallis recognizedthatmuchofthevolatilitylnOrdersandcustomerdemandforecasts

Symbiosexperiencedwasendogenouslygeneratedbyfeedbacksamongthemem- bersofthesemiconductorindustrysupplychain(Figure1l123).Eachfirminthe chain,followingItsownSelf-interest,orderstomeetanticipatedcustomerdemand

andadjustsitsinventoriesandbacklogsofpartsonordertoensureasteadysupply ofdeliveriesfromsuppliers･Theresultispowerfulamplificationofdemandfluc-

tuationsfromonelevelofthedistributionchaintothenext,CausingInstabilityfor allplayersintheindustry.Asachipmaker,Symbiosheldthetailpositioninthe

supplychainandexperiencedmorevolatilityindemandthanthosedownstream. ForSymbiostotemperthewildswingsinorderscausedbytheamplificationofin-

ventoryandsupplylineadjustmentsupthesupplychain,itcouldnolongerbase capacltyPlansonforecastsderivedfrompastactualorderrates.

WiththehelpofMarkPaich,anexperiencedmodeler,Wallisbegantodevelop

asystem dynamicsmodel･WallisalsorecruitedtwoSymbiosmanagers,Karl BraitbergandKevinGearhardt,fromlinepositionsintotheteam.Theybeganby mapplngthestockandflOwstructurethatgenerateddemandandquicklydeter一 minedthatthekeytoimprovedforecastswasthelinkbetweendesignwinsand

customerorders.Adesignwinoccurswhenacustomercommitstouslngaspecific Symbioschipinaspecificproduct.Designwinsarethefocusofthesalesforce's

FJGUREl1-23 Semiconductorindustrysupplychain

AsintheBeerDistributionGame,eachlayerinthedistributionchainampHfiesfluctuationsinfinal demanduntHordersforandproductionofsemiconductorsfluctuateslgnificantIy.

Semiconductors Products Products

orders Orders

(andcanceHations) (andcancellations) FinalDemand

Chapterll Delays 455

efforts.Togeneratebusiness,salespeoplemustpersuadeOEMstouseaSymbios chipintheirproducts.

TheprogressionofASICdesignwinsfromcustomercommitmenttoproduc- tionisshowninFigurell-24.Anapplication-specificchipcannotgointopro- ductionuntilthedetaileddesignisdeveloped,prototypesaretested,andthe chipISPeCifictoolinglnthefabisdevelopedandtested.Hencenewdesignwins accumulateinastockofDesignsinDevelopment･Asdesignsarecompletedand reviewed,prototypingstarts.Aftersuccessfultest(andconcurrentdevelopment andtestofthefabricationprocess),productionbegins.Productionvolumeand revenuedependonthenumberofproductdesignsinproductionandaveragesell- 1ngprlCeS.Thestockofdesignsinproductiondecreasesasthedesignsreachthe endoftheirusefullifeandarediscontinued.

TheconceptualmodelshowninFigure11-24wasdevelopedveryrapidly.It wasreadilyapparentthattherewerelongdelaysinthedesignandprototyplng process.Thelongdelaysmeanttoday'srevenuederivedfrompastdesignwins,So knowledgeoftherecentwinsinthedevelopmentandprototyplngplpelineshould provideabetterforecastoffuturebuildrequlrementSandrevenue.

ThenextstepwastoconverttheconceptualmodelshowninFigurell-24into anoperational,calibratedmodel.Theteamquicklyrealizedthatanaggregate modeltrackingthetotalnumberofdesignwinswasnotsufficient,sincedifferent designwinsgeneratedverydifferentproductionvolumesandprlCeS.However, previousattemptstofわrecastdemandbasedonindividualdesignwinshadnot beensuccessful.Thedelaybetweenanyparticulardesignwinandvolumeproduc- tionisquiteVariable,astheproductdevelopmenttimedependsonthecomplexlty

FIGUREll -24 Thestockandflowstructureofdesignwinsdeterminesvolumeandrevenue.

CurrentvolumeandrevenuedependonpastdesignwinsduetodevelopmentandprototypIngdelays. Thedelaysineachstagearehigh-orderprocesses.

Average Deve一opment

Time

Average Prototyping

Time

Average Product Lifetime

+ .U

productioni_Average Vohme vo山meper

.去 +

DesignWin

Average Revenued 卦一一 se"ing

Prjce

456 PartIV ToolsforModelingDynamicSystems

oftheparticularchip,thestabilityofcustomerspecifications,andotherattributes oftheproductdevelopmentprocess.Thesalesorganizationroutinelyestimatedthe volumepredictedtoflowfromeachdesignwin,butthemanufacturlngandmar- ketinggroupsconsideredtheseprojectionsunreliable.Indeed,somedesignwins neverresultedinvolumeproduction,forexamplewhentheOEM canceledthe productbeforeproductionbegan;Othersbecamewildsuccessesbeyondthehopes ofthecustomer.

Themodelingteamsettledonanintermediatelevelofaggregation.Knowl- edgeofthevolumesgeneratedbyindividualdesignwinswasnotnecessary.Pro- ductionplannersneededtoknOwhowmanywaferstostartandhowmanyunitsto buildatthelevelofeachproductiontechnologysuchasalineproducing8-inch waferswitha0.35micronlinewidthandacertainnumberoflayers.Salesand marketingneededtoknowlikelyfuturesalesatthelevelofproductfamiliesso theycouldallocateresourcesandsetsalesgoalsandsalesforcecompensation.The modelingteamdisaggregatedthemodelatthelevelofeachproductfamilyand processtechnology.Thedelays,volumes,andrevenuesfわrASICsareradicallydif-

ferentfromthoseforstandardproducts,andtherearedifferencesamongthedif- ferentstandardproductfamilies.Disaggregationallowedthemodeltogenerate informationneededbykeyorganizationalconstituenciesinaformtheycoulduse byprovidingforecastsofvolumeandrevenueattheproductfamilyandprocess technologylevel.

ThesimplestockandflowstructureinFigurell-24isapproprlateifthevol- umeandaveragepriceassociatedwitheachdesignwinarethesame.Inreality, volumeandpriceschangeovertimewithchangesintheproductmix,t∝hnology, andmarketconditions.Thevolumeandrevenuegeneratedbydesignwinscur- rentlyinproductioncouldbequitedifferentfromthevolumeandrevenueantici- patedfromdesignwinsfartherupstreamintheprocess.Tomodelthisvariability, theydisaggregatedthemodelfurtherbyaddingparallelstockandflowstructures, knownascoflows,totracktheprojectedvolumesandrevenuesassociatedwith eachdesignwin(FigureI1125).CoflOwstructureskeeptrackofvariousattributes oftheunitsinastockandflownetwork(Seechapter12).

Eachdesignwinaddsonedesigntothestockofdesignsunderdevelopment andaddsacertainexpectedvolumetothestockofanticlpatedproductionvolume fromdesignsunderdevelopment.TheratiooftheantlCIPatedvolumefromdesigns underdevelopmenttothetotalnumberofdesignsunderdevelopmentistheaver- agevolumeexpectedfromeachchipcurrentlylnthedesignphase.Whenthede- signmovesfrom developmenttoprototyplng,theaverageexpectedvolume associatedwiththedesignsunderdevelopmentalsomovesintotheparallelstock fortheexpectedproductionvolumeofdesignsinprototyplng.Whenthedesign movesintoproduction,theproductionvolumeexpectedfromthedesignsinproto- typlngalsomovesintothestockofantlCIPatedvolumefromdesignsinproduction Theoperationalmodelincludedanadditionalcoflowstructuretotracktherevenue expectedfromeachdesignwin.ProductionandcapacltyPlannerscouldusethe volumeprojectiontoplanwaferstartsbyapplyingtheexpectedyieldandwafer sizetovolumerequlrementS,andseniormanagementcouldusetherevenuepro- jectionstosetbudgetsandgenerateproformafinancialstatements.

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458 PartIV TわolsforModelingDynamicSystems

Calibratingthemodelrequired(1)estimatingthelengthanddistributionofthe developmentandprototypingdelaysforeachprocesstechnologyand(2)estimat-

1ngtheexpectedvolume,waferrequirements,andpricefordesignwinsineach productcategory.

GeneratlngandcollectingthedatawasamajorChallenge.Theteamneeded currentdataondesignwinsandtheirattributes｡Fortunately,ln1990thesalesor一

ganizationhadlaunchedanewprograminwhichsalesrepresentativesrecordedthe

characteristicsofeachwinatthetimeofthesale.Thedatabasetrackedtheprod- uct,customer,anticipatedvolumes,averagesellingprlCeS,andotherattributesfor thenext3years.Thesedatawereusedbythesalesorganizationtodeterminesales

goalsandcompensationbutwereconsideredunreliableandunstablebythemanu- facturlngandmarketingorganizations.

Theestimatesofpriceandvolumerecordedinthesalesforcedesignwindata-

basecouldnotbeusedinrawformbecausetheydidn'taccountforsubsequentor- dercancellations,changesinrequlrementS,andchangesinprlCeS.Butthe modelingteamrealizedthatthesalesforcedatabasedidn'thavetobeaccurateas

longastherelationshipsbetweenprojectedandrealizedvolumeandrevenuewere stable.Theteamthenassembledtheproductionhistoriesofeachproductfromdata

collectedbythemanufacturlngOrganization.Cross-tabulatingthesalesorganiza- tion'sdesignwindatabaseagalnSttheactualproductionhistoriesenabledtheteam toassesstheaccuracyofthesalesdatabase.Regressionsshowedfairlystablerela-

tionshipsbetweenthevolumeandrevenueprojectionsrecordedatthetimeacon- tractwaswonandtheactual,realizedvolumesandrevenueswhenthechipswere

actuallymade.Theserelationshipswereusedtocalibratethemodel.Combining thesalesforce'sdesignwindatawiththedesignandproductionhistoriesforeach productalsoallowedthemodelerstoestimatethelengthanddistributionofthede-

laysbyproductandprocesscategory.Sincethedesignandprototyplngprocesses arethemselvescomposedofmultiplestages(productdefinition,design,layout, masking,waferfabrication,sorting,prototypeassembly,testing,etc.),theteamex-

pectedthedelaystobeveryhigh-order(butnotpipelinedelaysasthereiscon- siderablevariationinprocessingtimesforeachstep)｡Whilethedelaysforany particulardesignwinwereunpredictable,themodelingteamfoundthatthedistri-

butionofthedelayoutnowsineachcategorywereapproximatedquitewellbyvar- ioushigh-ordermaterialdelays(generallybetweenninth-andtwentieth-order,a reflectionofthemanystagessubsumedinthedesignandprototyplngProcesses

andthedisaggregationofthemodelbyprocesstechnology).Figurell-26 ShowstheoverallresponseoftheestimatedmodelforASICstoasingledesign win(aunitpulse).Becausecustomchipshavealongdesigntime,thereisnore-

sponseatallforroughlyayear.Productionvolumesthenbuildrapidlytoapeak roughly3yearsafterthedesignwinbeforegraduallytailingoffasproductde- mandfalls.

Thecalibrateddesignwinmodelgeneratedmoreaccurateforecaststhanthe bottoms-upprocedure.Figure11127Comparestherevenueprojectionofthedesign

winmodeltoactualbillingsforproductlineA.Themodeltracksactualbillings moreaccuratelythanthebottoms-upforecasts.Themodelalsocaptureskeyshifts inrevenuegrowth,suchasthedeclineinsalesbetweenmonths50and64andthe recoverylnSalesbeginningaroundmonth78.

Chapterll Delays

FIGUREll-26 Estimatedrevenue

impactofadesign winforASICs

Thecurveshows thedistributionof revenueovertime

glVenaunitpu一se fromaslngle designwin.

FIGUREll-27 Actualand

projectedrevenue fromdesFgnWin modelforproduct lineA

Theprojection isdividedinto revenuederived

fromprJOryear, currentyear,and assumedfuture

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Notethatthemodelisfarfromperfect.Actualrevenuesfluctuatearoundthe projection.Theseerrorscausedintensediscussionwithinthemodelingteam.They foundthatsomeoftheerrorsarosefromvariationsinvolumeandprlCeSgenerated bytheoccasionalverylargeorverysmalldesignwinorotherunpredictable events.However,aftercarefulreviewofthedataandsomeadditionalmodeling, themodelingteamultimatelyconcludedthatmuchoftheunexplainedvariationin productionandbillingswascausedbyfluctuationsinoverallindustrydemand

aroundthelong-term growthtrend･Mostoftheseexcursionsarethemselves causedbyindustrywidesupplychainvolatility-situationswherecustomersover- reacttoshort-terminventoryandleadtimevariations･Walliscommented,"We donotattempttocapturetheseeffectswiththedesignWinmodeLInstead,Wethink ofthemodelresultsasrepresentlngthelonger-termgrowthtrendsforthebusi- ness.MForecastsbasedondesignwinshelpSymbiosdampouttemporaryover- reactionslncustomerorders,temperlngexpensiveswlngSinproductionand

capacltyaCqulSition. Thedesignwinapproachalsoprovidedinsightintothedriversofgrowth

forthebusiness.Figurell127breakstheprojectedrevenuestreamintorevenues

fromprojecteddesignwins,fromcurrentyeardesignwins,andfromearlierde- slgnWins.ProductsinlineAhaveshortwin-toIPrOductionandlifetimes.Design

winsalreadyinthepipelinewillsupportsalesforonlyabout2years･AfterJuSt

460 PartIV ¶)OlsforModelingDynamicSystems

18months,aboutathirdofprojectedrevenuesareassumedtoderivefromdesign

winsyettobewon.Thelong-termrevenueforecastforlineAisthereforehighly

sensitivetotheassumedrateoffuturedesignwins.ForproductlineAthebound-

aryofthemodelmightusefullybeextendedsodesignwinscanberelatedtothe

sizeandexperienceofthesalesfわrce,theircompensationincentives,andtherela-

tiveattractivenessoftheproducts.

Moreimportantly,thedriversofdesignwinsemergeasakeyleveragepolnt

forgrowth,asWallispolntedout:

Understandingtheseproductdesignwinandlifecyclecharacteristicsallowsour topmanagementteamtobalancetherequiredinvestmentsintechnology,produc- tioncapacity,andsaleseffectivenessagalnStthelikelytlmlngandmagnitudeofthe returnsonthoseinvestments.Priortodevelopmentofthedesignwinmodel,evalu-

ationsofproposedinvestmentsgenerallyunderestimatedthedelaysbetweeninvesL mentandresults.Withoutamodel,estimatesofthetotallifeofinvestmentreturns

aregenerallytooshort,Causingtotalinvestmentreturntobeunderestimated.

Thecalibrated,disaggregatedesignwinmodelgainedbroad,thoughnotuniversal,

acceptanceinthecompany.Itisusedtogeneratearollingestimateoffuturevol-

umerequlrementSandrevenuetomanageproductionandplaninventories.The

modelisalsousedasakeyinputtotheannualplanningprocess,tOlong-tem cap-

italplannlng,andaspartoftheproductdevelopmentplannlngCycle.

Consistentwiththeexperienceofothers,themodelingteamfoundthatab-

stractdescrlPtlOnandconceptualmodelsdidnotchangethethinkingorbehavior

ofkeydecisionmakersintheorganization.Rather,thementalmodelsandbehav-

iorofthemanagersresponsibleforproductionplannlngandcapacityaCqulSition

changedonlywhentheyactivelyworkedwiththemodeltoaddressimportantis-

sues.Themodelingteamworkedhardtoinvolvecurrentandfuturelinemanagers

inthedevelopmentandtestlngOfthemodel.Somemembersofthemodelingteam

weresubsequentlypromotedintolinepositionswheretheyusedthemodeltohelp

theminproductionplannlngandinventorymanagement.

KarlBraitberg,whobecamemanagerforstandardproducts,commentedonthe

businessimpactofthemodel:

Weusedtomanageinventorybygutfeel.Forexample,peoplewouldsay,"Thisis ahotproductsowebetterbuildahundredthousandofthemnow.HThey'dbasethis onsamplerequestsorotherunreliableinformationcomlng丘.omcustomers.Now wemakebetterproductionschedulingdecisionsandtimeinventorybuildsbetterby takingthedelaysbetweendesignwinsandvolumedemandintoaccount.Customer servicehasimproved:Ourabilitytomeetcustomerrequesteddeliverydateshasim- provedfromabout60%toabout80%,a.nldontimedeliverytoourcomirlitdateis 97%,whileinventorydaysonhandareata3-yearlow･Alltheinventorymetrics haveimproved.WehaveabettermixofproductinstockandinWIPlWorkin Processinventory].Nowwebuildtherightinventoryattherighttime.

Itisimportanttorecognizethatthemodeldoesnotreplaceotherconsiderationsin

theproductionplannlngandcapacitydecision.Managersdonotslavishlyfollow

themodel'soutput,norshouldthey.Rather,themodelinformstheviewpolntOf

keyparticipantsindiscussionsaboutproductionandcapacltyplannlng,providing

asanltyCheckonthecustomers'claimedrequlrementS･Short-te-,event-oriented

ChapterllDelays 461

thinkingstillexists,asWalliscommented:=Forsomepeople,whenacustomer

callsandscreamsatthem,theydon'tcarewhatyourmodelsays."Butthemodel

helpstemperthereactiontosuchpressure,helpingtostabilizetheoperation,raise

averageutilization,andincreasedeliveryreliability,allofwhichgeneratebene丘ts

forthecustomersaswellasfわrSymbios.Wallisrecalledthatintheolddays

duringrevenueshortfallswe'dbeatupthemarketingandsalesgroupstogooutand getsomemoredesignwinstofilltherevenueholenextquarter.Ofcourse,this neverworkedbecauseofthelongdelays,andprobablycausedmoreinstability.The modelhelpspeopleunderstandthesedynamics,stabilizingthebusiness,Increasing theefficiencyoftheorganization,andboostingOurgrowth.

Whilethemodelprovidesbetterforecastsofproductionvolumesandrevenues

thanthebottoms-upapproach,modelingteammembersarecarefultonoteitslim- itationsandmonitoritsaccuracyasthefirmandindustrycontinuetoevolve.

Themodeltreatsdesignwinsasacontinuousflow.Mostofthetime,thecon-

tinuousflowassumptionworkswell･However,Occasionalextremelylargeindi-

vidualdesignwinsviolatethecontinuousflowassumpt10nandmustbehandled

separately(theyareaddedexogenously).Similarly,somecustomerproductsfail,

leadingtocancellationofordersatvariouspointsintheprocess.Finally,assome

customersareboughtbyotherstheresultingconsolidationofOEMproductlines

canaffectthevolumeandrevenuegeneratedbydesignwinsalreadyinthe

plpeline.Theseissuesaregrowinglnimportance:Thecomputerindustrylnthe

1990sbecamesignificantlymoreconcentratedthroughmergersandacqulSitions･

Astheindustryconsolidates,thenumberofdesignwinsperyearfallswhiletheir

averagesizegrowsandforecastingbecomesmoredifficult(forallmethods,not

justthedesignwinmodel).IntemalchangesatSymbiosalsomeanthemodelmust

becontinuallyupdated:theprocessesunderlyingthedelaydistributionsestimated

fromthedatachangeastheproductmixandprocesstechnologychangeandasim-

provementprogramsshortenproductdevelopmenttimes. Forthesereasons,themodel(andallmodels)canneverbeconsideredfin-

ished.Modelsarealwaysworksinprogress,andthemodelusersmustconstantly

askwhethertheassumptionsOfthemodelarestillreasonableasconditionschange.

SustainedimplementationsuccessdependsoncreatinganOngOlngprocessOfmod-

elingratherthanasinglemodel,nomatterhowaccurateorcomprehensive(For-

rester1985).Teammembersnowcontinuouslytracktheirforecastingrecordand

compareittotheaccuracyoftheotherlbrecasts.Analysisoftheirerrorsgenerates

importantinsightintomodellimitationsandhelpsthemtocalibrateandimprove

themodel.Theycontinuetodevelopthemodelinconcertwiththeneedsandpar-

tiCIPaLLionofthepeopleresponsibleforproductionplanning,CaPaCltyaCqulSltion,

andstrategytohelpensurethatthemodelcontinuestobeunderstoodandused･

Modelingeffortsunderwayatthetimethisiswrittenexplicitlyaddresstheun-

certaintycausedbylumpydesignwinsthroughthedevelopmentofaMonteCarlo

versionofthemodelwhichwillgeneratetherangeofuncertaintyaswellastheex-

pectedtrajectoryofvolumeandbillings.Themodelingteamisworkingwithkey

customerstodevelopmodelstoreducefurtherthevolatilityofordersandimprove

deliveryperformance.Asonecustomersaid,"WeglVeyoutheworstinformation

wehaveandthenwonderwhywehaveaproblem･H

462 PartIV ToolsforModelingDynamicSystems

Asoftenfoundinmodelingprojects,thegreatestinsightintothestructureand behaviorofthebusinesscamewhenthemodelresultswerewrong.Yetbecause

manyorganizationspunishthosewhomakemistakes,mistakesareoftenhidden, denying血eorganizationtheopportunltytOlearn丘.omexperiencedThemodeling processhashelpedSymbiosovercomethenaturaltendencytofindthepeople responsibleforerrorsandblamethem･Seniormanagementisnowmorelikelyto interpretaforecastlngfailureasanopportunltytOdeepentheirunderstandingof thebusinessandlessasanoccasiontoblameabadoutcomeonsales,marketing, orcustomers.

ll.7 MATHEMATICSOFDELAYS:

KoYcKLAGSANDERLANG DISTR旧UT10NS

Thissectionpresentsthemathematicsofthebasicdelaytypesincontinuousand discretetime.SystemdynamicsmodelstyplCallytreattimeascontinuous･How- ever,thediscretetimeformulationsareusefulbecausethedatafromwhichdelays

areestimatedareusuallyreportedatdiscreteintervals･Inthefollowlnglassume thedelaytimeisconstant,sotheanalysisappliesequallytomaterialandinforma- tiondelays･TheassumptionOfconstantdelaytimesalsoallowsdelaystobe treatedaslinearoperators.Notethatifthedelaytlmeisendogenous,forexample whenthedelayprocessiscapacitated,thedelaytlmeWillingeneralbeanonlinear functionofthehistoryoftheinput.

11.冒.1 GeneraWormuはIionforDelays

Theshapeoftheresponseofadelaytoaunltpulsecanbeinterpretedastheprob- abilitydistributionoftheoutflowrate,analogoustothedeliverydistributionoflet- tersfollowingamassmailing.

Indiscretetime,theoutputofadelayattimetisaweightedsumofallpast valuesoftheinputuptothepresenttime:

Output(t)-wolt+wllt-1十 W2It-3+-

Or 00

o utp u t(t)-≡ wllnp叫Ⅰ-0 (ll-12)

wherethelagweightswaretheprobabilitiesofexitingthedelaylnanytime periodiaridirllLiStSuュ-(ItOunity,thatis,

li .wl-1 (11113,

Theconstraintthattheweightssumtounltyensurestheconservationofmaterial throughthedelay.Iftheweightssummedtolessthanone,thequantltyeXltlngthe delaywouldbelessthanthequantityaddedtoit;iftheweightstotaledmorethan one,morewouldleavethedelaythanentered,violatingtheconservationprlnCiple･ Ininformationdelays,WeightssummingtOOneensuretheequilibriumoutput equalstheinput,glVlnganunbiasedperceptlOnOftheinput･

Chapterll Delays 463

Takingthelimitofthediscretetimeformulationasthetimeintervalbetween

periodsshrinkstozeroyieldsthecontinuoustimeformulation.Theoutputisthe

integralofpastvaluesoftheinputweightedbytheprobabilityofdeliveryattime

t-S,wheretheprobabilityofdeliverystimeunitsafterenteringthedelay,p(S),is

glVenbyacontinuousdistribution:

Output(t)-

I.∞ I.m

p(S)ds- 1

p(S)Input(t-S)ds

Inprinciplethepatternofweights-theprobabilitydistributionofexitingthe

delay-isarbitrary,subjecttotheconstraintthattheinputtothedelaylSconserved

(thattheweightsarenonnegativeandsumtounity).However,inpractice,Onlya

fewpatternsarereasonableandrealistic.AttheinstantaquantltyOfmaterialisin-

jectedintoadelaytheoutputhasnotyethadanytlmetOrespond,sotheprobabil-

ityofexitattimep(0)-0(indiscretetime,theweightonthecurrentvalueofthe

inputw0-0).Theoutputofalldelaysmustapproachzeroafterasufficientlylong

timehaspassed;thatis,Oncetheitemsaredeliveredtheexitratemustfalltozero.

Thereforep(∞)-W∞-0.Thustheprobabilityofexitingadelay-itsresponseto

aunltpulse-muststartatzero,risetoamaximum,thenfalltozero. Itisreasonabletoassumetheexitdistributionissmoothandthatthedis-

tributionhasaslnglemaximum.Ifthedatasuggesttheoutputdistributionofa

delayhasmorethanonepeak,itisalmostcertainthetotaloutputistheresultof

twodifferentdelaysoperatinglnParallelandyoushouldmodeleachdelaysepa-

rately.Withintheseconstraints,therearetwomaintypesofresponses:adelayln

whichtheoutputrespondsimmediatelya氏erapulseInput,thengraduallydeclines;

andadelaylnWhichthereisnoresponseforsomeperiodoftime,followedbya

gradualincrease,peak,anddecline,Thefirst-orderdelaymodelstheformercase

andthehigher-orderdelaysprovideaflexiblefamilyofdistributionstomodelthe lattercase.

15Equation(11-14)Canalsobederivedbyapplyingtheconvolutiontheoremoflinearsystems theory.Ingeneral,theresponseofanylinearsystemtoanarbitraryInputCanbeexpressedasthe convolutionoftheinputwiththepulseresponseofthesystem,thatis,theproductoftheinputwith thelaggedpulseresponseofthesystem:

Otltput(t)-上Input(S)h(t-S)ds

vY,hereh()istheresponseofthesystemtoaunitimpulse. Ingeneral,thepulseresponseofalinearsystemcantakeonnegativeaswellaspositive

values,anditsintegralneednotbeumty,orevenfinite･Inthecaseofdelays,thepulseresponse mustbenonnegative,andconseⅣationofmaterialrequirestheintegraloftheresponsetoeqtlal unity,sowemaytreath()asaprobabilitydistributionp(),Theconvolutionintegralcanbederived byrewritingequation(11-12)as

i output(t'-芸 wIInputt-1-∑W卜lInputll=~〇〇

andtakingthelimitastheintervalbetweentimeperiodsbecomesinfinitelysmall.Furtherdetails canbefoundincontroltheorytextssuchasOgata(1997)orRowellandWormley(1997).

464 PartIV ToolsforModelingDynamicSystems

ll.7.2 F喜rst-OrderDe!ay

Thefirst-orderdelayassumesthecontentsofthestockofmaterialintransitare

perfectlymixedatalltimes.Perfectmixingrandomizestheorderofexitfromthe delay,1mplyingsomeitemsstayinthestockofmateriallntransitlongerthanthe averagedelaytlmeandsomestayforashorterperiod.Sincethefirst10rderdelay

isequivalenttothefirst10rderlinearnegativefeedbacksystem,itscharacteristicre- sponsetoapulselnputisexponentialdecay.Thatis,theprobabilityofexitlngthe

first-ordermaterialdelaylSglVenbytheexponentialdistribution

p(t)-(1/D)exp(-t/D) (ll-16)

wherethemeanofthedistributionistheaveragedelayD.

Whatistheaveragedelayormeanresidencetimeforitemsinthedelay?Isit

infactthedelaytimeparameterD?Bythemeanvaluetheoremofcalculus,the averageresidencetimeTrforanydelayprocessisthetime-Weightedaverageofthe outnowrate,givenaunitPulseinputattimezero:

･r-lo∽t･outflow(t)dt-I.班 ow(t)dt-It･p(t)dt (1ト17)

Notethatthetime-weightedaverageoftheoutflowfromaunltPulseisthesame

asthetime-weightedmeanoftheoutflowprobabilitydistributionp(t)IForthecase ofafirst10rdermaterialdelay,theoutflowisthestockofmaterialintransit,S,di-

videdbytheaveragedelaytimeD:

Outflow(t)-S(t)/D (11118)

Immediatelyafteraunitpulseinput,theinitialvalueofthestockofmaterialin transitisunity.Sincethefirst-ordermaterialdelayisthelinearfirsトordernegative feedbacksystem,thestockintransitthendecaysexponentiallywithtimecon- stantD:

S(t)-exp(-t/D)

Therefore,themeanresidencetimeisgivenby

･r-I.mt･[S(t)′D]dt-I.ut(1D,exp(-t/D,dt

(ll-19)

(1ト20)

Notethat(1/D)exp(-t/D)inthelatterexpressionispreciselytheexponentialprob- abilitydistribution.Integratingbyparts,

･rニーt･exp(-t′D,に十I.∞exp(-uD,dt-0-Dexp(-uD,E-D (ll-21)

whichconfirmsthatthemeanresidencetimeisinfactgivenbythedelaytime parameterD.

Indiscretetime,theweightswlforafirst-orderdelaydeclinegeometrically

(byafixedproportion)overtime:

wl-(1-L)Ll (ll-22)

ChapterllDelays 465

wherethelagweightparameterL,0≦しく1,isrelatedtotheaveragedelaytlme Dby

D-L/(1-L) (ll-23)

Thediscretetimegeometriclagformulationisqultecommonineconometricmod- elingwhereitisalsoknownasaKoycklag,afterKoyck(1954)whoshowedhow thelagparameterLcanbeestimated(Seeanygoodeconometricstextfordetails).

ll .7.3 Highe卜OrderDe一ays Cascadingnfirsトorderdelaystogetherinseriescreatesthehigher-orderdelays

discussedabove･Mathematically,theoutputofthenth-orderdelayistheconvolu- tionofthesequenceoffirst10rderdelays,eachwithidenticaldelaytlmeSequalto thetotaldelaytlmeDdividedbythenumberofstagesinthedelay.Incontinuous

timethehigher-orderdelaysareequlValenttotheErlangfamilyofdistributions, nameda洗ertheDanishtelephonepioneerknownasthefatherofqueulngtheory.

TheErlangdistributionofordernisglVenby

p(t)-器 tn-1exp卜(nの,t,;i,0 (ll-24)

Youcanusethemeanvaluetheoremtocheckthatthemeanresidencetimeofthe

nth-orderdelaylSinfactgivenbyD.TheErlangdistributionreducestothefirstl orderexponentialdistributionforn-1.

Indiscretetimethehigher-orderdelaysarealsoknownasPascallags,glVen bythedistribution

wl-(il l1)(1-L)nLl (i+n-1)!

i!(n-i)! (1-L)nLl;i∈‡0,∞) (ll-25)

whereagainthemeandelayisL/(1-L)･Justasthe丘rst-orderErlanglagisequiv- alenttotheexponentialdistribution,thePascallagreducestothegeometriclagfor ll-1.

Ifsufficientdataareavailable,theoutflowdistributioncanbeplottedanddi- rectlycomparedtotheErlangfamilytoseeifitisagoodmodelofthedelay

processandtoselecttheappropriateorderofthedelay(Seesectionll.5.1)･Some- times,however,onlysummarystatisticssuchasthesamplemeanandvarianceare available,whilethedataforthefulldistributionarenot.Inthiscasetheorderof

thedelaycanstillbeestimated,subjectonlytotheassumptlOnthatthelaglSWell approximatedbyamemberoftheErlangfamily.Thevarianceofthenth-order

ErlanglaglSglVenby(J2-D2/n･consistentwithintuitionandthesimulationre- sultsabove,thesmallerthevariancerelativetothemeandelaythehighertheorder

ofthedelay.Approximatlngthemeandelayandvarianceoftheoutflowfromtheir samplevalues,denotedDands2,respectively,yieldsasimpleestimatorforthe orderofthedelay:

a- INT (冒 )

(ll-26)

466 PartIV ToolsforModelingDynamicSystems

whereINT()istheintegerfunction.Ofcourse,theratioら/S2won'tingeneralbe aninteger,butroundingtothenearestintegergenerallyintroduceslittleerrorcom-

paredtothelikelysamplingerrorsinthedata･Remember,however,thatthisesti一 matorpresumesthedelaydistributionisamemberoftheErlangfamily;departures fromtheErlangdistributionwillyieldpoorestimates.Informationabouttheorder

ofadelaygleanedfromfieldworkshouldbeusedtocheckestimatesderivedfrom equation(11-26).

ll.7､4 RebtionofMaterial'lnC=nformationDelays

Asseenabove,theoutputsofmaterialandinformationdelayswithequaldelay timesareidenticalpr10Videdthedelaytimeremainsfixed.Toseewhy,considerthe

equationforthefirst-orderinformationdelaywithinputIandoutput0:

: -(II0)/D (11127)

Theoutputofthedelay,thestock0,hasaslnglenetratedeterminedbythegapbe-

tweentheinputandoutput.Thenetratecanbedisaggregatedintoexplicitincrease anddecreaserates:

dO I 0

dt D D (ll-28)

Equation(11-28)isequivalenttoafirst-ordermaterialdelaywithinflowIの,ouト flow0/D,andstockintransit0.Aslongasthedelaytlmeremainsfixed,thebe-

haviorofthetwodelaysisidentical.However,inamaterialdelaytheoutputisthe exitratefromthestock,whileintheinformationdelaytheoutputisthestock0.

Changlngthedelaytimecausesthebehaviorofthetwodelaystodiffer.Even

thoughtheirresponseunderconstantdelaytlmeSisthesame,modelersmustbe carefultousethepropertypeofdelays:AdelaytimeCurrentlythoughtofasfixed

maybecomev∬iableasamodelisdeveloped.

ll .8 SuMMARY

Thischapterdiscusseddelaysandshowedhowtheycanbemodeled.First,allde- 1aysincludeatleastonestock.Second,delaysinmaterialflOwnetworksmustbe distinguishedfromdelaysininformationfeedbackchannels:materialflowsare

conserved,whileinformationisnot.Thedifferenceaftbctshowthetwotypesof

delaysrespondtochangesinthedelaytlme･ Everydelayhastwomaincharacteristics:themeandelaytlmeandthedistrib-

utionoftheoILitPILltOfthedelayarourldthataverage.Thechapterdevelopedafam-

ilyofformulationsformaterialandinformationdelaysenablingmodelersto

captureawiderangeofplausibledeliverydistributions.First-orderdelaysare

characterizedbyanexponentiallydeclinlngOutputinresponsetoapulselnput･ ThelargestresponseoccursimmediatelyafterthepulseInput.Theresponseof

higher-Orderdelays,formedbycascadingfirsトorderdelaysinseries,1Sinitially zero,buildstoamaximum,andthendiesaway.Pipelinedelayspreservetheorder

ofentrytoadelaysotheoutputisexactlythesameastheinput,butshiftedbythe timedelay.Thefirst10rderdelayassumesthecontentsofthestockofmaterialin

Chapterll Delays 467

transitareperfectlymixedatalltimes,sotheoutflowisindependentoftheorder ofentry.Thehighertheorderofthedelay,thelessmixlnglSassumed;pipelinede-

laysassumenomixlngOfthecontentsofthestockintransitatall.Thehigherthe orderofthedelay,thelowerthevarianceinthedistributionoftheoutput.

Finally,thechapterdiscussedhowthelengthandoutputdistributionofdelays canbeestimated.Whennumericaldataareavailable,econometrictoolscanhelp

estimatedelaydurationsanddistributions.Whennumericaldataarenotavailable,

estimationbydirectinspectionoftherelevantprocesscanyieldgoodestimates･ JudgmentalestimatesaremoreaccuratewhenyoudecomposethedelaylntOits

constituentstepsandestimatethedelaysofeachseparately･Youshouldusemulti- plesourcesofinformationtohelpyouspecifydelays(andothermodelparameters) andinspecttheprocessfirsthandwheneverpossible.

Cs17_sE:s耶 aili轟Ji雲量報等仁王苫重量主音§

lMathematicaldemography]isconcernedwithcommonsensequestionsabout,

forinstance,theejfectofalowereddeathrateontheproportionofoldpeople

ortheeHectofabortionsonthebirthrate.Theanswersthatitreachesarenot

alwayscommonsense,andwewillmeetinstancesinwhichintuitionhastobe

adjustedtoaccofldwithwhatthemathematicsshowstobethecase･Evenwhen

theintuitiveanswergivestherightdirectionofaneHect,technicalanalysisis stillneededtoestimateitsamount.Wemayseeintuitivelythatthed710Pfroman

increasingtoastationarypopulationwillslowthepromotionfortheaverage

personinafactofTOrOHice,butnothingshortofanintegralequationcan

showthateachdropoflpercentintherateofincreasewilldelaypromotionto

middle-levelpositionsby2.3years. INathanKeyfitz(1977/1985),AppliedMathematicalDemography,p･viii･

ThestockandflOwstructuresdescribedinpreviouschapterskeeptrackofthe quantitiesflOwingthroughvariousstagesofasystem.Often,however,modelers mustnotonlycapturethetotalquantityOfmaterialinastockandflOwnetworkbut alsovariousattributesoftheitemsinthenetwork.Theseattributesmightinclude theaverageskiiiorexperienceofaworkt4orce,thequalltyofmaterlals,ortheen- ergyandlaborrequlrementSOfafirm'smachines･CoflOwsareusedtoaccountfor theattributesofitemsflowingthroughastockandflownetwork･Theoutflowrates ofitemsfromastockoftendependstronglyontheageoftheitems.Humanmor- talityratesdependonage,therateatwhichpeoplediscardandreplacetheirauto- mobilesdependsontheageoftheircars,machinebreakdownsinaplantdepend onthetimesincethemachineswerelastoverhauled,andtheprobabilityex-

convictsarere-arresteddependsonthetimesincetheirrelease･Agingchainsare usedtorepresentsituationswherethemortalityratesofitemsinastockandflow

469

470 PartIV ToolsforModelingDynamicSystems

structureareage-dependentandallowyoutomodelchangesintheagestructureof

anystock･Thischaptershowshowsuchsituationscanbemodeledandprovides examplesincludingglobalpopulationgrowth,organizationalaglng,On-the-job learnlng,andtechnicalchange.

12.1 AGINGCHAINS

ThestockandflOwstructureofsystemsisacriticaldeterminantoftheirdynamics,

andoftenthereareslgnificantdelaysbetweentheinflowofmaterialtoaprocess andtheoutflow.Inmaterialdelays(describedinsectionll.2)theflowofmaterial

through仙edelaylSCOnSerVed｡Materialentersthedelay,progressesthrougha numberofintermediatestages,andfinallyexits.Thereareneitheradditionstonor

lossesfromtheintermediatestages:everyItemthatenterseventuallyexits,andno

newitemscanenterotherthanatthestartofthedelayJnmanysituationsthereare additionalinflowsandoutnowstotheintermediatestages.Inthesecasesanaging

chainisusedtomodelthestockandflowstructureofthesystem.Imaginethe

skilledlaborforceatafirm.SinceittakestimefTornewhirestobecomefullyex- periencedandproductive,themodelermaychoosetodisaggregatethetotalstock ofemployeesintotwocategories,rookieemployeesandexperiencedemployees. Animportantaspectofthestructureisthedelayintheassimilationofrookies.

However,thissituationcannotbemodeledwithasecond-ordermaterialdelaybe- Causethefirm Canhirebothrookiesandexperiencedpeople,andbothrookiesand

experiencedemployeescanquit(Orbefired).Thereareinflowsandoutflowsto eachofthestocksinthechain(Figure1211).

12.1,1 Gene相室StructurerJfAgi;lgChains

Anagingchaincanhaveanynumberofstocks(calledcohorts),andeachcohort

canhaveanynumberofinflowsoroutflows.Figure12-2showsthegeneralstruc- tureforanagingchain.Thetotalstockisdividedintoncohorts,C(i),eachwithan

FlGURE121l

Exampleofan aglngChain

Chapter12 CoflowsandAgingChains

FIGURE12･2 Generalstructure

ofanaglngChain

471

inflow,I(i),andoutflow,0(i).Materialincohortimovestocohorti+1through

thetransitionrateT(i,i+1):

C(i)-INTEGRAL(I(i)+T(i-1,i)I0(i)-T(i,i+i),C(i)to) (12-1)

472 PartIV ToolsforModelingDynamicSystems

Thereisnotransitionrateintothefirstcohortandnotransitionrateoutofthelast

cohort:T(0,1)-0andT(n,n+1)-0.Ingeneral,thetransitionratescanbe eitherpositiveornegative(anegativetransitionratemeansitemsflowfromcohort

i+1tocohorti).Usually,however,thetransitionratesareformulatedasadelay andmostoftenasafirst-orderprocess:

T(i,i+1)-C(i)/YPC(i) (12-2)

whereYPC(i)isthenumberofyearspercohort(theaverageresidencetimebefore

exitingviamaturation)･Theaverageresidencetimeforitemsineachcohort YPC(i)candifferfromcohorttocohort.Recallfromchapterlithatafirst10rder

outflowfromastockimpliesthatthecontentsofthestockareperfectlymixedso thattheprobabilityaparticularitemexitsisindependentofwhenitenteredthe stock･Justasinhigher-ordermaterialdelays,theoverallbehaviorofanaglng chainwi血ncohortswillbesimilartothenth-ordermaterialdelay.Thenumberof cohortscanbeincreaseduntiltheassumptlOnOfperfectmixlngWithineachcohort becomesareasonableapproximation(Seesection1211･3foraformdationthatpre- servestheexactorderofentrytoeachcohort).

Theoutflowratescanbeformulatedinavarietyofways.Often,however,the outflowrepresentsthedeathrate(thatis,theexitratefromthestock)andisfor- mulatedas

O(i)-C(i)*FDR(i) (12-3)

whereFDRisthe丘･actionaldeathrateforcohorti.

Agingchainscanbeappliedtoanypopulationinwhichtheprobabilityofex-

itlngthepopulationdependsontheageoftheitemsinthepopulation.Besidesthe aglngandmortalityofapopulation,examplesincludethefailureofmachinesina factoryasafunctionofthetimesincethelastmaintenanceactivity,defaultandre-

paymentratesforloansofdifferentages,therateofdivorceasafunctionofmar- riageduration,orthelikelihoodofre-arrestfollowlngparole.

12ql.2 Examp日e:Popu日atiomame‖門菅FaS官Fueをure

inijrbanDyf7atrlぬき

Forrester'S(1969)UrbanDynamicsmodelincludesagingchainsforthreekey componentsofaclty:thestockofcommercialstructures,thehouslngStock,and thepopulation(Figure12-3).Forresterdividedthetotalstockofcom ercialstru c-

turesintothreecategories:NewEnterprlSe,MatureBusiness,andDecliningln- dustry.ThestockofNewEnterprlSeisincreasedbyNewEnterpriseConstruction.

ThetransitionrateofNewEnterprisetOMatureBusinessistheNewEnterprise Declinerate･Maturebusinessesageintothestockofdeclinlngindustrythrough theMatureBusinessDeclinerate.Finally,thestockofbuildingsintheDeclinlng IndustrycohortfallsthroughtheDecliningindustryDemolitionrate.Forrester chosetoassumethatallnewconstructionaddstotheNewEnterprisecohort(there arenoinflowstothematureordecliningindustrystocksotherthantheaglngrates fromthepriorcohort).Healsoassumedthatthedemolitionratefornewandma-

turebusinesseswassmallenoughtoIgnore,SOtheonlyoutflowfromtheaging chainisthedecliningindustrydemolitionrate.TheaglngChainforcommercial

u O !)!lO ∈ a凸

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473

474 PartIV ToolsforModelingDynamicSystems

structuresisthereforeequivalenttoathird10rdermaterialdelay(thoughthelife- timesofeachcohortarenotequalandvarywithchangesineconomicandsocial conditionsinthesimulatedcity).

ThehouslngStockchainismorecomplex.Forresterdividedthetotalhouslng stockintothreecategories-PremiumHouslng,WorkerHouslng,andUnderem- ployedHouslng-thatcorrespondtothethreetypesofpeoplerepresentedinthe model:Managerial-Professionalworkers,skilledLabor,andtheUnderemployed. NewhouslngOfeachtypecanbebuilt･Aseachtypeofhouslngagesitisgradually convertedintohouslngforthenexttypeofworker･Forexample,inmanycities largeVictorianhousesonceoccupiedbytheprofessionalclasswerelaterdivided intotwo-0rthreejamilyapartmentsoccupiedbytheworkingclass;asmiddle- classapartmentblocksintheBronxagedanddeterioratedmanybecametenements prlmarilyoccupiedbytheunderemployed･

Eachofthethreepopulationclassesincludedanetbirthrate(birthsless deaths),aninmigrationrate,andanoutmigrationrate.Theunderemployedcould, bygalnlngjobsandexperience,moveintotheworkerclass,andworkerscouldad- vanceintothemanagerial-professionalclass.Workerscouldalsosinkintounder- employment.

Asaninitialmodelofurbanproblemsandpolicies,Forresterdeliberatelykept themodelassimpleaspossible.NotallpossiblenowsintheaglngChainsarerep- resented,andthemodelisnomoredisaggregatedthannecessaryforthepurpose･ Forexample,ForresterIgnoredpossibledownwardmobilityoftheprofessional classanddidnotexplicitlyrepresenttheagestructureofthepopulationwithin eachclassofworkerJnrepresentlngtheinfrastructureofthecity,Forresteras- sumedthatstructuresbuiltforbusinessescouldnotbeconvertedtohousing,and viceversa,andthatold,decayedhouslngCOuldnotberehabilitatedintopremium houslng.Theexperienceofthepast30yearsshowsthatsomeoftheexcluded flowsdidbecomeimportantinmanycities.Agreatdealofoldindustrialspacewas convertedtohousing(e.g.,loftsinSohoandBrooklyn),gentrificationrehabilitated muchoftheolderhouslngStock,andmanynewbusinesseswerecreatedinpeo- ple'sgaragesandsparebedrooms.Thesemowscouldeasilybeaddedtotheaglng chainsinthemodel.Forexample,Homer(1979a,1979b)adaptedtheUrbanDy- namicsmodeltostudyinsuranceredlining.ThemodifiedmodelexplicitlyacI countsforgentrificationandrehabilitationofolderhousing,alongwitharsonfor profit.Mass(1974)andSchroeder,Sweeney,andAlfeld(1975)presentanumber

ofextensionsandelaborationsoftheorlglnalmodel,generallyshowingthat血e

policyrecommendationsoftheorlglnalmodelwererobusttomajorChangesin血e

modelboundaryandlevelofaggregation;seealsoAlfeldandGraham(1976).

12.1.3 Exampは:ThePopLぬtきonPyramidan仁i

theDemographic:T帽nSitior盲

AcommonuseforaglngChainsiscapturingtheagestructureofpopulations.EsI peciallyforlongllivedspecieslikehumans,youngandoldbehavedifferentlyand formanypurposescannotbeaggregatedintoaslnglestock.Chapter8described

Chapter12 CoflowsandAgingChains 475

thesimplestdemographicmodelwherethenumberofpeopleareaggregatedinto aslnglestock,Withbirthanddeathratesproportionaltothetotalpopulation:

Population=INTEGRAL(Births-Deaths,Populationt.) (1 2-4)

Bir[hs-FractionalBirthRate*Population (12-5)

Deaths-FractionalDeathRate*Population (12-6)

Inthisfirstl0rderstructurethoseJustborncanimmediatelyreproduceandarejust aslikelytodieastheoldestmembersofthepopulation.Formostrealpopulations

thesearepoorassumptions･Forhumans,mortalityrates(thefractionaldeathrate) arestronglyage-dependent:mortalityishighinthefirstyears,lowfromchildhood throughtheendofmiddleage,thenriseswithage.Thechildbearingyearsare

roughlybetween15and50,andfertilitylSnotuniformduringthisinterval.Vari- ationsinthepopulationgrowthratealtertheagestructureandaffectitsoverall

behavior･Forexample,anationwithhighlifeexpectancycanhaveahigherfrac- tionaldeathratethanonewithalowerlifeexpectancy.Ifpopulationinthenation withlowlifeexpectancylSgrowingrapidly,thenamuchlargerproportionofthe

populationwillbeyoung,reducingthetotalnumberofdeathsperyearperperson despiteloweraveragelifeexpectancyLThelagbetweenbirthandreproductioncan inducefluctuationsintheagestructure.Modelingtheeffectsofphenomenasuch asthebabyboomofthe1950S-includingtheextrademandplacedonschools,the

jobmarket,and,incomingdecadestheretirementsystem-requlreSamOdel血at distinguishesbetweenagegroups.

Demographersoftenrepresenttheagestructureofapopulationbythepopula- tionpyramid,agraphshowlngthenumberofpeopleineachagegroup,bysex (Figure12-4).Theagestructuresfortheworldasawholeandformanydevelop-

1ngnationssuchasNigeriaresemblepyramidsbecauserapidpopulationgrowth

meanstherearemanymoreyoungpeoplethanold･Theagestructuresofthede- velopednations,wheregrowthrateshavebeenlowforagenerationormore,are

moreuniform,thoughitisstillquiteeasytOSeethevariationsincohortsizecaused byphenomenasuchastheGreatDepression,WorldWarII,andthepostwarbaby boom.IntheUS,forexample,thedepressionandwarcutbirthrates,sothecohorts

bornbetween1930and1945aremuchsmallerthan也ebabyboomcohortsbomin the1950S(evenafteraccountingfornormalmortality).Theechoofthebabyboom

generation(thelargecohortsof5119yearoldsinthefigure,representingthechil- drenofthebabyboomers)isalsoclearlyvisibleintheUSagestmcture.Fora

numberofdevelopednations(includingJapan),fertilityhasbeenbelowreplace- mentratesforsometime,Sotheyoungestcohortsaresmallerthanthoseinthe prlmeChildbearlngyears.

Tbmodeltheseissues,thetotalpopulationcanberepresentedbyanaglng chaininwhichthepopulationisdividedintoncohorts,eachrepresentlngaCertain agerange,suchasthoseage5-10,ll-15,etc.Thefinalcohortrepresentsall

peopleoveracertainage.Thefollowlngequationsalsodisaggregatethepopula-

tionbysex:

Ps(0)-INTEGRAL(Bs+Is(0)-Ds(0)-Ms(0),Ps(0)to) (12-7)

476 PartIV ToolsforModelingDynamicSystems

FIGURE1214 Agestructuresofworldandselectednationalpopulationsin1998

Wor一d

400 300 200 100 0 100200 300 400

Population(millions)

USA

12 8 4 0 4 8

Populationfm=ions)

12 8 4 0 4 8

PopuFation(miHions)

Note:Scalesdiffer.

SouI℃e:USCensusBureau.

China

80 60 40 20 0 20 40 60 80

Population(minions)

6 4 2 0 2 4 6 Population(minions)

Brazjl

+44 Male #- Female

444444 # 蔓等登城襲来≡駁蔓

絞書柴≡投売完認諾縫綻類SaBS袋茸粥鍔怒諸表喜菜松茸菜#%%3g萱来室賢妻l SSE

怪宍§涼≡試琵深琵g賀来…無毒怒染繁栄学芸喜岩浴喜;-表決≡道議誤称指事喜*%i%:jggi

10 5 0 5 10

Population(miHions)

Chapter12 CoflowsandAgingChains

Ps(i)-INTEGRAL(Ms(i-1)+Is(i)-Ds(i)-Ms(i),Ps(i)t｡) foriE(1,...,nl l)

477

(12-8)

Ps(n)-INTEGRAL(Ms(n~1)+Is(n)-Ds(n),Ps(n)～) (12-9)

wherePs(i)is血epopulationincohorti,Bisthebirthrate,Ⅰ(i)isnetimmigration

toeachcohort,D(i)isthecohort-specificdeathrate,andM(i)isthematurationrate

fromcohortitoi+1.ThesubscriptSdenotesthesex(MorF).Eachcohortrep-

resentsYPC(i)yearspercohort.

Thebirthrateisthesumofthechildrenbomtoallwomeninthechildbearlng

years:

Bs-Ss TF

(CYFICYI+1)/afFY卜＼一一ノ~'＼一一/フ【̂一㌦ fFYI百) CYF CYF

∑W(a)pF(a),Where∑W(a)-1 (12-10)

Inthisformulation,PF(a)isthefemalepopulationincohortaandTFistotalfertill

lty-thetotalnumberofchildrenborntoeachwomanduringthechildbearing

years,whereCYlisthefirstandCYFisthelastchildbearingyearconsidered.The

ratioTF/(CYF-CYI+1)isthereforetheaveragenumberofbirthsperwoman

peryearduringthechildbearingyears,inclusive,usuallyassumedtobeages15to

49.Theage-specificweightsw(a)representthefractionoflifetimebirthsoccurring

ineachofthechildbearingyears(Figure12-5)anddependonbothbiologicalfac- tors,suchasnutrition,andsocioeconomicfactors,suchastheroleofwomeninthe

society,marriageage,andeducation.ThesexratioSsisthefractionofbirthsof

eachsex.Thesefractionsareusuallyclosetobutnotequalto0.5.Thesexratiois

alsonotconstantovertime:Insocietieswherethereisapreferenceformaleoff-

sprlng,technologynowenablespeopletoselectivelyabortfemalefetuses,reducl

lngSF.Femaleinfanticide,whichalsooccursinanumberoftraditionalsocieties,

Wouldbecapturedinthemodelbyhighermortalityratesfortheyoungestfemale cohort.

FIGURE1215

Worldaverage dLlstributi0nOf

birthsbymothers' age,1990-1995

([e to〓

0 % )s LJl L!g 5050

15-19 20-24 25-29 30-34 35-39 40･44 45-49

AgeGroup

Source:UnitedNationsPopulationDIVFSFOn,PopulationNewsletter,59(June1995).

478 PartIV ToolsforModelingDynamicSystems

OvertimepeoplemovethroughtheaglngChain.Theprocesscanbemodeled

withequations(12-1)-(12-3).Moststandarddemographicmodels,however,usea

slightlydifferentformulation.Manyofthesemodelsusediscretetimeintervals

equalindurationtothenumberofyearspercohort,YPC(i).Theyfurtherassume thatthedeathratewithinthecohortisconstantanddeductthetotalnumberof

deathsfromthecohortpopulationbeforemovingthepopulationfromonecohort tothenext:

Ms(i)-ExitRates(i)*(SFs(i)) (12-ll)

Ds(i)-ExitRates(i)*(1-SFs(i)) (12-12)

Thetotalrateatwhichpeopleleaveeachcohort(theexitrate)isdividedintotwo flows:thosewhomatureintothenextcohortandthosewhodie.TheSurvival

Fraction,SFs(i),isthefractionmaturingintothenextcohortand(1ISF)isthe

fractionthatdiedwhileinthecohort.Thesurvivalfractionsareeasilyderivedfrom

lifetablesorsurvivaldistributionsforthepopulation･1Theage-specificmortality

rate(theprobabilityofdeathperyearorfractionaldeathrateFDR)foracohort

withsurvivalfractionSFisgivenbytherateofexponentialdecaythatwouldleave

thefractionSFremainingafterYPCyears,orFDRs(i)- -1n(SFs(i))/YPC(i).

Iftheage-SpecificmortalityratesFDRareknown,thenthesurvivalfractionis

glVenby

SFs(i)- exp(-FDRs(i)辛YPC(i)). (12-13)

Iftheage-specificmortalityratefora10-yearcohortinapopulationwereFDR- 0･01/year,thenafter10yearstheexpectedsurvivalfractionwouldbe90.5%.The

fractionsurvivinglSgreaterthan90%becausethenumberofdeathsduringeachof

the10yearsfallsasthenumbersurvivingfalls.

Therearetwocommonformulationsfortheexitrate･Standarddemographic modelsassumediscretetimeintervalsandconstantdeathrateswithinthem.This

formulationcanbemodeledusingapipelinedelaywheretheexitratefromeach

cohortisthetotalrateatwhichpeopleenterthecohort(thesumofthosematuring

intothecohortplusanyimmigration),delayedexactlyYPCyears:

ExitRates(i)-DELAYP(Ms(i-1)+Is(i),YPC(i)) (12-14)

wheretheDELAYPfunctionrepresentsaplpelinedelaywithadelaytimehere

equaltothenumberofyearspercohortYPC(i).2

TheplpelinedelaylSapprOprlateforsituationswherethepopulationresidesin

eachcohortforexactlythesameperiod.Often,however,theresidencetimesfor

individualsarenotidenticalandthedeathratevariescontinuously.Attheotherend

ofthespectrum,suchsituationscanbemodeledbyafirst10rderdelay:

ExitRates(i)-Ps(i)/YPC(i) (12-15)

lKeyfitz(1977/1985),Lee(1992),andRosner(1995)describethemathematicsoflifetables andsurvivalanalysュsindiscreteandcontinuoustime.

2TheDELAYPfunctionisdefinedasfollows:Outflow-DELAYP(Inflow,DelayTime)im-

pliesOutflow(t)-Inflow(t-DelayTime).Seesectionll.2.3･

Chapter12 ConowsandAgingChains 479

Thefirst10rderexitrateimpliesthatwhiletheaverageresidencetimeineachco-

hortisYPC(i)years,somepeopleleaveearlierandsomeleavelater.Theformula-

tioninequation(12115)isappropriateinsituationswherethecohortsaredefined

notbyagebutbymembershipinacategorysuchasthelevelinanorganization

wheresomearepromotedtothenextlevelfasterthanothers(seethemodelinsec-

tion12･1･6)･Asthenumberofcohortsincreasesandthenumberofyearsperco-

hortfalls,thebehaviorofanaglngChainconsistlngOfnfirst-ordercohorts

convergestothepipelineformulation.

TwoFormulationsforMortality

Theformulationforthetransition(maturation)rateinequations(12-2)and(12-3)

differsfromtheformulationinequations(12111)-(12115).Intheformercase,the

maturationrateisgivenbythesizeofthecohortdividedbytheaverageresidence

time,whileatthesametime,deathsoccuratarateproportionaltothesizeofthe cohort.Inthelattercase,deathsareconsideredtooccuratthetimemembersexit thecohort.Thetwoformulationsaresimilarbutnotidentical.Considerfirst

equations(12-ll)-(12115),andforsimplicityassumetheexitrateisgivenby thefirst10rderformulationin(12115).ThetotaloutflowfromeachcohortP(i)is

M(i)+D(i)-ExitRate(i)-P(i)/YPC(i).Theintelpretationis血ateachmember

ofthecohortP(i)residesinthecohortforanaverageofYPC(i)periods.Onexit1

1ngthecohort,thetotaloutflowisdividedintothosematurlngIntothenextcohort

andthoseexitlngtheaglngChain.Thisformulationiscommonindiscretetime

demographicmodelsbasedontheplpelinedelaywhereeachcohortrepresentsa

particularagerangeandbydefinitionindividualsremaininthecohortforafixed

periodoftime.Itisalsoareasonablebehavioralmodelforsomeorganizational

structures,suchasconsultingfirms,lawpractices,Oruniversitieswherethereisan

up-or-outpromotionpolicy･InthesesettlngS,thestocksintheaglngChainrepre- sentcategoriessuchasassociate,seniorassociateandpartner.Ateveryrank,each

professionalisreviewedafteracertainnumberofyearsandiseitherpromotedor terminated(section12.1.6).

Inthecaseofequations(12-2)and(12-3),thetotaloutflowfromeachcohort

isM(i)+D(i)-P(i)/YPC+P(i)*FDR(i).Thissituationrepresentsacasewhere

deathscontinuouslyremovepeoplefromeachcohort･Theaverageresidencetime

islessthanYPCperiods･Thisformulationisapproprlate,forexample,inthe

UrbanDynamicsmodelwherethepopulationisdividedintodifferentsocio-

economiccategories:workersmove丘.omonecategorytoanotherwithacertain

probabilitybutalsocontinuouslyfaceachanceofdeath･3

Whichformulationisbetter?Returningtothecaseofalawfirmoruniversity

withanup-or-outpromotionpolicy,bothprocessesclearlyplayarole.Afteranav-

erageperiodof,say,8years,allfacultyarereviewedandeithergiventenureOrter-

minated,asinequation(12-11),butthereisalsoacertainrateatwhichuntenured

facultyleavetheuniversityPriortOtheirmandatoryreviewdate,asinequation

(12-2).Ifnecessaryforthepurposeofthemodelbothformulationscanbecom-

bined.Usually,however,thedataarenotgoodenoughtoallowtheseprocessesto

3statistically,thedistributionofthepopulationineachcohortisexponentialinthecaseof equation(12-11);inthecaseofequation(12-2),thedistributionishyperexponential.

480

FIGURE12-6

Projectedage structureofChina

comparedto currentdistribution

PartIV ToolsforModelingDynamicSystems

beestimatedseparately,andthedifferencesbetweenthetwoformulationsare

smallenoughthatitisnotnecessarytoincludeboth･

12.1.4 AgingChainsandPopulationnertzLa

Animportantconsequenceoftheagestructureofthehumanpopulationisthe enomousmomentumofpopulationgrowth.Worldpopulationcrossedthe6billion

markin1999withagrowthrateofabout78millionpeopleperyear(1.3%/year). Iffertilityaroundtheworldinstantlyfelltoreplacementrates,meanlngthatonav- eragepeoplehaveJustenoughchildrentoreplacethemselves,theworldpopulation

wouldnotimmediatelystabilize･Instead,populationwouldcontinuetogrowlIn theUnitedNations'1998instantreplacementscenario,worldpopulationwould reach8.4billionin2050and9.5billionin2150,ariseofmorethanathird.As

longastotalbirthsexceedtotaldeaths,thepopulationcontinuestogrow.Though

eachcohortJustreplacesitself,thosenowinthechildbearlngyearsaremuch greaterinnumberthanthoseintheoldercohorts･Becauseworldpopulationhas

beengrowing,moreandmorepeoplewillreachtheprlmeChildbearingyearsfor thenext30yearsorso,increasingtotalbirthsstillmore.Longhumanlifetimesand

thelongdelaybetweenbirthandreproductionmeanpopulationisveryslowtoad- justtOChangesinfertilityandmortality.

Thetremendousinertiacausedbytheagestructureofapopulationisfurther

illustratedbytheexperienceofChina･FertilityinChinafellbelowthereplacement levelbeginnlnginthelate1970sastheresultofthegovernment'sone-Childpolicy andotherchangesinsocialandeconomiccircumstances(SeeFigure12-4).Never- theless,thepopulationofChinagrewfrom985millionin1980to1.237billionin

1998,morethan25%inlessthan20years.AndalthoughtotalfertilitylSexpected toremainbelowreplacement,thepopulationisprojectedtogrowtoapeakofmore

than1･4billionby2030beforegraduallydeclining･Figure12-6comparesChina'S

80-84

70-74

60･64

50-54

a 40-44 <

30-34

20-24

10-14

00-04

80 60 40 20 0 20 40 60 80

Popuration (minions)

Sofidbars,1998;openbars,projectionfor2010 SouflCe.IUSCensusBureau

Chapter12 CoflowsandAgingChains 481

agestructurein1998totheagestructuretheUSCensusBureauprojectsfor2010. Whilethepopulationunderage35remainsaboutthesameorevenfalls,the populationoverage35increasesdramatically,simplybecausethoseaglnginto eachcohortoverage35aremuchmorenumerousthanthoseagingOut.

Theseexamplesshowthatapopulationcancontinuetogroweventhoughto-

talfertilityratesarebelowreplacementandcanshrinkevenwhenfertilitylS greaterthanreplacement･Variationsinfertility(moregenerally,intherateofad- ditionorremovalfromthecohorts)Caninducevariationsintheagestructureofa populationthatcancauseitsbehaviortodiffersignificantlyfromamodelinwhich allagesarelumpedintoaslnglestock.

12.1.5 SystemDynamicsinAction:World

PopulailionandEconomicDeve!opm耐電

Mostdemographicmodels,suchastheprojectionsoftheUSCensusBureauand UnitedNations,assumetotalfertility,births,mortality,andmlgrationareexoge- nousandcalculatetheresultingagedistributionsandtotalpopulations.Thesemod- elsareessentialtoolsforbusinessesandgovernmentagenciesseekingto understanddemographictrendsovertheshortterm,forpurposessuchasforecast1 1ngschoolagepopulationsorthenumberofpeopleenterlngtheworkforceorbe- comingeligibleforSocialSecunty.

Overlongertimehorizonsbirthsandlifeexpectancyshouldnotbetreatedas exogenousInputs.Factorssuchasnutrition,accesstohealthcare,thematerial standardofliving,pollution,andcrowdingalldependonthesizeandwealthofthe population,Creatlngahugenumberoffeedbacks.Nevertheless,virtuallyallde- mographicmodelsincludingthoseoftheUNcutalltheseloops.Officialprojec- tionsassumerecenttrendstowardlowerfertilitywillcontinue,untiltotalfertility fallsenoughtobringworldpopulationtoeventualequilibrium.TheUN'S1998 mediumfertilityscenario,forexample,assumesreplacementfertilitylSachieved worldwidein2055,leadingtoanequilibriumpopulationofaboutllbillion.

Forrester,inWorldDynamics(1971b),andthenMeadowsetal.(1972,1974)

developedthe丘rstintegratedmodelsofworldpopulation,theglobaleconomy, naturalresources,andthephysicalenvironment.Thesemodelsweredesignedto investlgatetheeffectsofpopulationandeconomicgrowthashumanactivityap- proachesthecarryingCaPaCltyOftheearth.Forrester'smodelrepresentedworld populationasaslnglestock.Meadowsetal.elaboratedandexpandedForrester's model,disaggregatingworldpopulationintofourcohorts(ages0-14,15-44, 45-64,and65andover)･Meadowsshowedthefourllevelagingchainbehaved qulteWellandprovidedsufficientprecisionwhenappliedtoworldpopulation wheremanydifferentpopulationsareaggregatedtogetherandthereisconsiderable measurementerroranduncertaintyaboutparameters･WangandSterman(1985), applyingtheMeadowspopulationsectortothepopulationofChina,useda66co- hortmodel(oneperyearuptoage65andoneforthoseover65).

Meadowsetal.Soughttomodelthedemographictransition.Thedemographic transitiondescribesthepatternofchangeinpopulationgrowthratesasnations industrialize.IntraditionalsocietiesprlOrtOeconomicdevelopment,bothcrude

482 PartIV ToolsforModelingDynamicSystems

birthanddeathrates(birthsanddeathsperthousandpeople)tendedtobehighand

variable･Averagelifeexpectancywascomparativelylow,andwomenboremany

childrentoensurethatafewwouldsurvivetoadulthoodandsupporttheirparents intheiroldage.Populationgrowthwasslow.

Accordingtothetheoryofthedemographictransition,lifeexpectancyrises sharplywiththearrivalofindustrializationandtheintroductionofmodernsanita-

tion,publichealthsystems,andmedicalcare.Deathratesfall.Birthrateseventu-

allyfallaswell.Higherlifeexpectancyandlowerinfantmortalitymeanmore

childrensurvivetoadulthood,sowomendonotneedtobearasmanytoachieve theirdesiredfamilysize.Further,desiredfamilysizetendstofallasthecostof

childrearlngrisesandasthecontributionofchildrentotheeconomicwelfareof

thefamilydeclines.Costsofchildrearingriseandcontributionsfallinindustrial

societiesbecausechildrenenterthelaborforcemuchlaterthanintraditionalagrl-

culturalsocietiesandmustbesupportedbytheirparentsformuchlongerandat

highercost･Thedeclineinbirthrates,however,isveryslow,sincenormsforfam-

ilysize,marrlageage,andotherdeterminantsoffertilityarestronglyembeddedin

traditionalculture,religiousnorms,andothersocialstructures;fertilitylSnOtthe

resultofeconomicutilitymaximizationbycouples.

Consequently,duringthedemographictransitionpopulationgrowthacceler-

atessharply,sincedeathratesfallwhilebirthratesremainhigh.Eventually,ac-

cordingtothetheory,fertilityfallsintoroughbalancewith mortality,and

populationapproachesequilibrium.Figure12-7showscrudebirthanddeathrates

(birthsordeathsperthousandpeopleperyear)forSwedenandEgypt.InSweden,

whereindustrializationbeganearly,deathratesfellslowly,sopopulationgrowth

wasmodestduringthetransition,taking120yearstodouble(1875to1995).In

Egypt,however,asinmanylater-developlngnations,thedeathratefellsharply

a洗erWorldWarII･Thebirthrate,whilestartlngtOfall,remainshigh,sopopula-

tiongrowthisveryrapid;populationdoubledinjust30years(1966-1996).Bythe late1990sthetransitionwasfarfromover.

TheMeadowsetal･globalmodelincludedafullyendogenoustheoryofthe

demographictransition.Todoso,theynotonlyhadtorepresenttheagestructure

oftheworldpopulationbutalsohadtomodeltotalfertilityandchangesinlife

expectancy.Aftertesting1-,4-,and151cohortmodels,theydeterminedthatthe

4-cohortmodelprovidedprecisionconsistentwiththestateofthedataatthattime

whilepreservlngmodelparsimonyandhelpingtokeepthemodelwithintheca-

pacltyOfthecomputersavailableintheearly1970S.Ingeneral,mortalityratesfor

eachcohortinthemodelshouldbespecifiedasaseparatefunctionoffood,health

care,materialstandardofliving,andotherfactors.Inpractice,thedatawerenot

availabletodoso･Meadowsetal.(1974)Showedthatthedistributionofmortality

byageisreasonablystableaslifeexpectancyvaries.MortalityfollowsaUIShaped

curve:mortalityratesarehighestforthevery young,lowestforpeoplebetween

aboutage10and30,andgraduallyriseaSPeopleage･4Asaveragelifeexpectancy

4Mortalityrateschangewithageandwithsocialandeconomicconditions･Debatecontinues aboutthemaximumhumanlifespanandtheeffectsofindustrializationandeconomicdevelopment onlifeexpectancy.Foranoverview,seeVaupeletal.(1998).

Chapter12 CoflowsandAgingChains

FuG URE 12-7 Thede mographic transition

( pu t!sn o

LJIL a

d )

at t2 tJ u tt2 a

凸

a P m

'a le E

LJt七 g a P n J U

(

pu t2Sn O

LJlJ a

d )

Oletl LJttZ a 凸

a P 2

.a lt2 t l

utJ!g a P nJ

Sweden

750 1800 1850 1900

Egypt

CBRCDR:'1.,I.･■: 日ケ̀､∫,.Population

P o p u la t io n ( m illion s )

P o p

ura

tj o n (

M i nion s )

1750 1800 1850 1900 1950 2000

7Top:Sweden,bottomr'Egypt,

Source:DanaMeadowsandDianaWright(personalcommuntcatl0n).

483

risesandfalls,thedistributionisshifteddownwardorupward,respectively,but retainsroughlythesameshape.Assumlngtheshapeofthedistributionremains

stable,age-specificmortalitycanthenbemodeledas

FDRs(i)-RFDRs(i)fs,.(LE) (12-16)

whereRFDR(i)isthereferencefractionaldeathrateforeachcohortandLEisav-

eragelifeexpectancyatbirth･Thereferencedeathrateisthefractionaldeathrate

inareferenceyear,Correspondingtotheyearinwhichlifeexpectancytakesthe

valuethatyieldsfs,i(LE)-1･Thedownward-slopinga苧e-specificfunctionsfs,i

relatemortalitytoaveragelifeexpectancyandcanbeestimatedfromactuarialor

demographicdata.

Meadowsetal.modeledaggregatelifeexpectancyasdependingonfourfac-

tors:foodpercapita,healthcareservicespercaplta,exposuretOPersistentpollu-

tion,andcrowding.Thesefactorsinteractedmultiplicativelytocaptureimportant

interdependenciesandtoensurerobustnessunderextremeconditions(e.g.,lifeexI

pectancymustapproachzeroasfoodpercapltaapproacheszero;lifeexpectancy

remainsfiniteevenifallconditionsareextremelyfavorable).Thedeterminantsof

484 PartIV ToolsforModelingDynamicSystems

lifeexpectancywereendogenouslygeneratedbyothersectorsofthemodel,clos-

1ngthefeedbackloopsinthemodel.

TotalfertilityTFdependsonbothabiologlCalmaximumanddesiredfamily

sizeofeachwomaninthepopulation.Theeffectivenessoffertilitycontroldeter-

mineswhethertotalfertilityisclosertothebiologlCalmaximumorthedesired

level.Avarietyofsocioeconomicfactorsdetermineddesiredfamilysizeandfer-

tilitycontroleffectivenessinthemodel.Themodelalsorepresenteddelaysinthe

adjustmentofculturalnormsfordesiredfamilysizetonewsocialandeconomic

conditions･Themodeldidanexcellentjobreplicatlngtheaggregatehistoricaldata

andprovidedthefirstfullyendogenousmodelofthedemographictransition,a

modelthat,aftermorethan25years,canstillbefruitfullyusedtoexplorediffer-

entpoliciesrelatingtopopulationgrowth.

BytreatlngInteractionsofpopulation,economicgrowth,andtheenvironment

inafullyendogenousfashion,ForresterandMeadowsetal.providedthefirstin-

tegratedglobalmodelstostudythedynamicsofgrowthinafiniteworld.Inthe

Meadowsetal.modelthedemographictransitionisnotautomatic,asassumedin

modelswithexogenousfertilityandmortality.Ifresourcesandenvironmentalca-

pacltyareSufficientandifeconomicgrowthanddevelopmentaredistributedfairly

soeventhepoorestpeoplehavesufficientfood,Cleanwater,accesstohealthcare,

anddecentjobs,thentheworldasawholemovesthroughthedemographictransト

tionandpopulationeventuallystabilizeswithhighlifeexpectancyandlowfertil1

1ty･Butifglobaleconomicdevelopmentpassesthehave-れotsbyorifpollution, resourceshortages,crowding,insufficientfood,orotherproblemscausedby

growthlimitdevelopment,thentheeconomicandsocialconditionsthateventually

leadtolowbirthrateswillnotariseandthedemographictransitionwillnotoccur.

Populationandeconomicgrowthcontinue,overshootingtheearth'scarrylngCa-

paclty･EnvironmentaldegradationreducesthecarrylngCapacityandmortality

rises.Withinahundredyears,populationandeconomicoutputfall.

Meadowsetal.(1972,pp･23-24)summarized血econclusionsofthestudyas follows:

1･Ifthepresentgrowthtrendsinworldpopulation,industrialization,pollution, foodproduction,andresourcedepletioncontinueunchanged,thelimitsto growthonthisplanetwillbereachedsometimewithinthenextonehundred years.Themostprobableresultwillbearathersuddenanduncontrollable declineinbothpopulationandindustrialcapaclty.

2.Itispossibletoalterthesegrowthtrendsandtoestablishaconditionofec0- 10glCalandeconomicstabilitythatissustainablefarintothefuture.Thestate ofglobalequilibriumcouldbedesignedsothatthebasicmaterialneedsof eachpersononeartharesatisfiedandeachpersonhasanequalopportunlty torealizehis[orher]individualhumanpotential.

3.Iftheworld'speopledecidetostrivefわrthissecondoutcomeratherthanthe first,thesoonertheybeginworkingtoattainit,thegreaterwillbetheirchances ofsuccess.

BothForresterandtheMeadowsteam soughttoencourageconversationand

debateaboutgrowthandstimulatefurtherscientificresearchleadingtoim-

provedmodels,improvedunderstanding,and,ultimately,actionsandpoliciesto

preventovershootandcollapseandencouragewhatisnowknownassustainable

Chapter12 CoflowsandAgingChains 485

development.Towardthatend,theauthorstookpainstopolntOutthelimitations

oftheirmodels.Meadowsetal･(197 2,p.21)wrote"Themodelwehavecon-

structedis,likeeveryothermodel,imperfect,oversimplified,andunfinished."

TheypublishedcompletedocumentationforbothworldmodelssoanyonewithacI

cesstoacomputercouldreplicate,revise,andmodifythemodels.Manydidso,

anddozensofcritiquesandextensionswerepublished･

ThemodeltnggeredavlgOrOuSandsometimesacrimoniouspublicdebateover

growth,adebatestillreverberatlngtoday.Italsostimulatedmanyotherglobal

modelingefforts,spannlngaWiderangeofmethods,modelboundaries,timehori-

zons,andideologlCalperspectives.Globalmodelswithnarrowmodelboundaries,

wheremanyofthefeedbacksarecut,tendtoreachmoreoptlmisticconclusions.

Modelsthatcapturethemanyfeedbacksbetweenhumanactivityandtheenviron-

menttendtoreachconclusionsconsistentwiththeorlglnalstudy･5

12.1.6 CaseStudy:GrowthandtheAgeStructure

ofOrganizations

Variationsinbirthrateshavedramaticeffectsontheagestructureoftheworld

population.Butgrowthalsohasprofoundimplicationsontheagestructureand

maturationoforganizations.Mostorganizationscontainvariouspromotionchains

thatrepresentthedifferentlevelsinthehierarchywithineachdepartmentorfunc-

tion.Consultingfirms,forexample,typicallyincludelevelssuchasassociate,

seniorassociate,partner,anddirector.

Thegrowthrateoftheorganizationhasadramaticimpactonthebalance

amongthelevelsinapromotionchainhierarchyandonopportunitiesforadvance-

ment.Figure12-8showsthepromotionchainforatypicalAmericanuniversity.

Therearethreefacultyranks:assistantprofessors,associateprofessors,andfull

professors.MostUSuniversitiesoperateanup10r-OutPromotionsystem:faculty

arereviewedafteracertainperiodandthosenotpromotedareterminated.Faculty

reachingfullprofessoraregrantedlifetenureandremainactiveuntiltheychoose

toretire(mandatoryretirementintheUSwasabolishedinthe1980S).While

occasionallyseniorfacultyarehiredfromotherinstitutions,thevastmaJOrltyOf

hiringlSatthenewassistantprofessorlevel.

Theup-or-Outpolicymeansthetransitionanddepartureratesareformulated

asfollows(theassistantprofessorflowsareshown;flowsforassociatesare

analogous):

AssistantPromotionRate-AssistantReviewRate*AssistantPromotionFraction

(12-17)

5Forrester(1971b)providesthefirstglobalmodelwithfullyendogenouspopulationandcarry-

ingcapacity.Meadowsetal一(1974)providesfulldocuTlentationforthemodel,calledWORLD3･ Meadowsetal･(1972)providesanontechnicaldiscusslOnOftheassumptionsandresultsofthe study･Meadows,Meadows,andRan°ers(1992)updatesthestudyandmodelandisthebest startlngpointfわrthosewishingtodigmoredeeplyIntotheseissues･0山erglobalmodelsandthe scienceofglObalmodelingitselfarecritiquedinMeadows,Richardson,andBruckmann(1982)･

486 PartIV TわolsforModelingDynamicSystems

FIGURE12-8 PromotionchainforatypicaEAmericanuniversity

HiringofassociateandseniorfacultylSOmitted.TheReviewRatefortheassistantandassociate

ranksisfirst-order;theFu"ProfessorRetirementRateisformu一atedasathird-orderdelayofthe

AssociatePromotionRate.AdaptedfromamodeldevelopedbyDavidPetersonandusedwith permission.

+ Total +

AssistantDepartureRate -AssistantReviewRate*(1-AssistantPromotionFraction)

AssistantReviewRate AssistantProfessors

AverageAssistantReviewTime

Notethattheassistantandassociateranksareform ulatedasfirst-orderprocesses

eventhoughcontractsarenominallyallforthesamespecifiedduration,sug-

gestingaPipelinedelay･Inpracticesomefacultyarepromotedearlierthanothers

duetothevaryingincidenceofpersonalandprofessionalleavesofabsenceandto

6TheformulationassumesallfacultyremainattheinstitutioI"ntiltheycomeupforreviewI Infact,thereissomeprobabilityfacultyleaveprlOrtO theirpromotionreviews.Amorerealistic modelwouldincorporatebotheffects,combiningthetwoformulationsformortality･Inpractice thedatatoestimatetheparametersarenotavailable,andtheerrorintroducedbyaggregating thosewholeavepriortOmandatoryreviewwiththosewholeaveafteranegativepromotion reviewisnegligible.

Chapter12 CoflowsandAgingChains 487

differingmarketpressures(ahotyoungprofessormaybepromotedearlytore- spondtooutsideoffersfromcompetinguniversities).Thesesourcesofvariation implythattheformulationfortheexitrateshouldallowsomemixlng.Thefirstl orderformulationassumesperfectmixlng,Certainlyanoverestimateofthevariance inpromotiontimes.However,glVentherelativelyshortresidencetimesineach Juniorrank,thefirst10rderformulationisnotlikelytointroduceslgnificanterror･

Incontrast,thelongtenureoffullprofessorsmeansafirst-orderformulation, withitsassumpt10nthattheyoungestfullprofessorsarejustaSlikelytoretireas theoldest,isclearlyinapproprlate.Inthemodelanalyzedhere,athird10rderfor- mulationfortheretirementrateisused.

GiventheseassumptlOnS,Whatisthedistributionoffacultyacrossthethree ranks?Thedistributiondependsontheaverageresidencetimesoffacultylneach rankandtheaveragepromotionfractions,aswellasthegrowthrateofthefaculty. Inmostuniversities,facultyremainassistantprofessorsforanaverageof3years beforepromotiontoassociate;associateprofessorsaretypicallyreviewedforpro- motiontofullprofTessorafteranaverageof5years.Fullprofessorstypicallyserve about35yearsbeforeretiringatanaverageageOfabout70.Thoughpromotion fractionsvaryovertime,typicalvaluesmightberoughly50%ateachrank.The equilibriumdistributiongiventheseparametersisreadilycalculated(byLittle's Law)tobeabout21%assistant,18%associate,and61%fullprofessors,adistri- butiontop-heavywithseniorfaculty.Wherethetotalsizeofthefacultyisfixed, Juniorfacultycanonlybegrantedtenurewhenafullprofessorretiresordies.

However,fewuniversitiesareinequilibrium･MostUSuniversitieswent throughaperiodofrapidgrowth丘･omtheendofWorldWarIIthroughtheearly 1970S,whenthebabyboomgenerationgraduatedfromcollege･Sincethen,dueto decliningcollegeagepopulationsandstagnatingfederalsupportforhighereduca- tion,growthslowedorevenbecamenegative.Figure1219showsthedistribution offacultyranksatMITsince1930(thepatternofbehavioratotherleadinguni- versitiesissimilar,thoughthetimingandmagnitudesdiffer)AUntil1970totalfac- ultygrewrapidly,averaglng3･7%/year･Theagedistributionwasskewedtoward theyoungerranks,withfullprofessorsaveraglngOnlyabout36%ofthefaculty from1930through 1969.Inthe1970sgrowthessentiallyceased,andthetotalfac- ultyremainedroughlyconstantthroughthemid1990S.Hiringofnewassistant professorsfell,andtheagedistributionbegantoapproachequilibrium･By1993 assistantprofessorsmadeuplessthan18%ofthefacultywhilemorethan63% werefullprofessors-veryclosetotheequilibriumdistribution.

Theconsequencesofthistransitionwereprofound.Duringtheeraofrapid growth,thehighproportionofyoung,untenuredfacultygavetheinstitution tremendousflexibilityandbroughtlargenumbersoftalentedpeopleintotheorga- nization.Becausetherewererelativelyfewseniorfacdty,thechancesofpromo- tiontotenureweregood.Relativelyyoungprofessorssoonfoundthemselves promotedtoseniorpositionssuchasdepartmentchairordean･A氏ergrowth stoppedandmostdepartmentsbegantofillwithtenuredfaculty,flexibilityde- clined.Itbecamemoredifficulttogettenure.Insomeparticularlytop-heavyde- partments(thosethathadgrownthefastestduringtheboomyears),therewas almostnotumover,littlehiring,andfewjuniorfaculty.Assimilardynamicsplayed outatuniversitiesthroughoutthecountry,manydoctoralcandidatesfoundthey

488

FlGURE12-9 Distributionof

facultyranks,MIT

PartIV ToolsforModelingDynamicSystems

1200

1000

800 >ヽ llll■

3 600 q LL

400

200

Tota一

＼ FullAssociate

州㌔〆--

1930 1940 1950 1960 1970 1980 1990 2000

t̂r

o e』

10 u O !tUt2 Jj

1930 1940 1950 1960 1970 1980 1990 2000

SouJ℃e:DataprovidedbyDavldPeterson;MIT.

couldnotgettenure-trackpositionsaftergraduation;asaresult,manywerefわrced

toacceptlow-payingPOStdoctoralpositionsorleaveacademiaaltogether･

TheaglngOfthefacultyalsohadimportantfinancialimplications.Because

seniorfacultyaregenerallypaidmorethanJuniorfaculty,theagingOfthefaculty

increasedthetotalcostofthefacultyfasterthantheriseinsalariesforeachrank･

Forindividualfacultysalariestokeeppacewithinflation,thetotalpayrollhadto

growevenfaster.Theresultingcostescalationhelpedpushtuitionupmuchfaster

thaninflationduringthe1970sand80S.Ultimately,lnParttOrelievebudgetpres-

sureandinparttomakeroomforfreshblood,MIT,alongwithothertopresearch

universitieswherethesamedynamicshadplayedout,implementedanearly

retirementincentiveprogram tospeedtheoutflowfrom theranksofthefull

professors.

Thediscussionabovesuggeststhatthehiringrateandpromotion丘.actionsare

notconstant;theychangeasconditionsintheuniversityeVOIve･Thedataonfac-

ultyateachrankcanbeusedtoestimatewhatthehiringandpromotionfractions

musthavebeenandthereforetestthesehypotheses,glVentheaveragetimespent

ineachrank.Figure12110showstheresults.Noattempthasbeenmadetospecify

thehiringandpromotionfractionseveryyear;instead,theseparametersaresetto

roundnumbersatwidelyspacedintervals.Despltethelowresolutionwithwhich

theinputsareestimated,themodelcloselytrackstheactualdata･Theexcellent丘t

showsthattheassumptionoffirst10rderexitratesfromeachjuniorcohort(and

Chapter12 ConowsandAgingChains

FJGURE12110

Simulatedfaculty agestructure,MIT

Top:SimuJated vs.actualfaculty byrankuslng imputedhiringrate andpromotion fractions,Midd/e:

lmputedassistant professorhiring rate.Bottom:

Imputedpromotion fractions.

1200

1000

800

>ヽ

≡ 600 q l⊥

400

200

--simulated Toti

- Actual FullAssociate

叫++㌦＼-一伽.＼r-㌧γ-

1930 1940 1950 1960 1970 1980 1990 20000

4 91

3 91

PO 1

0 u fO Jld

u O !tO t2JL

19601970198019902000

AssistantPromotionFraction

AssociatePromotionFraction

1930 1940 1950 1960 1970 1980 1990 2000

Source:Adaptedfromamodeldeve一opedbyDavidPeterson.

489

athird10rderretirementrate)isacceptableandthereislittleneedforfurther

disaggregationoftheagestructurewithineachfacultyrank.Consistentwiththe

discussionabove,promotionfractionsandhiringwerehighduringtheyearsof

rapidgrowthandfellwhengrowthstopped.Notealsothelargeburstofhiring

inthe1960S,whichdramaticallyincreasedtheranksoftheassistantprofessors.

Asintuitionwouldsuggest,thehiringsurgewasfollowedbyseveralyearsof

depressedhiring.Moreinterestlngly,theincreaslngnumberoffacultyintheupper

rankscomparedtothenumberofslotsavailablemeantthattheprobabilityof

490 PartIV ToolsforModelingDynamicSystems

promotionfrom assistanttoassociateafterthehiringboom inthe1960sfell significantly.

Inreality,thesizeandcompositionofthefaculty,andmoregenerallyany

workforce,feedsbackthroughthemarketandotherchannelstoaffTectthehiring rate,Promotionfractions,andotherparameters.Whileimportantinsightscanbe

gleanedfromthepromotionchainmodelwithexogenoushiring,promotion,and departureparameters,thesestructuresaremostusefulwhenembeddedinafull

modeloftheorganization.Thepromotionfraction,forexample,Canbemodeled

endogenouslyasdependingonthenormalspanofcontrolandthebalanceofsenior toJuniorpersonnel,Itisalsoaffectedbythefinancialhealthoftheorganization. TherateatwhichemployeesvoluntarilyqulttOtakebetteropportunitieselsewhere dependsontheirperceptlOnSOfthechancesforpromotion.Thesechances,intum,

dependontheagestructureandhencethegrowthrateoftheorganization.Since

themosttalentedemployeeswillhavethemostattractiveoutsideopportunities,a slowdowningrowth,byreducingpromotionopportunities,cansystematically drainanorganizationofitsbesttalent.Lossoftalentcanthenfreedbacktoworsen

performanceinthemarketplace,furthererodinggrowthinaviciouscycle(seesec- tion10.4.9).

ThefacultyexampleshowshowanaglngChaincanbeusedtomodelthede-

mographicstructureoforganizationsandillustratesthedramaticimpactofgrowth

onthedistributionofpersonnelamongthedifferentranks･Thesteadystateage structureofanypopulationdependsonitsgrowthrate･Changesinpopulation growthratesatthecommunlty,national,Orgloballevelschangetheratiosofchil-

drentopeopleofchildbearingageandoftheworkingagepopulationtoretirees,

significantlychangingthesocial,economic,andpoliticalpressuresfacedbythe population･Similarly,asthegrowthrateofabusinessorotherorganization changes,itnecessarilygoesthroughlargechangesintheratioofseniortoJunior employees,inpromotionopportunities,andintheaveragecostoftheworkforce.

Thesechangesarisesolelyasafunctionofchangesinthegrowthrateoftheorga- nization.Sincethegrowthofallorganizationsmustslowastheybecomelarger,

theagedistributiontendstobecometopheavy,poslnggreatChallengestoorgani- zationsseekingtorenewthemselveswhilepreservingattractivecareerpathsfor thosealreadyinthehierarchy.Thelargerandfasterthedeclineingrowthrates,the worsethisproblembecomes.Thefastest-growlng,mostSuccessfulorganizations alwaysfacethegreatestchallengewhentheirgrowthinevitablyslows.

12.1.7 PromoiionChainsand帥eLeaningCurve

CorlSideragalrlLLhetwo-1evelIPromotionchainforrookieandexperiencedworkers (showninFigure12-ll).Thisstructureisveryusefulinmodelingtheeffectof

trainlngandassimilationdelaysontheproductivityOfaworkforceasthegrowth ratevaries･7Thepromotionchainprovidesasimpleandeffectivewaytomodel thelearningCurvefornewemployees.Tokeepthemodelsimple,assumeitisnot

7oliva(1996)appliesthepromotionchainstructuretoservicequalityinamajorUKbank; Abdel-HamidandMadnick(1991)applyittosoftwareproductdevelopment;Packer(1964) appliesittoamodelofhightechgrowthfirms.

Chapter12 ConowsandAgingChains

FlGURE12･ll AtwoJeve-promotionchaintoexploreworkertraining

491

possibletohireexperiencedpeople.Insomeindustries,experiencedhiresare

unavai1ableortooexpensive.Morecommonly,becomingfullyproductivedepends

ontheaccumulationofsituation-specificknowledge,soprlOrexperienceisof limitedbenefit.

TheproductivltyOfrookieemployeesistypicallyafractionofthatforfullyex-

periencedemployees.ThetotalpotentialoutputoftheworkforceisthenglVenby

Potential_Experienced*

Output Productivlty RookieProductivity*Rookie +Experienced

Fraction Employees Employees (1 2-20)

AverageproductivltylS

AverageProductivity-PotentialOutputrrotalEmployees (1212I)

FormulatingtheflOwsasfirst-orderprocessesyields

RookieQuitRate-RookieEmployees*RookieQuitFraction (12122)

Experier.cedQuitRate -ExperiencedEmployees*ExperiencedQuitFraction

(12-23)

AssimilationRate-RookieEmployees/AssimilationTime (12-24)

Forpurposesoftestlng,assumetheworkforcegrowsataconstantexponentialrate.

Todoso,thefirmmustreplaceallthosewhoquitandcontinuouslyaddafraction ofthecurrenttotalwork丘)∫ce:

RookieHireRate-Tわtal(〕uitRate+GrowthRate*TわtalEmployees (12-25)

TotalQuitRate-RookieQuitRate+ExperiencedQuitRate (12126)

492 PartIV ToolsforModelingDynamicSystems

Whatistheequilibriumdistributionofemployeesbetweentherookieandexper i-

encedcategories?Theequilibriumconditions,whenthegrowthrateiszero,∬e

RookieHireRate-RookieQuitRate+AssimilationRate (12127)

AssimilationRate-ExperiencedQuitRate (12-28)

Giventhedefinitionsoftheflows,theequilibriumnumberofrookiesiseasily showntobe:

RookieE-ployeeseq-EEX:ep:?yneCeesd*(QEuxl:eFniea::ie.dn*Assi:iaetion) (12-29,

whichmeanstheequilibriumRookieFractionis

RookieFractioneq

Experienced*Assimilation QuitFraction Time

(1+QEuxiPteFniea::ie.dn*Ass;:action)

(12-30)

Equilibriumaverageproductivity,asa丘.actionof血eproductivltyOfexperienced employees,lS

Average

Productivltyeq

Experienced

Productivity

(1IRoo等rparc?id.unctivity*QEuxiPteIiea::ie.dn*Ass;:aetion)

(1+QEuxiPteFniea::ieodn*Ass諾 aetion)

Asintuitionwouldsuggest,thelowertherelativeproductivltyOfrookies,thelower

theequilibrium productivityOftheworkforcewillbe,unlessrookiesareas-

similatedinstantly.Longerassimilationtimesmeantheremustbemorerookies

intrainlng,andhigherexperiencedquitratesmeanmorerookiesmustbehired

tooffsetthoseexperiencedworkerswholeave.BotheffTectslowerequilibrium prodllCtivlty.

Notethattherookiequitfractionhasnoimpact(inthismodel),Becauserook-

iesarerepresentedasaslnglecohort,thosewhoqultareimmediatelyreplaced,So

rookiequltSCanceloutinthenetrateofchangeofrookies｡Ofcourse,higher rookiequltrateswouldincreasetheloadonandcostofthefirm'shumanresource

organization･Inamorerealisticmodelwheretherookiepopulationisdisaggre一

gatedintomorethanonecohort,orwherefillingvacanciestakestime,theequilib-

riumwoulddependonthequltratesOftheintermediatestocks.

Asanexample,Supposetheassimilationdelayis100weeks(about2years)

andexperiencedemployeesremainwiththefirmforanaverageof10years(the

experiencedquitfractionisO･002/week),Assumerookieemployeesquitata

higherrateofO.01/weekassomeoftherookieswashoutordecidethejobdoesn't

suitthem.Assumetheaveragerookieisonly25%asproductiveasexperienced

workers･Theequilibriumrookiefractionisthen%,andequilibriumproductivltylS O･8750ftheexperiencedlevel･8

8withoutlossofgenerality,theproductivltyOfexperiencedemployeescanbedefinedas1, allowingpotentialoutputtobemeasuredinfullltimeequivalent(FTE)experiencedpersonnel.

Chapter12 CoflowsandAgiTlgChains 493

TheassimilationdelayandrookieproductivityfractionJOlntlydeterminethe

learnlngCurvefornewemployees･Imaginehiringagroupofrookieemployees whentherearenoexperiencedemployees.ProductivltyInitiallywillbetherookie

productivityfractionandultimatelywillbeloo鞄oftheexperiencedlevel.Be- causetheassimilationprocessisfirst10rder,productivltymustapproachlOO%ex-

ponentiallywithatimeconstantequaltotheassimilationdelay.Iftheevidence

suggestedthelearningCurvefornewemployeeswasnotfirst-order,thepromotion

chaincouldbedisaggregatedfurthertoyieldtheappropnatepattemofproductiv- 1tyadjustment.

Whathappensifthe丘rmisgrowing?Figure12-12showsasimulationin

whichtheworkforcegrowsatanexponentialrateof50%/year(0.01/week),startl

1nglnWeek5.Theinitialnumberofexperiencedworkersis1000;therefore,the

initialhiringrateis100peryear.Thehiringrateimmediatelyrisesabovethetotal

qultrate,andtheworkforcebeginstogrowat50%/year.Becauseallnewhiresare

inexperienced,therookiefractionilnmediatelybeginstoriseandaverageproduc-

tivityImmediatelybeginstofall.Inthesteadystate,therookiefractionrisesto

54%andproductivityfallstoJust59%oftheexperiencedlevel.Though everyem-

ployeegoesthroughalearnlngprocessthatboostsindividualproductivityfrom

O･25to1,theshiftintheagedistributioncausedbygrowthlowersaveragepro-

ductivlty･Consequently,glVentheparametersintheexample,potentialoutput

(shownonthegraphinFTEexperiencedemployees)barelychangesforthefirst

6monthseventhoughthetotalworkforceandpayrollbegintoriseimmediately･

Afterayear,potentialoutputhasrisenbyonly36%comparedtothe50%growth intotalemployees･9

12乱8 Mentor岳ngandOmJ的e-JobTraining

Inthemodelsofarrookieemployeesgalnexperienceautomaticallyandwithout

cost･Inreality,on-thejob(OTJ)trainingoftenrequiresthehelpandmentoringof

experiencedemployees･Inexperiencedworkersreducethetimeexperiencedpeo-

plecandevotetotheirownjobsbyaskingquestionsandbycausingexperienced

peopletoworkataslowerrate･Modifyingthemodeltoaccountfortheimpact

ofmentorlngrequlreSreformulatingpotentialoutputasdependingonthenumber ofEffectiveExperiencedEmployees:

pstuetnpti:1-frx.pdeunftTvci:yd*(pr;:d:ucOct:venity*EmR,olO.?eeesIEEXE:f:perl:iety::C:esd) (12132)

wherethee-ffectivenumberofexperiencede王TnPloyeesisthetOtal王Iulmberlessthe

timedevotedtotrainlngtheinexperiencedemployees.Thatis,

Effectivmep?.xypeeer㌘nced-MAX(0,EEX:e,rli.eyneceesd-TraTi;negSRP.e.niies) (12-33)

9Notethatthepatternofadjustmentofproductivltyandtherookiefractionisexponential,a directconsequenceofthefirst10rderassimilationrate･Amorerealisticmodeldisaggregatlngthe rookiepopulationintomorecohortswouldshowanevenslowerincreaseinpotentialoutput･

494

FIGURE12-12

Responseoftwo- 1evelpromotion chaintogrowth

Thetota一work-

forcegrowsat 50%/yearstarting inweek5.The RookieProduc-

tivityFraction-

0.25,TheAssimi-

lationDelay-

100weeks,

theExperienced QuitFracrl0n-

0.002/week, andtheRookie QuitFraction-

0.01/week.

PartIV ToolsforModelingDynamicSystems

0 50

よ ¢a き

＼ a

rd o ad

8000

6000

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o> 4000 a .

≡ 山

2000

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0.8

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0.2

0.0

150 200

千Po1:entialOutput

._,__.]___..-..一一.-..:I:二二㌦少や沖 Ro.kies

_■■■"-■■-.■一一■■■-■■一■■-■■■-■I■】■-■--l■柵姐が榊が-Ⅳ沖が中村ががが洲がゆががh--〟

0 50 100 150 200 Weeks

Average Productivity

洲 ,-u- -..:.=.=く...-.-.-.､.-.榊こ.脚､'γ.､､~仙≠ ･.-.(∫-

Rookie

0 50 100 150 Weeks

TrainingRoohes-Rookies*FractionofExperiencedTime

TimeSpent

RequiredforTrainlng (12-34)

EachrookieconsumesanamountofexperiencedworkertimeequaltotheFraction

ofExperiencedTimeRequiredforTraining.Underextremecircumstances,the

numberofrookiesmightbesohigh,Ortheirtrainingdemandsmightbesogreat,

Chapter12 CoflowsandAgingChains 495

thatthetimeremainingforexperiencedworkerstoactuallydotheirjobsmayfall tozero.10

Mentorlnghasonlyasmallimpactontheequilibrium productivltyOfthe

workforce.Equilibriumproductivityforthecaseofmentorlngbyexperienced

workersiseasilyfoundtobe

Average

Productivityeq

Experienced

Productivity

Rookie

Productivlty Fraction

Fractionof

Experienced

TimeRequired

forTraining

Experienced

* Quit * Fraction

(1 +Experienced*Assimilation QuitFraction Time

(1 2-35)

Withtheparametersintheexampleaboveandassumlngaratherhighvalueof0.5

forthefractionofanexperiencedemployee'stimeconsumedintrainingeach

rookie,productivitylnequilibriumfallsto79%oftheexperiencedlevel,compared

to87.5%inthecasewithnomentoringbyexperiencedworkers.

Whilementoringhasonlyamodesteffectonequilibriumproductivlty,theim-

pactonproductivltyandpotentialoutputwhentheworkforceisgrowlngisdra-

matic.Figure12113showstheeffectofmentorlnginthesamescenarioasFigure

12-12.Inthesimulation,eachrookierequlreSmentOringbytheequlValentof0.5

experiencedpeople･Therookieandexperiencedemployeestocksfollowthesame

trajectory,butnow,astherookiefractionrises,thetotaltimespenttrainlngrook-

iesgrows,andthetimeexperiencedworkerscancontributetoproductiondrops.

Giventheparameters,productivityfallstoasteadystatevalueofO･32,Compared

t00.59inthecasewithnomentorlng,adropof46%.Intheshortrun,growthac-

tuallycausespotentialoutputtofall.Potentialoutputdropstoaminimum9%be-

lowtheinitialequilibriumandonlyreachestheinitiallevelafter67weeks.

Thelnteractio!1SOfTrainingDe一aysandGrowth

Thetrainlngmodelinsection12.1.8showsthatthehigherthegrowthrateofthe

laborforce,thelowerthesteadystateexperiencelevelandproductivityWillbe.

1. UsingthemodelwithOTJtrainlng,deriveanalgebraicexpressionforsteady

stateproductivityasafunctionofthegrowthrateandotherparameters,including

thefractionalqultrateOfexperiencedemployees,theassimilationtime,therelative

productivltyOfrookies,andthefractionofexperiencedtimerequiredfortrainlng･

lOMorerealistically,productionpressureswillslashthetimedevotedtotrainingrookiesbelow whatisrequiredlongbeforethenumberofeffectiveexperiencedemployeesfallstozero･Therefore tobefullyrobust,theassimilationtimeshouldbereformulatedasavariable,rislngWhentotalmen- tonngtlmeislessthanrequired･

496 PartIV TわolsforModelingDynamicSystems

8000

6000

の dJ q)

o> 4000 凸.

≡ LJJ

2000

4000

3000

07dJ4) o>2000 a.≡uJ

IOOO

1.0

0.8

⊂ 0.6 .9 O 応

丘 0･4

0.2

0.0

Potential Output

0 50 100 Weeks

150 200

Experienced Employees

＼ TimeSpent TrainingRoOkies

--___-_________ _______________---------------ムー-----

0 50 100 150 200 Weeks

Average

ProductivityRookie

0 50 100 150 200 Weeks

Howdotheseparametersaffectthelossofproductivltyinthesteadystateas

growthratesincrease?

2. Thecurrentmodelassumestheleam1ngandassimilationprocessisfirst10rder.

Inmanyhigh-Skillsettingsthisisunrealistic.Modifythemodeltoincludeathirdl

ordertrainingandassimilationprocess(Withthesamefractionalrookiequitrate

andaverageassimilationtime)iAssumerookieemployeesareequallylikelytoquit

ineachofthethreetraineecategoriesyoucreate.Besureyoumodifythetotalhir1

1mgratetOreplaceallemployeeswhoquit.EachcategoryofrookiesstillrequlreS

Chapter12 ConowsandAgingChains 497

thesametimefromexperiencedemployeesthroughOTJtrainlngandmentorlng. Ⅰnitially,assumetheproductivltyOfallrookiesisstill0.25也atofexperienced workers.RepeatthetestshowninFigure12-13(inwhichgrowthataconstant fractionalratebeginsfromaninitialequilibrium)･Next,assumemorerealistically thatrookieproductivityis0,0.25,and0.50thatofexperiencedworkersforrook- iesinstages1,2,and30ftheirtrainlng,reSpeCtively･Whatistheimpactofa higher10rdertrainingProcessOnthetransitionfromstabilitytogrowth?

3.Inmanyorganizations,suchasconsultingfirms,lawfirms,andotherprofes-

sionalserviceorganizations,experiencedemployeesnotonlymentorJuniorem- ployeesonthejobbutalsoparticipateinrecrultlngnewemployees.Modifythe modeltocapturethelossofproductivetimeduetorecrultlngeffort.Assumere- cruitlngeachnewemployeerequlreSaCertainfractionofanexperiencedperson's time(rookiesdonotparticipateinrecruiting).Paycarefulattentiontotheunitsof measure.Selectparameterstorepresentthecaseofconsultingfirmsrecrultlng MBAstudents.Theleadingconsulting丘rmsinvestheavilyintherecrultlng process･Besideson-campusrecrultlngeventsandinterviews,promlSlngCandト datesfacesecond,third,andoftenfourthroundsofinterviewsatcompanysites duringwhichtheymeetmanyseniormembersofthefirm･Seniorpeoplemustthen devotefurthertimetodiscussionandselectionofthefinalists.Further,manycan- didatesmustbeinterviewedforeachoneultimatelyhired.Maketheselectivityof thefirmanexplicitparameterinyourmodel,measuredasadimensionlessratioof thenumberofoffersmadepercandidateconsidered.Alsointroduceaparameter reflectingthefractionofoffersaccepted(theyield).Usingyourestimateofthese parametersandthetimesenioremployeesinvestinrecrultlngeachcandidate,run themodelforvariousgrowthrates.Whatistheimpactofrecruitingeffortonaver- ageproductivityandeffectiveproductioncapacity?Wh atistheimpactofgrowth onthetimeseniorpeoplehaveavailableforrevenue-generatingactivities?What wouldhappenifthe丘rmtriedtocutbackonthetimeseniorpeopleinvestinre- cruiting?Whatwouldhappenifthefirm becamelessselective?Ifthereputationof the丘rmdeclined,erodingtheiryield?Developacausaldiagramshowinghowpo- tentialoutputandaverageproductivitymightfeedbacktoaffectthefirm'sability todeliverhigh-qualityresultstotheirclientsandtorecruitandretainthebestcan- didates.Wh ataretheimplicationsforthegrowthstrategyofafirm?

12.2 CoFLOWS:MoDEuNGTHEATTRlBUTESOFASTOCK

ThestockandflOwnetworksdevelopedthusfarkeeptrackofthenumberofitems inastockandflowchain.Thesizeofastockindicateshowmuchmaterialisinthe

stockbutdoesnotindicateanythingaboutotherattributesoftheitems.Amodelof afirmmightincludestocksfordifferentkindsofemployees,butthesestocksonly indicatehowmanyemployeesthereareanddonotrevealhowproductivetheyare, theiraverageage,theirtraininglevel,orothercharacteristicsthatmightbeimpoト

tantforthemodelpurpose･Oftenitisnecessarytokeeptrackofattributessuchas theskillandexperienceofworkers,theproductivltyOfmachinetools,thedefects embodiedindesignsmovlngthroughaproductdevelopmentprocess,orthebook valueofafirm'sinventory.Conowstructuresareusedtokeeptrackofthe

498 PartIV ToolsforModelingDynamicSystems

attributesofvariousitemsastheytravelthroughthestockandflowstructureof asystem･

Asanexample,consideramodeldesignedtohelpacompanyunderstandhow

fastnewtechnologycanbedeployedandhowitchangesthenumberofworkersit

needs.Eachmachine也ecompanybuys丘.omequipmentSuppliersrequlreSaCer-

tainnumberofworkerstooperateit.Overtime,astechnologyImproves,thepro-

ductionprocessgrowsmoreautomatedandfewerworkersarerequired.The

companylSinterestedinknowinghowquicklythenew,labor-savingmachines

willbedeployedandhowfasttheirtotallaborrequlrementSWillchange.

Asimplemodelofthesituationbeginswiththefirm'sstockofcapitalplant

andequlpment,Suchasmachinetools･Thecapltalstockisaugmentedbycapital

acqulSltlOnSandreducedbycapitaldiscards.Forsimplicity,assumethediscard processisfirst-order:

CapitalStock (12-36) -INTEGRAL(CapitalAcquisition-CapitalDiscards,CapitalStock(to))

CapitalAcquisition-Exogenous (12-37)

CapitalDiscards-CapitalStock/AverageLifeofCapital (12-38)

ThetotallaborrequlrementSOfthefirm areequaltotheproductofthenumberof

machinesinthefirm'SplantsandtheaveragelaborrequirementsOfeachmachine:

TbtalLaborRequirements-CapitalStock*AverageLaborRequirements(12-39)

HowshouldaveragelaborrequlrementSbemodeled?Obviously,ifanewtypeof machinerequlrlngOnlyhalfasmanyworkerssuddenlybecameavailable,theav-

eragelaborrequlrementSWOuldchangeonlyslowlyasthenewmachinesgradually

replacedtheexistlng,laborintensivemachines.Thereisadelaybetweenachange

inthelaborrequirementsavailableinnewmachinesandtheadjustmentofaverage

laborrequirements.SimilarconsiderationsapplytootherfactorInputstOthe

productionprocesssuchastheenergyrequirementsOfthemachines,theirtotal

productivlty,andsoon･ItistemptingtOmodeltheadjustmentofthesefactorre-

quirementsaSaSimpledelaywheretheadjustmenttimeisequaltotheaveragelife

ofcapital:

AverageLaborRequlrementS (12-40) -SMOOTH(LaborRequirementsofNewCapital,AverageLifeofCapital)

However,thedelayformulationisfundamentallyflawedandwillleadtosignifi- canterrorsifthecapitalstockisnotinequilibrium.AnextremeconditionstestexI

posesthedefectintheproposedformulation.Supposethefirm'sequipment

suppliersintroduceanewtypeofmachinethatrequlreSOnlyhalfasmanyworkers.

Nowsupposethatatthesametime,the丘rmstopsbuyingnewequipmentalto一 gether(say,becauseofarecession).Thefirm thenmustcontinuetousetheexistl

lng,inefficientmachines,andthereisnochangeintheaveragelaborrequiredper

machine.However,thedelayinequation(12-40)willcontinuetoadjustaverage

laborrequirementstOthenew,lowlevelofthenewmachineseventhoughthefirm

isn'tbuyingany.Thefirm'srequiredlaborfTorcefallsasthedelaymagicallycon-

vertstheoldmachinestotheproductivltyOfnewoneswithouttheneedforanyIn-

vestmentorexpenditure･TherateofchangeinaveragelaborrequlrementSdepends

Chapter12 ConowsandAgingChains

FIGURE12-14 Coflowtotrackthelaborrequirementsembodiedinafirm'scapitalstock

Exogenous Capital

Acquisition Rate

CapitaE Acquisition

Requirements

Labor

RequlrementSOf NewCapitaf

CapitalStock

AverageLabor Requirements

Labor

RequlrementS

Average Lifeof

Capital

Capita一 Discards

Decreasein Labor

Requirements

499

Ontheratesatwhichnewmachinesareaddedtoandoldmachinesarediscarded

fromthecapitalstock.ThelaborrequlrementSOfthefirm 'sequlPmentareembod-

iedinthemachinesthemselves.Modelingtheadjustmentasadelaydivorces

changesinthisattributeofthestockofmachinesfromchangesinthestockitself.

TomodelsuchasituationrequlreSthemodelertokeeptrackofthelaborrequire-

mentsofeverymachineaddedandeverymachinediscarded.Coflowstructures

allowyoutodothis･ll

Figure12-14Showsthestructureforthecapitalstockmodeldescribedabove.

Thecoflowisastockandflowstructureexactlymirronngthemainstockandflow

structure.ThecoflOwtracksthelaborrequirementsembodiedinthecapitalstock

asnewmachinesareacquiredandoldonesarediscarded.

Thestockofcapitalisaugmentedbvacquisitionsandreducedbvdiscards.For

now,thecapitalstockistreatedasafirst10rderprocess.ThecapltalacqulSltionrate

isexogenous.

llsometrytosavethedelayformulationinequation(12140)bymakingtheaveragelifeof capitalavariableorrepresentingtheadjustmentprocesswithahigherl0rderdelay,butthecritique remainsvalid.Infact,therearemanymodelsintheliteraturewheretheadjustmentofinput requlrementSismodeledasadelay,1nCludingawiderangeofeconometricmodelsofenergyde一

mandinwhichtheenergyintensityoftheec?nomy(BTU/蛋ofoutputorBTU/yearperSofcapital stock)areasヲumedtoadjusttochangesinprl誓withsomeformofdistributedlag,independentof thecharacteristics,size,orturnoverofthecapltalstocksconsumlngthatenergy.

500 PartIV ToolsforModelingDynamicSystems

Thetotallaborrequiredtooperatethecompany'SexistlngmachinesisglVen

bytheLaborRequlrementSStock.Everytimeanewmachineisaddedtothecapl-

talstock,thetotallaborrequlrementSOfthefirmrisebythelaborrequiredforthat

machine.Everytlmeamachineisdiscarded,thetotallaborrequlrementSdecrease

bytheaveragelaborrequirementsOfthediscardedmachine:

IncreaseinLaborRequirements -CapitalAcquisition*LaborRequirementsOfNewCapital

(12-41)

Forexample,ifeachmachinerequlreS,Say,100workers,thenapurchaseof

10machinesincreasestotallaborrequlrementSby1000people･Sincethediscard

processisassumedtobefirst10rder,theprobabilityofdiscardisindependentofac-

quisitiontimeandofanyotherattributesofthecapitalstock.Therefわretheaver-

agelaborrequlrementSOfthediscardedmachinesequaltheaveragefortheentire

existlngStock.ThataverageisglVenbythetotallaborrequirementsdividedbythe

totalcapitalstock.Thus

DecreaseinLaborRequirements -CapitalDiscards*AverageLaborRequirements

(12-42)

AverageLaborRequirements-LaborRequirements/CapitalStock (12-43)

Reqtia,be:ents-INTEG可 RIenqctri:r:eSEreinnts-R:uiir:eebaaree:S,Requitea:Oernts(b)) (12-44)

Ifeachexistingmachinerequired200workers,thenthediscardof10machines

wouldreducelaborrequlrementSby2000people.Thereplacementofthesema-

chineswithnewonesrequlrlng100insteadof200peoplereducestotallaborre-

quirementsby1000people.

Thecoflowstructurehassomeobviousanddesirableproperties.Inequilib-

rium,capitalacqulSltionsanddiscardsareequal,and,if血elaborrequlrementSOf

newcapitalareconstant,thelaborrequlrementSOfthe丘rmwillalsobeconstant,

sincethelossofjobsassociatedwithdiscardedmachinesjustoffsetstheincrease

inlaborrequiredtooperatenewones･TheequilibriumlaborrequlrementSOfthe

firmwillbeLaborRequlrementSOfNewCapital*CapitalStock･ ChangesincapitalacqulSltlOnOrdiscardshavenoeffectonaveragelaborre-

qulrementSaSlongasthelaborrequirementsOfnewcapitalremainconstant･Now

imaglnethatanewlabor-savlngtechnologysuddenlybecomesavailablesothatall

newmachinesrequireOnlyhalfasmuchlabor.Figure12-15showstheresponseof

laborrequirementsovertime.Asexpectedgiventhefirst10rderstructureflorthe

capitaldiscardrate,thelaborrequlrementSOfthefirmapproachthenewequilib-

riumexponentially,withatimeconstantglVenbytheaveragelifeofcapital.

Iftheresponseofthesystemissimpleexponentialdecay,whyisacoflowfor-

mulationneeded?ThebehaviorshowninFigure12-15isexactlywhatwouldbe

generatedbythedelayformulationinequation(12140)IWhynotsimplymodelthe

adjustmentofaveragelaborrequlrementSWiththesimpleandeasytoexplainde-

lay?TheansweristhattheresponseofaveragelaborrequlrementSdependson血e

Chapter12 ConowsandAgingChains

FIGURE12･15

ResponseoHabor requJrementStO asudden50% reductioninthe

laborrequired tooperatenew machines

FIGURE12-16

Changesinthe growthrateof thestockalterthe

adjustmentofits attributes

lnallcasesthel∈ ト

borrequlrementS ofnewcapitaldrop by50%inyear51 Theresponsesin situationsof

10%/yeargrowth incapitalacquJSi- tions,equiJibrium, and10%/yearde- cHneinacqu∫si- tionsareshown.

1!u

n lt2)!dt23P rdood

■■l

n lt! l

!d t2

0P l

doa d

Average 1㌔hLaborRequirements

ofCapitalpI++4㌔一㌔叫〇枚や〇㌔e々一%a○>叫"I-和独叫.叫hv.叫〝1-x-bT叫"側軸Mm-nW《wyツ出納榊▲"Uv- LaborRequirements

20 40 60 80 100 Years

Average l訊. LaborRequirements ･､> ofCapital

＼ ◆㌔ -q ～ h｡戦わ.l‰℡

◆叫★←ーI←-◆ー★-★.-十I一一一1†ー-十一--一一一-帆-一一◆､--I--+.-†叫仙_…小､ 10%〝earDeclineinhvestment

ヽヽ＼＼

10Go:0./ニ;har＼ Jlul,ibrium～--∫..-一一≠ 一一一一■-I__- ～.------L--1---叩..._..一...一..

LaborRequirements

501

0 20 40 60 80 100 Years

behavioroftheacqulSltlOnanddiscardrates･Inequilibrium,withconstantacqui-

sitions,discards,andcapitalstock,thecoflowbehavesexactlylikeafirst10rderdel

laywithatimeconstantequaltotheaveragelifeofcapital.Butnowsupposethe

firmisgrowing,SOtheacqulSltlOnraterisesexponentiallyatsomerate.Newma-

chineswillbeaddedeverfaster,quicklydilutingthecontributionofoldmachines

toaveragerequirements.Orsupposethediscardratevarieswiththeutilizationof

thefirm'scapitalstock･Inthesecasestherateatwhicholdmachinesarereplaced

variesovertimeandsotoowilltheevolutionofaveragelaborrequlrementS･Fig- ure12-16Comparesthebehavioroflaborrequirementsinstationaryequilibriumto

thecaseswheretheacqulSltlOnrategrowsatlo啄/yearandwhereitshrinksat

lo啄/year.

Whenthecapltalstockisgrowlng,newmachinesareaddedatanever-greater

rate,SonewmachineswithlowlaborrequlrementSquicklydominatethestockof

capital･Averagelaborrequirementsfalltothenewlevelafteronlyabout35years,

comparedtomorethan90yearsintheequilibriumcase･Evenmoreinterestlng,1n

thecasewherethefirm isshrinkingatlO%/year,newinvestmentquicklybecomes

sosmallthataveragelaborrequlrementSneverreachthenewlevel.Afterabout

20years,newinvestmentisnegligibleandthefirmisstuckwithacapitalstock

consistlngPrlmarilyofold,inefficientmachines.Byexplicitlymodelingthe

502 PartIV TわolsforModelingDynamicSystems

attributesoftheitemsflOwlngIntoandoutofthestockofmachines,thecoflow

modelcorrectlytrackschangesinthetotalandaveragelaborrequlrementSOf thefirm.

ThelaborrequlrementSexamplecanbegeneralizedtoanyattributeofany stock.Figure12117showsthegenericstructureforacoflowforthecasewhere

thereisasingleinnowandsingleoutflowtothestock Ingeneral,themainstockmayhaveanynumberofinnowsandoutflows,say

minflowsandnoutflows:

Stock-INTEGRAL(TotalInflow-TotalOutflow,Stock(to)) (12-45)

rnl

TotaHnflow- ∑ Inflow(i) (12-46) 】-】

∩

TotalOutnow-∑outflow(j) (12-47)｣-1 0utflow(j)-Stock/AverageResidenceTimeforOutflow(j) (12148)

Eachoutflowismodeledasafirst-orderprocesswithanoutflow-specifictimecon- stant.Thetimeconstantscanbevariables.

ThecoflOwstructuretrackingtheattributeofthestockexactlymirrorsthe structureofthemainstock.EachunitflOwingIntothestockaddsacertainnumber ofattributeunitstothetotalattributestock,Intheexample,eachnewmachine addsacertainnumberofworkerstothetotalnumberrequiredtooperateallthe machines･Thenumberofattributeunitsaddedperstockunit,denotedthemarginal attributeperunit,candifferforeachinflow.Forexample,thefirmmightbuydif- ferenttypesofmachines,eachrequlrlngadifferentnumberofworkerstooperate it.Thus,

At7roiEalte-INTEGRAL(InACt;eSb:uttT-DAetC:rn芸aa:I;ei,nAttrTbO::t(t｡)) (12-49)

lHI

TotalIncreaseinAttribute-∑ MarginalAttributeperUnit(i)*Inflow(i)(12-50)l=1

Similarly,foreachoutflowfromthemainstockthereisacorrespondingdrainfrom thetotalattributestock.Eachunitleavlngthestockremovestheaverageattribute perunit.Theaverageattributeperunitissimplythetotalattributeleveldividedby thetotalnumberofunitsinthestock:

TotalDecreaseinAttribute-∑ AverageAttributeperUnit*Outflow(j)(12-51)J-1 AverageAttributeperUnit-TわtalAttribute/Stock (12-52)

Youcanmodelasmanydifferentattributesasyoudesire,eachcapturedbyasep- arateconowstructure.Forexample,onecoflOwmightrepresentthelaborrequire-

mentsofthefirm'scapitalstock,anothermightrepresenttheenergyrequirements,

athirdmightrepresenttheproductivityofthemachines,afourthmightrepresent thedefectrateintheoutputofthemachines,andsoon.

Chapter12 CoflowsandAgingChains 503

FIGURE12-17 Genericcoflowstructure

EachunitflowIngintothestockaddsthemarglnalattributetothetotalattribute.EachunitfIowIngOut removestheaverageattribute･lngenera一,therecanbeanynumberofinflowsandoutflowstothemain stock,eachwithacorrespondingflowintothetotalattributestock.

AverageResidence Timefor1Outflow

Co刊ows

BuildandtestcoflowsforthefollowlngSituations:

l･Afirmmaintainsamake-t0-Ordersystemforitsproducts.Theorderbacklog

isincreasedbytheorderrate;itisdecreasedasordersarefulfilledandbyorder cancellations.Assumetheaveragedeliverydelay(theorderfulfillmenttime)is constantandequalto4weeks.Assumealsothatonaveragei%ofordersarecan-

celledperweek.CustomerspayondeliverybutpaytheprlCeineffectatthetime theirorderwast)laced,evenif1)ricehaschangedinthemeantime.Createacoflow thattrackstheaveragevalueoftheordersinthebackloganddeterminestheaver

agepriceassociatedwiththeordersfilled.Alsoformulatetheequationforthe fim'srevenues(assumerevenueisrecordedwhenordersarefulfilled).

2･ ConsiderthenationaldebtoftheUnitedStates･Thedebtisincreasedbybor- rowlnganddecreasedbyrepayment.Therepaymentratedependsontheaverage maturltyOftheoutstandingdebt.ThemixofTreasurynotes,bills,andbondsde-

terminesaveragematurity.Assumetheaveragematurltyis5years.TheTreasury rollsovermaturingdebtandmustissuenewdebttofinanceanyfiscaldeficit.The

504 PartIV ToolsforModelingDynamicSystems

deficitisexpenditurelessrevenue.Assumerevenueisconstantat$900billion (900e9)peryear･Expendituresconsistofinterestonthedebtandspendingongov- emmentprograms.Assumeprogramspendingisalsoconstantat$900billion/year. Thesevaluesareapproximatelycorrectfor1988;in1988theoutstandingdebtwas about$2.5trillion(2.5e12).Interestpaymentsareequaltotheproductoftheouト

Standingdebtandtheaverageinterestrate.First,formulatetheaverageinterestrate asane呆ogenousconstantinitiallyequalto7%/year.Next,replicatethemodeland formulatetheaverageinterestratebyuslngaCOflow･ThecoflOwformulationacI countsforthefactthattheaverageinterestratedependsontheinterestratesat whicheachbill,bond,ornotewasissued,evenifinterestratesonnewdebthave

changed. Verifythatwhentheinterestratesinbothformulationsareconstantandequal,

thebehaviorofthetwoformulationsisidentical.Next,Comparethebehaviorof thetwofomulationsfわrthecasewheretheinterestratefallsfrom7%/yearto 3%/yearin1992.Whatdifferencedoesthecoflowstructuremake,andwhy?To approximateacontinuouscompoundingsituation,useasmalltimestep,suchas ii6year,forthesimulations.

3.Itisoftenimportanttomodeltheaverageageofitemsinastockortheaver- agedateatwhichtheitemsenteredthestock.Asanexample,consideramodelof afirm'slaborforce.Assumeaslnglestockoflabor,increasedbyahiringrateand decreasedbyanattritionrate.Assumethattheattritionrateis丘rst-orderandthat employeesstaywiththefirmanaverageof10years.Formulateacoflowthat keepstrackoftheaverageageofthepeopleinthelaborforceandalsotheaverage dateatwhichtheyjoinedthefin.Hint:Youonlyneedonecoflowstocktocalcu- lateboththeaveragedateatwhicheachpersonwashiredandtheaverageageof theworkers.Fomulatethemodelsoitbeginsinequilibrium.Demonstratethatin equilibriumtheaverageageoftheworkersisequaltotheaveragetenureinthejob plustheiraverageageat血etimeofhiring.Explore血eresponseoftheaverageage oftheemployeestov∬ioustestinputsSuchaschangesintheaveragetimepeople staywiththefirm,stepandpulsechangesinthehiringandattritionrate,andex- ponentialgrowthordeclineinthehiringrate｡Note:Thischallengerequiresthat youintroduceaflowthatalterstheattributestockforwhichthereisnocorre- spondingflowintooroutofthestockoflabor.Suchastructureiscalledanon- conservedcoflOwbecausetheattributestockcanchangeevenwhenthereisno inflowtooroutflowfromthemainstock.

4.Thecapitalstockofafirm isincreasedbyacquisitionsanddecreasedbydis- cards.Theaveragelifetimeofeachunitofcapitalis20years.Giventhecostof eachlJnitofcapltaicreateacofllOWthatlTT10delsthebookvalueofthelfirm'scapi- talstock.Assumethevalueofeachunitofcapitalisreducedbydepreciationwith anaveragedepreciationlifeofcapitalthatcandifferfromtheactuallifetime.

12.2.1 CoflowswithNonconservedFJows

Thecoflowstructuresdescribedsofarrepresenttheattributesofthestockascon- seⅣedquantities:theonlywaythetotalattributestockcanchangeisthrough血e

Chapter12 CoflowsandAgingChains 505

infloworoutflowofaunitfromthemainstock.Often,however,theattributesasI

sociatedwithastockcanchangewithoutanychangeinthemainstock.Retrofits

canchangethelabororenergyrequirementsOfafim'scapitalstockeventhough

thefirm doesn'tbuyordiscardanynewequlPment･Thevalueofafirm'sinventory canbewrittendowntoreflectchangesinitsmarketvaluethoughthephysicalin- ventoryltSelfdoesn'tchange.Inthesecases,thetotalattributeassociatedwitha stockisnotconservedandthecoflowstructureincludesadditionalflowsintoor

outofthetotalattributestock,flowsforwhichtherearenocorrespondingflowsaf- fectingthemainstock.

SupposeasinFigure12118youaremodelingafirm'slaborforce,whichis increasedbyhiringanddecreasedbyattrition.Forthepurposesofthisexample, thehiringrateand血.actionalattritionrateareassumedtobeexogenous,thoughin

FIGURE12-18 ExampleofanonconservedcofIow:trackingtheexperienceofalaborforce

Newemployeesbringacertainamountofexperiencewiththem;departingemp一oyeestaketheir experiencewiththem･lnaddition,experienceincreaseswithtenureinthejobanddeclinesasworkers forgetoraschangesintheprocessmakeexistingexperienceobsolete.

Fr.actional AttritionRate

506 PartIV ToolsforModelingDynamicSystems

generaltheywillbemodeledasendogenousvariables.ThecoflOwmeasuresthe

averageandtotaleffectiveexperienceoftheworkforce,ThestockTotalEffective

Experience(measuredinperson-weeks)istheeffectivenumberofweeksofser-

viceeachemployeehas,summedoverallemployees･Eachemployeehiredbrings

acertainamountofeffectiveexperience.Employeesleavlngthelaborforcetake

theaverageexperiencewiththem:

AverageExperience-TotalEffectiveExperience瓜aborForce (1 2-53)

TotalEffectiveExperience-INTEGRAL(IncreaseinExperiencefromHiring +IncreaseinOn-the-JobExperience-TLossofExperiencefromAttrition -ExperienceDecayRate,TotalEffectiveExperience(t.)) (12-54)

IncreaseinExperiencefromHiring -AverageExperienceofNewHires*Hiring (12-55)

LossofExperiencefromAttrition-AverageExperience*Attrition (12-56)

Eachemployeeaccruesadditionalexperienceattherateof1weekperweek

worked.Inthisexample,theunitoftimeforthesimulationistheyear,whileaver-

ageexperienceismeasuredinweeks･Theincreaseintotaleffectiveexperienceis

thenumberofweekseachpersonworksperyearsulnmedovertheentirelabor force:12

IncreaseinOn-the-JobExperience -LaborForce*WeeksWorkedperYear

(12-57)

Finally,effectiveexperiencealsodecaysaspeopleforgetrelevantknowledgeand

aschangesintheproductionprocessrenderexperienceobsolete･Thefractional

decayrateisassumedconstantherebutmightvarywithchangesinorganizational

structureorprocesstechnology｡Thetotallossofexperienceistheaveragelossof

experiencesummedovertheentireworkforce:

ExperienceDecayRate -LaborForce*AverageExperience*FractionalExpehenceDecayRate(12-58)

BecausethestockofeffectiveexperienceismodifiedbythenonconservedflOws

ofexperienceaccrualanddecay,theequilibriumexperienceoftheaverageworker

willnot,ingeneral,equaltheaverageexperienceofnewhires,asitwouldina

conservedcoflow.Inequilibriumthesumofthefourratesaffectingtotaleffective

experiencemustbezero.WhenhiringandattritionarealSoequalsothelaborforce

isinequilibriumwithHiring-Attrition-Labor辛FractionalAttritionRate,a

littlealgebrarevealsequilibriumaverageexperiencetobe:

12Timeinthesimulationofthisexamplelsmeasuredinyears,whileexperienceismeasuredin weeks.Thereisnocontradiction.Considertheunitsofequation(12-57).TheincreaseinOTJex- perienceismeasuredinperson-weeks/year,determinedbythelaborforceandtheaveragenumber ofweeksworkedeachyearJftimewasmeasuredinmonths,血eIncreaseinOn-the-JobExperience wouldbethelaborforcemultipliedbythenumberofweeksworkedpermonth.Notethatthe

numberofweeksworkedperyearwillnotingeneraleqtla152.ⅥlCationtime,sickleave,strike s ,

orpromotiontomanagementallreducetherateatwhichemployeesaccumulateexperience･

Chapter12 ConowsandAgingChains

Average

Experienceeq

Fractional *AverageExperience Weeks AttritionRate ofNewHires + per

(A慧?t諾nonRaiteIFractlBencaLyE;pa:erience)

507

Equilibriumtotaleffectiveexperienceissimplytheequilibriumaverageexperi-

encemultipliedbythelaborforce.Asexpected,thegreatertheexperienceofnew

hiresorthenumberofweeksworkedperyear,thegreatertheequilibriumaverage

experiencewillbe;thefasterexperiencedecaysorpeopleleavetheorganization,

thelowertheequilibriumexperiencelevelwillbe.

Greateraverageexperienceshouldtranslateintogreaterproductivity,higher

quality,andlowercost･LeamlngCurvetheoryprovidesavarietyofmodelstore-

lateexperiencewithaprocesstoattributessuchasproductivity,quality,orcost.

Onecomm onfolmulationforthelearningCurvepositsthatproductivltyrisesbya

glVenpercentageWitheachdoublingofrelevantexperience:

Productivity-ReferenceProductivlty* AverageExperience

(12-60)

whereReferenceProductivityistheproductivltyattainedattheReferenceExperi-

encelevel.TheexponentcdeterminesthestrengthoftheleamlngCurveandis

equalto

c=log2(I+fp)-1n(1+fp)nn(2) (12161)

wherefpisthefractionalchangeinproductivityPerdoublingofeffectiveexperi- ence(seethechallengeinsection9.3.4;seealsoZangwillandKantor(1998)fora

derivationofthisandotherfomsofleamingcurves).13similarequationscouldbe usedtomodelotherattributessuchasdefectrates,meantimebetweenfailurefor

equlpment,Orunitcostsastheydependonaverageexperience.

MostleamlngCurvemodelsmeasureexperiencebycumulativeproduction,a

stockthatcanneverdecline,soproductivltyCanOnlynseovertime.Themodelde-

velopedhererepresentsproductivltyaSdependentontheaverageeffectiveexperi-

enceofeachworker.ModelinglearnlngaSaprocessembeddedinthehuman capitalofthefin meansthat,incontrasttostandardlearnlngCurvemodels,itis

possiblefortheproductivityOfthefirmtofall.ProductivityCanfallifthereisa

suddenexodusofexperiencedworkersorifthereisalargechangeintechnology

thatmakespastexperienceobsolete.

Clearly,whileworker-specificknowledgeisimportant,learnlnglSalsoem-

beddedinlonger-livedstockssuchasplantandequlpment,Organizationalroutines,

andotherinfrastructure･Cumulativeexperiencewiththeseinfrastructurescouldbe

modeledinthesamewayaseffectivelaborexperience,thoughtheseotherele- mentsoffirm infrastructurewouldhavesmallerattritionratesthanlabor.Model-

1ngPrOductivltyaSdependentonexperienceembeddedinafirm'sresourcesand infrastructure,ratherthanasafunctionofsomedisembodiednotionofcumulative

13Thefractionalchangeinproductivltyfpwillbepositivebecausegreaterexperienceboosts productivityJftheleamngCurveisusedtorepresentunitcosts,㌔willbenegativesinceincreaslng experiencereducescosts.

508 PartIV ToolsforModelingDynamicSystems

experience,allowsproductivlty,cost,Orqualitytodecayshouldexperiencede- cline,whilestandardleamlngCurvesCannotexhibitsuchbehavior.

Thereissomeevidenceforsuch"forgettingcurves."Sturm (1993)estimated leamingcurvemodelsforthenuclearpowerindus仕yinEurope,theformerSoviet Union,andtheUSA.Surprisingly,thenumberanddurationofunplannedoutages actuallyincreasedwithcumulativeoperatlngexperienceinabouthalfthecoun- tries,prlmarilyinthenationsoftheformerSovietbloc.Sturmhypothesizedthat knowledgeofsafeoperationsfellinthewakeofthepoliticalandeconomicturmoil causedbythefallofthecommandeconomies.HendersonandClark(1990)fTound thatdominantfirmsinthesemiconductorequlPmentindustryoftenlosttheirlead- ershippositionwhentherewasachangeinproductarchitecturethatrendered也e cumulativeexperienceofthefirmobsolete,erodingtheircompetitiveadvantage andallowlngyoungerandlessexperienced丘rmstoovertakethem･Accurately modelingsuchsituationsrequlreSnOnCOnServedcoflows･

TheDynamicsofExper始nceandLearning

ExplorethebehavioroftheworkforceexperiencemodelinFigure12-18.Assume thehiringrateequalstheattritionrate(plusexogenoustestinputs)sothatthose leavlngareinstantlyreplaced.Assumetheinitiallaborforceis1000people.Con- siderthefollowingParameters:

FractionalAttritionRate-0.20/year.

AverageExperienceofNewHires-10weeks.

AverageWeeksWorkedperYear-50weeks/year.

FractionalExperienceDecayRate-0.10/year.

FractionallmprovementinProductivltyperDoublingofExperience

(fp)-0･30･

ReferenceProductivity-loo(widgets/week)/person.

ReferenceExperience-10weeks.

1.Whatistheequilibriumaverageexperienceperworker?Explorehowthe equilibriumvarieswiththevaluesofthediffTerentparameters.

2.Whathappenstoaverageexperienceandproductivltyifnooneeverleaves thefirm?GeneratethelearnlngCurveforacohortofnewemployeesby settingtheinitiallaborforcetoaverysmallnumber(one),Settingthe FractionalAttritionRatetozero,andthenaddingalargepulseOfnew employees(1000)atthestartofthesimulation･Withoutattrition, experiencedemployeesneverleave.Doeseffectiveexperiencerise indefinitely?Why/whynot?Whatistheequilibrium(ifitexists)for averageexperienceandproductivity?

3･ConsidertheresponseofaverageexperienceandproductivltytOChangesin thevariousparameters(fromaninitialequilibrium).Assumeemployee tumoverdoubles.Whatistheimpactonaverageexperienceand productivityandwhy?

Chapter12 CoflowsandAgingChains 509

4･Fromtheonglnalequilibrium,assumechangesintheproductionprocess accelerate,Soeffectiveexperiencesuddenlybeginstodecayattwiceits orlglnalrate･Whatistheimpactonaverageexperienceandproductivlty andwhy?

5･Wh atisthebehaviorofaverageexperienceifthefirmbeginstOgrow? Fromtheinitialequilibriumdescribedabove,assumethehiringratestarts togrowexponentiallyat30%/year.Whatisaverageexperienceinthe steadystate?Howlongdoesittaketoreachthesteadystate?Whatisthe impactonproductivity?Howdoesthebehaviorofthemodelcompareto thatoftherookie/experiencedworkermodelinsection12.1.7?

12t2.2 htegratingCofbwsandAgingChains

Theassumptionthateachunitleavlngthemainstockremovestheaverageattribute perunitisclearlyanapproximation.Inparticular,thefirst10rderstructureforthe decreaseinthetotalattributeimplicitlyassumesthatallitemsinthestockareper- fectlymixed･Asseeninchapterll,theassumptlOnOfperfectmixlngisoftennot approprlate:AbettermodelrequlreShigher-orderdelaysorahigh-orderaglng chain.Thecoflowstructure氏)rthesecaseswillexactlymirrorthestocksandflows inthehigher-orderdelayoraglngChain.

Forexample,Sterman(1980)developedageneralmodeltocapturethepro- ductionfunctionofafirmoreconomicsystem.ProductiondependsonInputsOf capital,labor,energy,andmaterials.TheselnputrequlrementSareembodiedinthe fim'scapitalstocks(asinthelaborrequirementsexample).However,economet- ricevidenceandfieldstudyshowthatthedistributionofdiscardsfromcapital stocksisnotfirsトorder;forexample,newmachinesandfacilitiesarenotnearlyas likelytobescrappedasolderunits.Thedistributionisclearlyhigher-order.Ithere- foredisaggregatedthecapitalstockintoanaglngChain,withcorresponding coflows･Ifurtherassumedthatthelabor,energy,andmaterialsrequlrementSOf capitalequipmentweredeterminedatthetimeconstructionstarts(theenergy requirementsOfanewofficebuildingcan'tbechangedsignificantlyafterground- breakingexceptbycostlyretrofit).Theresultingvintagingstructureandcorre- spondingcoflOwsfortheembodiedinputrequlrementSareShowninFigure12119. Thenumberofvintagescanbeincreasedasneededtofitthedataforthesurvival distributionofitemsinthemainaglngChain.Inthesimplifiedi-epresentationofthe modelshowninthefigure,theconstructiondelaylSassumedtobefirst10rder, whileathird-orderdelay,withacorrespondingthird-ordercoflOwstructureforthe factorrequlrementSOfcapitalunderconstruction,wouldbemorerealistic.Like- wise,capitalisdiscardedonlyfromtheoldestvintage.Ifthedatawarrantit,itis easytoincludeadiscardratefromeachvintage.Inthatcasethemodelermustalso includethereductioninthefactorrequlrementSOfeachvintagefromdiscards, equaltotheproductofthefactorintensityOfeachvintageandthediscardratefrom eachvintage.

Finally,notethatthemodelshowninthefiguredoesnotpermitchangesto thefactorrequlrementSOfcapital.Thisisknownasaputty-c′aymodelbecause factorrequlrementSCanbevariedpriortoinvestment,likeputty,butoncethefirm

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Chapter12 CoflowsandAgingChains 511

commitstoaninvestment,theembodiedfactorrequlrementSarefixeduntilthat

capitalisdiscarded(thefactorproportionshardenlikeclayfiredinakiln).Inreaレ

Ity,retrOfits,maintenanceactivlty,andwearandtearcanalterthefactorrequlre- mentsofexistlngCapital.Themodeliseasilymodifiedtoincorporatesuchchanges

infactorrequirements(Sterman1980developsageneralmodelofproductionin- cludingavariableretrofitpotentialwhichallowsthemodelertospecifyanydegree ofvariabilitylnthefactorrequlrementSOfexistlngCapital,frompureputty-clayto fullputty-putty).

ModelingDesignWinsintheSemiconductorIndustry

Sectionll.6describesthedesignwinmodelthatSymbiosusestoforecastitsreve-

nues･ThemodelconsistsofanaglngChainthattracksthenumberofdesignwins forSymbiosproductsastheymovefromtheinitialcommitmentofthecustomer

topurchaseaSymbioschipthroughdesign,prototyplng,andproduction,finally generatingaflowofrevenues.Ateachstagethereissomeprobabilitytheproject willbecanceledbythecustomer.AsshowninFigurell-25,themodelincludesa coflOwstructuretokeeptrackoftheanticipatedproductionvolumesassociated witheachdesignwin.

BuildamodelcorrespondingtotheaglngChainwithcoflowstructureforde-

slgnWinsshowninFigurelト25.Thoughtheactualmodelrepresentseachstage (designsunderdevelopment,prototyplng,anddesignsinproduction)asahigh- orderdelay,forthischallengeassumeeachtransitionrateisfirst-order.Includein yourmodelacancellationrateforeachofthethreestages(theseflowsarenot

showninthefigure).Ensurethatyourmodelisinitializedinequilibrium.Select reasonableparameters.

Symbios,likethesemiconductorindustrylngeneral,experienceslargeampli- tudecyclesindemand.Simulatetheseconditionsbytestlngyourmodelwi血a fluctuationindesignwinsandintheantlCIPatedvolumeofnewdesignwins.As-

sumeasinewavewithanaverageperiodofabout4years,andassumetheantici- patedvolumesassociatedwitheachwinareatapeakatthesametimethedesign winratepeaks.

12.3 SuMMARY

Agingchainsarewidelyusedtocapturethedemographicstructureofapopulation. ThepopulationneedllOtbealivingpopulationbutcanbethestockofmachinesin aplant,thenumberofcarsontheroad,Ortheaccountsreceivableofafirm.Any

timetherateatwhichitemsexitastockandflownetworkdependsontheirage, thatis,anytlmethemortalityratesofindividualsinthestockareage-dependent, anaglngChainmayberequiredtomodelthesituationwithsufficientaccuracyfor thepurposeofthemodel.

512 PartIV TわolsforModelingDynamicSystems

CoflOwsareusedtokeeptrackoftheattributesoftheitemsinastockandflow

network.Attributescanincludetheageoftheitems,theproductivltyandexperi-

enceoflabor,theenergyrequlrementSOrleveloftechnologyembeddedinplant

andequlPment,thelevelofdefectsinproductdesigns,OranypropertythatisasI sociatedwiththeitemsinthestockandflownetwork.Coflowsareusefulinsitua-

tionswherethequalitiesoftheitemsinasystem'sstocks,aswellastheirquantlty, affectthedecisionmakingoftheagentsinthesystem.

iWtjdelingDeeis呈o呈1き:-Eak毒首唱

Amodelforsimulatingdynamicsystem behaviorTlequiresformalpolicy descriptionstospecljyhowindividualdecisionswetobemade.Flowsof informationwecontinuouslyconvertedintodecisionsandactions.Noplea

abouttheinadequacyofourunderstandingofthedecision-makingprocesses canexcuseusfromestimatingdecision-makingcriteria.Toomitadecision

pointistodenyitspresence-amistakeoffarg71eatermagnitudethanany errorsinourbestestimateofthepy10CeSS.

-JayW.Forrester(1992,pp.51152)

Priorchaptersdiscussedhowtorepresentthephysicalandinstitutionalstructureof

systems,forexample,howtorepresentstockandflOwnetworksandselectthe levelofaggregation.Thischapterexplorestheformulationofthedecisionrules representlngthebehavioroftheagents.Thedecisionrulesinmodelsmustbefor一

mulatedsothattheyareappropriateforthepurposeofthemodel･Theymustbe consistentwithallavailableknowledgeaboutthesystem,includingnumericaland

qualitativedata.Theinfomationusedinthemodelofadecisionprocessmustbe avai1abletotheactualdecisionmakers.Andallformulationsmustberobustsothat

･n10matterhowextremetheinputs,theoutputbehavesappropriately. Thechapteralsopresentscommonandimportantformulationsthatconform to

theseprinciples,thestructureandbehaviorofeachformulation,andexamples･ Theseformulationsconstitutealibraryoffrequentlyusedcomponentsfromwhich youcanassemblealargermodel.

13.1 PRINCIPLESFORMoDELINGDECIS10NMAKING

Thestructureofallmodelsconsistsoftwoparts:assumptlOnSaboutthephysical andinstitutionalenvironmentontheonehandandassumptlOnSaboutthedecision

513

514 PartIV TbolslbrModelingDynamicSystems

processesoftheagentswhooperateinthosestructuresontheother.Thephysical

andinstitutionalstructureofamodelincludesthemodelboundaryandstockand

flowstructuresofpeople,material,money,infomation,andsoforththatchar-

acterizethesystem･Forexample,Forrester'S(1969)UrbanDynami?ssoughtto understandwhyAmericaヮslargecitiescontinuedtodecaydespitemasslVeamounts

ofaidandnumerousrenewalprograms.Todosothemodelrepresentedkeyphysi-

calcomponentsofatypicalcitylnCludingthesizeandqualityofthehousingStock, commercialstructures,andotherin丘･astructure;thesize,skillmix,income,and

otherattributesofthepopulation;themowsofpeopleandcapitalintoandoutof

thecity;andotherfactorsdescribingthephysicalandinstitutionalsetting.

Thedecisionprocessesoftheagentsrefertothedecisionrulesthatdetermine

thebehavioroftheactorsinthesystem｡ThebehavioralassumptlOnSOfasimula-

tionmodeldescribethewaylnWhichpeoplerespondtodifferentsituations.Inthe

UrbanDynamicsmodel,theseincludeddecisionrulesgovemlngmigrationand

construction.Inanotherpioneeringsimulationstudy,CyertandMarch(1963)

foundthatdepartmentstoresusedaverysimpledecisionruletodeterminethe

floorprlCeOfgoods.Inessence,therulewastomarkupthewholesalecostofthe

itemsbyafixedpercentage.Ifexcessinventorypiledupontheshelves,asalewas

heldandthemarkupwasgraduallyreduceduntilthegoodsweresold.Ifsales

goalswereexceeded,thenprlCeSWereraised.Priceswerealsoadjustedtoward

thoseofcompetitors.Thenormalmarkupwasdetemi nedbytradition-itadjusted

veryslowlytowardtheactualmarkuponthegoodssold(takingaccotlntOfany

salesorotherpricechanges).CyertandMarchfoundthattheserulesforpricingre-

producedthepricingdecisionsofthestoremanagersqulteWell･1

Accuratelyportraylngthephysicalandinstitutionalstructureofasystemisrel-

ativelystraightforward.Incontrast,discoveringandrepresentlngthedecisionrules

oftheactorsissubtleandchallenglng.Tobeuseful,simulationmodelsmustmimic

thebehavioroftherealdecisionmakerssothattheyrespondapproprlately,not

onlyforconditionsobservedinthepastbutalsoforcircumstancesneveryeten-

Countered･Youmustspecifyarobust,realisticdecisionruleateverydecisionpoint inthemodel.

13.1.1 DecisionsandDecisionRu一es

Modelersmustmakeasharpdistinctionbetweendecisionrulesandthedecisions theygenerate.Decisionrulesarethepoliciesandprotocolsspecifyinghowthe

decisionmakerprocessesavailableinformation.Decisionsaretheoutcomeofthis

process･Inthedepartmentstoreexample,thedecisionruleistheprocedurefor

marKlnguPWhoiesaiecostsandacLJuStlngtnemarkupDaSedoninventoryturnover,

lTheagentsinmodelsneednotbehumandecisionmakers･Theymightbeothertypesof organisms(suchaswolvesandmooseinapredator-preymodel)orphysicalobjects(suchasthe

sunandplanetsinamodelofthesolarsystem).Inthesecases,thedecisionrulesoftheagents representthewaysinwhich血emoose,wolves,andplanetsrespondtothestateofthesystems inwhichtheyoperate.Inthesolarsystemsimulation,themodelerwouldspecifytheforcesactlng oneachmassaccordingtoeitherNewtoniangravitationorgeneralrelativlty;inthepredator-prey ease,thedecisionrulesspecifyingthebehaviorofthemooseandwolves(fertility,mortality･forag- 1ngandhuntingbehavior,migration,etc.)Wouldbegroundedinfieldandperhapslaboratorystudy.

Chapter13 ModelingDecisionMaking

FIGURE13-1 Decisionrules

govemtherates offlowin

Systems. Decisionsarethe

resultofapplylng adecisionrule totheavailable informationcues. Thecuesare

generatedbythe physicaland institutional structureofthe

system,inc山ding measurement

andreporting PrOCeSSeSI Theoutputofa decisionprocess istherateof f一owthatalters thestateofthe

System.

515

competitorprices,andsoon･ThedecisionruleleadstodecisionssuchasprlClnga particularitemat,say,$9.95.

Itisnotsufficienttomodelaparticulardecision.Modelersmustdetectand representHtheguidingpolicyMthatyieldsthestreamofdecisions(Forrester1961)i Everyrateofflowinthestockandflowstructureconstitutesadecisionpoint,and themodelermustspecifypreciselythedecisionruledetermlnlngtherate.

Everydecisionrulecanbethoughtofasaninformationprocesslngprocedure (Figure1311).Theinputstothedecisionprocessarevarioustypesofinfomation, orcues.Thecuesaretheninterpretedbythedecisionmakertoyieldthedecision. Thecuesusedtorevisepncesinthedepartmentstorecaseincludewholesalecosts, inventorytumover,andcompetitorpnces.Decisionrulesdonotnecessarilyutilize allavailableorpotentiallyrelevantinformation.Thementalmodelsofthedecision makers,alongwithorganizational,political,personal,andotherfactors,influence theselectionofcues丘.omthesetofavailableinformation.Thosecuesactually usedindecisionmakingarealsonotnecessarilyprocessedoptlmally.Cyertand MarchfoundthatdepartmentstoreprlClngdecisionsdidnotdependoninterest ratesorrequiredratesofretum,storeove血ead,trade-olfsofholdingcostsagalnSt theriskofstockouts,estimatesoftheelastlCltyOfdemand,Oranysophisticated StrateglCreaSOnlng.

Thedecisionrulesinamodelembody,explicitlyorimplicitly,assumptlOnS aboutthedegreeofrationalityofthedecisionmakersanddecision-making process.Thespectrumofpossibilitiesisbroad.Atoneextreme,somemodelsrep- resentdecisionmakersassimpleautomata,makingdecisionsbyrotefromasmall, fixedrepertoireofchoices,withoutanypossibilityoflearnlngOradaptation,Atthe otherextremeliesthetheoryofrationalexpectationswhichholdsthatdecision

51!6 PartIV ToolsforModelingDynamicSystems

makersunderstandthestructureofthesystemperfectly,nevermakesystematicer- rorsintheirinferencesaboutitsfuturebehavior,andthereforealwaysmakeopti- maldecisions(Muth1961;Miller1994;Lucas1996)･NobellaureateGaryBecker (1976,p.14)summarizedtheviewofmanyeconomistswhenhesaid,"Allhuman behaviorcanbeviewedasinvolvingpartlCIPantSWhomaximizetheirutilityfrom astablesetofpreferencesandaccumulateanoptimalam Ountofinformationltodo so]･MInthisview,notonlydopeoplemakeoptimaldecisionsgiventheinforma- tiontheyhave,buttheyalsoinvestexactlytheoptlmaltimeandeffortinthedeci- sionprocess,ceasingtheirdeliberationswhentheexpectedgaintofurthereffort equalsthecost.

13.1.2 FiveFormu一ationFundamentals

ThellatureOfadecisionprocessanditsrationalityareemplrlCalquestions血at mustbeaddressedbyprlmaryfieldstudy,experimentaltests,andothermeans. Chapters15and16discussdifferentviewsontherationalityofdecisionmaking anditsimplicationsformodelsofhumanbehavior.Butwhateveryourviewabout thesophisticationandrationalityofdecisionmaking,yourmodelsmustconform tocertainbasicprinciples(Table13-1).

TheBakerCriterion:Theinputstoalldecisionrulesinmodelsmust berestrictedtoinformationactuaHyavailabletotherealdecision makers. In1973,duringtheUSsenate'ShearingsontheWatergateburglary, rumorsflewaboutthepossibleinvolvementofPresidentNixon.SenatorHoward Baker,amoderateRepublican,keptaskingthewitnessesbeforethecommittee, "Wh atdidthePresidentknow,andwhendidheknowit?"HispolntWasthatthe presidentcouldnotbeimplicatedinthescandalifhewasunawareoftheactions ofhisstaffandsubordinates.WhenitlaterbecameclearfromtheWh iteHouse

tapesthatNixonhadknownearlyonandhadpartlCIPatedinthecoverup,Baker hadtheanswertohisquestionandcalledforNixontoreslgn･

YoumustalsoapplytheBakerCriterionwhen氏)rmulatingthedecisionrules inyourmodels.Youmustask,Whatdothedecisionmakersknow,andwhendo theyknowit?Tbproperlymimicthebehaviorofasystem,amodelcanuseasan inputtOadecisiononlythosesourcesofinformationactuallyavailabletoandused bythedecisionmakersintherealsystem.Ifmanagersofanoilcompanydonot knowthetruesizeoftheundiscoveredresourceinabasin,thisinformationcannot

beusedinmodelingtheirdecisiontodrill･Ifshipownersdonotknowhowmany shipsareunderconstructionaroundtheworld,informationaboutthissupplyline cannotbeusedasanInputtOtheirforecastsoffutureratesnortheirdecisiontoexI

pandtheirfleets.Ifproductionplannersdonotknowthecurrentorderrate,they cannotusethatinformationtosettheproductionschedule.Thetruesizeofthe basin,theactualsupplylineofshipsonorder,andtheactualorderratewillbepre- sentinthemodel,butinformationaboutthemcannotbeusedaslnPutStOtheasI sumeddecisionrulesifthesedataarenotknownbytheactualdecisionmakers.

Thepnnciplethatdecisionsinmodelsmustbebasedonavailableinformation hasthreeimportantcorollaries.

First,nooneknowswithcertaintywhatthefuturewillbring.Allbeliefsand expectationsaboutthefuturearebasedonexperience･Modelersmustrepresentthe

Chapter13 ModelingDecisionMaking

TABLE13-1

PrincIPlesfor modelinghuman behavior

517

1･ TheBakerCriterion:Theinputstoalldecisionru一esinmodelsmust berestrictedtoinformationactuaHyavaHabletotherealdecision makers.

｡ Thefutureisnotknowntoanyone.Allexpectationsandbeliefsabout thefuturearebasedonhistoricalinformation.Expectationsandbeliefs

maythereforebeincorrect.

o Actualconditionsandperceivedconditionsdifferduetomeasurement

andreportingdelays,andbeliefsarenotupdatedimmediatelyon receiptofnewinformation.Perceptionsoftendifferfromtheactual situation.

o Theoutcomesofuntriedcontingenciesarenotknown.Expectations about"whatif"situationsthathaveneverbeenexperiencedarebased

onsituationsthatareknownandmaybewrong.

2･ Thedecisionru亘esofamodelshouldconformtomanagerial practice.

oA"Variablesandrelationshipsshouldhaverealworldcounterpartsand meanlng･

oTheunitsofmeasureinaHequationsmustbalancewithouHheuseof arbitraryscaFIngfactors.

o Decisionmakingshouldnotbeassumedtoconformtoanyprl0rtheory butshouldbeinvestigatedfirsthand.

3. Desiredandactualconditionsshouldbedistinguished.Physica日 constraintstotherea‖zationofdesiredoutcomesmustbe

represented.

｡ Desiredandactualstatesshouldbedistinguished.

o Desiredandactua一ratesofchangeshouldbedistinguished. 4. Decisionrulesshouldberobustunderextremeconditions.

5･ EquHbriumshou一dnotbeassumed.EquilibriumandstabHty may(ormaynot)emergefromtheinteractionoftheelementsof thesystem.

waylnWhichpeopleform andupdatetheirbeliefsfrom informationaboutthe

currentandpaststatesofthesystem.Youcannotassumethatdecisionmakers

haveperfectknowledgeoffutureoutcomesorthatforecastsarecorrect,evenon

aVerage･

Second,perceivedandactualconditionsoftendiffer.Informationaboutthe

currentstateofasystemisgenerallynotknown;insteaddecisionsarebasedonde-

layed,sampled,oraveragedinformation.Plantmanagersmayhavesomedata

abouttheorderrate,buttheirinformationmaydifferfromtheactualorderrate.

Modelsmustaccountforthedelaysandotherimperfectionsinthemeasurement

andreportlngOfinformation･MeasurementandreportlngnotOnlyintroducedel

lays,butcanalsocreatebias,noise,error,andotherdistortions.Modelsshouldrep-

resenttheprocessesbywhichinformationisgenerated,anddecisionsshouldbe

representedasdependingonthereportedinform ation,notthetruestateofaffairs･

Third,modelerscannotassumedecisionmakersknowwithcertaintytheout-

comesofcontlngenCiestheyhaveneverexperienced.Decisionsinvolvechoosing

518 PartIV ToolsforModelingDynamicSystems

fromvariousaltematives･Thechoicesleadtoconsequences･Peopleusually(but notalways)choosethealternativetheybelievewillyieldthebestoutcome(how- evertheydefineit).Someofthealternativesmayhavebeenchoseninthepast,and thedecisionmakermayhaveagoodideaoftheirlikelyconsequences.Butothers, probablymost,haveneverbeentried,eitherbythedecisionmakerorbyanyone elsefromwhomthedecisionmakermightlean.

Economictheoryrequiresfirmstoallocatetheirresourcestothoseactivities thatyieldthehighestreturn,forexample,tochoosethemixofcapital,labor,and otherinputstotheproductionprocessthatmaximizesprofit･Butmanagersina 氏rmdon'thaveanydirectknowledgeabouttheproductivltyOfmostofthepossi- blecombinationsoftheseactivitiesandfactorlnputS.Wouldanewfaxmachinein accountingincreaseProductivitymorethanoneinpurchasing?Shouldthefirm buyanewautomatedmachinetooltoreducethenumberofworkersrequired?No oneknowswithcertaintybecausethereisnoexperienceofthesesituations.in- stead,impressionsaboutwhichinvestmentsandcombinationsofinputsmightbe mostproductivearesketchy,Incomplete,andconjectural･Theseimpressionsare gleanedovertime丘'omanecdotes,Observationsofotherorganizations,experi一 mentsthefirmmightconduct,andsoon.Informationaboutthetrueconsequences ofcontlngenCiesandchoicesthathaveneverbeenrealizedcannotbeusedinmod- els.Instead,modelsmustrepresentthewaylnWhichpeopleformexpectations aboutthelikelyconsequencesoftryingnewthings.Thesebeliefsareoftenincor- rectandslowtoadjusttonewinformation.

Thedecisionrulesofamodelshouldconformtomanagerialpractice. Everyvariableandparameterinamodelmusthavearealworldcounterpart andshouldbemeaningfultotheactorsintherealsystem｡Equationsmustbe dimensionallyconsistentwithouttheadditionoffudgefactorsorarbitrarypa- rameters･ManagersandmodelusersareJustlysusplCiousofmodelswithvariables suchas"technicaladjustmentfactor"orparam eterswithunitsofmeasuresuchas widgets2/person-mile/leapyear,suspecting,Oftencorrectly,thattheyarefudge factorsusedonlytogetthemodeltoworkandlackanyempiricalortheoretical justification.

Manymodels,especiallylnoperationsresearchandeconomics,assumedeci- sionmakingisoptlmal｡Simulationmodels,incontrast,mustmi血°thewaypeo- pleactuallymaketheirdecisions,wartsandall.Modelersmuststudythedecision processesoftheactorsinthefield,throughlaboratoryexperiments,orother means.YoushouldnotassumepeoplewillbehaveaccordingtoanyaprlOritheory, suchastheassumptlOnSineconomicmodelsthatpeoplearemotivatedbynarrow self-interestandareperfectlyrational,orthattheyarena'1'veautomatonsandun- responsivetonewinformation.

DesiredandactualconditionsshouJdbedistinguished.Physicalcon- straintstotherealizationofdesiredoutcomesmustberepresented. Weliveinaworldofdisequilibrium.Changearisesfromthegapsbetweenthede- siredandactualstatesofaffairs.Modelsshouldseparatedesiredstates-thegoals ofthedecisionmakers-fromtheactualstatesofthesystem.Thedecisionrules inmodelsshouldexplainhowtheactorswouldrespondtoproblems,Shortfalls,

Chapter13 ModelingDecisionMaking 519

pressures,andotherindicationsthatthingsaren'twheretheythinktheyshouldbe.

Goalsarethemselvesdynamic,andmodelersoftenneedtorepresentthewaythe actorsinthesystemformandupdatetheirasplrations.

Modelersshouldseparate也edesiredratesofchangeinsystemstates血･omthe

actualratesofchange･Decisionmakersdeterminethedesiredratesofchangein systemstates,buttheactualratesofchangeoftendifferduetotimedelays,re- sourceshortages,andotherphysicalconstraints.Aplantmanagermaydetermine

thedesiredrateofproduction丘.omcuessuchasinventoryandorderbacklogs,but theactualrateofproductioncannotimmediatelyrespondtochangesinthedesired

rate･Actualproductiondependsonstocksoflabor,capitalequipment,andmateri- als,alongwithlesstangiblesystemstatesincludingtheworkweek,workforceef-

fTortandskill,andprocessquality･Decisionmakerscannotinstantlychangethese statesbutcanonlyaffectthedecisiontohire,theacqulSltlOnOfnewequlPment,the rateofworkertrainlng,andsoon.Actually,managerialdecisionsonlydetermine theauthorizationofvacanciesandtheorderingofnewequlpment.Theactualrate

ofhiringandinstallationofnewequipmentdependontheavailabilityofworkers andtheabilityoftoolmakerstoproduceanddeliver.

Decisionrulesshouldberobustunderextremeconditions.complex systemsoftengeneratebehaviorfarfromtherangeofhistoricalexperience.In-

deed,onepurposeofmodelinglStOdesignpoliciesthatmovethesystemintoan entirelynewreglmeOfbehavior.Tobeuseful,thedecisionrulesinmodelsmust

behaveplausiblyinallcircumstances,notonlythoseforwhichtherearehistorical

records･Robustnessmeansdecisionrulesmustgenerateoutcomesthatarephysi- callypossibleandoperationallymeaningfulevenwhentheinputstothosedeci-

sionstakeonextremevalues.Productioncanneverbenegative.Shipmentsfroma warehousemustfalltozerowhentheinventoryofproductiszero,nomatterhow manyordersthereare.Robustnessnecessarilymeansmodelswillincludemany

nonlinearrelationships･Undernormalsituations,afim 'Sliquidityhasnoimpact onemployment.Butifcashonhandapproacheszero,afirmmaybeforcedtolay

offitsworkerseventhoughthebacklogofworkishigh andthefirmisprofitable. Theimpactofliquidityonnethiringishighlynonlinear.

EquiJibriumshouldnotbeassumed.Equilibriumandstabilitymay(or maynot)emergefromtheinteractionoftheelementsofthesystem. Theexistenceandstabilityofanyequilibriainasystememergefromtheinter- actionsofthedecisionrulesoftheagentswiththephysicalandinstitutionalstruc-

tureofthesystem.Theyarecharacteristicsofsystembehavior.Modelersshould

notbuildintotheirmodelsthepresumptionthatthesystemhasaparticularequl -

1ibriumorequilibria,Orthatanyequilibriaarestable･Instead,modelersshouldrep- resenttheprocessesbywhichdecisionmakersrespondtosituationsinwhichthe

stateofthesystemdiffersfromtheirgoals.Modelanalysisthenrevealswhether

thesedecisionrules,interactingWithoneanotheralldwiththephysicalstructure, resultinstableorunstablebehavior.

TheseprlnCiplesmayseemtobenothingmorethancommonsense.Itseems

obviousthatpeoplecan'tbasetheirdecisionsoninfomationtheydon'thave,that desiresarenotinstantlyandperfectlyrealized,andthatphysicalimpossibilities

520 PartIV ToolsforModelingDynamicSystems

are,well,impossible.Yetmanymodelsroutinelyviolatetheseprinciples.Inpar-

ticular,manyeconomicandoptlmizationmodelsassumetheagentshavecomplete

andperfectinformationaboutthepreferencesofcustomers,theproductionfunc-

tiongovernlngOutput,andotherinformationthatrealmanagersperceivethrough

afog,ifatall.Manyothersgivedecisionmakersperfectforesight,endowlngPeo-

plewithcrystalballsthatglVethemperfectknowledgeofthefutureandtheabil1

1tytOpredicthowotherpeoplewouldbehaveinhypotheticalsituations.Decision

makersareassumedtobeconcemedsolelywiththemaximizationoftheirpersonal

utility(orprofitsinthecaseofafirm).Theseassumptionsareusedtoderivethe

equilibriumofthesystem,andeithernodynamicsareconsideredorthesystemis

assumedtobestable,retumlngSWi氏lyandsmoothlytoequilibriumafterashock･2

Attheotherendofthespectrum,Somemodelsassumedecisionsaremadeby

rotefromalimitedrepertoireofoptlOnS.Thesemodelsoftenshowthatverycom-

plexbehaviorcanarise血.omextremelysimpledecisionrules.EpsteinandAxtell'S

(1996)Sugarscapemodeldevelopsanartificialsocietyinwhichagentswithvery

simplerulescompeteforresources(sugar).Complexbehaviortheyinterpretas

coalitionfomation,trade,andwararisesfromtheinteractionoftheagents.There-

sultsarefascinatlngandcanhelpbuildunderstandingofthebehaviorofcomplex

systems.However,unlessthedecisionrulesaregroundedinfirsthandstudyofac-

tualdecisionmaking,suchmodelshavelimitedutilitytodecisionmakers,andthe

correspondencebetweentheirdynamicsandthebehaviorofrealsystemsremains

conJeCtural･3

FindingFor-mutationFlaws

Theformulationsbelowallappearedinactualmodels(Somesimplificationshave

beenmadeforclarity).Usingtheformulationprinciplesabove,critiqueeach

formulation.Ifyouidentifyaflaworflaws,proposearevisedformulationthat

correctstheproblem.

2ThereareofcourseexceptlOnS･Manyeconomicmodelsaredynamic･Others,suchasmany game-theoreticmodels,restricttheinformationavailabletotheagents.Afewexplorealternatives totheassumptionthatpeoplearemotivatedbyselfishutilitymaximization･Stillfewerare groundedinfirsthandstudyofdecisionmaking.Fullydynamic,disequilibriumbehavioralmodels groundedinprlmaryfieldworkremainrareineconomics･PsychologlStS,incontrast,oftenutilize fieldworkandexperimenttostudydecisionmakingandhavedevelopedmodelsthataccommodate motivesforactionotherthanutilitvmaximizationsuchasfairness.altruism,revenge,andothers. However,manyofthesemodelsexplainslngledecisionsattheleveloftheindividualinstatic, one-shotdecisioncontextsandcannotcapturethedynamicsofasystemororganization･

3There areexceptlOnS･Sincediscoverlngandunderstandingthedecisionprocessesofpeople incomplexsystemsisoftendifficult,itisoftenusefultodevelopmodelsthatassumedifferent degreesofrationalitytotesttherobustnessofresultstoawiderangeofassumptlOnSabouthuman behavior.Modelsoffullyrationalbehaviorcanalsobeusedtoestablishupperboundsfortheper formanceofasystemandhelpmeasurethevalueofpotentialimprovementsindecisionmaking. ModelssuchasSugarscapecangenerateusefulideasforfurtherresearchandillustratethewelレ knownpropertyofcomplexsystemsthattheirbehaviorarisesmorefromtheinteractionofthe elementsandagentswithoneanotherthanfromthecomplexityOftheindividualcomponents themselves(see,e.g.,Forrester1961andSimon1969).

Chapter13 ModelingDecisionMaking 521

1 . Inamodelofa丘rm'ssupplychainandinventorymanagementpolicies,

theinventoryoffinishedproductwasincreasedbytheproductionrateand

decreasedbytheshipmentrate. Thefollowlngformulationforproduction

wasproposed:

Production-Shipments+InventoryShortfall(13-1)

InventoryShortfa ll -DesiredInventory-Inventory(13-2)

where

Production-Rateatwhichproductsarecompletedandenterinventory, Shipments-Rateatwhichproductsareshippedtocustomersfrom inventory, InventoryShortfall-Shortageorsurplusofinventoryrelativetothe desiredlevel, DesiredInventory-Inventorylevelthefirmconsidersappropriate, Inventory-Actualstockofproductavailableforshipmenttocustomers.

2 . Inthesamemodel, themodelerinitiallyproposed

Shipments-Orders(13-3)

butthenrealizedthatinventorycouldbecomenegativeiforderswerelarge

enoughforalongenoughperiod. Themodelerthenproposedthefollowing formulationtocorrectthenaw:

Shipments-MIN(Orders, Inventory)(13-4)

3 . Amodelofafirm'sinvestmentincapltalplantassumedinvestmentwas

deteminedby血egapbetweenthedesiredlevelofcapitalstockandthe

currentlevel,p lusreplacementofwo

-Outcapital(thediscardrate):

Investment-CapitalDiscardRate +DELAY3[(Kx-K),ConstructionDelay]

(13-5)

where

K*-Desiredcapitalstock,

K-Capitalstock,

DELAY3-Third-ordermaterialdelay,

ConstructionDelay-Averageconstructiondelayforcapital.

4.Inthesamemodel,thedesiredstocksofcapitalandotherfactorsof

productionsuchaslaborweredeterminedbythesolutiontotheprofit

maximizationproblemforafirmunderperfectcompetition･Inequilibrium,

themarginalrevenuederivedfromuseofanadditionalunitofanyfactorof

productionFlisJustbalancedbyitsmarglnalcostPl:

p旦9-p. ∂FI

where

P-Priceofoutput(marginalrevenue),

(13-6)

522 PartIV TbolsforModelingDynamicSystems

Pl-Priceofaunitoffactori(marginalcostoffactor),

Q-Q(Fl,F2,...,Fn)-Production,givenbythefirm'sproduction function,

aQ/aFl-Marginalproductivityoffactori(additionaloutputgenerated byoneadditionalunitoffactori).

5.AmodeloftheUSdairyindustryspecifiedtheequilibriumconsumption andproductionofmilkasdependingongrossdomesticproduct(GDP)- ameasureoftheincomeofthenation-andtheprlCeOfmilkPm:

Consumption(t)-Production(t)-a+bGDP(t)+cPm(t)+e(t) (13-7)

wherea,b,andcareparametersestimatedfromhistoricaldataandeisa randomerror.

13.2 FoRMULATiNGRATEEQUATEONS

Thissectionpresentsalibraryofcommonformulationswithexamplesforeach Eachconformstotheguidelinesabove.Thesegenericstructuresarethebuilding blocksfromwhichmorecomplexandrealisticmodelscanbebuilt.Inanyrealpro- JeCtyouWilloftenhavetocustomizeandelaboratethem Inparticular,everycon- Stantinaformulationcanbemodeledasavariable,withitsowndecisionrules

governlngItsevolution.Whetheraconceptcanbeassumedconstant,exogenous,

ormustbemodeledasanendogenouspartofthesystemstructuredependsonthe purposeandtimehorizonofthemodel.

13.2,l Fractjona]IncreaseRate

ConsiderastockSwithinflowrateRI.Oftentheinflowisproportionaltothesize ofthestock.Thestockgrowsatafractionalincreaserateg,whichmaybeconstant orvariable:

R1-gS

Examples

BirthRate-FractionalBirthRate*Population

InterestDue-InterestRate*DebtOutstanding

(13-8)

(13-9)

(13-10)

WhenthefractionalgrowthrateglSaCOnStant,theformulationreducestothe

linearfirst-orderpositivefeedbacksystemdescribedinchapter8andgenerates exponentialgrowth.

Thegrowthratecanbelessthanzero,inwhichcaseRIbecomesthenetinflow rateandgbecomesthenet血.actionalgrowthrate.However,asshowninsection 13.3.3,itisgenerallypreferabletoseparatetheinflowsandoutflowsinsteadof lumplngthemintoaslnglenetrate.Differentdecisionprocessesandphysicalcon-

straintsoftengoverninflowsandoutflows,anditisdifficulttoformulateaslngle netratethatistransparentandrobust.Thenetrateofchangeofanystockcan alwaysbecalculatedasanauxiliaryvariablefromtheindividualinflowsand outflows.

Chapter13 ModelingDecisionMaking 523

13.2.2 FractionalDecreaseRate

ConsidertheoutflowrateRofromastockS･Theoutflowisoftenproportionalto

thesizeofthestock.Theoutflowcanbeformulatedeitherasdependingonthe

fractionaldecreaseratedorequlValentlyasthestockdividedbytheaveragelife- timeLIbrtheitemsinthestock:

Ro-dS-S瓜 (13-ll)

Examples

DeathRate -FractionalDeathRate*Population -Population/AverageLifetime (13-12)

DefaultsonAccountsReceivable-FractionalDefaultRate*AccountsReceivable -AccountsReceivable/AverageTimetoDefault

(13-13)

Theseexamplesallform linear,first10rdernegativeloopsandgenerateexponential

decaywithatimeconstantofL-i/d.Theyareequivalenttoafirst-ordermater-

ialdelay.Thefractionalratesoraverageresidencetimescanbevariables.

13･2.3 AdjustmenttoaGoa! Managersoftenseektoadjustthestateofthesystemuntilitequalsagoalorde-

siredstate.Thesimplestformulationforthisnegativefeedbackis

RI-Discrepancy/AT-(S* -S)/AT (13114)

whereDiscrepancyisthegapbetweenthedesiredstateofthesystemS*andthe

actualstateS･TheadjustmenttimeATistheaveragetimerequiredtoclose

thegap.

Examples

ChangeinPrice-(CompetitorPrice-Price)仲riceAdjustmentTime (13-15)

NetHiringRate-(DesiredLabor-Labor)/HiringDelay (13-16)

HeatLossfromBuilding-TemperatureGaprTemperatureAdjustmentTime

TemperatureGap-OutsideTemperature-InsideTemperature (13-17)

ProductionRate-PerceivedInventoryDiscrepancy/InventoryAdjustmentTime

PerceivedInventoryDiscrepancy-Desiredlnventory-PerceivedInventory (13-18)

"Desiredminusactualoveradjustmenttime"istheclassiclinearnegativefeedback

system,and,intheabsenceofotherrates,generatesexponentialadjustmenttothe

goal(seechapters4and8).Inequation(13-15)afirm adjustsitspricetomatchthe

competition.In(13-16)themodelerhaschosennottorepresenthiring,firing,and

qultSSeparatelybuttoaggregatethemintoaslnglenethiringrate.Thehiringdelay

representstheaveragetimerequiredtoadjusttheactualworkforcetothedesired

level･WhennethiringlSnegativethefirmisimplicitlylaylngOffitsworkers･In

(13117)therateofheatlossfromabuildingdependsonthetemperaturedifference

524 PartIV TbolsforModelingDynamicSystems

betweenthebuildingandtheairoutsideandthethermalresistanceorRjactorof

thestructure.Oftentheactualstateofthesystemisnotknowntothedecisionmak-

ers,whorelyinsteadonperceptionsorbeliefsaboutthestateofthesystem(seethe

BakerCriterion)AInthesecasesthediscrepancyisgivenbythedifferencebetween

thedesiredandperceivedstateofthesystem,asin(13118).Notethattoberobust

(13-18)Shouldbemodifiedsoproductionneverbecomesnegative.

13L2.4 TheStockManagemenモStructure:

Ra官e≡NormaヨRaモe+Ae!jusモmem昔s

Whenthereisanoutflowfrom astock,theadjustmentrateformulationRI-

(S*-S)/ATwillproduceasteadystateerror.IfthereisanoutflowR.,thestockS

willbeinequilibriumwhenS-S*-Ro*AT･Thelargertheoutfloworthelonger

theadjustmenttime,thegreatertheequilibriumshortfallwillbe.Thestockman-

agementstructureaddstheexpectedoutflowtothestockadjustmenttoprevent steadystateerror:

Innow-ExpectedOutflow+AdjustmentforStock (13-19)

AdjustmentforStock-(Sx-S)/AT (13-20)

Sincetheinstantaneousvalueofratescannotbemeasuredtheexpectedoutflowis usuallyformedbyaveragingPastOutflows.

Example

Amanufacturingfirmmaysetproductiontoreplacetheshipmentsitexpectsto

make,adjustedtobringlnVentOryinlinewiththedesiredlevel.Expectedsbip一 mentsareoftenestimatedbysmoothingpastshipments.

Production-ExpectedShipments+AdjustmentforInventory

AdjustmentforInventory -(DesiredInventory-Inventory)nnventoryAdjustmentTime

ExpectedShipments -SMOOTH(ShipmentRate,ShipmentAveragingTime)

Tbbefullyrobust,theproductionratemustbeconstrainedtobenonnegativeeven

whenthereisfartoomuchinventory.Additionaladjustmentscanbeincluded,for

example,toadjustforstocksofworkinprocessinventory,backlogsofunfilled orders,andsoon.

Thestockmanagementstructureisoneofthemostimportantandusefulfor-

mulatiOPISal-1disdiscIJSSedindetailinchapter17.

13.2.5 FlowIResourceIProductivity

TheflOwsaffectingastockfrequentlydependonresourcesotherthanthestockit-

self･TherateisdeterminedbyaresourceandtheproductivltyOfthatresource:

Rate-Resource*Productivlty (13-24)

OrequlValently,

Rate-Resource/ResourcesRequiredperUnitProduced (13-25)

598 PartIV ToolsforModelingDynamicSystems

betested.ChallengesgiveyouaChancetodesignandimplementpoliciesforim-

provedperformance.

15LI HuMANDECISIONMAKING:BouNDEi)RAT!ONAuTY

oRRATIONALExpECTATJONS?

Chapters13and14provideawiderangeofrobustformulationsforuseinmodels ofhumanbehavior.Buttheseformulationsstillleaveconsiderableroomfordif-

ferentassumptionsaboutthedegreeofrationalityinthedecision-makingprocess.

Giventheinformationavailabletothem,dopeoplemakerational,optlmaldeci-

sionsoristheirbehaviornaiveandmindless?Dopeoplemakesystematicerrors?

Howandhowquicklydoleamlngandadaptationoccur?

Anextensivebodyofexperimentalandfieldstudiesdocumenthuman

decision一makingbehaviorindiversecontexts.Asyoumightexpect,thewaypeo-

plemakedecisionsdependssomewhatonthesituation･Somedecisionsaremade

automatically(whichpairofsocksshouldIwearthismoming?)･Othersinvolve considerabletime,resources,anddeliberativeeffort,alongwithemotionsandfee1-

ings(whatkindofcarshouldIbuy?).Humandecisionmakinggenerallyfallsin

betweentheextremesofmindlessrotebehaviorandtheperfectrationalityofeco-

nomictheory.Theevidencesuggests血attherationalityofhumandecisionmaking

isbounded(see,e.g.,Simon1957,1982;CyertandMarch1963;andNelsonand

Winter1982;Conlisk1996Surveystheevidenceanddiscussestheoreticalissuesin thecontextofeconomics).

Boundedrationalityarisesbecausehumancognitivecapabilities,aswonderful

astheyare,areoverwhelmedbythecomplexltyOfthesystemswearecalledupon

tomanage.Chapter1discussedboundedrationality;hereIrepeatHerbertSimon'S

(1957,p.198)principleofboundedrationality:

ThecapacltyOfthehumanmindforformulatingandsolvingcomplexproblemsis verysmallcomparedwiththesizeoftheproblemwhosesolutionisrequiredforob- JeCtivelyrationalbehaviorintherealworldorevenforareasonableapproximation tosuchobjectiverationality.

Boundedrationalityresultsfromlimitationsonourknowledge,cognltlVeCapabil-

ities,andtime.OurperceptlOnSareSelective,Ourknowledgeoftherealworldisin-

complete,ourmentalmodelsaregrosslysimplifiedandimperfect,andourpowers ofdeductionandinferenceareweakandfallible.Emotional,subconscious,and othernonrationalfactorsaffectourbehavior.Deliberationtakestimeandwemust

oftenmakedecisionsbeforeweareready.

Asanexample,considerabasicproblemfacingthemanagersofanybusiness:

capitalinvestment.Managersmustdecidewhenandhowtoinvestincapacltyand

onlydesiretoinvestwhentheybelievetheinvestmentwillbeprofitable･Todoso

optlmally,theymustchoosetherateofinvestmentthatmaximizesthenetpresent

valueofthefirm'sexpectedprofits,fTorallfuturetime,asthecompetitiveenvironェ

ment,inputCOStS,demand,interestrates,andotherfactorsaffectingprofitschange･

TheymusttakeintoaccountallpossiblecontlngenCiesincludingthewaysin wbichotheractorsintheenvironment(Suppliers,competitors,workers,customers,

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 599

govemment,etc.)mightreacttoanydecisionthe丘rmmakesJngeneral,these

lnPutSarelinkedinacomplexnetworkoffeedbackrelationshipsandmayalsobe influencedbyrandomshocks.

ChooslngInvestmentOPtlmallyrequlreSthefirm'smanagerstoformulateand

solveanexceedinglycomplexstochastic,dynamicoptlmizationproblem.¶)doso

themanagersmusthave(1)knowledgeofthecostanddemandfunctionsfacing thefirm;(2)knowledgeofthefuturebehaviorofallvariablesandotheractorsin

thesystem,or,equivalently,aperfectmodelofthesystemfromwhichthefuture

behaviorofthesevariablesandactorsmaybededuced(therationalexpectations

hypothesis,seeMuth1961);(3)thecognitivecapabilitytosolvetheresultingop- timizationproblem;and(4)thetimedoso.

Noneoftheseconditionsismetinreality･Inpractice,thecomplexltyOfthe

problemissooverwhelmingthatnoonecansolveitorevenagreeonwhat血ere1-

evantvariablesandpolicyoptlOnSare.Economistsworkingwithinvestmentmod-

elsmustmakeseveresimplifyingassumpt10nStOrendertheproblemtractable,for

example,assumlngInputandproductmarketsareperfectlycompetitive,discount

ratesareconstant,andadjustmentcostsarequadratic.Eventhen,asPindyckand

Rotemberg(1983)commentwithdryunderstatement,

Stochasticcontrolproblemsofthissortaregenerallydifficult,ifnotimpossibleto solve.This,ofcourse,raisesthequestionofwhe也errationalexpectationsprovides arealisticbehavioralfoundationforstudyinglnVeStmentbehavior.

Optimaldecisionmakingisimpossibleevenforproblemsmuchsimplerthancap-

italinvestment,suchaschooslngWhichjobcandidatetohireorwhichstudentsto

admittoauniversity.TbdosorequlreSaSSeSSlngallrelevantcandidatecharacter-

isticsandpredictingthelikelysuccessandfailureofthecandidatesglVentheat-

tributesandperformancehistoryofallsimilarapplicants,includingthosewho

werenotselected･Manystudiesshowthatsimpledecisionrulesbasedonasmall

numberofinputsoftensignificantlyoutperform theexpertsinawiderangeof

tasks,frompredictingtheperformanceofstudentsandthelifeexpectancyofcan-

cerpatientstopredictingbusinessfailuresandstockmarketperformance(Dawes 1979;Camerer1981).

ThischapterbeganwithHerbertSimon'sbluntassessment,inhisNobelPrize

address,thatthe血eoryofrationalchoiceunderlyingeconomicsdoesnotHevenre-

motelydescribetheprocessesthathumanbeingsuseformakingdecisionsincom-

plexsituations.HSuchaboldstatementsuggeststhreequestions:First,whatisthe

evidencethatpeopledon'tbehaveaccordingtotheprlnCiplesofrationalchoice

andeconomictheory?Second,howthendopeoplemakedecisions?Finally,how

carl+thewayspeoplemakedecisiorlSbemodeled?

15.2 CoGNmVEL朋ITAT旧NS

Humanshavealimitedabilitytoprocessinformation.Asaconsequence,"percep-

tionofinformationisnotcomprehensivebutselective"(Hogarth1987,p･4;orig-

inalemphasis).Forbothphysiologicalandpsychologicalreasons,Weperceiveand

attendtoonlyasmallfractionoftheinfTomationavailableintheenvironment.In-

stead,peopletakeveryfewcuesintoaccountwhenmakingdecisions･Attentionis

600 PartIV ToolsforModelingDynamicSystems

ascarceresourceandmustbeallocatedamongcompetingdemands.Wefocusour

attentiononsomecuesandignoreorremainunawareofother,potentiallyimpor- tantcues.Undernomalcircumstances,ourattentionmovesfromonecuetoan-

otlleraStheirsalienceandperceivedimportancechangeandaswebecome distractedbyevents,Instressfulsituationsthefloodofinformationcanoverwhelm

ourprocessingCapabilitiesandwefailtoperceivenewinfomation,regardlessof itsimportance.Studiesofpilotsincrises,forexample,showhoweasilyinforma- tionoverloadcanarise.Insomecases,thepilotsaredoingsomanythingsatonce

andarebombardedbysomanydifferenttypesofinformation(visuals,instru- ments,radioinstructions,auditorycues,andothers)thattheyareliterallyunableto noticecriticalcuessuchasthecopilotshoutingemergencylnStruCtions.Crashes haveresultedfromsuchinformationoverload.

Ourcognitivecapabilitiesaresimilarlybounded･Miller(1956)famously showedthatshort-termworkingmemorylSlimitedtoH7±2"chunksofinforma- tion;constraintsonthestorageandrecallofinformationinlong-term memoryand onintuitivecomputationalpowerhavealsobeenidentified.Ideallyattentionand

cognitiveeffortshouldbeallocatedoptlmallyaccordingtotheimportanceandutil- 1tyOfthedifferentcuesavailabletothedecisionmaker,butpeopledonothavethe

timeorcognltlVeCapabilitytodecidewhatthatoptimalallocationis.Indeed,血e attempttodosocomplicatesthedecisionproblem,aggravatesinformationover- load,andcanleadtoevenworsedecisionmaking.Rather,peopletendtofocus theirattentionandeffortoncuesthatarereadilyavailable,salient,andconcrete.

Wefocusoncueswebelievetoberelativelycertain,systematicallyunderweight-

inguncertainorremoteinformationevenwhenithasdiagnosticvalue(Hogarth 1987;Kahneman,Slovic,andTversky1982,chap.4)AOurmentalmodelsaffect whichofthemanycuesinanenvironmentwethinkareimportantanduseful,dL

rectlngattentiontothosecuesattheexpenseofothers･However,asdiscussedin

chapter1,peoplearenotoriouslypoorjudgesofcausalityandco汀elation,andsys- tematicallycreatementalmodelsatvariancewiththeknownsituation,sothatour

expectationssometimesleadustonoticecuesthathavelowdiagnosticpowerand preventusfromattendingtomoreusefulcues.

BecauseourcognltlVeanddecision-makingcapabilitiesarelimited,Wecannot

makedecisionsaccordingtotheprescnptlOnSOfoptlmizationtheory.Instead,we use,consciouslyandunconsciously,awiderangeofheuristicstomakedecisions･

Alargeanddiversebodyofempiricalandexperimentalresearch,generallyknown asbehavioraldecisiontheory(BDT),documentstheheuristicspeopleuseinjudg一 mentanddecisionmaking･1

Whilesomeheuristicsworkwellundersomesituations,theresearchshows

thatmanyyieidsystematic,significant,andpersistenterrors･WhiletrainingCan moderatesomeoftheerrors,manyarerobustinthefaceofexperienceandaredif- ficulttoovercome.

lTheliteratureislarge.Forgoodoverviews,SeeHogarth(1987);Kahnemanetal.(1982);Plous (1993);RussoandSchoemaker(1989);andThaler(1991,1992).

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 601

15.3 】NDIVIDUALANDORGANIZATIONALRESPONSES

TOBouNDEDRAT10NALITY

Sinceoptlmaldecisionmakingwithperfectmodelsisimpossible,peopleand

organizationshavedevelopedanumberofwaystosimplifythetaskofdecision making.

15.3,1 Habit,Routines,andRulesofThumb

Habitsandroutinesareproceduresfollowedrepetitivelyandwithoutsignificant deliberativeeffort.Insteadofdecidingwhattodoeachmomingbyconsideringthe

costsandbenefitsofallouroptlOnS,mostOfusfollowaroutine:Exercise,shower,

getdressed,andsoon.Wedon'tthinkaboutit,WeJustdoit･ Routinesarenearlyautomaticprocedurestrlggeredbyparticularconditions･

Theyaretheorganization'sstandardoperatlngprOCedures･Routinesmaybeinfor一

malorhighlycodifiedprotocols.Theymayberigidorpermitsomeflexibilityln responsetolocalconditions.Theyoftenevolvewithexperience･Organizational routinesaresimultaneouslyembeddedin,justifiedby,andreinforcetheorganiza- tion'straditions,culture,andfolklore.

Anothercom onmethodtoreducethecomplexityOfdecisionmakinglS

throughrulesofthumb.Aruleofthumbisaproceduredesignedtoyieldapretty gooddecisionquicklyandeasily.Rulesofthumb,ordecision-makingheuristics, arebasedonsimplified,incompletemodelsoftheproblemsituation･Theytendto

relyonrelativelycertaininformationreadilyavailabletothedecisionmaker･Inthe departmentstoreprlClngexamplecitedinsection13･1,managersdonothavethe information,cognltlVeCapability,OrtimetosettheprlCeSOfeachitemtooptlmize

storeprofits.Settingfloorpncesbymultiplyingwholesalecostsbyatraditional markupratioisaruleofthumbthatallowsstoremanagerstosetpricesquickly･ Theruleisnotoptimalbutperformswellenoughinmostsituations･Whenprices

provetobetoohighortoolow,otherrulesofthumbsuchasHholdasaleforslow movlngprOductsMallowmanagerstocorrecterrors･

'i5.3.2 ManagingAttenモSon

Sinceattentionisascarceresource,controllingtheinformationpeoplehaveaccess

andattendtoisanimportantsourceofpower･Organizationshavedevelopedmany structuresandroutinestocontrolaccesstoinformation,directingtheattentionof

itsmemberstowardsomecuesandawayfromothers.Thesedevicesincludefor-

malreportlngrelationships,agendasettlng,thegeographicalstmctureoftheorga- nizationaridphysicallayoutofitsfacilities,andaccoldntlngalnldinforlmation

systems.Informalnetworksofcommunicationalsocriticallyinfluencethealloca- tionofattention.Someofthemostpowerfulpeopleinanylargeorganizationare theexecutivesecretaries-thepeopleyoumustpersuadetoglVeyouaccesstO

busyseniorexecutives.

15.3t3 GoalFomlationandSatisficing

AnotherstrategytoreducethecomplexltyOfthedecisiontaskisgoalsettlng･In- steadofmakingdecisionsbyexplicitlysolvingoptimizationproblems,people

602 PartIV ToolsforModelingDynamicSystems

insteadtendtosetgoalsandadjusttheirbehaviorinanattempttomeetthem.Once thegoalsaremet,problemsolvingeffortsoftenstopsotheattentionandcognitive resourcestheyconsumecanbeusedelsewhere.HerbertSimoncoinedtheterm

"satisficing"todescribebehaviorinwhicheffortisreducedonceasatisfactoryso- lutiontoaproblemisfoundorasatisfactorylevelofperformanceisattained.Stu-

dentsoftenreducetheirstudyeffortoncetheyachievethegradestheydesire; consumersstopsearchingforbargalnSOncealowenough priceisfoundforthe

itemtheydesire;employersoftenhirethefirstcandidatemeetingtherequirements forthejobratherthansearchingforthebestone.

Settingspecificgoalsprovidesdecisionmakerswithaconcretetargetagainst

whichtheycancomparetheactualperformanceofthesystemandinitiatecorrec- tiveactionwhenthereisadiscrepancy.Themoreconcreteandspecificthegoal,

theeasieritisforpeopletodeterminewhichinformationcuesareimportantand whichcanbeignoredandtodecidewhichactionstotaketoreachthegoal.

Aspirationsandgoalsthemselvesareadaptiveandrespondtoexperience.In thedepartmentstoreprlClngexample,thestandardmarkupoverwholesalecosts adaptedtoexperience.Storemanagersgraduallyadjustedtargetmarkupstotheac- tualmarkupsrealizedbythestoreafterrespondingtocompetitorpricesandhold- 1ngSalestomovesurplusinventory.Thequotaforasalesforceisoftenbasedon anaverageofrecentsalesplusacertainmarglntOencouragegreatere放)rt,anda student'sdesiredgradepolntaveragetendstoadjusttotheactualgradesreceived,

againperhapsbiasedbyamargintoencouragegreaterachievement(Cyertand March1963;Lant1992;Morecroft1985).

15.3L4 .ProbiemDecomposifionandDe!?er絹r品目zed Deeis昏0円Mak岳mg

LimitedinfTormationprocesslngCapabilityforcespeopletodividethetotaltaskof makingadecisionintosmallerunits.Byestablishingsubgoalsthecomplexityof

thetotalproblemisvastlyreduced. Decompositionofdecisionproblemsintosubgoalsisalsoanimportantmoti-

vationfororganizationalspecialization.Eachorganizationalsubunitischarged withachievingasmallnumberofsubgoals:Thesalesorganizationischargedwith

meetlngSalesgoals;themanufacturlngOrganizationmustdeliverontimeandbel lowcertaincosttargets.Withineachofthesefunctions,furtherdecomposition

takesplace:InsidethemanufacturlngOrganization,individualmachineoperators musthit也eirdailyquotasandmaintenancetechniciansstrivetoclearthebacklog ofworkorders.Typically,tlhegoalsofeachorganizationalsuburlitarebroken downintostillsmallersubgoalsuntiltheconnectionsbetweenthedecisionsthe

agentcanmakeandtheagent'sgoalsareclearandunambiguous. Indecidinghowtoachieveagoal,decisionmakerstendtolgnOre,OrtreataS

exogenous,thoseaspectsofthesituationtheybelievearenotdirectlyrelatedtoit (Simon1957,p.79):

IndividualchoicetakesplaceinanenvironmentofHgivens"-premisesthatareac- ceptedbythesubjectasbasesforhischoice;andbehaviorisadaptlVeOnlywithin thelimitssetbythese"givens.H

Chapter15 ModelingHuman】】ehavior:BoundedRationalityorRationalExpectations? 603

Forexample,afirmmaylowerprlCeStOincreasemarketshareontheassumption

thatcompetitorprlCeSWillremainatcurrentlevels;arealestatedevelopermaybe-

glnCOnStruCtionofanewpropertyontheassumptlOnthatlowvacancyratesand

highrentswillpersistuntilthebuildinglSreadyforoccupancy;amachineopera-

torstrivlngtOhitthedailyquotamaychoosetodeferscheduledmaintenance,1g-

norlngtheeffectofthisactiononfutureyieldandquality.Theimplicitassumpt10n

ofproblemdecompositionanddecentralizeddecisionmakingisthatachieving

eachsubgoalwillenablethedecisionmakerororganizationtoachievetheirover-

allgoals.Thisassumpt10nisoftenincorrect.

15.4 lNTENDEDRAT10NAしけY

CognltlVelimitationsandtheotherboundsonrationalitymeandecisionsareoften

madeasiftherewerenotimedelays,sideeffects,feedbacks,ornonlinearities･

Sincerealsystemsofteninvolveconsiderabledynamiccomplexity,decisionsmade

inthisfashionoftencausepolicyresistance,instability,anddysfunction.Doesthis

meandecisionmakersareirrationalorJustPlainstupid?Notatall.Humanbehav-

iorisusuallypurposeful.Mostdecisionsaremotivatedbyacertainlogic.The

modelermustuncoverandrepresentthementalmodelsofthedecisionmakersand

representtherationalefortheirdecisionrules.WhataretheimplicitassumptlOnS

thatmaketheirbehaviorsensible,fromtheirpointOfviewandgiventheirgoals?

Thatis,isthedecisionruleintendedlyrational?

Adecisionruleislocallyorintendedlyrationalifitwouldproducereasonable andsensibleresultsiftheactualenvironmentwereassimpleasthedecisionmaker

presumesittobe,thatis,ifthepremisesacceptedbythesubjectweretrue･Forex-

ample,itissensibleforafirmtocutprlCeStOStimulatemarketsharewhencapac-

ityutilizationislowlfthemangersbelievethatcompetitorswon'torcan'trespond

bycuttlngtheirownprices.Figure15-1showsacausaldiagramofthesituation･

ThecompanycutsprlCeSWhencapacltyutilizationfallsbelowsomenormalortar-

getlevel,forminganegativefeedbackasmanagersattempttoFilltheLine(loop

Bl).Ifthesystemwereassimpleasthemanagerspresumeittobe,thatis,ifthe

prlCeOfcompetlngproductswereinfactexogenous,thencuttlngpricestOStimu-

1atedemandandboostprofitswouldmakesense.Butthemanagers'mentalmodel

isliketheproverbialtipoftheiceberg:ItincludesonlyasmallfractionofthefTeed-

backstructureinthesystem.Competitorsarelikelytosetpncesuslngthesamefill

thelinelogic.CuttingprlCeSWhenutilizationdropscreatesareinforcingfeedback

(Rl)inwhichadropinpricecausesthemarketshareandhenceutilizationofcom-

petlngfirmstofall,leadingthemtocuttheirprices.Thecompanyfindsitsmarket

shareandljfilizationdonotimproveaseLXPeCtedandCIJ-tSPriceagalnラCloslngthe

positiveloop.WhenthepresumptionOfexogenouscompetitorprlCeSisfalse,10-

Callyrationalattemptstofillthelineleadtoanunintendedpricewarthatdestroys

profitabilityforall･2

2NotallpricewarsareunanticIPatedorilTational･FirmsmaystartaprlCeWarinanattemptto bankruptrivalstheybelieveareweakerortopunishdefectorsfromacartel(e.g.,GreenandPorter 1984).

604 PartIV ToolsforModelingDynamicSystems

FFGURE15-1 Anintendedlyrationalpricingpolicycanleadtoaninadvertentpricewar.

Top:Mentalmodelofafirminwhichcompetitorpncesarebelievedtobeexogenous.Cuttingpnces

toFi‖theLine(Bl)whencapacityutilizationfa"sislocaHyrationaliftheboundaryofmanagement's mentalmodelcutsthefeedbackstocompetitorprlCeS.

Bottom,JWhen_Competitorfirmsbehavethesamewayanda一socutprlCeStOboosttheirowncapacity

utilization(B2),thentheintendedlyrationaldecisiontolowerpricesinthehopeofstimulatingdemand

createsthereinforcingfeedbackRl(shownbythethicklines)andapricewar?nsueswhenever industrydemanddropsbelowcapacity.Forclarity,additionalfeedbacksfrompncestoindustrydemand andfromdemandtocapacityarenotshown.

Theaccountabovedoesassumethemanagersexplicitlyconsidercompetitor

prlCeSbutdecidethatthecompetitorswon'trespondtoapnCeCutWithapriceCut

oftheirown.Altematively,themanagersmayneverconsidercompetitorpricesat

all,assumlngImplicitlyandwithoutreflectionthatlowerprlCeSStimulatedemand

andwillhelpfilltheline.

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 605

15･4･l TestingforIntendedRationaMy: PartialMode一¶∋Sts

Partialmodeltestshelpyoudete-in°whetherthedecisionrulesinyourmodel

∬eintendedlyrationaHnapartialmodeltesteachorganizationalfunctionorde-

cisionpointisisolatedfromitsenvironmentuntiltheenvironmentisconsistent

withthementalmodelthatunderliesthedecisionrule.Thesubsystemcanthenbe

challengedwithvariousexogenouspatternsinitslnPutS･Doesafirm 'sinventory

managementpolicybehaveappropnatelywhendemandsuddenlyincreases?Does

thecapitalinvestmentprocessadjustcapacltytoappropnatelevelswithoutexcesI

siveinstability?Howdoesthefirm'Spncerespondtoachangeinunitlaborcosts?

IntheprlCeWarexampleabove,themanagerscutprlCeStOfillthelinewhenuti-

1izationislowbecausetheybelievecompetitorpnCeSWillnotrespond･Apartial

modeltestofthispnclngrulewouldbeimplementedbymakingthecompetitor

prlCeeXOgenOuS,thenchallengingthemodelwithadeclineindemand.Lower

prlCeSwouldboostdemandandfilltheline,demonstratlngthatthedecisionrule

issensibleinaworldwherethefeedbacktothemarketiscut,asthemanagers believe.

15.5 CASESTUDY:MoDELINGHIGH-TECHGROWTHFiRMS

Fo汀eSter'S(1968)HmarketgrowthHmodelillustrateshowboundedrationalitycan

berepresentedinmodelsandhowtheintendedrationalityofamodelcanbe

tested･3ThemarketgrowthmodelgrewoutofForrester'sexperienceadvisingen-

trepreneursandcompa血esinthehigh-techindustryJtisoneofseveralmodelsof

high-techgrowthfirmsForresterbuiltduringthe1960S(Forrester1975a;seealso

Packer1964andNord1963).Thesemodelsaddressedapuzzlethatisstillanissue

today･Mostnewcompaniesfail.Somegrowforawhilebutthenstagnate.Still

fewermanagetogrowbutexperienceperiodiccrises,ofteninducingturnoverof

topmanagement･Onlyaverysmallnumberseemabletogrowrapidlyandsteadily

forextendedperiodsoftime(seeFigure316). Forrestercoulddiscernnoobviousdifferencesbetweenthesuccessesandfai1-

uresinthequalityoftheproducts,thecreativltyOftheirengineers,OrOtherfunda-

mentals･Hebecameconvincedthattheexplanationforthedifferingoutcomeslay

inthedifferentdecisionrulesusedtomanagetheenterpnseandtheunantlCIPated

sideeffectsofpoliciesthatappearedtoberationalandwell-intentionedwhen viewedinisolation.

Inthemarketgrowthmodel,Fo汀eSterSetOuttOCreatethesimplestpossible

modelthatcouldstillcapturethekeydecisiorlrulesoftheerltrePrenelLirSarldchief

executivesheknew Thoughbasedonthecaseofaparticularfirm ,themodelis

3Theanalysisofintendedrationalityinmemarketgrowthmodelwasinspiredbyanddraws pnMorecroft(1983)IMorecroftpioneeredthedevelopmentoftheconceptsofintendedrationality lnSystemdynamics(seealsoMorecroft1985)forwhichhewontheJayForresterprizein19901 TheversionofthemarketgrowthmodeldevelopedherediffersfrombothForrester'soriginaland Morecroft'S1983versioninsomedetails,buttheessenceofkeyformulationsisthesame,asare thebehaviorandimplicationsofthemodel.

606 PartIV Tわolsfb∫ModelingDynamicSystems

qultegeneralanditslessonsapplytogrowlngOrganizationsinanyindustry.The parametersarethereforechosentoberepresentativeoftypicalhigh-techproducts andnottoreplicatetheexperienceofanyonecompany.

Toillustratehowinteractionsofintendedlyrationalpoliciescouldproduce failure,ForresterdeliberatelymadethestrongsimplifyingassumptlOnthatthe

marketforthefirm'sproductwasunlimited･Thepotentialofthecomputerand high-techindustryinthe1960sseemedtohimtobesogreatthatthiswasarea-

sonableassumptlOn.

15.5.1 ModelStructure:Overview

Themodelrepresentsasinglefirm competlnglnapotentiallyunlimitedmarket.To

keepthemodelassimpleaspossible,FoITeSterdeliberatelyomittedmanyorgani- zationalfunctionsandstructures.Forexample,thereisnoincomestatementorbal- ancesheet,andcompetitorsareincludedimplicitlylnaSimplemarketsector.The

representationofthefirm itselfconsistsofthreesectors,eachrepresentingadif-

ferentorganizationalsubunit(Figure1512):sales,orderfulfillment,andcapacity acqulSltlOn｡

FIGURE15-2 Sectorsofthemarketgrowthmodel

Themodeldividesthefirmintodistinctorganizationalsubunits,Eachfunctionoperatesonthebasisof differentinformation.

Source:AdaptedfromMorecroft(1983).

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 607

Interactionsoforganizationalfunctionscreateimportantfeedbackloops,such asthebalancingloopB3,whichcouplesthefirmtothemarketthroughproduct availability.Anincreaseinordersbooststhebackloganddeliverydelay,causlng somedelivery-Sensitivecustomerstotaketheirbusinesstothefirm'scompetitors･

ThemodelrepresentsthefirmanditsmarketasanecologyofinteractlngagentS- theindividualorganizationalfunctions-eachwiththeirowngoalsanddecision rules.

Consistentwiththeprinciplesofboundedrationality,managersoperatlngln theindividualsubunitsarenotassumedtounderstandtheoverallfeedbackstruc-

ture.Eachsubunitisassumedtohaveaccesstoanduseasmallnumberofinfor-

mationalcues,notthefullsetofinformationpotentiallyavailable･Forexample,

thecapacltyexpansiondecisionisbasedonproductavailabilityasmeasuredbythe deliverydelayanddoesnotdependonforecastsoffuturesalesgeneratedbythe marketingorganization,whicIIWeregenerallydistrustedandignoredbysenior

management･

15.5.2 0rderFuJfiHment

Figure15-3Showsthestructureoftheorderfulfillmentfunction･

FIGURE15-3 0rderfulfillment

Therectanglewithroundedcornersdenotestheboundaryofasubsystemororganizationalsubunitjn

themodel(Morecroft1982)･Variablesoutsidetheboundaryaredeterminedinothersubsystem.S･Often themembersofthesubunitviewtheseInputsaSeXOgenOuSgNenS.Here,productioncapacitylstaken tobeoutsidethecontroloftheorderfulfi"mentorganization.

608

FIGURE15-4 Capacity utiljzation

PartIV ToolsforModelingDynamicSystems

Forresterassumedthefirmmanufacturedacomplexhigh-techproductandop-

eratedabuild-t0-Ordersystem.Ordersaccumulatedinabackloguntiltheycould

beproducedandshipped.Theactualaveragedelayindeliveringorders(themean

residencetimeofordersinthebacklog)isgivenbytheratioofthebacklogtothe

currentshipmentrate(Seesectionll.2.6).Thebook-to-billratioisacommon

measureofthehealthofhigh-techcompanies.Book-to-billratiosgreaterthanone

indicatetheorderbooklsgrowlng.

Backlog-INTEGRAL(OrderRate-ShipmentRate,Backlogb) (15-1)

DeliveryDelay-Backlog/ShipmentRate (15-2)

Book-toIBillRatio-OrderRate/ShipmentRate (15-3)

Thedesiredproductionratedependsonthebacklogandthenormaldeliveryde-

lay-thenormaltimerequiredtoprocess,build,andshipanorder:

DesiredProduction-Backlog/NormalDeliveryDelay

Productioncapacltyandcapacltyutilizationdetemineshipments:

ShipmentRate-Capacity*CapacityUtilization

CapacityUtilization-i(DesiredProduction/Capacity)

(15-4)

(15-5)

(1 5-6)

FromthepointOfviewofthemanagersresponsiblefororderfulfillment,capacity

isaglVen,OneOfthepremisespeopleacceptasabasisfortheirchoices.Capacity

isnotundertheirdirectcontrolandrespondsonlyslowlytoseniormanagement's

decisionstoinvesLOperationsmanagersmustaccommodatevariationsindemand

throughchangesinthelevelofcapacltyutilization.Thehigherthebacklog,the

highertheutilizationrate,thoughofcourse,utilizationsaturateswhenthefirm's

plantsareoperatingattheirmaximumrate.Figure15-4showstheassumedcapac-

1tyutilizationfunction.Bydefinition,whendesiredproductionequalscapaclty,util

lizationisunity.Whendesiredproductionislessthancapaclty,plantmanagerscut

utilizationbackgradually,preferringtorunthebacklogdownratherthanidling

theirplantsandlayingOffemployees.Thereforetheassumedutilizationcurvelies

abovethe450referencepolicy.However,whenthebacklogiszero,utilizationand

LL)

1(SS a 一u O!S u a ∈

!P)

u (VFt e

N≡ In

)̂!3t2dd 3

0.00 0.25 0.500.75 1.00 1.25 1.50 1.75 2.00

DesiredProduction/Capacity (dimensionless)

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 609

shipmentsmustalsobezero:Iftherearenoorderslnthebacklog,therearenocus-

tomerstowhomaproductcanbeshipped,andthe丘rmneveraccumulatesinven-

tory.Utilizationrisesaboveonewhendesiredproductionexceedscapacitybutat

sharplydiminishingratesuntilitreachesamaximumassumedtobe25%above nomal.4

Theintendedrationalityoftheorderfulfillmentdecisionrulecanbeexamined

throughtwopartialmodeltests.First,theformulationforshipmentsshouldallow

thefirmtomeetitsdeliverygoalswhencapacitylSnotaCOnStraint.Iftherewere

nocapacltyConstraintonshipmentssocapacityutilizationwasperfectlyflexible,

utilizationwouldliealongthe450lineinFigure1514.Theformulationforthe

shipmentratewouldthenreduceto

ShipmentRate-Capaclty*CapacityUtilization -Capacity*(DesiredProduction/Capacity) -DesiredProduction

-Backlog/NormalDeliveryDelay (15-5a)

whichistheformulationforafirst-ordermaterialdelay.IfcapacltyWerenevera

constraintonshipments,theproductionschedulingdecisionrulewouldalwaysen-

ablethefirmtofulfillorderswithinthenormaldeliverydelay.

Thesecondpartialmodeltestexaminestheintendedrationalityoftheentire

orderfu岨11mentprocess.NowcapacitylStakenasexogenousandconstant,and

theshipmentformulationischallengedwithastepincreaseinorders(Figure1515).

Capacltyis500units/month.Theinitialbacklogis1000units.Sincethenormal

deliverydelayis2months,desiredproductionis500units/monthandinitialuti-

lizationislO0%.Inmonth0ordersincreaseto600units/month･Thebacklogbe-

glnStOriseandmanagersincreaseutilization.Sincecapacityisfixed,thedelivery

delayrlSeSabovethenomallevel.Shipmentssmoothlyapproachthenewequilib-

riumrateof600units/month.Ⅰnthenewequilibrium,utilizationhasreached120%

ofnomalandthedeliverydelayrlSeStO2.7mon血S･

Thesetestsdemonstratetheintendedrationalityoftheformulationfororder

fulfillment.Inisolation,theorderfulfillmentdecisionruletrackschangesinorders

inasmoothandstablemannerandmaintainsthedeliverydelayaslowaspossible

glVenthecapacltyCOnStraint.Note,however,thatifordersweresustainedatarate

greaterthan125%ofcapacity(themaximumrateofoutput),theshipmentrate

wouldalwaysbelessthanordersandthebacklogwouldincreaseindefinitely.Such

behaviorwouldstillbeintendedlyrational:Thebestthemanagerscoulddoispro- duceatthemaximumrate.

15.5.3 CapaeityAcquisition

Figure15-6showsthestructureof血ecapacltyaCqulSitionsector.

4Thebacklog--Shipmentstructureisanexampleofacapacitateddelay,discussedinchapter14, alongwiththeconstructionofthenonlinearutilizationfunction.Themodeldefinesutilizationof loo鞄tobethenormalrateachievedwhendesiredproductionequalscapaclty.Manyfirmsdefine utilizationasthefractionofmaximumoutputachieved.Sincethemaximumutilizationis25% abovenormal,theformulationisequivalenttoassumingthefirmnormallyoperatesat80%of maximumcapaclty.

610

FLGURE15-5 Responseoforder fulf川mentsectorto

astepindemand

CapacitylSfixedat 500units/month. Ordersincrease from500to600 units/monthat timezero.

PartIV ToolsforModelingDynamicSystems

600

.°= ･l･･■ ⊂ ○

3 550 の := 】= ≡)

500

【〇

〇

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u O !8 12 N ≡

l n

12 Month 24 36 48

CapacityUtilization

(leftscale)_㌔ ...-.-一一--.--.---

■●-′~'' -elivery-elay

D e Bive r

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(mo nths

)

-12 0 12 Month 24 36 48

RatherthanmodelthecapacityOrderingandacqulSitionprocessindetail,ca-

pacltylSassumedtoadjusttothedesiredlevelofcapacltyWithathird10rderdelay.

Thecapacityacquisitiontimeissetto18months,atypicalvalue(sectionll.5.1).5

Capacity-SMOOTHS(DesiredCapacity,CapacityAcquisitionDelay) (15-7)

TheformulationfordesiredcapacltyCapturesSeveralimportantaspectsof

boundedrationality.Forresterobservedthatseniormanagersinthecompanyupon

whichhismodelwasbased,asinmanyfirms,Wereveryconservativeaboutcapi-

talinvestment.Investmentsincapacityareexpensiveandlargelyirreversible.Se-

niormanagers,inparticularthefounderandCEO,Werereluctanttoinvestuntil

therewasclearevidenceofneedanduntiltheycouldbesurethatanynewcapac-

1tyWOuldnotgounutilized.Thoughthesalesandmarketingorganizationspro-

ducedsalesforecasts,seniormanagementdidn'ttrustthem.Seniormanagement's

viewwasthatHmarketingcanforecastthemoon,andplantmanagersarealways

complainlngaboutcapacltyShortages.Theonlyreliableevidencethatweneed

morecapacityCOmeSWhenwestartmissingdeliverydatesで

5NotethatbecausethemodeldoesnotrepresentthephysicalflowsofcapacityOrders,arrivals, anddiscards,theinformationdelay(SMOOTHS)isusedra血erthanamaterialdelay(section11.3; chapter17developsformulationstomodelcapacityacqtlisitionexplicitly)･

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 61i

FlGURE15-6 Capacityacquisition

TherectanglesaroundDeliveryDelayPerceivedbyCompanyandCapacityrepresentdelayswithout showingtheirfunstockandflowstructure.

DeHveryDeqay Perceivedby Company

Pressureto

Expand

Timefor

Companyto Perceive

DeliveryDelay

Company

･dd- gee.監禁; Delay

+ Desired

Capacity

J. Effectof

Expansjon Pressur.eon

Desjred

r Capacity +

Thedesiredcapacitydecisionismodeledasananchoringandadjustment

process(section13.2.10).Managementformsdesiredcapacitybyanchoringon

currentcapaclty,thenadjustlngltuPOrdownbasedonvariouspressures･Because

cuessuchassalesforecastsarenoisy,unreliable,anduntrustworthy,thepressure

toexpandcapacltyderives丘.omthefirm'sperceivedabilitytodelivercomparedto

itsgoal.

DesiredCapaclty -Capacity*EffectofExpansionPressureonDesiredCapaclty

EffectofExpansionPressureonDesiredCapaclty -i(PressuretoExpandCapacity)

PressuretoExpandCapaclty DeliveryDelayPerceivedbyCompany

CompanyGoalforDeliveryDelay

(15-8)

(15-9)

(15-10)

perc?ievltvdebqyDce.1:ypany-SMOOTH(Delivery Delay, t.p:,ic:?vfeo諾 :vme:yam,yelay) (15-ll)

612

FIGURE15-7

Effectofproduct availabilityon capacity expansion

PartIV ToolsforModelingDynamicSystems

( s

s a ]u o!Su aL u !P )

^ l!3 t2d t2U

Pa J!S a 凸 u O

a Jn s s aJ d u O 叩S u e d x

1010 8- 1山

0.00 1.00 2.00 3.00 4.00

PressuretoExpandCapacity (dimensionless)

5.00

Pressuretoexpandcapacltyistheratioofthedeliverydelayseniormanagement perceivescomparedtotheirgoalfordeliverydelay.Managers'beliefsaboutprod-

uctavailabilityareassumedtolagthetruedeliverydelayduetothedifficultyof measunngavailabilityanddelaysinupdatingtheirbeliefsoncedatabecomeavail-

able.FirsトorderexponentialsmoothinglSassumed,withaperceptlOndelayof 3months.Fornow,thecompanygoalfordeliverydelaylSconstantandequalto thenormaldeliverydelay.InForrester'sorlglnalmodelthegoalwasitselfavari-

able(seethechallengebelow). Thepressuretoexpandcapacityhasanonlineareffectondesiredcapacity,aS

showninFigure15-7.WhenperceiveddeliverydelaylSVerylowcomparedtothe goal,managementconcludesthereissubstantialexcesscapacltyandcutsdesired capacitybelowthecurrentlevel.Whentheperceiveddeliverydelayexceedsthe

goal,desiredcapacltyrlSeSabovethecurrentlevel.Tocapturemanagement'scon- servativeapproachtocapacltyeXPanSiontheadjustmentisweak:A10%increase inexpansionpressurecausesalessthanlo啄increaseindesiredcapaclty,andthe effectsaturatesatamaximumvalue.

Management'scapacltyexpansionbehaviorisconsistentwiththeprlnCiplesof boundedrationality.Managementhadlittleconfidenceinsalesforecasts,market

research,andotherpossibleslgnalsoffuturedemandandinsteadbaseditsdecision ondeliverydelay-animportant,directmeasureofthefirm'sabilitytomeetde- mand.PerceptlOnSOfdeliverydelaylagbehindtheactualsituation.Atemporary

increaseindeliverydelaywillthereforenotresultinmuchinvestment,Onlywhen deliveryschedulesareconsistentlymisseddoesmanagementbecomeawareofand deemtheneedforcapacltySufficientlycompellingtoJustifyinvestment.

Totesttheintendedrationalityofthecapacitydecision,firstconsiderasimu- lationinwhichthedeliverydelayperceivedbythecompanylSeXOgenOuS.This

partialmodeltestcutsthebalancingCapaCltyexpansionloopB2andteststhere- sponseoftheanchoringandadjustmentformulationfordesiredcapaclty.InFigure 15-8thepressureforexpansionbeginsatthenormalvalueofone.Management

believesproductavailabilitylSatthedesiredlevel･Theperceiveddeliverydelay thenjumPSby25%foraperiodof2yearsbeforereturnlngtOnormal.Inmonth60,

perceiveddeliverydelaydropsto75%ofnormalbeforereturningtOnormala fte r

another2years.

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 613

l8 110

琵

叩岬

( L J l u O L u J S l ! u n )

^ l

!O e d t2 3

人

0 24 48Month 72 96

Ex p a

ns i o n P r

es s

u re

(d im e nS

ion一e ss)

TheincreaseintheperceiveddeliverydelaycreatespressureforcapacityeX-

pansion･Managementincreasesdesiredcapacltyaboveitscurrentlevel･Capaclty

graduallybeginstorise.BecausethefeedbackfromcapacitytOProductavailabill

ltylSCut,theincreaseincapacitydoesnotreducedeliverydelay.Managerscon-

tinuetoexperiencepressureforexpansion.Thoughcapacityhasincreased,the

continuinghighdeliverydelaytheyperceiveisevidencethatcapacityhasnotyet

increasedenough.Desiredcapacityremainshigherthancapaclty,andcapacltyad-

juststothedesiredlevel,closing仙epositiveCapacityGoalloop(RO).Thefort

mulationfordesiredcapacityenablesmanagementtosearchfortherightlevelof

capaclty,Whateveritmayturnouttobe･Whenproductionpressurereturnstonor-

malinmonth30,managersconcludethatthecurrentlevelofcapacltyis,finally,

therightone･Desiredcapacityfallsbacktothelevelofactualcapacity･Actualca-

pacltyrlSeSforafewmoremonthsduetothedelaylnCapacityaCqulSitionbutthe

effectismodest.TheresponsetoevidenceofexcesscapacltylSSimilar.Aslongas

thepressureforexpansionislessthanone,indicatingthepresenceofexcessca-

pacity,managementgraduallyreducescapacity.Notethatthefinallevelofcapac-

1tylSnotequaltotheinitiallevel.TheassumedchangeinavailabilitylSSymmetric,

butthenonlinearformulationforcapacityaCqulSitionmeanstheresponseisnot.In

equilibriumthemanagersarecontentwiththecapacitytheyhavebecausethereis

nopressuretochangeit･ Havingestablishedtheintendedrationalityoftheformulationfordesiredca-

pacltyandcapacityaCqulSlt10n,thenexttestconsiderstheoverallperformanceof

thecapacitysubsystembyclosingthebalancingCapacityExpansionloop(B2)Jn

Figure15-9thecapacltySubsystembeginsinaninitialequilibriumwithorders,ca-

paclty,andshipmentsallequalto500,capacltyutilizationatlO0%,anddelivery

delayatthenormalvalue.Theorderrateisexogenous.Attimezeroordersincrease to600units/monthandremainatthatlevel.

Asinthetestoftheorderfulfillmentsector,thefirstresponseisanincreasein

thebacklogandcapacltyutilization･Asutilizationbeginstosaturate,deliveryde-

laynses･Eventually,Seniormanagersbecomeconvincedthathighdeliverydelays

aresignificantandpersistentenoughtowarrantcapacltyeXPanSion･Capacltygrad-

uallyrisesJnalittleoverayear,capacityhasrisenenoughthatutilizationpeaks

andbeginstodrop.Deliverydelayfallsbacktowardthedesiredlevel･Thepressure

toincreasecapacltygraduallydiminishes.CapacitySmoothlyapproachesthenew

614

FdGURE15-9 Responseof capacity expansion subsystemto20% increaseinorders

PartIV ToolsforModelingDynamicSystem s

OrderRate //〟/■㌦､

Shipment Rate

24 Month 48 72

･1

■l

(s s a 盲

0 !S ua ∈ !P )

O !l t2N ≡ l ⊃

人U

D e ニv e r

y D e la y

(m o

nths )0 24 Month 48 72

equilibriumof600units/month,andbothutilizationanddeliverydelayretumto normalvalues.

Theresponseisintendedlyrational.CapacitylnCreaSeSinasmooth,stable

fashion,withoutsignificantovershootorinstability.Consistentwiththe18-month

c叩aCltyacquisitiondelayandmanagement'scautiousapproachtoinvestment,the

fulladjustmenttakesseveralyears.

ShipmentsdoovershootordersbeforereturnlngtOequilibrium.Theovershoot

isaninevitableconsequenceofthephysicalstructureofthesystemandnotaflaw

inthedecisionrulesIThecapacltyaCqulSltlOnlagmeansshipmentsfallbehindthe

desiredratea洗erthesteplnCreaSeinorders･Thebackloganddeliverydelayrise

abovetheirequilibriumvalues･Theonlywaybackloganddeliverydelaycanfall

backtonormalisforshipmentstoexceedorders.Inthetest,therequiredincrease

inshipmentsisaccomplishedthroughutilization.Alargeenoughincreaseinorders

wouldsaturatetheutilizationloop,forcingcapacltytOriSeaboveorderslong enoughtocleartheexcessbacklog.

Noticethatthesimulatedmanagersincreasecapacitybyexactlytherequired

amounteventhoughtheydonotknowtheoptlmallevelofcapacity.Thefomula-

tionfordesiredcapacltylSanexampleofthehill-Climbingstructuredevelopedin

section13･2･12･Hilトclimbingoptl血zationuseslocalknowledge一也eslopeofthe

terrainaroundyou-todecidewhichwayleadsmoststeeplyuphill.Iftheterrain issmoothenoughandthemountainhasonlyaslnglepeak,youwillalwaysendup atthesummit.

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 615

Inthecontextofcapacltyacquisition,movinguphillmeansmanagersadjust

capacltyinthedirectiontheybelievewillimproveperformancebyeliminatingthe

pressureforcapacltyexpansion.CapacltyIncreasesWhendeliverydelaylSPer-

ceivedtobehighandfallswhenlowdeliverydelayslgnalsexcesscapacity.Be-

causetheyalwaysanchorthedesiredcapacltydecisiononthecurrentlevelof

capacity,theycontinuetomoveuphilluntiltheslopeofthehill(productionpres-

sure)iszero.Note丘.omFigure15-7thatthe虫.actionalexpansionincapacityfalls

asthepressuretoexpandcapacitydrops･Thecautiousinvestmentpolicymeans expansionslowsasthesummitisapproached,reducingthechanceofovershooL6

H=C的tlbing

YouproposethecapacltyaCqulSitionformulationinFigure15-6inamodeland

demonstrateitsintendedrationalitytoyourclientbyshowl‡lgthetestsinFigure

15-8andFigure1519･YourclientobjectsthattheresponseofcapacltytOChanges

inordersinFigure15-9istooslow,polntlngtO血econservativecapacltyexpan-

sionfractionastheproblem･Exploretheimpactofmoreaggressiveresponsesto

expansionpressurebyrepeatingthepartialmodeltestswithasteeperexpansion

policy.

TestapolicylnWhichtheexpansionfractionrisesbythesameproportionas

thepressuretoexpandcapaclty.IfthepressuretoexpandcapacltyWere1.5,indi-

catlngdeliverydelaywasperceivedtobe50%abovenormal,thefirmwouldset

desiredcapaclty50%aboveitscurrentlevel.ThereferencelineinFigure15-7 showsthecapacityexpansionfractionforthispolicy.Whatisthebehaviorofthe

capacltySubsystemwiththisaggressivepolicy?Istheresponsestillintendedlyra-

tional?WhathappenswhenthecapacltyexpansionpolicylStwiceasaggressiveas

thereferenceline(theslopeoftherelationshipis2)?Underwhatcircumstances

couldyouJustifytheuseofsuchaggressivepoliciesinyourmodel?

15.5.4 TheSa一esForce

Figure15-10Showsthepolicystructureforthesalesforce.

6Hi11climbinglSnotthemostefflCientorreliableoptimizationheuristlCIMoresophisticated methodssuchassimulatedannealing,taboosearch,andgeneticalgorithmshavebeendevelopedto solvethelocaloptlmum,ruggedlandscape,andovershootproblems･Indifferentways,theyeach strikeoutatrarldorrlfrcimtimetotiirleaSaWaytOgetOffalocallPeakaildirlCreaSethechancethat youeventuallymakeyourwaytothemainsummit(theglobaloptimum).Fordetailssee,forexam -

ple,AartsandLenstra(1997);Rayward-Smithetal.(1996);andBarhenetal.(1997).Thesemeth- odshaveproventobeeffectiveinmanyoptlmizationcontexts,includingnp-hardtaskssuchasthe travellingsalespersonproblem･SomemodelersfindittemptingtOreplacethesimplehill-Climbing heuristicembeddedinthecapacityaCqulSitiondecisionrulewithoneofthesemoresophisticated methods.However,fewfirmsarewillingtoconductsuchexperiments.Theconservativemanagers inthefirmForresterstudied,andinmostfirms,WereunwillingtoinvestinexpensivecapacityJust toseeifbychanceitwouldimproveperformance.Whiletheseheuristicsareoftenexcellentopt1- mizationmethods,theyareusuallypoormodelsofactualhumanbehavior･Tojustifytheuseofone ofthesemethodswouldrequireevidencefromfieldstudyofthedecisionmakersthattheybehaved inafashionconsistentwi血血emoresophisticatedprocedure･

616 PartIV ToolsforModelingDynamicSystems

FIGURE15-10 Structureofthesalesorganization

ThegraylinkfromBacklogtoShipmentRaterepresentstheorderfulfillmentprocess(Figure15-3)and c一osestheSalesGrowthloopRl.

SalesForce

Adjustment Time

1-･r I

Costper Sales

Representative

y Fractionof Revenueto

Sales

Target Sales Force

モ Sa事es

HiringRate

Revenue Reporting

DeLay

Sales Effectiveness

Theorderratedependsonthenumberofsalesrepresentativesandtheireffec-

tivenessasmeasuredbyordersbookedperpersonpermonth:

OrderRate-SalesForce*SalesEffectiveness (15112)

Saleseffectivenessdependsonthenumberofcustomercallseachsalespersoncan

makepermonth(assumedtobeconstant)andthefractionofcallsresultingina

sale(theclosingrate),whichdependsontheattractivenessoftheproductinthe

marketplace(seethemarketsubsystem).

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 617

Theactualsalesforceadjuststothetargetsalesforcethroughthenethiring

rate.Theadjustmenttimeforthesalesforcerepresentsthetimerequiredtorecog-

nizeandfillavacancyandfornewsalespeopletobecomefullyeffective･7

SalesForce-INTEGRAL(SalesForceNetHiringRate,SalesForceto) (15-13)

SalesForceNetHiringRate (TargetSalesForce-SalesForce)

SalesForceAdjustmentTime (15-14)

Thenumberofsalesrepresentativesthesalesorganizationcansupportisdeter一

minedbythesalesbudgetandtheaveragecostofasalesrepresentative,including benefitsandoverhead.

TargetSalesForce SalesBudget

CostperSalesRepresentative (15-15)

Budgeting,asinmanyorganizations,isbasedonexpectedrevenue･Expectedreve-

nuesareregularlyupdatedandaremodeledbysmoothingactualrevenuewitha

31mOnthrevenuereportlngdelay.Thefractionofexpectedrevenueallocatedto

thesalesorganizationisassumedtobeconstant･Shipmentsandpricedetermine revenue.

SalesBudget-FractionofRevenuetoSales*RecentRevenue

RecentRevenue

-INTEGRAL(ChangeinRecentRevenue,RecentRevenuet｡)

ChangeinRecentRevenue -(Revenue-RecentRevenue)/RevenueReportingDelay

Revenue-Price*ShipmentRate

(15-16)

(1 5-17)

(15-18)

(15-19)

Consistentwiththeprinciplesofboundedrationality,theformulationsforthesales

budgetandforthetargetsalesforcedonotinvolveanyattempttodeterminethe

optlmalnumberofsalesrepresentativesJnstead,asinmanyorganizations,･each

majorOrganizationalfunctionreceivesatraditionalfractionofthebudget,perhaps

adjustedslightlyasotherfactorsvary.Budgetsarebasedonrecentactualrevenue

anddonotinvolvecomplicatedforecastlng.

Isolatlngthesalesorganizationfromtherestofthesystemteststheintended

rationalityofthesalesorganization'sdecisionrules.Theaveragecostissetto

$8000perpersonpermonth.Thefractionofrevenuetosalesissetto20%,andthe

productpriceis$10,000/unit.InthesimulationinFigure15-ll,capacityisas-

sumedtobeperfectlyflexible,Soorderscanalwaysbefilledinthenormaldeliv-

erydelay,andsaleseffectivenessisassumedtobeexogenous.

Forthefirst60months,saleseffectivenessishigh-10units/person/month.As

aresult,thesalesforcegeneratesmoremoneyfわrthesalesorganizationthanit

costs.Asrevenuegrows,andwithitthesalesbudget,thesalesforcerises.Thead-

ditionalsalespeoplebookevenmoreorders,leadingtostillmorerevenuegrowth

7AmorerealistlCmodelwouldseparatenethiringIntoSeparatehiring,qult,andlayoffrates sincethedecisionprocessesandtimedelaysaffectingeachoftheseflowsaredifferent(section 13.3.3).However,Forrester'snethiringformulationprovidesareasonablefirstapproximationfor thepresentpurpose.

618

FIGURE15-ll

PartialmodeHest ofthesales

organization

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firmenjoysrapidexponentialgrowth･Inmonth60saleseffectivenesssuddenly

dropsto25%ofitsorlglnalvalue.Ordersimmediatelyfall.Thesalesforcecontin-

uestogrowforafewmonthsduetorevenuesgeneratedbyordersalreadyinthe

backlogandthedelaylnreVislngthesalesbudget.Soon,however,thesalesorga- nizationisforcedtodownsize.Withsaleseffectivenesssolow,thesalesforcenow

costsmorethanltgeneratesinsalesbudget.Thesalesforcedeclinesexponentially

andwouldeventuallyreachzero･8

Asinthecaseofcapacityexpansion,thedecisionrulesforbudgetingandfor

investlngfundsinthesalesorganizationinvolvenooptlmization.Thefirmisnot

8Thecompanywillgrowwhenevertheopen-loopsteadystategain(OLSSG)ofloopRlis greaterthanone.ForaloopconsistingOfnvariables,xl,･.･,Xn,theOLSSGisdefinedbyfirst breakingtheloopatanypolnt,SayXl,defininganlnPutVariablexT.andanoutputvariablex?.The

OLSSGisthenglVenbythesteadystatechangeintheoutputinresponsetoapresumedchangein theinput:

OLSSG-.tljT票 -(慧 )(忠 )･･･鹿 )

TocalculatetheOLSSGfortheSalesGrowthloop,recallthatinequilibriumtheoutputofafirstl ordernegativefeedbackprocesssuchasexponentialsmoothingequalsitsInput.Thusinsteady state,SalesForce-¶lrgetSalesForce,Shipments-Orders,andRecentRevenue-Revenue･

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 619

abletocalculatetheoptlmalallocationofitsresourcesamongdifferentactivities

anddoesnotknowtheoptimalsalesforce.Thedecisionrulesthefirmusesfor

budgetingandsalesforcemanagementembodyaslgnificantdegreeofbounded

rationality.

Yetthesedecisionrulesenablethesalesorganizationtobehaverationally･

Whenevereachdollarofrevenuegeneratesmorethanadollarinnewbookings, thecompanygrows.Wheneachdollarofrevenuereturnslessthanadollarinnew

bookings,thesalesorganizationandcompanyshrink.Therulesofthumbforbud一

getlngandsalesforcemanagementenablethefirm togrowuntilitreachesthe

equilibriumpredictedbystandardeconomictheory,eventhoughtheagentsinthe

modeldonothavetheinformationorcapabilitytosolvetheprofitmaximization

problem(seethechallengebelow).

15.5.5 TheMarket

Inthefullsystemsaleseffectivenessisnotconstant.Figure15112showsthestruc- tureofthemarketsector.

Saleseffectivenessdependsontheattractivenessoftheproductinthemarket-

place･Forsimplicity,Forresterassumedattractivenessdependedonlyontheavail-

abilityoftheproduct,measuredbydeliverydelay.Inreality,theattractivenessof

theproductdependsonahostofattributesbesidesavailability,1nCludingprlCeand

financlngterms,quality,supportandservice,andsoon.Forrester'sfull"corporate

growthmodel"(Forrester1964,1975a;Packer1964),aswellasmanymodels

since,representsmarketshareanddemandasdependingonawiderangeofattri-

butes(seeFigure3-7).

SalesEffectiveness-NormalSalesEffectiveness*EffectofAvailability (15120) onSalesEffectiveness

EffectofAvailability ,/DeliveryDelayPerceivedby

onSalesEffectiveness J＼ MarketTargetDeliveryDelay (15-21)

Delivery

pe?cei1Fvyed -SMOOTH(percEevli:ebryyCD.eE芸any,perTcieTveefBre:vaerrkyeBteolay)(15-22)

byMarket

Aone-unitchangeintheSalesForcethereforeproducesasteadystatechangeintheTargetSales Forceof

OLSSG SalesEffectiveness*Price*FractionofRevenuetoSales

CostperSalesRepresentative

LoopswithOLSSG>1exhibitexponentialgrowth,thosewithOLSSG<1exhibitexponential decline,andthosewithOLSSG-1haveneutralstability.Withtheparametersofthebasecase growthrequlreS

SalesEffectiveness>8000S/person/month 10,000S山nit*0.20 4units/person/month

WhiletheOLSSGdetermineswhetherthefin growsordeclines,therateofgrowthdependson thetimeconstantsofthedelaysintheloop:Theshorterthedelays,thefasterthegrowthrate.

620 PartIV ToolsforModelingDynamicSystems

FIGURE15-12 Structureofthemarketsubsystem

ApplyingtheBakerCriterion(whatdocustomersknowaboutavailability,and whendotheyknowit?),itisclearthatcustomersarenotawareoftheactualde- liverydelaybutmustestimateitfromdeliveryquotesprovidedbythecompany (andtheirownexperience).Themarket'sperceptionofavailabilitythereforelags thecompany'sownperceptlOnOfthedeliverydelayusedtoprovidedelivery quotes.Themarket'sreactiontoavailabilityisfurtherdelayedbecauseittakestime forcustomerstoupdatetheirperceptlOnSOfdeliverydelayandstillmoretimeto shifttheirbusinesstoorawayfromthecompany.TheperceptlOnandreaction delayforthemarketresponsetodeliverydelaylSassumedtobe12months,long enoughtocaptureboththeperceptlOntimeandthetimerequiredtorespond, Alargeincreaseinleadtimesinducessomecustomerstodropthecompanyandgo withacompetitor,butittakestimeforthemtoselectandqualifyanewsupplier andtoreconfiguretheirownproductsandoperationsaccordingly.Figure15-13 showstheassumedeffectofperceivedproductavailabilityonsaleseffectiveness.

Whenthemarketperceivesthatdeliveryleadtimesequaltheirtarget,salesef- fectivenessequalsitsnormalvalue.Asdeliveryleadtimesincreaserelativetothe acceptablelevel,saleseffectivenessfalls.Thedeclineinsaleseffectivenessaccel- eratesasdeliverydelayrisesabovetheacceptablelevel,untiltheonlycustomers leftarethosewhoarewillingtowaitfortheproductduetoitsunlqueSuitabilityto

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 621

FIGURE15-13

Marketresponse toproduct availability

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loyalcustomersaway.

Themarket'sresponsetoavailabilitycreatesthebalancingAvailabilityfeed-

back(B3).An increaseinleadtimescausesthemarkettoshifttoothersuppliers,

reducingordersandeventuallyhaltingfurtherincreasesinleadtime.Thedelayln

themarketresponseensuresthatcustomersdon'toverreacttoshort-term fluctua- tionsinleadtimes.

15N5.6 BehavioroftheFuI≡System

Thepartialmodeltestsaboveshowthateachorganizationalfunctionanddecision-

makingcenterinthemodelf+irm isintendedlyrational.Eachumitcanrespondinan

appropriate,stablefashiontochangesinitsenvironment･Operationsmanagersc.an meetdemandaslongastheyhavesufficientcapacity･SeniormanagementIn-

creasescapacitysmoothlyandbytherightamountwhendemandincreases･The

salesorgamizationgrowswhenitisprofitableandshrinkswhenitisnot. Eachfunctionintheorganizationbehavesinasensiblefashionfromthelocal

perspectiveofitsmanagers.Ifeachsubsystemisintendedlyrationalandsmoothly

adjuststomeetitsgoals,shouldn'ttheorganizationasawholereachitsobjectives asweu?

Figure15-14shows血ebehaviorof血ewholemodel.Nowtheindividual functionsinteractwithoneanotherandwiththemarket.

Thebehaviorofthef+irmasawholeisfarfromoptimalorevendesirable.Sales

dogrow,butunanticIPatedinteractionsofthedifferentorganizationalfunctions

createsevereproblems･First,㌢ow也ismuchslowerthanpotential.(Compare salestothecurvelabeledPotentialRevenue,whichshowshowfastsaleswould

growifthe氏rmwerealwaysabletodeliverontime.)Second,growthisfarfrom

smooth.Thefirm goesthroughrepeatedboomandbustcycles,asseeninthefluc-

tuationofthebook-to-billratio.Duringsalesslumpsordersfallbyasmuchas

50%.Revenuealsodropsduringtheslumps,thoughlessthanordersasthef+irm

drawsdownitsbacklog.Withtheparametersofthebasecase,thesalesslumpsare

sosevereitislikelyseniormanagerswouldbefiredandquitepossiblethecom-

panywouldbetakenoverduringoneofthedownturns･

FIGURE15-14 BehaviorofthefuH

marketgrowth model

Thepotential revenueCurve

showswhat revenuewouldbe

ifthefirmalways hadenough

capacitytofill ordersontime.

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Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 623

Theslowgrowthandboom-bustcyclesareentirelyselfjnflicted.Theyarise

throughtheinteractionofthefeedbackloopscouplingthedifferentorganizational

functionsofthefirmtooneanotherandtothemarket･Specifically,thelocallyra- tionalcapacltyaCqulSitionandsalesforceexpansionpoliciesinteractwiththemar- ket'sresponsetoavailabilitytocreateapersistentmismatchbetweenordersand

capacity.Atfirst,capacitylSample,andthefirmexperienceshealthygrowthin salesastheSalesGrowthloopdominatesthebehaviorofthesystem.Growingrev- enueleadstoexpansionofthesalesforceandstillmorerevenue.Afterabout3 years,Capacitybeginstoconstrainshipments,utilizationrisesabovenormal,and

deliverydelaystartstorise.AfterwaitlngtOensuretheriseinleadtimesisn'ttem-

porary,Seniormanagementbeginstoexpandcapaclty･Duetotheirconservative investmentpolicyandthelongcapacltyaCqulSitiondelay,however,capacltyCOn- tinuestolagbehindorders,allowingdeliverydelaytobuildupevenhigher.

Whilethefirmstrugglestoexpandcapacity,Customerslearnthatleadtimes forthefirm'Sproductsareveryhighandbegintodesignthefirmoutoftheirown productswhiletheyseekothersourcesofsupply.Saleseffectivenessdrops.Orders falljustascapacltyStartstOincrease.Thebook-to-billratiosoondropsbelowone

andthebacklogdeclines.Deliverydelaynowimproves,butittakestimeforthe

markettorespond･CapacltyOrderedduringtheearliershortagecontinuestoarrive. Utilizationanddeliverydelaysoonfallbelownormal.Management,respondingto theexcesscapaclty,scalesbackitsinvestmentplansandsooncapacltygrowth slows.Atthesametime,saleseffectivenessbeginstoriseascustomersrespondto

thereadyavailabilityofproducLSalesrepresentativesfinditmucheasiertoclose, andanewspurtofordergrowthbeginsJustaSCapaCltygrowthslows.Ordersand

capacltyfluctuateoutofphase,WithcapacitygrowthlaggingWellbehindorders. Managersineachorganizationalfunctionbelievetheyaremakingsensibleand

rationaldecisions.Theirmentalmodelstreatvariablesoutsidetheirfunctionasex-

ogenousInputs-theglVenSOftheirsituation･Theorderfulfillmentorganization takesordersandcapacltyaSglVenandoutsideitscontrolanddoesitsbesttoship

productundertheseconstraints.Thesalesorganizationdoesthebestitcantogen- erateordersglVenthesalesbudget.Butbecauseeachfunctionislinkedwiththe

othersinanetworkoffeedbackloops,theseInputsareactuallynotexogenous

glVenSbutarestronglyinfluencedbytheirownbehavior･Becausethemanagersof theindividualfunctionsdonotaccountfortheseloopstheirdecisionsgenerate

unanticIPatedsideeffects,inthiscase,effectscountertotheirgoals.Becausethey

don'tunderstandthesystemicorlglnOfthesedynamics,theindividualmanagers arelikelytoblametheirproblemsontheincompetenceoftheircolleaguesinother functions,thefickledecisionsofthecustomers,orJuStPlainbadluck.

Imaglnehowmanagementmightreacttothefirstcrisis,whichbeginsaround month48.TheprlnCIPalsymptomofdifficultylSaPreCIPltOuSdeclineinorders.

Examinlngthemonthlynumbers,Seniormanagersimmediatelyseethatthesales forcehascontinuedtogrowandthatthecauseoftheslumpISthereforeasharp droplnSaleseffectiveness.Howmighttheyinterpretthisinformation?Often,as

Forresterobserved,theyblamedthesalesslumpontheweakleadershipandmis一 managementofthevicepresidentforsales,apoorlymotivatedorunskilledsales force,increaslngCOmPetition,orotherexternalfactors.Theseattributionsarecon- sistentwithbehavioraldecisiontheory.Peopletendtoviewcauseandeffectas

624 PartIV TわolsforModelingDynamicSystems

closelyrelatedintimeandspace:Ordersdependonthenumberandeffectiveness ofsalesrepresentatives;ifordersfall,thesalesforcemustbeatfault.

Thetendencytoblameoutcomesonindividualsorindividualcharacteristics

insteadofsituational,systemicfactors-thefundamentalattributionerror-rein-

forcestheproblem(chapterI)･Inthecontextofthesimulatedcompany,managers arelikelytoreasonthatpoorsalesforceperformancemustindicatethesalesforce

lsburnedout,poorlymanaged,orJuStplainlazy･Seniormanagementrespondsby attackingtheseapparentcauses,firingthesalesVP,sendingthesalesforcetoa

motivationalworkshoptoboostsaleseffort,startlnganewadcampaign,OrCuttlng prlCeS･Fromtheperspectiveofthefirm'smanagers,withtheiropen-loopmental models,thesepoliciesmakesense.Thepoliciesdirectlyattackwhattheyhavecon- cludedarethecausesoftheproblem.

Infact,theactualcauseoftheproblemisseniormanagement'sconservative capacltyaCqulSitionpolicyandtheunintendedinteractionsofthatpolicywiththe delaysincapacltyacquisition,thepoliciesofthesalesorganization,andthere-

sponseofthemarkettoavailability.However,thesesystemiccausesaredistantin timeandspacefromthesymptomsofdifficulty.Insidiously,policiesdesignedto

attackthesymptomsappeartoworkintheshortterm.AfterreplaclngthesalesVP, salesrebound,reinforcingthemanagers'erroneousbeliefsaboutthecausesofdif-

ficultyandpreventingthemfromdiscoverlngthehighleveragepointsforim-

provement(RepenningandSterman1999Showhowamajorautomakerwasable

toovercometheseself-reinforcingattributionerrors).

Po⊇icyDesig!lir!帥eMarketGrowthMode一

ThischallengeasksyoutoextendanddeepenyouranalystsOfthemarketgrowth

modeltobuildconfidenceintherealismandintendedrationalityoftheproposed decisionrules･Youalsoareaskedtodesignandimplementvariouspoliciestoim-

provetheperformanceofthefirm.

1.Policyanalysis:Salesforceproductivity

Considerthebasecasebehaviorofthefullmodel･Supposesenior managementrespondstothefirstsalesslumpbyfiringthevicepresident

forsales,improvlngSalesforcetraining,andbringlnglnanexpensive motivationalspeakertopumpupthetroops.Assumethesepoliciesareinfact successfulinpermanentlyincreaslngtheenergy,Skill,andeffortofthesales

force,boostlngnormalsaleseffectivenessby25%･Further,ignoreanycosts associatedwiththenewpolicy(specifically,assumethereisnochangein

thecostpersalesrepresentativeoranyotherparameters)･Also,ignoreany implementationdelays･Implementthepoliciesinmonth60.Obviously, replacingtheVPforsalesandtheotherpoliciesareunlikelytoyieldsuch alarge,permanentincreaseinsalesproductivltyandwillhavesignificant

costs.Examinlngthecostless,permanentlyeffectivepolicymayprovide insightintothedynamicsofthebusiness.

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 625

a. Beforesimulatingthemodel,writedownwhatyouexpect.Sketchthe behavioryouexpectforthevariablesinFigure15-14underthenew

policy.Brieflyexplaintherationaleforyourjudgment.

b. Simulatethepolicy.Whatistheshort-runeffectofthepolicy?What isthelong-runeffect?Why?Doestheinterventionsolvetheproblems facingthefirm?Wh y/whynot?Howdidtheactualbehaviordifferfrom

yourexpectations,andwhy?

C. Howdoyouthinkseniormanagersmightinterprettheoutcomeofthe

policylnterVention?Whatmighttheydonext?

2.Flexiblegoalsforavailability

ThecapacltyaCqulSitionformulationassumesseniormanagement'sgoal

fordeliverydelaylSCOnStantandequaltothenormaldelayof2months･ Becauseproductiontechnologyandproductdesignsareconstantlychanglng

thenormaltimerequiredtofillorderscouldvary.Forresterfoundthat management'sgoalfわrdeliverydelay-thedeliverydelayseniorexecutives

consideredtobeacceptable-adjustedovertimetothedeliverydelay

perceivedbythecompany(aflOatinggoal,Seesection13･2･10)AHealso foundthatseniormanagementtendedtothinkthatdeliverydelayswere lowerthantheyactuallywere.Management'sperceptlOnStendedtobebased

onthefirm'sownleadtimequotes,notontheactualdeliveryexperienceof customers.Forresterfound,intum,thatleadtimequotes,especiallythose

providedtoseniormanagement,tendedtobeoveropbmistic･Consequently, management'sperceptlOnOfdeliverydelaywasbiasedandwasactually lowerthanthedataindicated.

Figure15-15showsonewaytomodelthegoal-settlngprocess.The

formulationforthepressuretoexpandcapacltySubtractsthebiasfromthe deliverydelayperceivedbythecompany.Thecompanygoalfordelivery

delaybecomesaweightedaverageofafixedgoalandthetraditionaldelivery delay.Thetraditionaldelayadjustsviafirst10rdersmoothingtothedelivery delayperceivedbythecompany｡

a. AddthegoalsettlngStructureinFigure15-15toyourmodel.Assume thefixedgoalfordeliverydelayis2months,asintheorlglnalmodel, andthetimetoadjustthetraditionaldeliverydelayis24months.Setting thedeliverydelaybiastozeroandtheweightonthetraditionaldelivery

delaytozeroisthenequlValenttotheorlglnalmodelinwhichthetarget deliverydelaylSCOnStant.Makesureyourfomulationisdimensionally COnSIStent.

b. Next,designandimplementpartialmodelteststoexaminetheintended

rationalityofthegoaトsettlngprOCeSS･Assumetheweightonthe traditionaldeliverydelaylSOneandthedeliverydelaybiasiszeroJsthe formulationintendedlyrational?Howmighttheformulationbejustified

intermsoftheprinciplesofboundedrationalityandtheempirical findingsofbehavioraldecisiontheory?Repeatthetests,settlngthe

biasto,forexample,0.5months･Aretheresultsstillintendedlyrational? Why/whynot?Howmightthedeliverydelaybiasbejustifiedinterms

626 PartIV TわolsforModelingDynamicSystems

FIGURE15-15 Revisedstructureforthedeliverydelaygoal

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Weighton Traditionaf

DeliveryDelay

ofthetheoryofboundedrationalityandtheresultsofbehavioral

decisiontheory?

C. Afteryouhavetestedthegoalsettingformulationinisolation,runthe

fullmodelunderthefollowingCOnditions:

i･ Settheweightlbrthetraditionaldeliverydelaytoone;keepdelivery

delaybiassetatzero.

ii･ Settheweightforthetraditionaldeliverydelaytooneanddelivery

delaybiast00.5month.

Howdoesthegoal-settlngProcessaffectthedynamicsofthefirmasa whole?

3.Designingahighleveragepolicy

a･ Desigr.arevisedcapacrLyaCquiSitiorlPOlicyfo‡thefifrrltOovercomethe

limitationsoftheorlglnalpolicy.Yourpolicyshouldenablethefirmto

avoidtheboomandbustandslowgrowthoftheorlglnalmodel.Keep yourpolicysimple.Yourpolicymustbeconsistentwiththeformulation

prlnCiplesdiscussedinchapter13andwiththeprlnCiplesofbounded

rationalityandbehavioraldecisiontheory.Ifyourpolicyutilizes

differentinformationcuesthantheorlglnalpolicy,besuretoconsider

possibledelaysintheacqulSltlOnandinterpretationofthesecues.

Chapter15 ModelingHumanBehavior:BoundedRationalityorRationalExpectations? 627

b. Testyourrevisedpolicyforintendedrationality.Whenordersare

consideredtobeexogenous,willyourreviseddecisionruleadjust

capacltylnanapprOprlateandreasonablefashionwhendemand

changes?

C･ Finally,testthebehaviorofyourrevisedformulationinthefullsystem. Discusstheresults.Considerthereasonsforthedifferencesand

improvementsinthebehaviorofthemodel,thefeasibilityof

implementlngSuchapolicylnrealorganizations,andtherobustnessof

yourpolicyintherealworld.Forexample,Willyourpolicyworkina

worldwheremarketpotentialisnotunlimitedandthemarketmight saturate,decline,orfluctuate?

4｡Effectivenessofsearchforprofit-maximlZlngequilibrium

Returntothepartialmodeltestofthesalesorganizationintheorlglnal

model.Inthediscussionofthesalesorganization'sbehavior,Iassertedthat

therulesofthumbforbudgetlngandsalesforcemanagementenablethefirm

togrowuntilitreachestheequilibriumpredictedbyeconomictheoryeven

though theagentsinthemodeldonothavetheinformationorcapabilityto

solvetheprofitmaximizationproblem･However,inthetestshowninFigure 15-llthereisnoequilibriumbecausethemarketpotentialisassumedtobe

unlimited･Thetestshowsonlythatthecompanygrowswheneversaleseffort

yieldsmorerevenuethanitcosts,andviceversa･Amorerealisticassumption isthatmarketpotentialisfiniteandthattheeffectivenessofsaleseffortfalls

asthatlimitisapproached･Inthatsituationthesalesforceshouldgrowuntil

saleseffectivenesshasfallenenoughsothatthecostofadditionalsales

representativesJustequalstheadditionalsalesbudgettheygenerate.

a･ Evaluatetheabilityoftheformulationforthesalesorganizationtoreach

theprofit-maximlZlngequilibriumpredictedbyeconomictheory.

Assumesaleseffectivenessdeclinesasthecompanygrows.Specifically,

assumesaleseffectivenessdeclineslinearlyasthesalesforcegrows relativetosomemarketpotential:

SalesEffectiveness-f(SalesForce)-NormalSalesEffectiveness

*MAX 0.1 SalesForce*NormalSalesEffectivenessl (15123) MarketPotential

whereMarketPotentialisaconstant.Usingthisformulationforsales

effectiveness,replicatethepartialmodeltestofthesalesorganizationby

assumlngtheshipmentrateisalwaysequaltothedesilredshipmentrate. AssumeMarketPotential-2000units/monthandNormalSales

Effectiveness-10units/person/month･

b･ Doesthesalesforcereachanequilibrium?Ifthereisanequilibrium,is theapproachtothatequilibriumsmoothandstableordoesthemodel

fluctuatearoundit?Ifthereisanequilibrium,isittheprofit-maximizlng

equilibriumpredictedbyeconomictheory?Toanswerthislastquestion,

treatthesalesorganizationasaprofitcenter.Thenetprofitofthesales

628 PartIV TわolsforModelingDynamicSystems

departmentrTTisdefinedasitsrevenue(thesalesbudgetitreceives)less

itsexpenditures(thecostofthesalesoperation):

¶ -Sales】〕udget-SalesExpenditures (15-24)

Revenueandthefractionofrecentrevenueallocatedtosalesdetermine

thesalesorganization'sbudget(15-16);thesalesforceandcostpersales

representativedetermineexpenditures:

7T= Fractionof *Recent Sales小 Costper RevenuetoSales Revenue Force SalesRepresentative

(15-25)

Inequilibrium,RecentRevenue-Revenue-Price*Shipments- Price*OrderRate.Thesalesforceandsaleseffectivenessyieldthe

orderrate(15112)).Therefore,equilibriumprofitsare

･ - Fiicv:1芸neuseof*price*EffeStallveesness*FS.ai:: FS.aiec:*RepCr:os蔓enp;eartive (15-26)

From(15-26)youcanderiveanexpressionfortheprofitofthesales

organizationasafunctionofthesizeofthesalesforce.Themaximum

profitoccurswheretherateofchangeofprofitsasafunctionofsales forceiszero,thatis,when

d′汀

d(SalesForce)

F ractiono f

Revenue *Price *

toSales

Sa le s

Effectiveness

Costper Sales

Representative (15-27)

Derivetheequilibriumsalesforcefromtheexpressionforequilibrium

profits,assumingsaleseffectivenessisspecifiedaccordingto(15-23).9

Comparetheeconomicequilibriumtothebehaviorinyourpartialmodel

test.Doestheboundedlyrationalformulationforsalesmanagement

enabletheorganizationtoreachtheprofit-maximlZlngequilibriumeven

thoughtheorganizationdoesnotknowwhatthatequilibriumis?What

circumstancesmightpreventthesalesorganizationfromconvergingtO

theprofit一maximizlngequilibrium?

5｡Generalizingthehill･dimbinghellristic

Giveotherexampleswherelocallyrationaldecisionmlesenablepeopleor

organizationstosearchfortheoptlmalstateofasystemwithoutglobal

knowledgeoftheterrain.

9Technically,(15127)isthefirst-orderconditionforprofitmaや ization･Tobesureanyvalueof salesforcesatisfying(15127)maximizesprofitsinsteadofminimlZlngthemrequiressatisfyingthe second-orderconditionthatthesecondderivativeofprofitswithrespecttosalesforcebenegatlVe. Confirmthatthisissoforyoursolution.

Chapter15 ModelingHumanBehavlOr:BoundedRationalityorRationalExpectations? 629

15.6 SuMMARY

SimulationmodelsaredescrlptlVe.Thedecisionrulesinmodelsmustconformto

actualpractice,wartsandall.Themodelercanthendesignpoliciestoimproveper- formance.Anextensivebodyofevidenceshowsthattherationalityofhumande- cisionmakingisbounded.BoundedrationalityarisesbecausethecomplexltyOf

thesystemsinwhichweliveandthedecisionswemustmakeoverwhelmourcog- nitivecapabilities.Consequently,weusevariousheuristics-rulesofthumb-to enableustomakereasonabledecisionsinthetimeavailable.However,Sometimes

theseheuristicsproducesystematicerrorsandcausethequalityofdecisionmak-

1ngtOfallfarshortofrationalbehavior.Researchinbehavioraldecisiontheoryhas documentedawiderangeoftheseheuristicsandidentifiedmanyerrorsandbiases towhichtheyfrequentlylead.

Thechaptershowedhowmodelsconsistentwithboundedrationalityand behavioraldecisiontheorycanbeformulatedandhowtheintendedrationalityof thedecisionrulescanbetested.Partialmodeltestsenableyoutoassesswhether thesimulatedagentsandorganizationalsubunitsarelocallyrationalglVentheir mentalmodels,localincentives,andknowledgeofthesystem.Partialmodeltests helpuncovernawsinmodelformulationsandhelpbuildconfidencethatyourrep- resentationofthedecisionrulesofthepeopleinthesystemaresensibleandcon- sistentwithyourknowledgeofhowtheythinkandbehave･Partialmodeltestshelp youtoidentifysituationswheresensiblepeopleoperatingWithintendedlyrational decisionrulescaninteracttocreatedysfunctionaldynamicsforthesystemas awhole.

ぎ童re開き蔓sa重責喜て･lg-ge吾寵短丁至ミ‥ 主毎垂e呈言訳等FLX葺準∈短号圭導き_-3F葺きデA-1!_露呈珊

Stockshavereachedwhatlookslikeapermanentlyhighplateau.

IIrvlngFisher,ProfessorofEconomics, YaleUniverslty,October1929

Thetrendwillcontinueuntilitends.

-JamesDines,stockmarketanalyst (TheWallStyleetJoumal,21May1992)

Expectationsarefundamentaltodecisionmaking.Modelersmustportraytheway

theagentsrepresentedintheirmodelsformforecastsandupdateexpectations.

Thesemodelsmustbeconsistentwiththepnnciplesofmodelformulationdeve1-

0pedinearlierchaptersandmustbegroundedinempiricalstudyinthefield.This

chapterdevelopsaboundedlyrationalformulationfb∫modelingforecastlngand

expectationformation,particularlvforsituationswherethevariableofinterestisノ

growlng.Examplesusedtotestthemodelincludeforecastsofinflation,commod-

1typrlCeS,andenergyconsumptlOn.

16.1 MoDELJNGExpECTATl0NFoRMATl0N

Alldecisionsdependonourmentalmodelsofthesituation.Expectationsaboutthe

futurebehaviorofthesystemformacriticalcomponentofthesementalmodels.

Weconstantlyformexpectationsaboutwhatislikelytohappen,andtheseexpec-

tationsguideouractions.Businessesandgovernmentsspendenormoussumson

631

632 PartIV ToolsforModelingDynamicSystems

forecasts,frompredictionsofeconomicgrowth,inflation,andexchangeratesto thechanceofarevolutionorterroristattack.

ModelsoftheforecastlngProcessmustCapturethewaypeopleformexpecta-

tions･Areforecastspreparedjudgmentallyorwithformaltechniques?Arethefor-

maltoolssimple(e.g.,exponentialsmoothing)Orcomplex(e.g･,large-scale

econometricmodeling)?Themodelmustcapturethecuesusedintheforecasting

processandthewaylnWhichthecuesarecombinedtoyieldthefわrecast.Howis

thispossible?Afterall,differentorganizationsforecastindifferentways.Someuse

complexmodelstoprepareforecasts;inthatcase,domodelershavetoincludethe

actualmodelusedbythedecisionmakerintheirsimulationsoftheorganization?

Therearecaseswheresimulationmodelsdoincorporatetheothermodelsusedby

theorganization.Inpractice,however,suchcomplexltylSrarelyneeded.Inasur-

veyofforecastlngpracticesatabout100UScorporationsSandersandManrodt (1994)foundthat

Althoughmanagersaremorefamiliarwithquantitativeforecastlngmethodsthanin thepast,thelevelofusagehasnotincreased.Practitionerscontinuetorelylargely onjudgmentalforecastlngmethods...Further,whenquantitativeforecastlngmethl odsareused,theyfrequentlyarejudgmentallyadjusted.

Realisticmodelsmustalsocapturethesocialandpoliticalforcesthatinfluencean

organization'sforecastsanddecisionmaking.Anorganizationmayusealarge econometricmodelwithhundredsofvariablestoforecasttheeconomicenviron-

ment,butifseniormanagersIgnorethemodel'soutputandgowiththeirgutfeel-

1ngS,thenyourmodeloftheforecastlngprocessCan'tassumethesophisticationof

thelarge-scalemodel.insteadyoumustcapturethewaysinwhichthemanagers'

intuitivejudgmentsareformed,thatis,howtheinformationtheyconsumeandthe

waytheydigestitleadtothatcertainfeelingintheirgut.

Thoughmanyorganizationsspendconsiderableresourcesgeneratlngandpur-

chasingforecasts,forecastinglSasocial,political,andbureaucraticactivlty,nota

scientificone.GalbraithandMerrill(1992)studiedtheforecastingpracticesof

largecompaniesandfoundthatmanagementfrequentlyadjusted,tweaked,andig-

noredtheforecastsgeneratedbycorporateforecastingstaff(Table16-1).

Thesocialandpoliticalnatureofforecastlngmeansmanyjudgmentalheuris-

ticsandothermanifestationsofboundedrationalitymayhaveconsiderableinflu-

enceontheforecastlngprocessandcanleadtopersistent,systematicforecasting errors.

Expectationsareusuallymodeledinsystem dynamicsasadaptivelearnlng

processessuchasexponentialsmoothing.AdaptlVeexpectationsarecommonin

economicmodelsaswell.1Adaptiveexpectations(singleexponentialsmoothing)

Outperformmanyotherforecastingmethodsoverlongertimehorizons(Makridakis etal.1982;Makridakisetal.1984;CarboneandMakridakis1986).

iForexample,IrvingFisher'S(1930)theoryofinterestrates,Nerlove'S(1958)cobwebmodel, Friedman'S(1957)permanentincomehypothesis,‖oltetal.'S(1960)productionscheduling models,thebehavioralmodelsofCyertandMarch(1963),AndoandModigliani'S(1963)life cyclehypothesisofsaving,andEckstein'S(1981)theoryof"coreinflation."

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFo-ation 633

TABLE16-1

ForecastinglSa

socialandpolitical

activity,nota

purelyscientific One.

Resultsofa

suⅣeyof

corporate

forecastingstaff inasampleof NewYorkand

AmericanStock

Exchange listedfirms

andcomparab一e

prlvate】yheld firms.

Managementrequestsstaffrevisionstoshowmorefavorableoutcomes 45%

Managementmakesownrevisionstoshowmorefavorableoutcomes 26%

Managementrequestsbackcasts(modelusedtojustify

preselectedoutcome)

Incorrecttechniquesorassumptionsused:

Accidentally

De=berately

Managementignoresmodels/forecasts

Departmentswithholdinformationfromothers

Departmentssupplymisleadinginformationtoothers

Modelsaredeliberatelymisspecified

38%

1 6

1 2

Source:GalbraithandMerriH1992.

★ProbablyanunderestimateslnCethesurveyswerereportedbytheforecastingstaff,whohaveanin- centivetobelleVethelrworklSuSeM,arelikelytobetoldtheirworkisLmPOrtantbysuperiors,andare notalways(orevenusua=y)privytotheactualdecision-makingprocess･

However,sometimesexpectationsrespondnotJusttOthehistoryofthevari-

ablebuttoitspastgrowthrateaswell.Forexample,thepastvaluesandpasttrend

inordersmaybeusedtoestimatethelikelyfutureorderrate.Exponentialsmoothl

lngdoesn'tworkwellfortrends.Theoutputalwayslagsbehindtheinput,Causlng

asteadystateerrorwhenevertheinputissteadilygrowlng.Steadystateerror

meanstheoutputneverequalstheinput,evenaftersufficienttimefortransientad-

JuStmentShaspassed･2

AllprocedureslbrestimatlngatrendrequlreCOmparlngrecentValuestohis-

toricalvaluesinsomefashion.Forexample,acompanymayestimatethefuture

growthrateofrevenuebycomparlngCurrentyearrevenuetOrevenuefrom the

prioryear.Severalissuesariseinthisseeminglysimpletask(Figure16-1). First,theforecastermustgetup-to-dateinfom ationonthevariableofinterest,

Oftentherearesignificantmeasurementandreportingdelays.Afirmmayhaveto

waituntilthecloseofthefiscalyeartogetanaccurateestimateofannualrevenue

tocompareagalnStprlOryearSales.

Second,mostvariablesaresomewhatnoisy-theirvaluesfluctuateinanun-

predictablefashionaroundthetrend｡Short-termnoisemustbefilteredoutsothe

expectedtrenddoesnotbouncearoundwithtemporaryvariationsinthecurrent

value.Acompanycanshortenthedelaylngettlngrevenuedatabyuslngunaudited

quarterlyormonthlyestimatesratherthanwaitlngforthecloseofthefiscalyear. However,quarterlyormonthlydataaremorelikelytovaryWithseasonalandother

temporaryfactorsthatdivergefromtheunderlyingtrendandaremorelikelytobe

revised.Shorteningreportingdelaysreducesthereliabilityofthedata.

2RecallthatinadaptlVeeXPeCtat10nStherateofchangeintheexpectationXxisgivenby dXヅ/dt-(X-X史)a),whereXistheinPutvariableandDisthetimeconstant.SupposeXgrows linearlyatraterunits/timeperiod.InthesteadystateXHmustalsobegrowlnglinearlyatrater, requiring(X不-x)/D-r,yieldingasteadystateerrorgivenbyX虫-x-rD.Section16.6derives thesteadystateerrorwhentheinplltgrowseXpOllentially.

634

FJGURE16-1

Theforecasting challenge

Hypothetical forecastsof avariabJe. Measurementand

reportingdelays meantheactual currentva一ueof thevariableto

beprojectedis unknown,

introducingerror. Thelengthof thehistoricaltime horizonusedto estimatethe

trendintheinput dramatically affectsthe forecast.

PartIV TわolsforModelingDynamicSystems

Third,theforecastermustdecidehowfarbackinhistorytoconsider.Inesti-

matlngfuturerevenuegrowth,ShouldthefirmcomparerecentsalestoprlOryear

salesortosalesoveralongerhorizonsuchas5years?Ashorthistoricaltimehori-

zonwillleadtoanearlierresponsetochangesintrendsbutalsoamplifiesthere-

actiontotemporary恥ctuations.Theanswerstothesequestionsdependonthe

purposeforwhichthefわrecastisused,theamountofnoiseinthedata,andinstitu-

tionalfeaturessuchasthefrequencyofdatacollection,alongwiththevarious

judgmentalheuristicspeopleuse-deliberatelyandinadvertently-toprocessthe data.

16.1,̀き ModelingGrow帥 Expecモal.-ions: TheTRENDFunction

Growthexpectationsinsystem dynamicsareoftenmodeledwiththeTREND

function(Sterman1987).TheinputtotheTRENDfunctioncanbeanyvariable･

Theoutputisanestimateofthefractionalgrowthrateinthevariable･ButTREND

isnotJustaCleverwaytocalculategrowthrates｡Astheinputtodecisionrulesin

models,TRENDrepresentsabehavioraltheoryofhowpeopleformexpectations

andtakesintoaccountthetimerequiredforpeopletocollectandanalyzedata,the

historictimehorizontheyuse,andthetimerequiredtoreacttochangesinthe

growthrate.ThecausalstructureoftheTRENDfunctionisshowninFigure16-2･

TheTRENDfunctiongeneratestheexpectedrateofchangeintheinputvari-

able,expressedasafractionoftheinputvariablepertimeunit･TheTRENDfunc-

tioninvolvesthreeparameters,eachthetimeconstantofafirst10rderexponential

smoothingprocess:

PerceivedTrend-TREND(INPUT;TPPC,THRC,TPT)

TREND-INTEGRAL(ChangeinTREND,TRENDb)

TRENDt｡-<specifiedbyuser> ChangeinTREND-(ITREND-TREND)/TPT

ITREND-[(PPC-RC)/RC]/THRC

RC-INTEGRAL(ChangeinRC,RCt｡) RCt｡-PPCt｡/(1+THRC*TRENDt｡) ChangeinRC-(PPC-RC)/THRC

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation

FIGURE16-2 CausalstructureoftheTRENDfunction

Theoutputisanestimateofthefractionalgrowthrateintheinputvariable.Thestructurehasthree

parameters:thetimetoperceivethepresentstateoftheinput,TPPC;thehistoricaltimehorizon

agalnStWhichtheperceivedconcHtioniscompared,THRC;andthetimeforbeliefsaboutthetrend torespondtochangesinitsindicatedvalue,TPT.

OUTPUT

(ExpectedFractional GrowthRateoflNPUT)

PPC-王NTEGRAL(ChangeinPPC,PPCt｡)

PPCt｡-INPUTt｡/(1+TPPC*TRENDt｡)

ChangeinPPC-(INPUT-PPC)/TPPC

where

INPUT-Inputvariable(units),

TREND-Perceivedfractionalgrowthrateoftheinputvariable

(1/timeunits),

ITREND-IndicatedTrendintheinput(1/timeunits),

635

OUTPUT

(16-1)

636 PartIV ToolsforModelingDynamicSystems

RC-ReferenceConditionoftheinput(units),

PPC-PerceivedPresentConditionoftheinput(units),

TPT-TimetoPerceivetheTrend(timeunits),

THRC-TimeHorizonfortheReferenceCondition(timeunits),

TPPC-TimetoPerceivethePresentConditionoftheinput(timeunits).

Howistheperceivedgrowthratedeterminedfromtheinput?3Tobegln,thein-

stantaneous,rawvalueoftheinputvariableissmoothed,generatingthePerceived

PresentCondition.FirsトordersmoothinglSaSSumed･Thetimetoperceivethepre-

sentconditionTPPCrepresentstwofactors.First,assesslngthecurrentstatusof

anyvariabletakestime;TPPCmustthereforenotbelessthanthemeasurementand

reportingdelaysfortheinputvariable.Inthecaseofcorporateandeconomicdata, thedatacollectionandreportinglagmayrangefromseveralweekstoayear.Inthe

caseofdemographic,environmental,andsocialindicatorsthedelaysmaybeeven

longer.Second,eveniftherawdatawereavailableimmediately,forecastersmay

smooththereportedvaluesoftheinputtofilterouthighjrequencynoise.Noise

arisesfromtheprocessitself,frommeasurementerror,andfromsubsequentrevi-

sionsinthereporteddata.Theextentofnoiseinoneimportantandwidelypre-

dictedeconomicvariableisshowninFigure16-3,therateofinflationintheUS

consumerpriceindex(CPI).TheCPIisreportedmonthly･Between1947and1986 thestandarddeviationofinflationfrommonthtomonthwasl11% ofitsmean

value,clearlyshowlngtheneedtofilteroutshorトtermnuctuations.

Decisionmakersthencomparetheperceivedpresentconditiontoitspastval-

ues,measuredbytheReferenceConditionRC,todeterminewhethertheinputis

rislngOrfalling.Thereferenceconditionoftheinputisformedbyfirst-orderexI

ponentialsmoothingoftheperceivedpresentcondition.Thetimehorizonforthe

referenceconditionTHRCdeterminesthehistoricalperioddecisionmakerscon-

sidertoberelevantintheforecastingprocess.Equivalently,1/THRCistherateat

whichpastvaluesoftheperceivedinputarediscounted･4

TheoutputoftheTRENDfunctionisexpressedasafractionalgrowthrateper

timeperiod.HencetheindicatedtrendITRENDisthedifferencebetweentheper-

ceivedpresentconditionoftheinputandthereferencecondition,expressedasa

fractionofthereferenceconditionandthendividedbythetimehorizonfortheref- erencecondition.5

Theindicatedtrendprovidesthemostup-to-dateinformationonthecurrent

fractionalrateofchangeintheinput.However,beliefsdonotadjustinstantlyto

3Theinitialvaluesofthereferenceandperceivedpresentconditionaresettoinitialize theTRENDfunctioninsteadystateattheinitialperceivedgrowthratesetbythemodeler (section16.6).

4NotethattheRCisnotthevalueoftheinputatsomeparticularpolntinthepastbutanexpo- nentiallyweightedaverageofallpastvaluesoftheinput.ThelongerthehistorichorizonTHRC, themoreweightisglVentOOldervaluesoftheinpllt.

5whiletheequationfortheindicatedtrendappearstocomputethelinearandnotcompound growthratetheexpressionfortheindicatedtrendactuallyyieldsthecontinuouscompoundingfrac- tionalgrowthrateintheinputbecausethereferenceconditionisformedbyexponentialsmoothing oftheinput(section16.6).

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 637

FIGURE16-3 ConsumerprlCe inflationinthe

UnitedStates, 1947-1986

Thegraphshows theannualized fractionalrate

ofchangeinthe mon州yvaluesof theCPl.

0.20

0.15

0.10

の卜II

謡 0.05 と ▼~

0.00

-0.05

-0.10

Source:Sterman(1987).

newinformation.TheTRENDfunctionallowsthedecisionmaker'sbeliefabout

thetrendintheinputvariabletoadjustgraduallytothevalueindicatedbythemost

recentdata･Firstl0rderinformationsmoothinglSassumedwithadelaygivenby theTimetoPerceivetheTrendTPT.Thelaglntheadjustmentoftheperceived

trendrepresentsthetimerequiredforachangeintheindicatedtrendtoberecog- nizedandacceptedbydecisionmakersasabasisfortheiractions.

HowshouldtheparametersoftheTRENDfunctionbeinterpretedandesti-

mated?Thetimetoperceivethepresentconditionisatleastaslongasanymea- surementandreportlngdelaysbutmaybelongeriftheinputvariableishighly noISyanddecisionmakersapplyadditionalaveraglngOrSmoothing.Thetimehori- zonforestablishingthereferenceconditionTHRCrepresentsthetimeframeover

whichthetrendisassessedandwilldependonthepurposeoftheforecast.Ingen- eral,thelongerthetimehorizonfortheforecast,thelongerthehistoricalhorizon shouldbe.However,thetimehorizonforestablishingthereferenceconditionisa

subjectivejudgmentandisinfluencedbythememoriesandexperiencesofindi- vidualdecisionmakers.Duringthe1970Stherateofeconomicgrowthinthein-

dustrializedworldslowedsignificantlyfrom theratesofthe1950sand60S.

However,economicforecasterswhoseprofessionalexperiencewasgainedduring

thehigh一growthdecadescontinuedtoforecasthighgrowthformanyyearsdespite theloweractualgrowthratesofthe1970sandSOS.Theybelievedtheslowgrowth after1973wasatemporaryaberrationandthattheeconomywouldsoonresume thegrowthratethatcharacterizedthepast.Thedelayintheacceptanceofanew

trendasanoperationalinputisoftenslgnificant.Theadjustmentlagdependsnot onlyonthetimerequiredforindividualdecisionmakerstorecognlZethechange butalsoonorganizationalinertia.Anewtrendmayhavetobecomepartofthecon-

ventionalwisdombeforesomearewillingtoact.Insuchcases,perceivedtrends maychangeonlyasfastasmanagementturnsoverandisreplaced.

638 PartIV n)OlsforModelingDynamicSystems

TheTRENDfunctionrepresentsforecastlngaSaboundedlyrationalprocedure

inwhichforecasterssmoothrecentdataandprojectrecenttrends･Isthereanyev- idencethatpeoplefわrmfわrecastsuslngSmoothingandtrendprq】ection?Sanders

andManrodt'S(1994)surveyfoundjudgmentalme血odssuchas"manager'sopin- ion,"à〕uryofexecutiveoplnion,Hand"salesforcecompositeHoplnionswerethe mostcommonmethodsusedinsalesforecastlnginUScorporations.Studiesof

judgmentalforecasting(erg"Makridakisetal.1993)showthatmostjudgmental forecastsarequlteSimilartosimplesmoothingwithtrendextrapolation.Among

theformaltechniquesusedbythesurveyedfirms,themostpopularweremovlng averages,exponentialsmoothing,regression,straightllineprojections,andnaive models.AlloftheseareformsofadaptlVeexpectations.Naivemodelsandmovlng

averagesaresimilartoexponentialsmoothing,differingonlyintheweightsacI

cordedtopastdata･Regressionandstraightllineprojectionlikewiseaverageout noiseandfluctuationsinthepastdata,thoughunlikesimplesmoothingtheyalso accountforgrowthtrends.

16.1.2 BehavioroftheTRENDFunction

TheTRENDfunctionhasthedesirablepropertythatitprovides,inthesteadystate, anunbiasedestimateofthefractionalgrowthrateoftheinput.Iftheinputgrows exponentiallyatrateg,thesteadystateoutputoftheTRENDfunctionisalsog(See section16.6foraproof).

TheparametersoftheTRENDfunctiondetermineitstransientresponseto changesinthegrowthrate･Figure16-4Showspartialmodeltestsillustrating,fora

rangeofparameters,itsresponsetoachangeinthegrowthrateoftheinput.Inthe simulations,aone-quarter-yearmeasurementandreportingdelay(TPPC)isas- sumed-avaluetypicalofmanycorporateandmacroeconomicdataseries.Thein- put,initiallyconstant,suddenlybeginstogrowataconstantexponentialrateof

5%/year･TheperceivedtrendinthevariablegeneratedbytheTRENDfunctionat firstdoesnotchange-thoughtheinputhasstartedtogrow,ittakestimeforthe newvaluestobereported.Theperceivedtrendthengraduallyrisestothetrue valueof5%/year.Thelongerthetimehorizonforestablishingthereferencecon-

ditionorthelongerthetimerequiredfordecisionmakerstoperceivethetrend,the moregradualtheresponse.

16.2 CASESTUDY:ENERGYCoNSUMPTEON

Whatwillenergyconsumptionbeintheyear2020?HowmuchelectrlCltyWilluti1-

itieshavetosupply10yearsfromnow?Long-termforecastsofenergyconsump- tion,bothattheaggregatenationallevelandatthefuel-andregion-specificlevel,

arecriticaltobothenergysuppliersandtothegovernment.Powerplants,refiner-

ies,andoilfieldsinvolvesomeofthelongestleadtimesofanyconstructionproI JeCtS,Oftenadecadeormore.Fortunatelyforutilitiesandoilcompanies,energy consumptlOnintheindustrializedworldgrewatfairlysteadyexponentialratesfor

mostofthepostwarperiod,andforecastlngWaseaSy･Butafterthefirstoilshock in1973economicgrowthslowed.Energyconsumptionfellsignificantly,andeven aftertheeconomyrecoveredfromtherecessionof1974-75,consumptiongrowth

wasbothslowerandmorevariable･ThebreakinhistoricenergyconsumptlOnpat-

Chapter16 ForecastsandFlldgeFactors:ModelingExpectationFormation 639

FlGURE16･4 Behaviorofthe TRENDfunction

Theinput,initiaHy constant,begJnStO growexponentiaHy at5%/yearat timezero.The

parametersare asindicated,with TPPC-0.25

yearsinalfcases･

(sJt=a ĴL)a l

t2tJ LJtn O J9 P

a 13

a d x 山

Jt28 ĴL) a

te tl LJt≧ 0 J9 P a 10

a d x 山

1 2 Years 3 4 5

ternsprovidesanaturalexperimenttoexaminetheabilityofforecasterstoantici- patethecrisis.Inshort,theydidn't-the1973CrisiscameasasurpnSetOnearlyall

energyproducers,governments,andforecasters.Itmaybeunreasonabletoexpect forecasterstohaveforeseensuchadramaticshiftintheglobaleconomicsandpol- iticsofoil.Howwell,then,didforecastersdoinadaptingtothenewworldof

volatileenergyprlCeSandslowereconomicgrowth? Thefirstoilshockin1973ledtothegrowthofahugeenergymodelingindus-

try,whichsoonoffereddetailedmodelsofeveryaspectoftheenergysystem.

Manyofthesemodelsareamongthemostcomplexpublicpolicymodelseverde- veloped.Unfortunately,theirforecastlngrecordispoor.

ForecastsofenergyconsumptionintheUnitedStates(andothernations)ad-

justedveryslowlytothenewrealitiesoftheenergysystem･Figure16-5Shows forecastsoftotalUSenergyconsumptionfor1985alongwithactualconsumption. After1973,asactualconsumptionfell,forecastsofenergyconsumptioninthe

UnitedStatesalsobegantodrop.Forecastsmadeintheearly1970sprqectedUS energyconsumptlOnin1985tobeabout130quadrillionBTUsorHquadsH (1quad/year-1015BTU/year).Actualenergyconsumptionin1985waslessthan

74quads,a75%overestimation.Similarerrorswereobservedintheforecastsfor othernationsandtimehorizonsandforelectricityandotherfuels(Lynch1994; NelsonandPeck1985).Thelargeerrorsandseeminglyreactivenatureofthefore-

castssuggesttrendextrapolationmayhavebeenusedbymanyoftheforecasters.

640

FIGURE16-5 ForecastsofUS

totalenergy consumptionin 1985

Eachpoint representsa forecastof

consumptionin theyear1985, plottedinthe yeartheforecast wasmade.

PartIV ToolsforModelingDynamicSystems

∧U

:■■Jt=â

JS P t2 n O

金運也匿せ㊤

◆ ◆f i . ;

皆 … 芸鵜 ÷ ◆鎗頼義浮㌔

1955 1965 1975 1985

Manyearlyforecasts,particularlyprlOrtOtheoilshocksofthe1970S,wereindeed madebyextrapolation.Buttrendextrapolationseemsnaivetomanyobservers, whopolntOut-qulteCOrreCtly-thatenergydemandforecastsareoftentheresult ofextensivestudiesinvolvingdetailed,multidisciplinaryanalysisandsophisti- catedmodels.

InSterman(1987,1988b)ItestedtheabilityoftheTRENDfunctiontomodel theevolutionofforecastsoftotalUSprimaryenergyconsumptionin1985(Figure 16-5).Theinputtotheforecastswasactualenergyconsumption.Theexpected fractionalgrowthrateestimatedbytheTRENDfunctionwasthenprojectedto continuefromthecurrenttimetotheforecasthorizonof1985.

Specifically,theforecastmadeinyeartofenergyconsumptioninforecastyear FY,denotedFCFY(t),WasCalculatedby

FCFY(t)-PPC(t)*(1+TREND(t)*TPPC)*exp(TREND(t)*(FY-t))(16-2)

wherePPCistheperceivedpresentconditionofactualenergyconsumptlOnand

TREND(t)-TREND(C(t);TPPC,THRC,TPT) (16-3)

istheexpectedtrendinactualconsumptionCestimatedbytheTRENDfunction. Inequation(1612)forecastersrecognizethatthemostrecentdataareoutof

dateduetomeasurementandreportlngdelaysandadjusttheperceivedpresent conditionbythegrowthexpectedtohaveoccurredbetweenthedaterepresented bythemostrecentdataandthepresenttime.ThegrowthcorrectionisTREND(t) *TPPC･Asshowninsection16,6,thiscorrectionensuresthattheperceivedpre- sentconditionwillequaltheactualvalueoftheinputwhentheinputisgrowlngat asteadyexponentialrate.Theforecastforsomefutureyearisthenconstructed fromtheestimateofcurrentconsumptiongivenbyPPC*(1+TREND*TPPC) byassumlngCOnSumptlOnWillgrowatthecurrentperceivedTRENDbetweenthe presenttimeandtheforecasthorizonFY.Equations(16-2)and(16-3)therefore yieldanunbiasedforecastinthesteadystateofexponentialgrowthintheinput.

IestimatedtheparametersoftheTRENDfunctioneconometricallyforfore- castsofenergyconsumptlOnin1985.TheestimatedparameterswereTPPC-1,2, THRC-5.4,andTPT-3.2years,respectively.Dataforannualenergycon-

sumptlOnatanytimewereonlyavailablethroughtheprlOryear,atbest,dueto measurementandreportlnglags,SotheestimatedvalueofTPPCisreasonable.The

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 641

FIGURE16-6

Responseof TRENDfunction

withparameters estimatedfor

energyforecasts

Theinput beglnSgrOWFng exponentially at5%/yearat timezero.

FIGURE16-7 Simulatedand actualforecastsof

USprlmaryenergy consumptionin 1985

(sJ t 2

a ĴL) a

lt2tJ Lll≧ 0 )9 P ¢ IU ad x

JIt=aN ⊃ トg u O !lJ!J P t2n

1945 1950 1955 1960 1965 1970 1975 1980 1985

Source.ISterman(1987).

Otherparametersarealsoreasonable.Energyconsumptionistiedtothesizeofthe

capltalstockintheeconomy,astockthattumsoveronlyslowly,glVlngCOnSump-

tionsignificantinertia.Forecastsoflong-term growthinenergyconsumptlOn

shouldbebasedonacorrespondinglylong-termhistoricalviewandarelikelyto

reactslowly;long-termforecastsshouldnotriseandfallwithshorトtermmove一

mentsinenergyconsumptlOnCausedbybusinesscyclesandothertemporaryvari- ations.Figure16-6showstheresponseoftheTRENDfunctionwiththeestimated

parameterstoastepchangeinthegrowthrateoftheinput.Theresponseisqulte

slow.IAfter5years,theexpectedgrowthratehasadjustedonly25%ofthewayto

achangeinthegrowthrateoftheinput;twodecadesarerequiredfortheexpected

growthratetoadjust95%oftheway.

Figure1617Comparesthesimulatedforecaststotheactualforecastsfor1985.

AsthegrowthrateofactualconsumptlOnroseduringthepostwarboom,thesim-

ulatedforecastsrisefromabout70quads/yearintheearly1950stoabout125

quads/yearin1973.Theforecastssteadilyfallafter1973asactualconsumption

growthslowedinthewakeof1973and1979Oilshocksandthedeeprecessionsof

1974175and1979-82.ThesimulatedforecastspassqulteClosetothemedianofthe

642

FlGURE16-8 Forecastand actuaHotal

electricity consumption intheUS

Forecastsofthe NorthAmerican

Electricity Reliability Counci一(NERC), 1974-1990.

PartIV Too一sforModelingDynamicSystems

( u 喜

王

suoI" ) )i

1960 1965 1970 1975 1980 1985 1990

Source:NelsonandPeck(1985).ReprintedwithpermlSS10nfromtheJoumafofBuslneSS andEconomicStatistJCS.Copynght1985bytheAmencanStatlStlCalAssociationlA"nghts resen/ed.

actualforecasts.Themeanabsoluteerrorbetweenthemodelandtheforecastsasa

percentofthemedianforecastexceedstheminimumpossibleerrorbyjust1%.6

Similarbehaviorisalsodocumentedforotherfuels･Forexample,10-year

forecastsoftotalUSelectricitydemandproducedbytheNorthAmericanElectric

ReliabilityCouncil,anindustryassociationofelectricutilities,exhibitsimilar

overshooting(Figure16-8).Electricitygrowthbefore1973hadbeenrathercon-

stantatabout7%/year･After1973thegrowthratefell.Theforecastsonlyslowly

adaptedtothechange,leadingtomorethanadecadeofgrosslyoveroptlmistic forecasts.NelsonandPeck(1985)showthattheNERCforecastsaremodeledex-

tremelywellbyexponentialextrapolationofcurrentconsumptlOnaSSumlngthe

historicgrowthratewillcontinue.Theymodeledthehistoricgrowthratewithfirst-

ordersmoothingoftheyear-to-yeargrowthrate,aproceduresimilartotheTREND

function･Theyfoundthesmoothingtimeduringthe1970Stobeabout5years,

consistentwiththeestimatedparametersfortotalenergyconsumption.

Forecastsofenergyconsumptionhavebeenmadewithawiderangeoftech-

nlqueSandmodels･ManyofthesemodelsarequlteCOmplexanddonotappearto

besimpleunivariateextrapolations.Yetnomatterhowsophisticated,eachmodel

reliesuponexogenousvariablesorparameters･ThesemightincludeGDP,popula-

tion,energyprlCeS,andtechnologlCalprogress.Theoryprovidesnostrongguid-

anceinselectingtheassumedfuturevaluesoftheseInputs,allofwhichmustbe

forecastjudgmentally･Alongwithhighlyuncertainparameterssuchastheprice

elasticitiesofenergydemandandthesupplycurvesfordifferentresources,theexl

ogenousinputsServeaSfreeparametersmodelersusetomanipulatetheforecasts

tobeconsistentwiththeconventionalwisdomoftheday.Thecorrespondenceof

thesimulatedandactualforecastssuggeststhattherecenttrendactsasastrong

constraintuponchoiceofthesefudgefactors.

IfrequentlyobservedsuchbehaviorwhenIworkedattheUSDepartmentof

Energyinthelate1970S･Seniorofficialsinthedepartmentwerekeenlyawareof

6sincethereareoftenmultipleforecastsforagivenyear,theminimumpossibleerrorisgreater thanzero.

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 643

theforecaststheiragencyandotherorganizationshadmadetheprioryear;these forecastsconstrainedwhattheydeemedtobepoliticallyacceptableforthecurrent

forecast.Someofficialsbelievedthedepartmentcouldnot,forpoliticalreasons, forecastfutureconsumptlOntObeaslowasprojectedbyenvironmentalgroups. Forecastsinwhichtheeconomywasassumedtogrowatlessthanhistoricalrates

orinwhichconservationreducedenergyconsumptlOnperCapltaWereCOnSidered unacceptable.Atthesametime,theyfeltitwouldbeunseemlyforthegovernment

toprojectCOnSumPtlOnexceedingtheaggressiveforecastsofoilcompaniesand energyindustryassociations.Thedepartment'sforecastsgenerallyfellnearthe highendoftherange.

Astrongherdmentalityamongforecastersreinforcedthedominanceoftrend

extrapolationbyensurlngthatnextyearヮsforecastswerebasedonandnottoodif-

ferentfromlastyear'S･In1972forecastsofUSprlmaryenergyCOnSumPt10ninthe year2000rangedfromahighofnearly200quads/year,projectedbytheDeparト

mentofthelnteriorandFederalPowerCommission,toalowof125quads/year, proJeCtedbyenvironmentalactivistAmoryLovins.By1983,asthetrendextrapol

lationmodelsuggests,theforecastshadfallenbyafactoroftwo.Governmentand industrygroupsprojectedconsumpt10nin2000tobeabout100quads/year,while Lovinsprojectedthatconsumptioncouldbelessthan50quads/yearifthenation

pursueda"softenergypath"emphasizingefficiencyratherthanproduction. ThoughtheforecastsfellbyafactoroftwoinjuStadecade,therankorderoffore-

Castswithinanyyearremainedremarkablystable.Yearafteryearthehighestfore- Castswerethoseoftheenergyindustry,followedcloselybygovernmentagencies, withenvironmentalistsprojeCtlngthelowesttotals.Thecloseattentioneachfbre-

casterpaidtotheprojectionsofothersandthepoliticalconstraintsondepartures fromtherangeofpriorforecastsslowedtheadjustmentoftheforecaststoreality.

Themedianforecastfollowedthepathpredictedbysimpletrendextrapolationof pastgrowthinactualconsumptlOn,Withtheforecastsofindividualgroupsandor一

ganizationsadjustedaboveorbelowthemedianinaccordancewiththeirparticu-

1arideologyandpoliticalagenda･ Insuchhighlypoliticizedenvironmentsitissmallwonderthatmanymodelers

cherishthefreeparametersenablingthemtoadjusttheirforecaststomatchtheex- pectationsoftheirclients.

16.3 CASESTUDY:CoMMOD汀YPRICES

SmoothingandtrendextrapolationalsoexplainforecastsoftheprlCeSOfmany commodities.Asanexample,Figure1619showsthecashpriceofcattleintheUS from i972to1986,aperiodOIgreatPrlCeVOiatility･7Alsoshownaretheone-

quarter-aheadforecastsofGlennGrimes,aprofessorofagrlCulturaleconomicsat theUniversityOfMissouriandarespectedprofessionallivestockmarketanalyst.

Grimes'forecastsarewidelycirculatedthroughtheagriculturalextensionsystem incattlecountry.Grimes'forecastsarealsointerestingbecause,asBesslerand Brandt(1992)show,his31mOnth-aheadforecastsareactuallymoreaccuratethan

7Figure20-2showsamuchlongerhistoryofthecattlemarket,illustratlngthepersistentcycles inprices,production,andstocks.

644

FIGURE16-9

Ca川eprlCeSand forecasts

Actualand forecastcash

prlCeforcattlein Omaha,令/CWT

(hundredweight). Forecastsare

one-quarter-ahead forecastsofGFenn

Grimes,plotted agalnSttheactual outcomes.

PartIV TわolsforModelingDynamicSystems

ト 60 ≧ O一. 鯛~50

Grimes Forecast

Actua■CattlePrice憾霊鮎 i t

,F iI

lifu..I,棚 tIlpW iilii

1971 1973 1975 1977 1979 1981 1983 1985 1987

Source.JBessFerandBrandt(1992).

thecattlefuturesmarket(specifically,Grimes'forecastshavelowermeansquare errorthanthe3-month-aheadfuturesprice).InspectionofGrimes'forecasts,how- ever,revealatendencytomisstheturnlngpOlntSinthemarketandtoovershoot

aftersustainedprlCemovements,forexample,afterthelargeriseinprlCeSbetween 1977and1979.

ThephaselagandovershootinthepredictionssuggestsGrimesmaybefore-

castingbysmoothingrecentprlCeSandthenextrapolatingtherecenttrend.The sameformulationusedtomodeltheenergydemandforecastsisspecifiedtotest thishypothesis.Theone-quarter-aheadforecastofcattleprices,P等(t),ismodeled

byextrapolatingtheperceivedpresentconditionbytheexpectedgrowthrateg'k overtheone-quarter-yearforecasthorizonFH:

Px(t)-PPC(t)*[1十TPPC*g*(t)]辛exp(FH*g*(t)) (16-4)

g弓(t)-TREND(P(t),TPPC,THRC,TPT) (16-5)

Asinthecaseofenergydemand,theperceivedpresentconditionisadjustedfor

thechangeexpectedtooccuroverthetimerequiredtoperceivethepresentcondi- tionTPPC.Theformulationforthesimulatedforecastwillthereforeyieldanun-

biasedestimateofprlCeinthesteadystateofexponentialgrowth･ TheparameterswereestimatedeconometricallyandfoundtobeTPPC-0.60,

THRC-6.00,andTPT-0.56years,allreasonablevalues.Figure16110Shows

thecorrespondencebetweenthesimulatedandactualforecasts･Themodelrepl i -

catesGrimes'forecastswell:Themeanabsolutepercenterrorisabout4.5%,and theR20fthemodelisO･95･Becausesmoothingintroducesadelay,thesimulated forecasts,liketheactualforecasts,missmajorturningPOlntSinprice.Becauseit

takestimeforexpectationsaboutthetrendtochange,themodelalsocapturesthe overshootoftheforecastsafterthelargepriceriseinthelate1970swhenGrimes, liketheTRENDfunction,predictedprlCeincreasestocontinueforawhileeven

thoughactualpricefell･ ProfessorGrimesreportedthatheforecastsbycloselymonitorlngfundamen-

talsinthemarket.HestaysinclosetouchwithmarketparticlpantSincluding

breeders,producers,andpackers,anddrawsonextensivesupply-sidedatain- cludingstocksofcattleonfeedlots,breedingstocks,andslaughterrates.Onthe

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 645

FIGURE16-10 Simulatedand

actualcattleprlce 70 forecasts

Top:Simulatedvs･ actualforecasts. Bottom:The sJlmulated

expectedgrowth rateincatt一e

PrlCeS･

ト 60 >

O■■■ヽ ∽ 50

(sJt23̂ J L)

a o

!Jd a lll e3

u! P

ua Jト P ¢ 1

3adx

GrirnesForecast

/㍗㌔.-.-､グ i＼ simu.ated

Forecast

1971 1973 1975 1977 1979 1981 1983 1985 1987

0.08

0.06

0.04

0.02

000

1971 1973 1975 1977 1979 1981 1983 1985 1987

demandside,hetriestoassessnotonlytheimpactofpricesbutalsochangesin people'slifestylessuchasthetrendinthepastdecadestowardleanerdietswith lessredmeat.Hisexperience,contacts,andfocusonfundamentalsdidallowhim

toforecastsignificantlybetterthanpartlCIPantSinthefuturesmarket.Nevertheless,

asobservedinthecaseofenergyconsumptlOn,univariateextrapolationexplains thebulkofthevarianceintheforecasts,1eavlngOnlyasmallresidualtobeex- plainedbytheinfluenceofothervariablessuchasthenumberofcattleonfeedlots,

breedingandslaughterrates,theprlCeSOfothercommodities,andsoon.Past prlCeSformapowerfulanchoronjudgmentsoffutureprlCe.Subjectiveadjust- mentsinresponsetootherfactorshaveonlyaweakeffectduetotheirvariability,

uncertainconnectiontoprlCemovements,andlackofsaliencecomparedtoprlCeS themselves.Nodoubtthesefactorsdohavesomeimpactonthefわrecasts.Butsub-

jeCtiveassess_7nentSOflifestylechangescalJrSirI_gpeOPletoeatlessbeef,andeveIl reportsthatcertainbreederswanttoincreasetheirherds,arelikelytohaveaweak

effectindeedcomparedtoapowerfultrendinpnceitself.

16.4 CASESTUDY:tNFLATl0N

Inflationexpectationsarecriticaltodecisionsthroughoutallsectorsoftheeconl

omy,1nCludingmonetarypolicy,theprlClngOfstocksandbonds,capitalinvest- ment,collectivebargalnlng,prq】eCtionsoftax revenue and government expenditures,andyourowninvestmentdecisions.Thestakesarehighandthetask

646 PartIV ToolsforModelingDynamicSystems

isdaunting:Inflationisvolatile(Figure1613)andisaffectedbyahostofeconomic

eventsandvariables.Consequently,inflationisoneofthemostintensivelystudied

economicindicators･Asmallarmyofprofessionaleconomistsinacademia,private

businesses,governmentagencies,andprofessionalforecastingfirmsdevotethe

betterpartoftheircareerstoforecastlnginflation.Howwelldotheydo?

Formorethan50years,beginnlngin1946,thePhiladelphia-basedfinancial

JOurnalistJosephLivingstonconductedasurveyofeconomicforecasters,The

panelincludedawiderangeofprofessionalforecastersandeconomistsfrombusi-

ness,government,andacademia.Oneofthesurveyquestionssolicitedforecastsof

theCPI,6and12monthsahead.Theseinflationforecastsprovideoneofthe

longestcontinuousseriesdirectlymeasurlngpeOple'sexpectationsandhavebeen

extensivelyanalyzedintheeconomicsliterature･8

Figure16-llcomparestheLivingstonpanel'S6-and12-monthforecaststothe

actualinflationratethrough1985.ActualinflationwasquiteVOlatilefromtheend

ofWorldWarIIthroughtheKoreanwar.Inflationwaslowduringthelate1950s

andearly60S.Betweenthemid60sand1980,inflationgenerallyacceleratedand

fluctuatedsubstantiallyoverthebusinesscycle.After1981inflationfellsharply.

ComparlngtheforecastsagalnSttheactualoutcomehighlights

l･Bias:Thefbrecastersconsistentlyunderpredictinflationduringthe1960s

and1970S,wheninflationaccelerated,andoverestimatesomewhatduring the1980S,wheninflationfTell.

2･Phaseshift:Thepeak(trough)oftheexpectedinflationratelagsthepeak

(trough)oftheactualinflationrate.Forecastersconsistentlymissedthe

turnlngpointsininflationcausedbythebusinesscycle.

3･Attenuation:Theactualrateofinflationfluctuatessignificantlyoverthe

businesscycle,particularlyinthe1970sand1980S.Theamplitudeofthe

forecastsissubstantiallylessthanthatofactualinflation.

Thebias,phaselag,andattenuationareallsuggestiveofsmoothingandtrend

extrapolation.How wellcantheTREND functionreplicatetheforecastsof

thepanel?

InSterman(1987)IexaminedtheabilityoftheTRENDfunctiontomodelthe

6-monthLivingstonforecasts･TheoutputoftheTRENDfunctionwascompared

againstthepanel'sforecastsoftheinflationrateoverthenext6months:9

ExpectedInflation-TREND(CPI;TPPC,THRC,TPT) (16-6)

Inmostmodelingsituationsactualexpectationsdataareunavailableandthe

modelermustestimate血eparametersJudgmentally･Whl上etheparametersfb∫the

8E.g.,Croushore(1997),Caskey(1985),PeekandWilcox(1984),BombergerandFrazer (1981),JacobsandJones(1980),Pearce(1979),Mullineaux(1978),andPesando(1975).

9ThepanelactuauyforecasttheleveloftheCPI,However,becausetheCPIhasrisensomuch since1946itisdifficulttoassessforecastaccuracyfromthepredictedlevelsoftheCPI,Ⅰnsteadthe rateofinflationimplicitinthepanel'sforecastsiscompareddirectlyagalnSttheexpectedgrowth rategeneratedbytheTRENDfunction.

FIGURE16-ll

TheLivingston panel'sinflation forecasts

comparedto actualinflation

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 647

6-MonthForecastvs.ActuaHnflation

12-MonthForecastvs.Actua一lnflation 0.15

0.10

∽ ｢■■

3 0.05 と ▼~

0.00

-0.05

energyandcattleforecastswereestimatedeconometrically,Iusedjudgmental

estimatesoftheparameterstomodeltheinnationforecasts. Thevalueschosentomodelthe6-monthforecastswereTPPC-2,THRC-

12,andTPT-2months.TheLivingstonforecastsweredatedJuneandDecember

ofeachyear.Carlson(1977)ShowsthatduetolagsinreportingtheCPIandinthe

timerequiredtoadministerandtabulatethesurveytheLivingstonpanelmadetheir

forecastsknowlngtheCPIonlythroughAprilandOctober,respectively.Thusthe

panelmemberswereactuallymaking8-and14-monthforecastsandTPPCisset

to2monthstocapturethedelaylnperCeivlngthecurrentvalueoftheCP110

TheI-yeartimehorizonforthereferenceconditionwasselectedasfollows.

First,iyearisacomm on,convenient,andeasilyjustifiedreferencepoint.Second,

ComparingthemostrecentdataagalnSttheyear-agovalueisasimplewaytofilter

outanyresidualseasonalvariationsininflation(thepanelusedtheseasonally

10Afterthe1970ssomeforecastersprobablyknewtheMayandNovemberCPIvalues,but Livingston'Sproceduredoesnotdefinitivelyindicatewhichvaluesthepanelused･

648

FIGURE16-12 TRENDfunction

comparedtothe Livingstonpanel'S 6-monthforecast

Theparameters oftheTREND functionare

TPPC-2, THRC-12,and TPT-2months.

PartIV ToolsforModelingDynamicSystems

adjustedCPIbuttheadjustmentsarenotperfect)･Third,therawinflationdata

(Figure16-3)aredominatedbyhigh-frequency(monthly)noise.Six-and12-

monthforecastsshouldnotbeoverlysensitivetomonthlychangesinreportedin-

flationthatmayberevisedorreversednextmonth.Forprofessionalreasons

(consistency)andcognitivereasons(minimizingdissonance)forecastersareun-

likelytorevisetheirexpectationsdramaticallyfrommonthtomonthdespitethe

volatilityofthedata.WithasmoothingtimeOf12months,thereferencecondition

attenuates97%ofthemonth-tO-monthnoiseyetadjuststo63%ofachangeinthe

perceivedpresentcondition(Forrester1961,p･417).

ThetrendperceptlOntimeof2monthsimpliesrespondents'beliefsadjust

nearlycompletelytoachangeintheindicatedtrendwithin6months(threetime

constants),meaningtheforecastersassimilateandrespondtoapparentchangesin

thetrendsincetheirlastforecast.OnewouldexpectTHRCandTPTtobeslightly

longerforthe12-monthforecasts.ll

Figure16-12showsthesimulationresultsforthe6-monthforecasts･The

TRENDfunctionreproducesthebias,attenuation,andphaseshiftapparentin

theactualforecasts,butthesimulatedforecastsarehighonaveragecomparedto

theLivingstondata.InfacttheTRENDfunctionyieldsabetterforecastthanthe

Livingstonpanel!Themeanabsoluteerror(MA巴)betweensimulatedandactual

forecastsis0.014(Table1612).TheTheilinequalitystatistics(Theil1966;Sterman

1984)decomposethemeansquareerror(MSE)intothreecomponents:bias,un-

equalvariation,andunequalcovariationsosystematicerrorcanbeseparatedfrom

unsystematicrandomdifferencesbetweenthesimulatedandactualdata(seechap- ter21).Aful140%oftheMSEiscausedbybias.Theremainderisduetounequal

covariation,meanlng60%oftheMSEisunsystematic.Theunequalvariationterm

isvirtuallyzero(thetwoserieshaveequalvariances).

TherearetwoprlnCIPalcompetlngexplanationsforthebias.Theactualfore-

castlngprocessusedbytheLivingstonpanelmaybemoresophisticatedthanthe

univariateTRENDfunction.Othereconomicvariablesmaybeconsidered,suchas

llButonlyslightly･The6-monthforecastdeterminestheinflationpathforthefirsthalfofthe annualforecasts.Forecastersareunlikelytoprojectaradicallydifferentinflationrateforthesecond halfoftheforecastyear.Infact,the6-and12-monthforecastsarequitesimilar(Figure16-11),

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 649

TABLE16-2

ErroranalysISOf simulatedinflation forecasts

MAヒ-Mean

Abso山teError; MSE-Mean

SquareError; UM-Fractionof

MSEduetobias; US-Fractionof MSEdueto

unequalvariation; UC-Fractionof MSEdueto

unequal covariation; ｢-Correlation coefficient betweensimulated andactualfore- casts.Seetext

forexplanationof thethreemode一s; Seechapter2Hor explanationoHhe Theilstatistics.

MAE MSE UM uS uC r

Model (1/years) (1/years)2 (dimensionJess)

Noanchor 0.0140 4.0E-4 0.40 0.00 0.60 0.88

Fixedanchor 0.0099 2.41E-4 0,08 0.15 0,77 0.88

Seaanchor 0.0088 1.92E-4 0.16 0.03 0.81 0.91

moneysupplygrowth,thegovernmentbudgetdeficit,andtheunemploymentrate. Inaddition,differentinformationprocesslngroutinesmaybeused.Somere- searchers,suchasCaskey(1985),assumethattheLivingstonforecastersdrawon

awiderangeofmacroeconomicindicatorsanduseoptlmalBayesianupdatingto predictinflation･Thisseemsunlikely･Experimentalevidencesuggestspeopleare muchmoreconservativeinbeliefupdatingthanBayes'Theorempredicts(Plous

1993)･Further,anytheorythatpeopleoptimallycombineawiderangeofcues mustexplainwhythismoresophisticatedprocessisdecidedlyinferiortounivari- atetrendextrapolation.Thefactthatsimpleextrapolationofrecentinflationrates outperformstheprofessionalforecasterssuggestsaccuratemodelingoftheinfla-

tionfbrecastlngprocessrequlreSevengreaterboundsontherationalityoftheex- pectationformationprocessthantheTRENDfunctionpresumes.

TheTRENDfunctionassumesforecasterstracktheactualrateofinnation,

Withadelay.Overtimeerrorswillbegraduallycorrected.However,behavioralde-

cisiontheorysuggestsforecastersmaybeinfluencedbyseveralheuristicsknown

tocausesystematicerrorsinjudgment･Inparticular,pastinflationitselfislikelyto actasastronganchoronpeople'sforecasts.Anchoringandadjustment,asde- scribedinsection13.2.10,isacommonandpowe血 1judgmentalheuristic,one

thatoftenaffectsjudgmentsinadvertently.Theadvantageoftheanchoringandad-

justmentStrategylSitssimplicityandintuitiveappeal･Thedisadvantageisthe commontendencytounderpredict,thatis,torevisepriorbeliefstoolittlewhen facedwithnewdata.Judgmentsareoftenunintentionallyanchoredtoreference

pointsthatareimplicit(suchasevenoddsinabetortheaxisofagraph).People'S judgmentsexhibitanchoringevenwhentheirrelevanceoftheanchortothetaskis madesalient.

Theseconsiderationssuggesttheforecasters'judgmentsmaybeinfluencedby ananchorthatbiasestheforecastdownwardfromthevaluesindicatedbyex-

trapolationoftherecentinflationrate･Theanchoringandadjustmentstrategycan bemodeledasfollows:SIJ-PPOSetheLivingstonpanelformsinflationaryexpecta- tionsas

ExpectedInflation -(1-W)*TREND(CPI;TPPC,THRC,TPT)+W*ANCHOR

(16-7)

In(16-7),thesimulatedLivingstonforecastisaweightedaverageoftheTREND

functionandanANCHOR,withtheanchorgivenaWeightw.Theparametersof theTRENDfunctionarethesameasthoseusedin(1616).Theanchorcanbe

thoughtofasanunderlyingreferencepointthatthepaneluses,consciouslyorun-

consciously,whenforecastlng.

650

FIGURE16-13

Simu一ated6-month

Livmgston

forecasts:fixed- anchormodel

PartIV ToolsforModelingDynamicSystems

Thesimplestassumptionisthe"fixed-anchor"modelinwhichANCHOR-0.

ZeropnCeChangeisanaturalchoicefortheanchor:Zerochangeisthesimplest naivemodel("tomorrowwillbeliketoday")andzeroinflationisacommonly

statedgoalofpolicymakers.Equation(16-7)thenreducesto

ExpectedInflation-(1-W)*TREND(CPI;TPPC,THRC,TPT) (16-8)

whichimpliesforecasterswillalwaysunderpredictthemagnitudeofinflation･Fig- ure16-13showsthefitofthefixed-anchormodeluslngW-0.20.Thefitisim-

provedsubstantiallycomparedtothe"no-anchorHmodel:TheMA芭fallsby29%. TheTheilstatisticsshowthebiasisreducedt08%oftheMSEandthebulkofthe

remainingerrorisunsystematic(unequalcovariation). TheanchoringandadjustmentmodelfitstheforecastsbetterthantheTREND

functionalone.However,thefixed-anchormodelassumesforecastersalwaysun-

derpredictandwouldneverlearntocorrecttheiroptimisticbiaseveniftherateof inflationheldsteadyindefinitely.Thefactthattheno-anchormodelisgenerally

highbetween1947and1983suggeststhatthepanelfelttheunderlyinginflation ratewaslowerthantheactualrateofinflation,biaslngtheirforecasts.However, theunderestimationbytheno-anchormodelafter1983suggeststheanchorhad

risenduringthehigh-inflation70S,causlngthepaneltocontinuetoforecasthigh

inflationinthemid80sdespitemuchloweractualrates･ Theideathattheanchorrepresentsthepanelmembers'long-termexperience

ofinflationsuggestsamodelinwhichtheanchoritselfadjustsveryslowlyto changesintheinflationrate-a"sea-anchor"model.Aseaanchorisalargeobject, usuallyaconeofsailcloth,suspendedbyacableinthecalmerwatersbelowaship. Seaanchorsstabilizeaship'spositioninwaterstoodeepforconventionalanchors toattachtothebottom.Theshipstillmoveswiththewind,waves,andcurrents,

buttheseaanchorslowsitsmotionbycreatlngextradrag.Similarly,panelmem-

bers'lifeexperiencewithinflation,theirbeliefabouttheunderlyinginflationen- vironment,mayactasaseaanchorontheirjudgmentsofshort-runinflation.

TheanchorisnowspecifiedbytheTRENDfunction,butwithmuchlonger

parameters:

ANCHOR-TREND(CPI;TPPCA,THRCA,TPTA) (16-9)

FIGURE16-14 Simulated

Livingston forecast:sea- anchormodel

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 65l

wheretheparameterTPPCAisthetimetoperceivethepresentconditionforthean-

chor,andsoon.Theanchorshouldrespondslowlytochangesintheunderlyingln-

nationrateandshouldnotrespondsignificantlytotemporarychanges.The

parameterswerechosentoreflectthelong-termnatureoftheanchor:TPPCA-1,

THRCA-10,andTPTA-3years.Thesevaluesarelongenoughtoattenuate

changesininflationmorerapidthantheshort-termbusinesscycle.Theinitial

(1947)valueoftheanchorwassett0-3%/year,implyingthatthepanel'sjudg一

mentswereinitiallybiasedtowardmilddeflation.Manyeconomists,recallingthe

deflationoftheGreatDepressionandtherecessionandfallingpricesthatfollowed

WorldWarI,worriedthattheUnitedStateswouldreturntodepressionafterWorld

WarII.Theweightontheanchorwassetto0.25.Figure16114comparesthesea-

anchorandactualforecastsandshowsthecomponentsofthesea-anchorforecast.

Theanchorreducestheforecastsuntil1983,wheninflationfallssubstantially.The

anchorthenkeepsthesimulatedforecasthigh,improvlngthefitbetween1983 and1985.

Thesea-anchormodelistheoreticallymoresatisfyingandalsomorerobust thanthefixed-anchormodel.Itallowsforlearnlng:Ifinflationremainssteadythe

modeleventuallyproducesunbiasedforecasts(asseemstohaveoccurredbetween

Sea-AnchorMode一vs.6-MonthLivingstonForecast

ComponentsofSea-AnchorForecast

SJI e a

し

くL

0.15

0.10

0.05

0.00

-0.05

652

FIGURE16-15 Six-month

Livingstonforecast vs.actua一inflation, 1947-1997

Theplottedvalues ofactualinflation

differslightly comparedto Figure16-lldue torevisionsinthe CPIsince1985.

FIGURE16･16

Ljvingstonpanel's b-mOnTnTOreCaSI

comparedtosea- anchormodel, 1947-1997

PartIV ToolsforModelingDynamicSystems

1958and1965).Inahyperinflationthefixed-anchormodelwouldseriouslyunder-

predictinflation,whilethesea-anchormodelwouldlearntoexpectit.Thesea-

anchormodelreducestheMA巴byanotherl1%･TheMSEisstillprlmarily

unsystematic,andthecorrelationbetweenthesimulatedandactualforecastsim-

provesslightly.

TheanalysisinSterman(1987)reportedherewasdonewithdatafrom 1947

through1985.Thesea-anchormodeldoesqulteWellinexplainlngthebehaviorof

inflationforecastsoverthis40-yearspan.Since1985,however,thedynamicsof

inflationhavechangeddramatically.Inflationcontinuedtofall,andtheeconomy

attainedvirtualprlCeStabilitybythemid1990S.By1997manyrespectedecono-

mistswere,forthefirsttimesincetheGreatDepression,seriouslydiscusslngthe

dangersofdeflation.Howdoesthesea-anchormodelholduplntrackingthistur-

bulentperiod?SinceLivingston'sdeathin1990theFederalReserveBankof

Philadelphiahascontinuedthesurvey.Figure16-15showsthe6-monthforecasts

agalnStactualinflationthrough1997.Consistentwiththesea-anchorhypothesis, forecastersgenerallycontinuedtoexpectinflationtobesomewhathigherthanit

tu川edouttobethroughoutthelate1980sand1990S.

Figure16116Comparestheperformanceofthesea-anchormodeltotheactual

forecasts,uslngthejudgmentallyestimatedparametersorlglnallychoseninthe

1987analysis.Themodelsuggeststhattheunderlyinglong-termtrendanchoring

0.15

0.10

め i_

冨 0.05 >. i::ヨ T-

0.00

ェ0.05

Actual lnflation

＼

＼ LivingstonPanel■S

1945 1955 1965 1975 1985 1995

0.15

0.10

のトl■■

3 0.05 >･ li::≡ ■-

0.00

-0.05

1945 1955 1965 1975 1985 1995

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 653

theinflationforecastspeakedaround1985atabout6.5%/yearandfilltoaround 4%/yearby1997･Thesimulatedforecaststracktheactualforecastsreasonably well,thoughthemodelforecastsarehighbyanaverageofabout0.3%/yearbe- tween1985and1997,asmall血･actionofthestandarddeviationoftheindividual

forecastscomprlSlngthepanelmean. Clearly,thefitbetweenthedataandmodelisnotperfect.Thefitcouldbeim-

provedbyincorporatingtheinfluenceofothereconomicvariablesandbyestimatl lngtheparameterseconometricallyratherthanuslngtheorlglnaljudgmental estimatesselectedinthe1987paper.

Thehistoricalfitofthemodelcouldalsobeimprovedbyallowingthepara- metersofthemodeltovaryovertime.Overthe50yearsexaminedherethebasis forandmethodsofcomputlngtheCPIhavechangeddramatically.Theserevisions intheCPImeanthehistoricrateofinflationisnowdifferentfromwhatitwasat

thetimetheforecastsweremade.Thequalityandavailabilityofotherpotentially relevanteconomicdatahaveimprovedmarkedly,andthetoolsavailabletofore- Castersweretransformedfromsliderulesandgraphpapertocomputersandso- phisticatedeconometricmodels.Andofcourse,themembershipoftheLlvingston panelhaschangedcompletely.Forecasters,reactlngtOthegreatervolatilityofin- flationsincethe1970S,mayhavebecomemoresensitivetorecentprlCeChanges.

Nevertheless,theabilityofthesea-anchormodeltotracktheforecastsaswell asitdoesforhalfacentury,thoughitreliesononlyasinglecueandusesfixed, judgmentallyestimatedparameters,suggeststhattheunderlyingcognltlVe processespeopleusetoforecastinflationarerathersimpleandstable.

TheTRENDfunctionandthesea-anchormodelportrayinflationforecastlng asaprocessthatishighlyboundedinitsrationality.Whiletherearedozensofeco-

nomicvariablespeoplebelievetobecausallyorstatisticallyrelatedtothelikely futurerateofpricechange,thesea-anchormodelassumesforecastsareformed solelythroughconsiderationofthepasttrendinprlCeSitself.Whilemanyfore- castersusecomplexeconomicmodelsandsophisticatedforecastingmethods,the sea-anchormodelassumespeopleforecastthatrecentinflationrateswillcontinue butadjusttheirestimatesbytheirintuitivefeelingabouttheunderlyinginnation environment.Theclosecorrespondenceoftheactualforecaststothesea-anchor modelsuggeststheimpactofotherpotentiallyrelevanteconomicvariablesonthe panel'sforecastsisweak.

Theweakinfluenceofotherindicatorsinthepanel'sforecastsisconsistent withbehavioraldecisiontheory.Peopleareincapableofcorrectlydeducingthe consequencesofintricatedynamicsystemssuchastheeconomyandtendinstead toprocessinformationwithsimple,incomplete,anderroneousmentalmodels.In doingsopeoplepreferrelativelycertaininformationtouncertain,noisyinforma- tion･Thefuturevaluesofpotentiallyrelevantvariablessuchasthemoneysupply, interestrates,unemployment,economicgrowth,exchangerates,andbudget deficitsarethemselvesnoisy,uncertain,variable,controversial,anddimcultto forecast.Thereissubstantialdisagreementamongeconomistsaboutthenatureof therelationshipsbetweenthesevariablesandtherateofinflation.Recentinflation itself,incontrast,providesapowerful,salient,andrelevantcue,measuredinthe sameunitsasthetargetvariable,andislikelytofわrmastronganchoronpeople's forecasts.

654 PartIV ToolsforModelingDynamicSystems

Asdiscussedfわrthecaseofenergydemand,decisionaidssuchaseconometric

modelsdonotsolvetheproblemsincethemodeler'sjudgmentisalwaysneededto specifythemodelstructureandthefuturevaluesoftheexogenousvariables.In

fact,theforecastsofmanyeconometricmodelsareheavily"add-factored"bythe modelers･Anaddfactorissimplyaquantltyaddedtotheoutputofaneconometric

modeltobringtheforecastinlinewiththemodeler'sintuition;itisafudgefactor. AmodelmightpredictinflationwasgolngtObe2%overthenextyear,butiffore-

Castersbelievedthatwastoolow,theymightaddafudgefactorof,say,1%to bringtheforecastuptotheirintuitivejudgmentthatinflationwillbe3%/year(See chapter21).Defendersofaddfactoringarguethatitallowsthemtotakethelatest availabledataintoaccount,Overcomeslimitationsofthemodels,andenablesthem

tobringtheirexpertknowledgetobear.Butexpertsarepronetomanyofthesame judgmentalbiasesobservedinthepublicatlarge(TverskyandKahneman,1974;

Kahneman,Slovic,andTversky,1982)Jndeed,Caskey(1985)showstheLivings-

tonpanel'sforecastsofinflationarevirtuallyidenticaltothosegeneratedbyDRI (DataResources,Inc.),oneofthelargestandmostsuccessfuleconometricfore-

castingfirms･Inaworldofgreatuncertainty,inflationforecastsarestronglyinflu-

encedbyrecenttrendsininflationitselfdespitethefactthatforecastersclaimto

considerawiderangeofvariablesandspendconsiderableresourcesoncomplex econometricmodels.

Theclosecorrespondenceoftheforecastsproducedbydifferentforecasters

anddifferentmethodsalsoreflectsaherdmentalitylntheforecastlngcommunity. Professionalforecasterspaycarefulattentiontotheprojectionsoftheirrivalsand

colleagues･Herdingbehavioramongforecastersarisesinpartfrombasicpsychol logicalfactorsandsocialpressures.Researchshowspeopletendtorevisetheir

opinionstowardthoseofothers,evenstrangers･Asch(1951,1956)hadpeoplese- lectwhichofthreelineswasthesamelengthasareferenceline.Alone,peoplegot itrightmorethan99%ofthetime.Thenpeoplewereaskedtojudgethelengthof

thelinesafteragroupofothersannouncedtheiroplnions･Theotherpeople,se- cretlyworkingwithAsch,woulddeliberatelyglVeerroneousanswers,Saylngthat alineof,forexample,3incheswasthesamelengthasanotherof3.75inches.Asch

foundthatgroupsassmallasthreecausedone-thirdofthepeopletestedtoagree thatthe3-inchlinewasinfactequalinlengthtothe3.75-inchline.Thetendency toreviseoplnionstowardthoseofothersinagrouplSStrongerWhentheother

groupmembersareknowntoandrespectedbythesubjectandwhentheoplnion concernsmattersmoreambiguousanduncertainthanthelengthofaline-forex- ample,thefuturerateofinflation.

TheincentivesfTorecastersfacealsoreinforceherding.Manybelieveitismuch

worsetobetheonlyonewrongthantobeoneofmanymakingthesameerror. Whenmiserylovescompanyltisrationalforindividualstoshadetheirforecasts

towardtheconsensusviewevenwhenmarketfundamentalsortheirprlVateinfor一 nationindicateadifferentforecast･Forecastersherdtogether,adjustingtheirfore-

caststowardtheviewsofandemphasizingthecuesusedbywhomeveramong themhasgottenluckylatelyandproducedanaccurateforecast(Froot,Scharfstein,

andStein1992developarelatedgame-theoreticmodelofherdinglninvestor behavior).

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFo-ation 655

16.5 iMPLICATlONSFORFoRECASTCoNSUMERS

Theresultssuggestimportantlessonsforforecastersandespeciallyformanagers anddecisionmakerswhomustchoosewhichfわrecastsandforecastlngmethods tobuy.

First,mostforecastsarenotverygood.Forecastsaremostaccuratewhenthe underlyingdynamicsarestable,aswhenpredictingtheinfluenceofregularphe- nomenasuchasseasonalvariations.Butfbrecastlngmethodsareparticularlypoor whentherearechangesintrends,noise,andothersourcesofturbulence.Theseare

preciselythetimeswhenpeoplearemostinterestedinforecasts.

Second,mostforecastingmethodsfrequentlymisschangesintrendsandturn- 1ngpOlntSincycles,lagglngbehindratherthananticlpatlngthem.Thesystematic

errorsinforecastsofinflation,comm odityprlCeS,energyuse,andothervariables stronglysuggestadaptlVeexpectationsandsimpletrendextrapolationoftendomi- nateprofessionalforecasts.Thesemethodsdocorrecterrorsovertime,butbecause theylnVOIvesmoothingpastdata,theyInevitablyintroducedelaysthatcausethe

forecaststomisskeyturnlngpointsandshiftsingrowthrates. Third,smoothingandextrapolationofthepasttrendinthevariableitself

seemstodominateotherconsiderationsinforecastlng.Thoughforecastersoften

claimto(andindeedmay)examineawiderangeofvariablesinmakingtheirfore-

casts,pastvaluesandpasttrendsstronglyanchortheirforecasts.Theinfluenceof

othervariablesisweakbecausetheirconnectionstothetargetvariablearepoorly understood,unstable,noISy,andambiguous.Forecastersoftenbehaveasifthey

wereuslngSimplesmoothingandnaiveextrapolationevenwhentheyareuslng complicatedformalmodels.Theyadjusttheparametersandvaluesofexogenous

lnputSuntiltheoutputofthemodelis"reasonable,"thatis,untilitmatchestheir intuitionJntuition,however,isbiasedbyavarietyofjudgmentalheuristicsand

tendstobestronglyanchoredtorecenttrends. Fourth,forecasterstendtounderestimateuncertaintyintheirforecasts,often

failingtoprovidearange,alternativescenarios,Oralistoffactorstowhichtheir forecastsaresensitive(seetheoverconfidencebias,section8.2.5).

Howthencanmanagersimprovethevaluetheygetfromforecasts?Fight agalnSttheoverconfidencebiasbyexplicitlychallenglngaSSumPtlOnSandasking

howyourexpectationsmightbewrong(forpracticalexamples,seeRussoand Schoemaker1989).Requireforecasterstodocumenttheirassumptions,maketheir

datasourcesexplicit,andspecifythemethodstheyareuslng･Don'tallowfore- casterstouseaddfactoring(chapter21discussesstandardsforreplicabilityand rigorinmodeling).

EverlSO,improvingforecastaccuracyisdifficuit･Thebestwaytoimprovethe benefit/costratioofforecastinglStOreducethecost.Theprojectionsofexpensive forecastlngServicesandmodelstendtobedominatedbysmoothingandtrendex-

trapolation.Managerscansaveagreatdealofmoneybysmoothingandextrapo- 1atlngthedatathemselves.Forecastaccuracymaynotimprove,butthecostof acqulrlngtheforecastswillfall.

Finally,focusonthedevelopmentofdecisionrulesandstrategleSthatarerO- busttotheinevitableforecasterrors.TherealvalueofmodelinglSnottOanticipate

656 PartIV TわolsfわrModelingDynamicSystems

andreacttoproblemsintheenvironmentbuttoeliminatetheproblemsbychang-

1ngtheunderlyingstmctureofthesystem.Modelersandtheirclientsshouldbede-

slgnerS,notdiviners.InthewordsofAntoinedeSainトExupとry,HAsforthefuture,

yourtaskisnottoforesee,buttoenableit."

ExtrapoiationandSモabiFi吋

Theexpectationformationprocesscandramaticallyaffectthestabilityandperfor-

manceofasystem.Tbexploretheimpactofextrapolativeexpectationsindynamic

models,considerthemodelsofnew-productgrowthdevelopedinchapters9and

10.Thesemodelsdidnotexplicitlyincludeexpectationsaboutfuturedemand.Be-

causeittakestimetobuildcapacity,however,managersingrowthmarketsmust

forecastthedemandfortheirproductsfarinadvance.Forecastingtoolittlegrowth

leadstocapacityshortages,erodingmarketshare(youcan'tsellmorethanyoucan

make).Forecastingtoomuchgrowth,ontheotherhand,leadstoexcesscapacity,

destroylngProfitability.

Considerthetypicallifecycleofasuccessfulnewdurableproduct.Salesrise

initiallyatrapidexponentialrates.Asthemarketgrows,thefractionalgrowthrate

slows.Eventually,salespeak,thenfalltoaratethatcoversreplacementofdis-

cardedunitsandgrowthinthetotalcustomerbase.Thedi軌lSionofVCRsinthe

USshowninFigure10-8providesanexample･

Figure9122insection9.3.6presentsasimplemodelofthelifecyclefor

durableproducts.BasedontheBassdi軌lSionmodel,themodelrepresentssalesas

thesumofinitialandreplacementpurchases:

SalesRate-InitialPurchaseRate十 RepeatPurchaseRate (16-10)

Themodeldoesnotincludeproductioncapacityatall,implicitlyassumlngCapac-

ityisalwaysadequateandneverconstrainssales(ordersalwaysequalsalesequal

deliveries).Theassumptionthatcapacityisalwaysadequaterequireseitherthatca-

pacltyCanbeadjustedinstantlyorthatdemandforecastsarealwaysperfect･Both

assumptionsarefalse.Capacltyacquisitiondelaysinmanyindustriesarelong,and forecastsareoftenerroneous.

ModifythemodelshowninFigure9122toincludedemandforecastsandca-

pacltyadjustments.Tobegin,notethatintheorlglnalmodeltherearenodistinc-

tionsamongorders,sales,anddeliveries.Allareimplicitlyassumedtobeequal｡

Whencapacityadjustmentlagsareintroduced,youmustdistinguishbetweenthese

concepts｡Letthesalesrateinequation(16-10)representtheorderrate(demand)

fortheproduct･Thefirmcanonlydeliverproductifcapacityexceedssales:12

DeliveryRate-MIN(SalesRate,Capacity) (16-ll)

12Theformulationforthedeliveryrateassumesthatanysales(orders)thatcan'tbedelivered duetocapacityconstraintsarelostforeverJmplicitly,customersarehighlydeliverysensitiveand foregoadoptlOnWhentheproductisunavailable･Morerealistically,anyunfilledordersaccumulate inabacklog,andthedesireddeliveryratedependsonthesizeofthebacklog,notthecurrentorder rate.Forthepurposesofthischauengeignorethebacklog(andpossibleinventories)･Youmight addbacklogstotesttherobustnessofyourresultsinthischallengetothisimportantassumpt10n aboutmarketstructure.YoucanalsoreplacetheMINfunctionwithitsfuzzycounterpart(section 13.2.8).

Chapter16 ForecastsandFudgeFactors:ModelingExpectationFormation 657

ItisnotnecessarytomodelthestockandflOwstructureforcapacltyaCqulSlt10nin detail(chapter17developsthisstructure).Instead,itissufficienttoassumecapac-

ityadjuststothedesiredlevelwithadelay(asassumedinthemarketgrowth

modeldevelopedinchapter15)･Forsimplicity,assumethelagincapacityisthe

sameforincreasesanddecreases.Athird-orderdelayprovidesarealisticrepresen-

tationofthecapacityadjustmentprocess(chapterll):

Capacity-SMOOTHS(DesiredCapacity,CapacityAcquisitionLag) (16-12)

Desiredcapacltyrepresentsdemandprqectedintothefuturebythecapacltylead

timeandthenadjustedbythenormalcapacltyutilizationlevel:

DesiredCapaclty-ProjectedSales/NormalCapacityUtilization (16-13)

1.Adaptiveexpectations

First,assumethefirmhasmyopicexpectationsandsetsprojectedsalestoits beliefabouttherecentsalesrate.

PrqjectedSalesRate-RecentSalesRate (16-14)

Asexplainedinchapterll,ittakestimetomeasureandreportsalesand additionaltimetofilteroutshort-termnoiseinsales.Hencetherecentsales

rateismodeledwithadaptiveexpectations(assumefirst-orderexponential

smoothing):

RecentSalesRate-SMOOTH(SalesRate,SalesPerceptionTime) (16-15)

Tomeasurethefirm'sabilitytomatchcapacltytOdemand,definethe

adequacyofcapacltyaSthegapbetweennormalproductionandsales.

NormalproductionistheproductionrateglVenbycapacltyatnormal utilization.

AdequacyofCapaclty (NormalProduction-SalesRate)

SalesRate (16-16)

NormalProduction-Capacity/NormalCapacityUtilization (16-17)

BeginwiththeparametersforthemodelshowninFigure9-23.Assumea

half-yearcapacityacquisitiondelay,aone-quarter-yeardelaylnPerceiving

sales,andnormalcapacltyutilizationof90%.Comparethebehaviorof

capaclty,Projectedsales,andsales.Howwelldoescapacitymatchdemand?

DotheforecasterrorsandadequacyofcapacltyVarySystematicallyoverthe

productlifecycle?Explain.Explorehowtheforecastandcapacityerrors

varywiththeparameters(boththelagsincapacityadjustmentandthe

parametersgovernlngtheproductlitreCycle). I＼

2.Extrapolativeexpectations

ForecastlngbyadaptiveexpectationswillalwayscausecapacltytObe

inadequatewhendemandisgrowing.Modifyprojectedsalestoincludethe

expectedgrowthinsales,Assumemanagersbelieverecentsalesgrowthwill continueovertheforecasthorizon:

ProjectedSalesRate-RecentSales *(1+ExpectedGrowthinSales*ForecastHorizon) (16-14a)

658 PartIV ToolsforModelingDynamicSystems

TheforecasthorizonisthecapacltyaCqulSltlOnlag.Assumethefirm

forecastssalesgrowthusingtheTRENDfunction:

ExpectedGrowthinSales-TREND(SalesRate,SalesPerception Time,HistoricalHorizonforSales,TimetoPerceiveSalesGrowth)

(16-18)

Assumethefilm looksbackoverthepastyeartoestimatethetrendinsales

(HistoricalHorizonforSales-1year)andthattheTimetoPerceiveSales

Growthisone-quarteryear.BysettingTPPCtotheSalesPerceptionTime,

theperceivedpresentconditionequalstheRecentSalesRate.

ComparethebehavioroftherevisedforecasttothemyoplCCaseOf

simplesmoothing.Doesincorporatlngthegrowthindemandimprovethe

abilityofcapacltytOtrackdemandduringthegrowthphaseoftheproduct

lifecycle?Wh athappenswhenthemarketsaturates?Isthereatrade10ff

betweentheabilitytomatchdemandgrowthduringthegrow血phaseandthe

saturationphase?Explain.

Commentontheeffectivenessofextrapolativeexpectationsasa

forecastlngmethodinproductlifecyclesettings.Whatareitsadvantagesand

disadvantages?Doyouthinkrealfirmsforecastbyextrapolationofrecent

salesgrowth?Whatalternativemethodsmightworkbetter?13

16.6 きNmAuZAT10NANDSTEADYSTATERESPONSE oFTHETRENDFuNCT10N

Tobeareasonablemodelofgrowthexpectationformation,TRENDshouldpro-

duce,inthesteadystate,anaccurate(unbiased)estimateofthegrowthrateinthe

lnputVariable｡Thatis,if

Input-Ioexp(gt)

then

limTREND(Input)-g((I:

(16-19)

(16-20)

Theproofreliesonthefactthatthesteadystateresponseof丘rsトorderexponential

smoothingtoexponentialgrowthisexponentialgrowthatthesamerateasthe

Inputbutwithasteadystateerror:WhentheinputisgrowingeXPOnentially,the

13Notei_haHheform.J,lationforProjectedSalesRatedoesnotcorrectforthelagintheperception ofsales(therecentsalesrate).Byequation(16-22),recentsaleswilllagactualsalesbyg*Sales PerceptlOnTime.Further,sincecapacitylSmodeledasathird-orderdelay,thepropergrowthcor- rectionforthecapacitylagisl1+g*(CapacityAcquisitionLag/3)]3(youcanderivethisexpresI sionfromtheanalysisinsection16.6),However,thereisnoreasontoexpectrealfirmstomake suchprecisecorrectionsortoavoidsteadystateerrorundergrowth･DoingsorequlreSthemto understandthelengthanddistributionofthesalesperceptlOndelayandcapacltyaCqulSitiondelay. Inexperimentalproductlifecyclemarkets(PaichandSterrrtan1993),subjects,includingmany withbusinessexperience,generallydidnotforecastaggresslVelyenollghtocoITeCtforsteadystate error.Mostsubjectsfoundthemselvesshortofcapacityduringth einitialgrowthphase,failedto anticipatethesaturationofthemarket,andexperiencedasignificantcapacltyovershootasboom turnedtobust.

Chapter16ForecastsandFudgeFactors:ModelingExpectationFormation 659

smoothedvariablelagsbehindtheinputbyaconstantfractionofthesmoothed value.

Theequationforfirst-ordersmoothingofanInputis

dOutput dt -(Input-Output)/D (16-21)

whereDistheadjustmenttime.Thesteadystatesolutionofequation(16121)for

thecaseofanexponentiallygrowlngInputCanbefoundinmanydifferentialequa- tionstexts:

Output-Input/(1+gD) (16-22)

Thatis,thesmoothedvariablelagstheinputwithasteadystateerrordependingon

theproductofthegrowthrateoftheinputandtheaveragelagbetweenlnputand

output.Thesolutioncanbeverifiedbysubstitutioninthedifferentialequation.In-

tuitively,thegapbetweenInputandoutputmustbejustgreatenoughtocausethe

fractionalrateofchangeoftheoutputtoequalthefractionalgrowthrateofthein-

put,thatis,insteadystate,d(Output)/dt-(Input-Output)A)-gOutput.

ⅠntheTRENDfunction,PPCisasmoothoftheInput,Sointhesteadystateof

exponentialgrowthatrateg/period,PPCwillalsobegrowlngeXPOnentiallyat

rateg.SincethereferenceconditionRCisasmoothofPPC,itwillalsobegrowl

lngat丘.actionalrateg:

警世〒g ButbyequatlOn(16-21)

dRC (PPC-RC) dt THRC

g-警/RC

(PPC-RC) THRC

(16-23)

(16-24)

(16-25)

whichispreciselytheexpressionfortheindicatedtrend,ITREND,equation

(16-1).SinceTRENDisasmoothofITREND,TREND-ITREND-蛋inthe

steadystate.Thus,inthesteadystate,TRENDyieldsanunbiasedestimateof

theexponentialgrowthrateintheinput.Duringtransients,ofcourse,TRENDwill

differfromthetruegrowthrateoftheinput.

WhenusingtheTRENDfunction,themodelermustspecifytheinitialcondi-

tionforeachstatevariable.Themodelersetstheinitialvalueoftheperceivedtrend

atsomevalue,denotedTREND(t｡).Usually,theinitialvaluesoftheperceivedpre- sentconditionandreferenceconditionshouldbesetsothattheTRENDfunction

isinitializedinsteadystateattheassumedinitialgrowthrate.From equation

(16-25),thesteadystateinitialconditionsarereadilyfoundtobe

INPUT(to)

(1+TREND(to)*TPPC)

PPC(t｡)

(1十TREND(to)*THRC)

660 PartIV ToolsforModelingDynamicSystems

TheseinitialconditionsavoidunwantedtransientsintheadjustmentofTRENDto theactualgrowthoftheinput.

16,7 SuMMARY

Forecastsandexpectationsarefundamentaltodecisionmaking.Theoriesoffore- Castlngrangefromrationalexpectations,inwhichpeopleareassumedtohavea nearlyperfectunderstandingofcomplexsystemsandnevermakesystematicer- rors,totheoriesinwhichbehaviorissimpleandpeopleneverlearn.Experimental andfieldstudiessupportanintermediatetheorylnWhichrationalityisbounded. Behaviorandexpectationsdoadapt,butslowly.Weoftenlearnthewronglessons fromexperienceandfrequentlymakesystematicerrorsinforecastingandcontrol1 1ingcomplexsystems.

Thechapterintroducedandtestedaboundedlyrationalformulationformod- elingtheformationofgrowthexpectations,theTRENDfunction.TheTREND functionmodelsthewaylnWhichpeopleformexpectationsabouttherateof growthinavariablebasedonthehistoryofthevariableitself.

TheTRENDfunctionwastestedwithseveralexamples,includingforecastsof inflation,commodityprices,andenergyconsumption･Inallcases(andmanymore discussedintheforecastingliterature)theforecastscanbemodeledwellbyadap- tivelearnlngprocessesSuchasexponentialsmoothingandtrendextrapolation･ ForecastersfrequentlymissturningPOlntS,overreacttOtrends,andgenerateother systematicerrors.LearningisoftenquiteSlowrelativetothedynamicsofthevari- ablespeopleseektoforecast.

Forecastsareoftendominatedbysimpleadaptationtopasteventseventhough forecastersclaimtoconsiderawiderangeofvariablesandusecomplicatedmod- elstogeneratetheirforecasts.Thepasthistoryandtrendinavariableactasa stronganchoronpeople'Sjudgmentsandconstraintherangeofvaluestheycon-

siderreasonable･Insituationswheretherelationshipsamongvariablesinthesys- temarenoISy,unstable,orobscure,thetrendinthetargetvariablewillloomlarge intheforecastingProcessanddominatetheeffectofotherpredictors.Similarly, forecastersoftenadjusttheinputstotheirmodelsuntiltheoutputsconformtotheir intuitionandtosocialandpoliticalpressures.

S嘩筆写yC畠表童設S義認産油e i:jit圭等呈至言串ぎ0§∈皇呈盲裏芸串三号§

Thedistinctionbetweenstocksandjlowsiswellknown...Yeteconomic

theoriesstillrevolveprimarilyaroundjlowconceptsofsupplyanddemand‥. lS]tock-Variableconceptsofsupplyanddemandmustbeincorporated explicitlylneconomicmodelsinofldertocapturetherichdisequilibrium behaviorcharacteristicsofrealsocioeconomicsystems.

-Nathaniel∫.Mass(1980,p.97)

Asupplychainisthesetofstructuresandprocessesanorganizationusestodeliver anoutputtoacustomer.Theoutputcanbeaphysicalproductsuchasanautomo- bile,theprovisionofakeyresourcesuchasskilledlabor,Oranintangibleoutput suchasaserviceorproductdesign.Asupplychainconsistsof(1)thestockand flowstructuresfortheacquisitionoftheinputstotheprocessand(2)themanage- mentpoliciesgoverningthevariousflows.Thenextseveralchaptersconsiderthe structureandbehaviorofsupplychainsinvarioussettlngS.Supplychainsoften exhibitpersistentandcostlyinstability.Thischapterlaysthefoundationbyillus- tratlngthebehaviorofsupplychainsinimportantcontextsanddeveloplngafun- damentalformulation-thestockmanagementstructure-usefulinmodeling supplychainsinalltypesofsystems,notonlybusinesssystems,butalsophysical, biologlCal,andothersystems.

ThestockmanagementstructureisusedtoexplaintheorlglnOfoscillations. OscillationrequlreSboththattherebetimedelaysinthenegativefeedbacksregu- latingthestateofasystemandthatdecisionmakersfailtoaccountforthese

663

664 PartV InstabilityandOscillation

delays-1gnOrlngthesupplylineofcorrectiveactionsthathavebeeninitiatedbut havenotyethadtheireffect.ThoughitisfoolishtoIgnoretimedelays,experi- mentalevidenceshowspeopleoftendojustthat･Casestudiesofvariousindustries suggestthesemlSPerCePtlOnSOffeedbacklieattherootofthepersistentcyclesin realestate,shipping,andrelatedindustries.

dW.1 SupplyeMAMS日NBusbNESSANDBEYOND

Afirmcanbeviewedasasetofprocesses:Aprocessfororderfulfillment,for manufacturlngtheproduct,forprlClng,foradvertislng,forhiring,andsoon.Each oftheseprocessesrequlreSVariousinputs,Whichmustbeacquiredfromsuppliers･ Asupplychainisthestructurethroughwhichtheinputsareacquired,transfo-ed intoanoutput,andthendeliveredtoacustomer.Thecustomercanbeexternalor intemal.Theinputsandoutputscanbetangible,suchasanautomobileanditsparts andrawmaterials,orintangible,asinproductdevelopmentwheretheoutputisa completeddesignandtheinputsincludecustomerspecifications･

SupplychainsconsistofastockandflowstructurefortheacqulSition,storage, andconversionofinputsintooutputsandthedecisionrulesgovernlngtheflowsI Theautomobilesupplychainincludesthestockandflownetworksofmaterials suchassteel.SteelmovesfromrollsofsheetmetalthroughstamplngIntobody partstoassemblyandshipmenttodealers.Ateachstageintheprocessthereisa stockofpartsbufferingthedifferentactivities(aninventoryofsheetsteelbetween steelacqulSitionandusage,aninventoryofstampedpartsbetweenstamplngand assembly,aninventoryofcarsbetweendealeracqulsltlonandsales)･Thedecision structuregoverningtheflowsincludespoliciesfororderingsteelfromsuppliers, schedulingthestamplngOfbodypartsandassembly,shippingnewcarstodealers, andthecustomers'purchasedecision.

Supplychainsoftenextendbeyondtheboundariesofasingleorganization.Ef- fectivemodelsmustrepresentdifferentactorsandorganizationsincludingsuppli- ers,thefirm,distributionchannels,andcustomers.Becausetheyinvolvemultiple chainsofstocksandflows,withtheresultingtlmedelays,andbecausethedecision rulesgovernlngtheflOwsoftencreateimportantfeedbacksamongthepartnersin asupplychain,systemdynamicsiswellsuitedforsupplychainmodelingandpol- icydesign.Severalexamplesofsupplychainshavealreadybeendiscussed(See chapter2andsections6.3andll.6).

TheconceptofasupplychainneednotberestrictedtobusinesssettlngSOr eventohumansystems.Forexample,thesupplyofglucoseprovidingtheenergy requiredformetabolicactivitylnyourbodyistheoutputofasupplychainbegin- nlrigWithtlheConsumptionOffbodariderldir.gwiththemetabolismofgllLiCOSearid excretionofwastes.Thereareimportanttimedelaysintheprocess,includingde- 1aysinthedigestionandtransportofsugarsandinthesynthesisanddiffusionof insulin(seeSturisetal.1991forasystemdynamicsmodelofthehumanglucose- insulinsystem).

17.1.-I 0sciHatior毒,AmphLfica的 n,andPhaseLilg

Thepurposeofasupplychainistoprovidetherightoutputattherighttime･As customerrequlrementSChange,themanagersofthesupplychainrespondby

Chapter17 SupplyChainsandtheOriginofOscillations 665

adjustlngtherateatwhichresourcesareorderedandused･Supplychainsarethus

governedprimarilybynegativefeedbackBecausesupplychainstypicallyinvolve

substantialtimedelays,theyarepronetooscillation-productionandinventories

chronicallyovershootandundershoottheapproprlatelevels.Figure17-1shows

industrialproductionintheUS.Thedataexhibitseveralmodesofbehavior,

First,thelong-rungrowthrateofmanufacturlngOutputisabout3.4%/year.Sec-

ond,asseeninthebottompanelofthefigure,productionfluctuatesslgnificantly

aroundthegrowthtrend･Thedominantperiodicityisthebusinesscycle,acycleof

prosperltyandrecessionofabout3-5yearsinduration,butexhibitingconsider-

ablevariability.

Theamplitudeofbusinesscyclefluctuationsinmaterialsproductionisslgnif-

icantlygreaterthanthatinconsumergoodsproduction(Figure17-2;again,theex-

ponentialgrowthtrendhasbeenremoved).Thepeaksandtroughsofthecyclein materialsproductionalsotendtolagbehindthoseinproductionofconsumer

goods.

Thesethreefeatures,oscillation,amplification.,andphaselag･arepervasivein supplychains.Typically,theamplitudeoffluctuatlOnSincreasesastheypropagate

fromthecustomertothesupplier,witheachupstreamstageinasupplychaintend1

1ngtOlagbehinditsimmediatecustomer,

TheamplificationoffluctuationsfromconsumptiontOProductioniseven

greaterinspecificindustries.ThetoppanelinFigure17-3showsthepetroleum

FIGURE17-1 lndustrial

productionin theUS

Top:USindustrial productionsince 1947.Bottom: Detrended industrial

production showlng fluctuationsinthe

USmanufacturlng sector.

■ll

■■■

(o o L

N 6 6 L )

u O !13 n P O J d

re !) 1 S n P u l S

ー

1ー

一.一

(o oL

= P u OJ

l)P u 巴 1 0 1 8 ^ 慧叩一a∝

O!)O nP

OJd rt2!JllS n P u

1950 1960 1970 1980 1990 2000

SouflCe.IUSFederalReserve,seriesB50001.

666

FIGURE17-2

0sci‖ation, amplification, andphaselagln theaggregate supplychain

PartV InstabilityandOscillation

,LL

■l

rLトr

(

o o L = P u

a jl) P u

巴 1

01a ^ !

) e la

u O !P

n P O

Jld

lt2!Jl tSn P u

I 1950 1960 1970 1980 1990 2000

Source:USFederalReserve,senesB51000andB53010

supplychain(thefigureshowstheannualizedgrowthrate;allmonthlydataare shownas121mOnthcenteredmovlngaveragestOfilteroutthehigh-frequency month-t0-monthnoise).Theamplificationissubstantial.Productionfluctuates morethanconsumptlOn.Intum,drillingactivityfluctuatesaboutthreetimesmore

thanproduction,imposlnglargeboomandbustcyclesonthesuppliersofdrillrigs andequlpment･Themiddlepanelshowsthemachinetoolindustry｡Fluctuationsin economicgrowthleadtomuchlargerswlngSinmotorvehiclesales.Duringreces-

sions,peoplekeeptheiroldcarsgolng,leadingtounantlClpatedinventoryaccu一 mulationandforclngevenlargerproductioncutbacks.Theautomotiveindustry generatesalargeshareoftotalmachinetoolorders.Duringaproductiondownturn,

theautocompaniespostponeorcanceltheircapitalinvestmentplans,Causlngeven largerdropsintheorderstheyplacefわrmachinetools,Duringthenextupswlng theyscrambletobuildcapacltyandorderssurge.Thephaselagbetweenvehicle productionandtheinducedchangesinmachinetoolordersisclearlyvisible.The bottompanelshowsthesemiconductorindustry･Semiconductorproductionisat theupstreamendofthesupplychainforcomputersandelectronicequlpmentand fluctuatesmuchmorethanindustrialproductionasawhole.

17.2 THESTOCKMANAGEMENTPROBLEM

Supplychainsconsistofcascadesoffirms,eachreceivlngOrdersandadjusting

productionandproductioncapacltytOmeetChangesindemand･Eachlinkinasup- plychainmaintainsandcontrolsinventoriesofmaterialsandfinishedproduct.To understandthebehaviorofasupplychainandthecausesofoscillation,amplific a-

tion,andphaselag,ltisfirstnecessarytounderstandthestructureanddynamicsof aslnglelink,thatis,howanindividualfirmmanagesitsinventoriesandresources

asitattemptstobalanceproductionwithorders･Suchbalanclngprocessesalways involvenegativefeedbacks.

A11negativefeedbackprocessesinvolvecomparingthestateofthesystemto

thedesiredstate,theninitiatlngacorrectiveactiontoeliminateanydiscrepancy･In suchastockmanagementtask,themanagerseekstomaintainastock(thestateof thesystem)ataparticulartargetlevel,oratleastwithinanacceptablerange.

Stocksarealteredonlybychangesintheirinnowandoutflowrates･Typically, themanagermustsettheinnowratetocompensateforlossesandusageandto

Chapter17 SupplyChainsandtheOriginofOscillations 667

FIGURE17-3

Amp.ificationin

supplychains

Top:Oilandgas

dri川ngfluctuates farmorethan

productionor consumption. Thegraphshows 12-monthcentered

mOVlngaverages oftheannualized

fractionalgrowth ratecalculated

fromthemonthly data.

Source.･USFederal Reserve,series S13000andA13800.

Middle:Ordersfor

machinetools fluctuatefarmore thanthe

productionoftheir majorcustomer

(theautoindustry). Graphshows

annualgrowth rates.

Source:Anderson,Fine andParker(1996).

Bottom:

Semiconductor

production f一uctuatesfarmore

thanindustrial

productionasa whole.Thegraph shows12-month

cente｢edmovlng averagesoHhe annualized

fractiona一growth ratecalculated

fromthemonth一y data.

Source:FederalRe- seⅣe,seriesB50001 and136790.

(J t2 3 ^ ]

% ) alt2E LJtJVtO L

9 一t2 u

O !T3 t2丘

人 U

1970 1975 1980 1985 1990 1995 2000

で t=

a [̂%

) a le E LJlN LO J

Ft2u O !13空

:: 百土 MachineTool

島 Orders＼ ft"tBzK 兵了ヽ十∴十 r-小--..PPL/.▲､トへ-⊆ ～ル-r-iL--i 叫~-.計-一㌢〆~~

/ 説叫菅が4 もぎMotor f!Vehicle

1970 1975 1980 1985 1990 1995

0 0

(Jt2 3

^ [% ) O l

正

LJtき 0)9

1t2 u

O!IOt2Jj

Semiconductors

㌔冒EPt制 i門甑滞ア /-

1960 1965 1970 1975 1980 1985 1990 1995 2000

Counteractdisturbancesthatpushthestockawayfrom itsdesiredvalue.Often

therearelagsbetweentheinitiationofacontrolactionanditseffectandlagsbe-

tweenachangeinthestockandtheperceptlOnOfthatchangebythedecision

maker･Thedurationoftheselagsmayvaryandmaybeinfluencedbytheman-

ager'sownactions.

Stockmanagementproblemsoccuratmanylevelsofaggregation.Atthelevel

ofafirm ,managersmustorderpartsandrawmaterialstomaintaininventoriessuf-

ficientforproductiontoproceedatthedesiredrate.Theymustadjustforvariations

intheusageofthesematerialsandforchangesintheirdeliverydelays.Atthe

individuallevel,youregulatethetemperatureofthewaterinyourmomlngShower,

668 PartV InstabilityandOscillation

guideyourcardownthehighway,andmanageyourcheckingaccountbalances.At

themacroeconomiclevel,theUSFederalReserveseekstomanagethestockof

moneytostimulateeconomicgrowthandavoidinflation,whilecompensatingfor

variationsincreditdemand,budgetdeficits,andinternationalcapltalflows.

17L2.1 ManagingaStock:Structure

Thestockmanagementcontrolproblemcanbedividedintotwoparts:(1)thestock

andflowstructureofthesystemand(2)thedecisionruleusedbythemanagersto

controltheacquisitionofnewunits,

Tobegin,considerasituationinwhichthemanagercontrolstheinflowrateto

thestockdirectlyandthereisnodelayinacquiringunits(Figure17-4).1Fillinga

glassofwaterfromafaucetprovidesanexample:Thedelaybetweenachangein

thestateofthesystem(thelevelofwaterintheglass)andtheinflowtothestock

(therateatwhichwaterflowsfromthetap)isshortenoughrelativetotheflowthat

itcansafelybeignored.

Thestocktobecontrolled,S,istheaccumulationoftheacqulSitionrateAR lessthelossrateLR:

S-INTEGRAL(AR-LR,St｡) (17-1)

Lossesincludeanyoutnowfromthestockandmayarisefromusage(asinaraw

materialinventory)ordecay(asinthedepreciationofplantandequipment).The

lossratemustdependonthestockitselfllossesmustapproachzeroasthestock

isdepleted-andmayalsodependonsetsofotherendogenousvariablesXandex-

ogenousv∬iablesU.Lossesmaybenonlinearandmaydependontheagedistrib- utionofthestock:

LR-i(S,X,U) (17-2)

HowshouldtheacqulSitionratebemodeled?Ingeneral,managerscannotaddnew

unitstoastocksimplybecausetheydesiretodoso･First,theacquisitionofnew

unitsmayInvolvetimedelays.Second,theacquisitionofnewunitsforastock

usuallyrequlreSresources:Productionrequireslaborandequlpment;hiringre-

qulreSreCruitlngeffort.Theseresourcesmaythemselvesbedynamic.There-

sourcesavailableatanymomentimposecapacltyCOnStraints･Fornow,assumethe

capacityOftheprocessisampleandthattherearenosignificanttimedelaysinac-

qulrlngnewunits.ThereforetheactualacqulSltionrate,AR,isdeterminedbythe

desiredacqulSltionrate,DAR:

AR-MAX(0,DAR) (17-3)

TheMAXfunctionensuresthattheacqulSltlOnrateremainsnonnegative.Inmost

situations,theacquisitionratecannotbenegative(onceconcreteisdeliveredand

lThediscussionassumes血emanagercontrols也elnflowto仇estockandmustcompensatefor changesintheoutflow.Therearemanystockmanagementsituationsinwhichthemanager'stask istoadjusttheoutflowfromastocktocompensateforchangesintheinflow.Afirmmustadjust shipmentstokeepitsbacklogundercontrolasordersvary;managersofahydroelectricplantmust adjusttheflowthroughthedamtomanagethelevelofimpoundedwaterastheinflowvaries.The principlesforstockmanagementinthesesituationsareanalogoustothoseforthecasewherethe managerscontroltheinnowalone.

FIGURE17-4 Structurefor

managlngaStock whenthereareno

acqulSit'rondelays

669

pouredataconstructionsiteitcannotberetumedtothesupplier).Inthosecases

whereexcessunitscanberetumedordiscarded,theseprocessesareusuallygov-

ernedbydifferentcostsandcriteriaandshouldbemodeledseparately,notasa

negativeacqulSlt10nrate･2

TheformulationforthedesiredacqulSltionratecapturesthedecision-making

processofthemanagers.Therearemanypossibilities.FollowingtheprlnCiples

outlinedinchapterl3,suchformulationsmustbebasedonlyoninformationactu-

allyavailabletothedecisionmakers,mustberobustunderextremeconditions,and

mustbeconsistentwithknowledgeoftheactualdecision-makingprocess,evenif

thewaypeopleactuallymakedecisionsislessthanoptlmal.Inmoststockman-

agementsituationsthecomplexltyOfthefeedbacksamongthevariablesmakesit

2Seesection13･331Al1theMINandMAXfunctionsintheformulationsinthischaptercanbe replacedwiththeirfuzzycounterpartsifthepurposeofthemodelrequlreSit.

670 PartV InstabilityandOscillation

impossibletodeteminetheoptlmalstrategy.Instead,peopleuseheuristicsorrules ofthumbtodeterminetheorderrate.Theorderingdecisionruleproposedhereas-

sumesthatmanagers,unabletooptlmize,insteadexercisecontrolthroughalocally rationalheuristic.Themodelthusfallsfirmlylnthetraditionofboundedrational-

ityasdevelopedbySimon(1982),CyertandMarch(1963),andothersandasde- scribedinchapter15.

Thedesiredacquisitionraterepresentstherateatwhichmanagerswouldlike tobeaddingunitstothestock.Twoconsiderationsarefundamentaltoanydecision rulefordesiredacqulSltlOnS.First,managersshouldreplaceexpectedlossesfrom thestock.Second,managersshouldreducethediscrepancybetweenthedesired

andactualstockbyacqulrlngmorethanexpectedlosseswhenthestockislessthan desiredandlessthanexpectedlosseswhenthereisasurplus.Thusthedesiredac-

qulSitionrateistheexpectedlossrateELplusanadjustmentforthestockASto bringthestockinlinewithitsdesiredlevel:

DAR-EL+AS (17-4)

Theformulationcanbeinterpretedasanexampleoftheanchoringandadjustment

heuristic(TverskyandKahneman1974;chapter13)･HeretheanchoristheexI pectedlossrateEL.Adjustmentsarethenmadetocorrectdiscrepanciesbetween thedesiredandactualstock.

WhydoesthedesiredacqulSitionratedependonexpectedlossesratherthan

theactuallossrate?Thecurrentvalueofaflowrepresentstheinstantaneousrate ofchange.Actualinstruments,however,Cannotmeasureinstantaneousratesof

changebutonlyaverageratesoversomefiniteinterval･ThevelocltyOfanobject iscalculatedbymeasuringhowfaritmovesoversomeperiodoftimeandtaking theratioofthedistancecoveredtothetimeinterval,Theresultistheaveragespeed

overtheinterval.Theactualspeedthroughouttheintervalcanvary,andthevelocl ltyatthefinishlinemaydifferfromaverage.Similarly,thesalesrateofacompany rightnowcannotbemeasured.Insteadsalesratesareestimatedbyaccumulating totalsalesoversomeintervaloftimesuchasaweek,month,Orquarter.There-

portedsalesrateistheaverageoverthereportlnginterval,andsalesattheendof theperiodmaydifferfromtheaverageovertheinterval.Nomatterhowaccurate theinstruments,therateofchangemeasuredandreportedtoanobserveralways

differsfromtheinstantaneousrateofchange.

WhileinprlnCipleal1flOwsaremeasuredandreportedwithadelay,1nPractice thedelaylSSOmetimessoshortrelativetothedynamicsofinterestthatitcansafely beomittedfromyourmodels.Inastockmanagementsituation,thelossrateis

sometimesdirectlyobservablebythedecisionmakerwithessentiallynodelayor measurementerrorsothatitisacceptabletoassumeEL-LR･Mostoften,how- ever,thelossrateisnotdirectlyobservableandmustbeestimated,introducing

measurement,reportlng,andperceptiondelays.Theexpectedlossratemightthen bemodeledasaninfわrmationdelayoftheactuallossrate(seechapter11).Some- timesdecisionmakersextrapolaterecenttrendsinreportedlossestocompensate forexpectedgrowth.InthesecasestheTRENDfunctioncanbeusedtomodelthe

processbywhichmanagersformtheexpectedlossrate(Seechapter16). ThefeedbackstructureoftheheuristicisshowninthebottompartofFigure

1714.TheadjustmentforthestockAScreatesthenegativeStockControlfeedback

Chapter17 SupplyChainsandtheOriginofOscillations 671

loop.Thesimplestformulationistoassumetheadjustmentislinearinthediscrep-

ancybetweenthedesiredstockS*andtheactualstock:

AS-(S*-S)/SAT (17-5)

whereS*isthedesiredstockandSATisthestockadjustmenttime(measuredin

timeunits).Thestockadjustmentformsalinearnegativefeedbackprocess.The

desiredstockmaybeaconstantoravariable,

17.2.2 SteadyStateError

TheinclusionoftheexpectedlossrateintheformulationforthedesiredacqulSl-

tionrateisanimportantbehavioralassumptlOn.Expectedlossesareincludedfor

tworeasons:First,omittingreplacementofexpectedlossesleadstoasteadystate errorinwhichthestockdiffersfromitsdesiredvalueeveninequilibrium.Steady

stateerrormeansagapbetweendesiredandactualstatespersistsevenafterthe

systemhashadtimetosettleintoitssteadystate(i.e,,evenaftertherelationships

amongthestatevariablesstopchanging).Steadystateerrorcanarisedespitethe

existenceofanegativefeedbackloop,suchasthestockadjustmentloop,which

strivestoeliminatediscrepanciesbetweenthedesiredandactualstateofthe SyStem･

Imaglneafirm thatsetsitsproductiontargetbasedonlyonthegapbetweenits

desiredandactualinventorylevels･Thestocktobecontrolledisinventory,ship-

mentsdete-in°thelossrate,andproductionistheacqulSltionrate.Supposetheir

decisionruleistoeliminateanygapsbetweendesiredandactualstocksovera periodof1week:

Production-(DesiredInventory-Inventory)乃nventoryAdjustmentTime (17-6)

wheretheInventoryAdjustmentTime-7daysandthenonnegativltyCOnStraint

onproductionisomitted.

TheequilibriumconditionforinventoryisProduction-Shipments.Therefore

thestockofinventorywillreachbalanceonlywhen

Production (Desiredlnventory-Inventory) inventoryAdjustmentTime

Shipments (17-7)

orwhen

Inventory-DesiredInventory-Shipments*InventoryAdjustmentTime (17-8)

ProducinglnresponsetOthesizeoftheinventoryshortfallguaranteesthatthefirm

will,inequilibrium,beoperatlngWithlessinventorythanitdesires.Wheninven-

tory-desiredinventory,productionwillbezero･Butifthereareshipments,in-

ventorywilldecline,Openlngagapbetweendesiredandactualinventory.Thegap

growsuntilitlSJustlargeenoughtoinduceproductionequaltoshipments.The

biggerthelossrateortheweakerthestockadjustment,thebiggerthesteadystate error.

Thesolutionistoincludetheexpectedlossrateintheproductiondecision.Ex-

pectedlossesmightbebasedontheaverageorderrate:

Production-AverageOrderRate +(DesiredInventory-Inventory)仙lVentOryAdjustmentTime

(17-6a)

672 PartV InstabilityandOscillation

lnequilibrium,averageordersnowequalactualorders,orderswillequalship- ments,andinventorywillequalitsdesiredlevel.Averageratherthanactualorders areusedbecausetheinstantaneousvalueoftheorderrateisnotmeasurableand

firmsdeliberatelyaverageincomlngOrderstosmoothouthigh-frequencynoise andavoidcostlychangesinproduction.

Automaticreplacementofexpectedlossesimprovestheperformanceofthe decisionruleforthedesiredacqulSitionrate.However,youmaynotincludeafor- mulationinyourmodeljustbecauseitwouldmakesense.Youmustalsohaveev- idencethatpeopleactuallydomakedecisionsthatway･Thesecondreasonfor includingtheexpectedlossrateinthemodelisthattheevidencesuggestspeople doinfactaccountforthelossestheyexpectwhenmanagingstocks(see,e.蛋 .,

Sterman1989a,b)-providedlossrateinformationisavailable.Insomesituations, lossrateinformationisunavailableorunreliable.Inthesecasesthereislikelytobe asteadystateerror.Closeinspectionofthedecisionprocessmayrevealthatthede- siredstockincludesasafetymarglnthatroughlycompensatesforthesteadystate error.

17.2.3 ManagingaStock:Behavねr Thesimplestockmanagementstructure,asbasicasitis,yieldsimportantinsight intothesourcesofamplificationobservedinsupplychainsIToillustrate,consider afirmmanagingItsStockofplantandequipment.ThelossraterepresentsthedisI cardofoldbuildingsandequipment.Assumelossesfollowafirst10rderprocess withanaveragelifetimeof8years.Alsoassumethedelaysinreportingthediscard ofbroken-downorobsoleteequlpmentareShortrelativetothedynamicsofinter- est,Sotheexpectedlossratecanbesetequaltotheactuallossrate.Thestockad- justmenttimeissetto3years.Theseparametersareconsistentwiththevalues estimatedbySenge(1978)forcapitalinvestmentinvarioussectorsoftheUS economy(Seesectionll.5.1).

Thedesiredcapltalstockdependsonthedemandforthefirm'sproducts.To explorethebehaviorofaslnglelinkinasupplychain,desiredcapltalisexoge- nous.Figure17-5showstheresponseofthesystemtoastepIncreaseindesired capltal｡Thesystembeginsinequilibriumwithadesiredstockof100unitsand throughputof12.5units/year.Atthestartofyear1thedesiredstocksuddenlyln- creasesto120units.ThestepIncreaseindesiredcapitalimmediatelyopensupa gapof20unitsbetweenthedesiredandactualstock.The叫iustmentforthestock ofcapitaljumpsby20units/3years-6.67units/year,increaslngthedesiredac- qulSltlOnratetO19.17units/year.BecausetherearenodelaysorcapacltyCOn- straintsontheacquisitionrate,thestockbeginstorise.Asitdoes,thecapital shortfalldiminishes,reducingthestockadjustment.TheacqulSltlOnrategradually fallsbacktothelossrate.Asthestockrises,sotoodoesthelossrate.Becausethe

expectedlossrateisassumedtoequaltheactuallossrate,thenetchangeinthe capltalstockisequalsimplytothestockadjustment:

NetChangeinCapitalStock-(S太一S)/sAT (17-9)

whichisthefamiliarfirst10rderlinearnegativefeedbacksystem.Therefore,as seeninthefigure,afterthreeadjustmenttimes(9years),thecapitalstockhasad- justedabout95%ofthewaytoitsnewequilibrium.

Chapter17 SupplyChainsandtheOriginofOscillations

■_

1-r

Jea ^ JS I P

FIGURE17-5

Responsetoa steplncreasein

thedesiredstock

0 2 4 Years 6 8 10

2 4 Years 6 8 10

673

Theconsequencesofthestockmanagementstructureforsupplychainman-

agementareprofound･First,theprocessofstockadjustmentcreatessignificant

amplification.Though thedesiredstockincreasedby20%,theacqulSlt10nratein-

creasesbyamaximumofmorethan53%(thepeakacquisitionratedividedbythe

initialacquisitionrate-19.2/12･5).Theampllficationratio(theratioofthemax-

imum changeintheoutputtothemaximum changeintheinput)istherefore

53%/20% -2.65.A1%increaseindesiredcapacltyCausesa2.65%Surgeinthe

demandfornewcapital.Whilethevalueoftheamplificationratiodependsonthe

stockadjustmenttimeandcapltallifetime,theexistenceofamplificationdoesnot.

Alongeradjustmenttimereducesthesizeoftheadjustmentforthestockforany

glVendiscrepancybetweenthedesiredandactualstocksandthusreducesam-

plification,butalsolengthensthetimerequiredtoclosethegapandreachthe

newgoal.

Second,amplificationistemporary･Inthelongrun,al%increaseindesired

capltalleadstoa1%increaseintheacqulSitionratedButduringthedisequilibrium

adjustment,theacqulSitionrateovershootsthenewequilibrium･Theovershootis

aninevitableconsequenceofthestockandflowstructure･Theonlywayastock

canincreaseisfortheacqulSltlOnratetOexceedthelossrate･TheacqulSitionrate

mustincreaseabovethelossratelongenoughtobuildupthestocktothenewde-

siredlevel.Thefirm'ssuppliersfacemuchlargerchangesindemandthanthefirm

itselfandmuchofthesurgeindemandistemporary･

674 PartV InstabilityandOscillation

Exp一oringAmplification

Explorethebehaviorofthesimplestockmanagementmodelwiththeparameters intheexampleshowninFigure17-5.Trythefollowlngtests:

l･ExploretheresponseoftheacqulSitionratetodifferentmagnitudesforthestep increaseindesiredcapitalstock.Howdoesthesizeofthestepaffecttherateof adjustmentofthecapitalstocktothenewequilibrium?Doestheamplification ratiofortheacqulSltionratedependonthesizeofthestepindesiredcapital? Why/whynot?

2.WhatistheresponseoftheacqulSlt10nratetOa20%stepdecreaseindesired capital?Whatistheresponsetoa60% decrease?Arethereanydifferences? Why/whynot?

3.Howdoestheamplificationofchangesindemanddependonthestockadjust-

menttime?Withanadjustmenttimeof3yearsittakes9yearstoreach95%ofthe desiredcapitalstock･Somemanagersinthefirmarguethisistoolong.Whatisthe amplificationratiogeneratedbyanadjustmenttimeof2years?1year?Whatare theimplicationsofamoreaggressivestockadjustmentpolicyforthefirmandits equlpmentSuppliers?

4. Explorethedependenceoftheamplificationratioonthelifetimeofcapital. Whathappenstotheamplificationofdemandchangesasthelifetimeofcapitalin- creases?Why?Howdoesthishelpexplainwhytheamplitudeofbusinesscycles intheconstructionindustrylSgreaterthanthatoftheservicesector?

5. Canthesimplestockmanagementsystemoscillate?Withthebasecasepa- rameterstheresponsetoasteplnCreaSeindesiredcapltalisaslngleovershootof theacqulSitionrate:Thesystemampl泊esdemandchangesbutdoesnotgenerate oscillation.Arethereanyparametersthatcaninduceanoscillatoryresponse? Why/whynot?

6.ThesteplSaSimpleinputthatteststheresponseofasystemtoanunexpected changeintheenvironment.Intherealeconomythedemandforafirm'sproduct (andhenceitsdesiredcapitalstock)exhibitsmorecomplexbehavior,including fluctuations,randomshocks,andgrowth.Testtheresponseofthesystemtoafluc- tuationbyassumingdesiredcapitalstockfluctuatessinusoidally(assumethesys- temremainsinequilibriumuntilthestartofyear1):

S*-100*[1+Asin(2′汀(t-1)/P)]fort>1

whereAistheamplitudeofthenuctuationandPistheperiod.Tobegin,set A-0.10andP= 1year.Calculatethesteadystateamplificationratiointhe acquisitionrate･Theamplificationratioistheratiooftheamplitudeofthefluctu- ationintheacquisitionratetotheamplitudeofthefluctuationindesiredcapital. Steadystatemeansyoushouldmeasuretheamplitudeofthevariablesafterinitial transientshavediedout(afteraboutthreetimeconstantsSAThavepassed).How doestheamplificationratiodependontheperiodofthecycleP?Howdoesitde- pendonthestockadjustmenttimeSAT?Itishelpfultomakeagraphshowingthe amplificationratioasafunctionoftheratioP/SAT.

Chapter17 SupplyChainsandtheOriginofOscillations 675

7. Nowexploretheresponseofthesystemtogrowthin血edesiredcapitalstock.

Considertwocases,andonceagaln,assumedesiredcapitalstockisconstantuntil

thestartofyear1:

a. Lineargrowth(startwithaslopeof20units/year).

b･ Exponentialgrowth(startwithagrowthrateoflO%/year).

Isthereasteadystateerrorforthecaseofgrowthinthedesiredstock?Thatis,

doestheactualstockeventuallyequalthedesiredstock?Why/whynot?Findanal-

gebraicexpressionforthesteadystatestockSintermsoftheinputS*andtheother

parametersinthesystem.

8. Sofarthelossratehasbeenassumedtobefirst-order,meaningthelikelihood

anyunitinthestockisdiscardeddoesnotdependonitsage･Inreality,theproba-

bilityofdiscardusuallyrisessharplyforoldervintages.Disaggregatethecapital

stockintoathird-orderagingchain.Eachvintage(stockofagivenaverageage)

shouldhavearesidencetimeequaltoone-thirdtheaveragelifetime.Assumethere

arenodiscardsfromthefirsttwovintages(thelossratewillthereforebeequiva1

lenttoathird-orderdelayoftheacquisitionrate).Whatistheimpactofanexplicit

vintaglngStructureOnthebehaviorofthemodel?

17.3 THESTOCKMANAGEMENTSTRUCTURE

Thesimplemodelaboveyieldsimportantinsightsintothebehaviorofsupply

lines;however,themodelinvokesanumberofunrealisticassumptlOnS.Mostseri-

ousistheassumptionthatthereisnodelayintheacqulSltionprocess･Afirmseek1

1ngtOincreaseitscapitalstockcannotacqulrenewunitsimmediatelybutmust

awaitconstructionordelivery.Newworkerscannotbehiredandtrainedinstantly.

Ittakestimeforyourcartostopafteryousteponthebrakes,andittakestimefor

theeconomytorespondafter血eFederalReservechangesinterestrates.

Figure1716modifiesthestructureofthestockmanagementsystemtoinclude

adelaybetweenordersandacqulSltlOn.Asbefore,thestockisincreasedbyacqu1 -

Sitionsanddecreasedbythelossrate;theseareformulatedasinequations(17-2)

and(17-3).ThestockandflOwstructurenowincludesasupplylineofunfilled

orders-thoseordersthathavebeenplacedbutnotyetreceived:

SL-INTEGRAL(OR~AR,SLt｡) (17-10)

TheorderrateORisnowthemanagers'decisionpolnt.Theacquisitionratede-

pendsonthesupplylineSLofunitsthathavebeenorderedbutnotyetreceived

andtheaverageacqulSitionlagAL:

AR-L(SL,AL) (17-ll)

AL-I(SL,X,U) (17112)

wherethelagfunctionL()denotesamaterialdelay.Theacquisitionlagcouldbea

pIPelinedelay,afirst10rderdelay,Oranyotherdistributionofarrivalsaroundthe

averageacqulSitionlagJngeneral,theacqulSltionlagmaydependonthesupply

lineitselfandontheotherendogenousandexogenousvariables.Often,theaver-

ageacqulSitionlaglSrelativelyconstantuptothepolntWheretherequiredacqul-

sitionrateexceedsthecapacltyOftheprocess,asforexamplewhenthedesired

676 PartV instabilityandOscillation

FIGURE17-6 Thegenericstockmanagementstructure

ThedeterminantsofthedesiredsupplyFinearenotshown(seetext)･

constructionrateforcapltalplantexceedsthecapacltyOftheconstructionindustry.

TheacqulSitionlagcanalsobeinfluencedbythemanager'sdecisions,aswhena firmchoosestoexpeditedeliveryofmaterialsbypaylngPremiumfreight.

ThestructurerepresentedbyFigure17-6isqultegeneral･Thesystemmaybe nonlinear.Theremaybearbitrarilycomplexfeedbacksamongtheendogenous variables,andthesystemmaybeinnuencedbyanumberofexogenousforces, bothsystematicandstochastic.ThedelaylnaCqulrlngnewunitsisoftenvariable

andmaybeconstrainedbythecapacltyOfthesupplier･Table17-1mapscommon

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678 PartV InstabilityandOscillation

examplesintothegenericform.Ineachcase,themanagermustchoosetheorder

rateovertimetokeepthestockclosetoatarget.Notethatmostofthesesystems tendtogenerateoscillationandinstability.

Managersstillordertoreplaceexpectedlossesfromthestockandreduceany

discrepancybetweenthedesiredandactualstock･InthepresenceofanacqulSition delaymanagersmustalsomaintainanadequatesupplylineofunfilledorders,ad- justingltSOthatacqulSltionsareclosetothedesiredrate.Toformalizethisheuris- tic,firstnotethattheorderrateinmostreallifesituationsmustbenonnegative:

OR-MAX(0,IO) (17-13)

whereIOistheindicatedorderrate,therateindicatedbyotherpressures.Order cancellationsaresometimespossibleandmaysometimesexceedneworders(e.蛋., theUSnuclearpowerindustrysincethe1970S).Asbefore,thecostsofandad一 ministrativeproceduresforcancellationsarelikelytodifferfromthosefornewor- ders.Cancellationsshouldthereforebemodeledasadistinctoutflowfromthe

supplyline,governedbyaseparatedecisionrule,ratherthanasnegativeorders (Seechapter19forasuitableformulation).

Theindicatedorderrateisformulatedasananchoringandadjustmentprocess.

ThedesiredacqulSltionrateDARistheanchor,whichisthenadjustedbyan amountdesignedtobringthesupplylineofunfilledordersinlinewithitsgoal(the adjustmentforthesupplylineASL):

10 -DAR+ASL (17-14)

Theadjustmentforthesupplylineisformulatedanalogouslytotheadjustmentfor thestock:

ASL-(SLx-SL)/SLAT (17-15)

whereSLkisthedesiredsupplylineandSLATisthesupplylineadjustmenttime. ThesupplylineadjustmentformsthenegativeSupplyLineControlloop.

Figure1716doesnotshowthefeedbackstructureforthedesiredsupplyline. Insomecasesthedesiredsupplylineisconstant｡Moreoften,however,decision makersseektomaintainasufficientnumberofunitsonordertoachievetheac-

quisitionratetheydesire.ByLittle'sLaw(chapterll)thesupplylinemustcontain

ALperiod'Sworthofthethroughputthedecisionmakerdesirestoachieve.Several

measuresfわrdesiredthroughputarecO- on･Thedecisionmakermaysetthesup- plylinetoyieldthedesiredacqulSltlOnrateDAR:

SL*-EAL*DAR (17-16)

whereEAL,theexpectedacqulSitionlag,representsthedecisionmaker'scurrent beliefaboutthelengthoftheacquisitiondelay(which,ingeneral,maydifferfrom theactualacquisitiondelay).

Equation(17-16)assumesaratherhighdegreeofrationalityonthepartofde- cisionmakers.Theyareassumedtoadjustthesupplylinetoachievethedesired

acqulSitionrate,whichincludesreplacementofexpectedlossesandcorrectionof temporarygapsbetweendesiredandactualinventory.Asdescribedinsection17.4, experimentalevidenceshowsdecisionmakersareoftennotsosophisticated.Man-

agersfrequentlydonotadjustthesupplylineinresponsetotemporaryimbalances

Chapter17 SupplyChainsandtheOriginofOscillations 679

inthestockbutbasethedesiredsupplylineontheirestimateoflong一mnthrough-

putrequirements-theexpectedlossrateEL:

SL*-EAL*EL (17-16a)

Thefomulationforthedesiredsupplylinemustdependonempiricalinvestigation oftheactualdecision-makingprocess.

Wh icheverformulationforthedesiredsupplylineisused,thelongertheex-

pecteddelaylnaCqulrlnggoodsorthelarger血edesiredthroughputrate,thelarger thesupplylinemustbe.Ifaretailerwishestoreceive1,000widgetsperweekfrom thesupplieranddeliveryrequlreS6weeks,theretailermusthave6000Widgetson ordertoensureanuninterruptedflOwofdeliveries.Theadjustmentforthesupply

linecreatesanegativefeedbackloopthatadjustsorderstomaintainanacqulSition rateconsistentwithdesiredthroughputandtheacqulSltlOnlag.Withoutthesupply linefeedback,orderswouldbeplacedevenafterthesupplylinecontainedsuffi-

cientunitstocorrectstockshortfalls,producingovershootandinstability(section

17･4).Thesupplylineadjustmentalsocompensatesforchangesintheacquisition lag.IftheacqulSltlOnlagdoubled,forexample,thesupplylineadjustmentwould inducesu任icientadditionalorderstorestorethroughputtothedesiredrate.

Therearemanypossiblerepresentationsfbr山eexpectedacqulSltlOnlagEAL, rangingfromconstantsthroughsophisticatedforecasts･Itissometimesacceptable

toassumetheexpectedacqulSltlOnlagequalstheactuallag,EAL-ALUsually, however,ittakestimetodetectchangesindeliverytimes.Customersoftendonot

knowthatgoodstheyorderedwillbelateuntilafterthepromiseddeliverytlmehas

passed.TheexpectedacqulSltlOnlagcanthenbemodeledbyaperceptiondelay representlngthetimerequiredtoobserveandrespondtochangesintheactual delay:EAL-i(AL,TPAL),whereTPAListheTimetoPerceivetheAcquisi- tionLag.

Finally,toensuretheformulationisrobust,theequationforthedesiredacqu1- SitionratemustbemodifiedsothatDARremainsnonnegativeevenwhenthereis

alargesurplusofinventory.

DAR-MAX(0,EL+AS) (17-4a)

Everyfomulationshouldbeevaluatedintensofitsrobustness,itsunderlyingln- formationalandcomputationalrequirements,anditsconsistencywiththeformul

lationprinciplesdescribedinchapter13.Theformulationfortheorderrate conformstotheseprinciples.First,theformulationisrobust:Ordersremainnon- negativenomatterhowlargeasurplusstocktheremaybe,andthesupplylineand stockthereforeneverfallbelowzero.Second,informationnotavailabletorealde-

cisionmakersisnotutilized(suchasthesolutiontothenonlinearoptimization

problemdete-inlngtheoptlmalorderrateortheinstantaneousvalueoftheloss rateoracquisitiondelay).Finally,theorderingdecisionruleisgroundedinwell- establishedknowledgeofdecision-makingbehavior,inparticular,theanchoring andadjustmentheuristic.Expectedlossesform aneasilyantlCIPatedandrelatively

stablestartlngpointforthedetemi nationoforders･Lossrateinformationwilltyp- icallybelocallyavailableandhighlysalienttothedecisionmaker.Replacing losseswillkeepthestockconstantatitscurrentlevel.Adjustmentsarethenmade inresponsetotheadequacyofthestockandsupplyline.NoassumptlOnismade

680 PartV InstabilityandOscillation

thattheseadjustmentsareoptimal.Rather,pressuresarisingfromthediscrepancies betweendesiredandactualquantitiescausemanagerstoadjusttheorderrateabove orbelowthelevelthatwouldmaintainthestatusquo.

17.3.1 BehavioroftheStockManagementStructure

Toillustratethebehaviorofthestockmanagementstructure,consideragaina firm'scapitalinvestmentdecision.ThestockisthetotalquantltyOfcapitalequlp- mentandthesupplylineistheamountofplantandequlpmentOnOrderorunder construction.Asbefore,thelossrateisafirst10rderprocesswithanaveragelife- timeof8yearsandthestockadjustmenttimeissetto3years･Ⅰnthissimplever- sionofthemodel,theacquisitionprocessisassumedtobeafirstl0rdermaterial delay(morerealistic,higher-orderdelaydistributionsareconsideredbelow),and therearenocapacltyCOnStraints.Theaverageacqtlisitiondelayisthereforecon- stantandissetto1.5years,consistentwiththe17-monthaveragefoundbyMont- gomery(1995).Assumethedelayinobservingandreactingtothediscardofold equlpmentisshortrelativetotheothertimeconstants,Sotheexpectedlossratecan besettotheactuallossrate.Likewise,assumetheacqulSitiondelaycanbeper- ceivedimmediately,sothattheexpectedacqtllSltlOnlagequalstheactuallag.

FollowingSenge'S(1978)results,thesupplylineadjustmenttimeissettoO･75 years.Thesupplylineadjustmenttimeisshorterthanthestockadjustmenttime. Adjustingthecapitalstockisdifficult,expensive,andtimeconsumlng;thelong lifetimeofplantandequlPmentmeansmistakesarenoteasilyundone･Hencefor bothmanagerialandadministrativereasons,gapsbetweendesiredandactualcap- italareclosedonlyslowly.Incontrastthesupplylineoforderscanbeadjusted muchmorerapidly.ThecostofadjustingOrdersismuchlowerthanthecostofad- JuStlngthecapitalstock,andthedelaylnaCqulrlngnewunitsismuchshorterthan thelifeofnewcapital.Itstilltakestimetoadjustthesupplyline.Ittakestimeto renegotiatecontracts,Specifyandexecutechangeorders,andmakeotheradjust- ments.Further,firmsareoftenreluctanttomakelargechangesinthequantities theyorderfromtheirsupplierssincemanycontractsspecifyexpeditingcostsor cancellationfees.Figure1717showsthestockmanagementstructureadaptedto thecapitalinvestmentexample･

Figure17-8showstheresponseofthesystemtoa20%stepIncreaseindesired capital.Capitalstocksmoothlyapproachesthenewgoal,andthetimerequiredto reachthenewequilibriumislittlechanged丘.omthecasewithoutanacquisitionde- lay.However,theacquisitiondelaydramaticallyincreasestheamplificationgen- eratedbythesystem.Themaximumchangeintheorderrateis160%greaterthan theinitiallevel,anamplificationratioof8.00(Comparedt02.65withouttheac- quisitiondelay).

Whendesiredcapitalincreases,thedesiredacqulSltlOnrateSuddenlyrises (throughthestockadjustmentloop)･Therearetwoeffectsontheorderrate:First, theorderrateriseswiththedesiredacqulSltlOnrate;Second,thedesiredsupplyline increasesinproportiontotheriseinthedesiredacqulSltlOnrate･Asthedesired supplylinerisesabovetheactualsupplyline,ordersriseabovethedesiredacqu1- sitionrate.Becausethesupplylineadjustmenttimeisrelativelyshort,theadjust- mentforthesupplylineisinitiallylarge(infactlargerthantheadjustmentforthe

Chapter17 SupplyChainsandtheOriginofOscillations

FIGURE17-7 Adaptingthestockmanagementstructuretocapitalinvestment

681

stock).Afterabout1year,thesupplylinehasincreasedenoughtoequalthedesired supplylineandtheorderratefallsbacktothedesiredacqulSltlOnrate.AsacqulSl- tionsraisethecapitalstock,theadjustmentforthestockfalls,andasitdoes,sotoo

doesthedesiredsupplyline.Because血eactualsupplylinelagsbehindthedesired level,thefirmfindsitselfwithslightlymorecapitalonorderthanitrequires,Caus-

ingthesupplylineadjustmenttobeslightlynegative.Theorderratecontinuesto

exceedthelossrate,however,duetothestockadjustment,untilcapitalreachesthe newdesiredlevel.

TheamplificationcreatedbytheacqulSltlOndelaydependsofcourseonthe

parameters,particularlythelengthofthedelayandthesupplylineadjustment time.Thelongertheacquisitiondelay,Ortheshorterthesupplylineadjustment time,thegreatertheamplification.GiventherealisticparametersinFigure1718,

theamplificationoforderswithrespecttodesiredcapitalisafactorofeight,a valueroughlyconsistentwiththeamplificationobservedintheoilandmachine toolindustries(Figure17-3).

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Chapter17 SupplyChainsandtheOriginofOscillations 683

Explor岳ngtheStockManagementStructure Explorethebehaviorofthestockmanagementstructurewith血eparametersused inFigure17-8.

1.Repeatthetestsinquestions1and20fthechallengeinsection17.2.3.How doestheinclusionofthesupplylineaffecttheresponseofthesystemtoincreases

anddecreasesindesiredcapital?

2.Howdoestheamplificationofdemanddependonthestockadjustmenttime? WiththeparametersusedinFigure17-8,ittakesabout8yearsforcapitaltoin- crease95%ofthewaytodesiredcapital.Howmuchcantheadjustmentbeaccel-

eratedbymoreaggressivestockand/orsupplylineadjustments?Whatistheeffect ofthesechangesontheamplificationoforders?

3･Canthesystemoscillate?Withthebasecaseparameterstheresponsetoastep increaseindesiredcapitalisaslngleovershootoftheorderandacqulSltlOnrate.

Arethereotherparametersthatcaninduceanoscillatoryresponse?Why/whynot? HowdoesthiscomparetothecasewherethereisnoacqulSitiondelayorsupply line,andwhy?Contrastthebehaviorofthesystemwiththetwoformulationsfor thedesiredsupplyline,equations(17-16)and(17-16a).Whichismoreresponsive?

Canthesystemoscillatewiththeformulationin(17116a)?Explain･

4･Testtheresponseofthesystemtoafluctuationinthedemandforitsproduct byassumingdesiredcapitalstockfluctuatessinusoidallyasinsection17.2.3:

S*-100*[1十Asin(2rTT(t-1)〟)]fort>1

Calculatethesteadystateamplificationratiointheorderrate,acqulSlt10nrate,and capitalstock.Howdoestheamplificationratiodependontheperiodofthecycle

P?HowdoesitdependonthestockadjustmenttimeSATandsupplylineadjust-

menttimeSLAT?HowdoesitdependontheacqulSitionlagAL?Makegraphs showlngtheamplificationratioasafunctionofthecycleperiodrelativetothese parameters･

5.Repeattheanalysisin(4)withtheamplitudeofthesinewaveindesiredcapi-

talA-0･50･Howdoesthebehaviorofthesystemdifferfromthesmallamplitude case?Calculatetheamplificationratiosoforders,acquisitions,andthecapital stockwithrespecttodesiredcapital.Whatisthesteadystateaveragevalueofthe capltalstock,andwhy?

61 Sofartheacquisitiondelayhasbeenassumedtobefirst10rder.Asshownin chapter11,theactualcapltalacqulSltlOnProcessisactuallyahigher-orderprocess｡ Replacethe丘rst-orderacquisitiondelaywithathird-orderdelay(withthesame

averagedelaytime).Whatis血eimpactofahigher-orderacquisitiondelayonthe behaviorofthestockmanagementstmcture?Considerresponsetimeandshape, amplification,andstability,andconsiderthesensitivltytodifferentvaluesofthe

parametersincludingSATandSLAT,notonlythebasecase.Considertheimpact ofspecifyingthedesiredsupplylineSL*byequation(17-16a).

684 PartV InstabilityandOscillation

17[4 THEORFGきNOFOscILLAT旧NS

Chapter4discussedthegenericstructureresponsibleforoscillations:negative

feedbackswithtimedelays.Ineverynegativeloopthestateofthesystemiscom-

paredtothedesiredstateandanydiscrepancyinducesacorrectiveaction.When

therearenotimedelays,thecorrectiveactionsrespondimmediatelytothedis-

Crepancyandimmediatelyalterthestateofthesystem･Theresultisasmoothap- proachtoequilibrium.Asshowninchapter4andsection8.5.2,negativefeedback

systemswithouttimedelayscannotoscillate･Oscillationscanariseonlywhen

therearetimedelaysinatleastoneofthecausallinksinanegativefeedbackloop･

Butnotallnegativeloopswithdelaysoscillate･Whatarethecausesofoscilla- tions?Underwhatcircumstanceswillasystemoscillate?

Delaysalwaysinvolvestocks(chapterll).Whentheinputandoutputofade-

laydiffer,thedifferenceaccumulatesinastockofmaterial(orinfomation)intran-

sit.Timedelaysbetweencorrectiveactionsandtheireffectscreateasupplylineof

correctionsthathavebeeninitiatedbutnotyethadtheirimpact.Themereexis-

tenceofthetimedelayandsupplyline,however,doesnotleadtooscillations.In

thestockmanagementstructureadaptedforcapitalinvestment,forexample(Fig-

ure17-7),thereisal･5-yeardelaybetweenorderingandreceivingnewcapital,yet thesystemdoesnotoscillate(withtheestimatedparameters).Eventhoughtheac-

qulSltlOndelaymeansordersplacedtodaydonothingtoreducethegapbetween

thedesiredandactualstock,managersareassumedtorecognizeWhenthesupply

linefillsenoughtosolvetheproblem-andreduceordersappropriately.Tooscil-

1ate,thetimedelaymustbe(atleastpartially)ignored.Themanagermustcontinue

toinitiatecorrectiveactionsinresponsetotheperceivedgapbetweenthedesired

andactualstateofthesystemevenaftersufficientcorrectionstoclosethegapare

inthepipeline.

17.4.1 Mis汀はnagingtheSupp吋L;ne: TheBeerDistributionGame

TheBeerDistributionGameillustrateshowoscillationsarise･3Thegameisarole-

playingsimulationofasupplychainorlglnallydevelopedbyJayForresterinthe

late1950stointroducestudentsofmanagementtotheconceptsofsystemdynam-

icsandcomputersimulation.Sincethenthegamehasbeenplayedalloverthe

worldbythousandsofpeoplerangingfromhighschoolstudentstochiefexecutive

officersandseniorgovernmentofficials.

Thegameisplayedonaboardportrayingatypicalsupplychain(Figure17-9).

Ordersforaridcasesofbeei-arerePi-eSeiltedbyir.arkefSaridchips.Eachbrewery

consistsoffわursectors:retailer,wholesaler,distributor,andfactory(良 ,W,D,F).

Onepersonmanageseachsector.Adeckofcardsrepresentscustomerdemand.

3ThegameisdescribedindetailinSterman(1989b,1992)andSenge(1990)･InformatioTon thegameandmaterialsareavailablefromtheSystemDynamicsSocietyat<system.dynamics @albany.edu>.Thereisnorealbeerinthebeergameanditdoesnotpromotedrinking･Whenthe gameisusedwith,e･g･,highschoolstudents,itiseasilyrecastastheHappleJUICEgame･"Many firmshavecustomizedthegametorepresenttheirindustry･

685

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686 PartV InstabilityandOscillation

Eachweek,customersdemandbeerfromtheretailer,fillingtheorderoutofin-

ventory.Theretailerinturnordersbeer丘.omthewholesaler,whoshipsthebeerre-

questedfromwholesalestocks.Likewisethewholesalerordersandreceivesbeer fromthedistributor,whointumordersandreceivesbeerfromthefactory.Thefac-

toryproducesthebeer.Ateachstagethereareorderprocessingandshippingde-

lays.Eachlinkinthesupplychainhasthesamestructure･

Theplayers'objectiveistominimizetotalcostsfortheircompany.Inventory

holdingcostsareusuallysetto$0.50percaseperweek,andstockoutcosts(costs

forhavingabacklogofunfilledorders)are$1.00percaseperweek･Thetaskfac1

1ngeachplayerisaclearexampleofthestockmanagementproblem.Playersmust

keeptheirinventoriesaslowaspossiblewhileavoidingbacklogs･4IncomlngOr-

dersdepleteinventory,soplayersmustplacereplenishmentordersandadjusttheir

inventoriestothedesiredlevel.ThereisadelaybetweenplacingandreceivlngOr-

ders,CreatlngaSupplylineofunfilledorders.

Thegameisfarsimplerthananyrealsupplychain.Therearenorandom

events一momachinebreakdowns,transportationproblems,Orstrikes.Thereareno

capacltyconstraintsorfinanciallimitations.Thestructureofthegameisvisibleto

all.PlayerscanreadilyinspecttheboardtoseehowmuchinventorylSintransitor

heldbytheirteammates.Thegameistypicallyplayedwithaverysimplepattem

forcustomerdemand.Startingfromequilibrium,thereisasmall,unannounced

one-timeincreaseincustomerorders,from4to8casesperweek.

Despltetheapparentsimplicityofthegame,peopledoextremelypoorly･

Amongfirst-timeplayersaveragecostsaretypicallyanastonishing10times

greaterthanoptlmal.Figure17-10showstypicalresults･Inallcasescustomeror-

dersareessentiallyconstant(exceptforthesmallstepincreasenearthestart)･In

allcases,theresponseofthesupplychainisunstable.Theoscillation,amplifica-

tion,andphaselagobservedinrealsupplychainsareclearlyvisiblein血eexperト

mentalresults.Theperiodofthecycleis20125weeks.Theaverageamplification

ratiooffactoryproductionrelativetocustomerordersisafactoroffour,andfac-

toryproductionpeakssome15weeksafterthechangeincustomerorders･

Mostinterestlng,thepatternsofbehaviorgeneratedinthegameareremark-

ablysimilar(thereare,ofcourse,individualdifferencesinmagnitudeandtiming)･

StartlngWiththeretailer,inventoriesdeclinethroughoutthesupplychain,andmost

playersdevelopabacklogofunfilledorders(netinventoryisnegative)･Inre-

sponse,awaveofordersmovesthroughthechain,growinglargerateachstage･

Eventually,factoryproductionsurges,andinventoriesthroughoutthesupplychain

starttorise.Butinventorydoesnotstabilizeatthecost-minimlZlnglevelnearzero･

Instead,inventorysignificantlyovershoots.Playersrespondbyslashingorders,of-

tencuttlngthemtozeroforextendedperiods.Inventoryeventuallypeaksand

slowlydeclines.Thesebehavioralregularitiesareallthemoreremarkablebecause thereisnooscillationincustomerdemand.Theoscillationarisesasanendogenous

consequenceofthewaytheplayersmanagetheirinventories｡Thoughplayersare

4MinimumcostsareobtainedwheninventorylSZero,butsinceincomngordersareuncertain andbacklogsaremorecostlythaninventories,itisoptlmaltosetdesiredinventorytoasmall positivenumber.

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688 PartV InstabilityandOscillation

freetoplaceordersanywaytheywish,thevastmajoritybehaveinaremarkably uniformfashion.

Tounderstandtheorlginoftheoscillation,amplification,andphaselag,con- siderthestructureandbehaviorofatypicallinkin血edistributionchainFigure 17-llmapsthestructureofaslnglelinkintothestockmanagementframework (chapter18developsmorerealisticsupplychainmodelsformanufacturing)･Net inventorylSthestocktobemanaged.Thesupplylineisthestockofordersthe playerhasplacedbutnotyetreceived,includingordersintransittothesupplier, thesupplier'sbacklog(ifany),andthegoodsintheshippingdelays･Adapting theorderingdecisionruletotheproduction-distributionsettlnginthegameis straightforward･Theexpectedlossrateistheplayer'sforecastofincomlngOrders･ Analysisofthebeergameandrelatedstockmanagementexperiments(Sterman 1989a,b;DiehlandSterman1995)showedthatmostpeopleformtheirforecasts

bysmoothingoraveragingpastOrders･Thedataalsoshowthatpeopledonot

FIGURE17-ll CausalstructureoftheBeerDistributionGame

ShowsthestructureofasIngFefinkinthesuppfychain.Customerordersareexogenous･Managers mustplaceorderswiththeirsuppllerStOreplaceshipmentstocustomersandrestoreinventoriestothe desiredlevel.

Chapter17 SupplyChaiIISandtheOriginofOscillations 689

managethesupplylineinthesophisticatedmannerassumedinequation(17-16).

Thedesiredsupplylinedoesnotrespondtotheinventoryadjustmentbutonlythe

replacementofexpectedlosses,asinequation(17-16a)･

Table17-2Showswhathappenswhenmanagerscompletelyignorethesupply

line.Thesystemissimulatedindiscretetimeintervalsof1week,justasintheac-

tualexperiment.Forillustration,desiredinventoryis400unitsandthedeliveryde-

layis3weeks.Customerorders,andexpectedcustomerorders,areconstantat100

units/week.Assumethemanagercon-ectstheentirediscrepancybetweeninventory

anddesiredinventoryeachweek(SAT-1week)･Toknockthesystemawayfrom

theinitialequilibrium,100unitsofinventoryareunexpectedlylostduringweek1,

reducingInventoryatthestartofweek2to300cases･Themanagerrespondsby

ordering200:100toreplacecustomerordersand100torestoreinventorytothe

desiredlevel.Thesupplylinerisest0400units.Duetothedeliverydelay,lnVen-

torylnWeek3isstillonly200.Themanager,1gnOrlngthesupplyline,agalnre-

spondstotheinventorygapandorders200.Thesupplylinerisest0500units.In

week4themanageragainfindsinventoryisloounitsshort,againIgnoresthesup-

plyline,andagainOrders200units.Thefifthweekisthesam e･

Bytheendofthefifthweekthefirstorderof200finallyarrives.Week6be-

glnSWithinventoryrestoredtoitsdesiredlevel･Themanagercutsordersbackto

theequilibriumrateof100units/week.Butthesystemisfarfromequilibrium:The

supplylinehasswollento600units.Thenextweek,200moreunitsaredelivered,

boostingInventorytO500.Facingasurplusof100units,themanagernowcuts

orderstozero.Toolate:Overthenext3weeksinventorysoarsto700units.

Sinceorderscannotbecanceledandgoodscannotbereturned,inventoryre一

mainshighuntilthesupplylineiscompletelydrainedanddeliveriesfalltozero

(week10).Ittakes3weekstoeliminatetheexcessinventory.Inweek13inventory

agalnequalsthedesiredlevel,soordersrisetotheequilibrium rateof100

units/week.Butthereisnownothinginthesupplyline･Nothingisdeliveredin

week14.Inventoryfallsto300,forcingorderstorise100unitsabovetheorder

rate.Again,nothingisdeliveredinweek151Inventoryfallsanotherloounits,and

themanagernowmustorder100toreplacecustomerdemandplus200torestore

inventorytothedesiredlevel.Bythestartofweek16inventoryhasfallento100,

forcingthemanagertoorder400units.Bythestartofweek17thefirstorderof

100amives,StabilizingInventoryat100units.Themanager,respondingonlytothe

inventoryshortfall,agalnOrders400.Thesupplylinehasnowswollento1100

units.Overthenext3weekstheseordersaredelivered,SoonpushinglnVentOry

abovethedesiredlevel.Thoughthemanagerslashesorderstozero,deliveriescon-

tinue,swellinginventorytoapeakof1200units.Andsothecyclecontinues(Fig-

ure17-12).5

5Giventhechosenparameters,theno-supply-linecontrolcasegeneratesalimitcycle:Theequト libriumisunstableandcycleamplitudeincreasestoamaximumdete-inedby血enonlinearitiesin thesystem,SpecificallythenonnegativltyOforders.Youshouldexperimentwithdifferentparame- ters(deliverydelay,inventory,andsupplylineadjustmenttimes)toexplorehowstabilityvaries withthestrengtbsoftheinventoryandsupplylinecontrolloopsandthelengthofthedelayinthe responseofinventorytoorders･Seesection4･3･3･

⊂〉 ⊂〉⊂) ⊂) ⊂)⊂)⊂)⊂) ⊂) ⊂〉⊂〉⊂) ⊂〉 ⊂) ⊂) ⊂)⊂〉 ⊂)⊂)⊂)⊂)⊂〉 ⊂) ⊂)⊂)⊂〉 ⊂) ⊂) ⊂) ⊂)⊂)⊂) ⊂) ⊂〉⊂) ⊂) ⊂)⊂)⊂〉 ⊂)⊂)⊂) ⊂) ○ くつの勺-LLつ (ロくO LL)CV) T- T のくD O) 7- 7-の寸 7-r ■▼'''II

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Chapter17 SupplyChainsandtheOriginofOscillations

FlGURE17-12 0sc‖ationcaused

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supply=ne

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TheoscillationinFigure17-12arisesnot血.om thetimedelayalonebut

becausethemanagerplacesorderswithoutregardtothesupplylineofunfilled

orders･Theonlythingthemanagercaresaboutiswhetherthereisenoughinven- toryrightnow.

Whathappenswhenthemanagerfullyaccountsforthesupplyline?Table1713

showsasimulationofthesystemforthesamesituationexceptthatnowthesupply lineisglVenaSmuchweightasinventoryonhand,thatis,SLAT-SAT-Iweek.

Asbefore,inventoryunexpectedlydropsby100unitsinweek1.Alsoasbefore,

themanagerorders100unitstoreplaceexpectedcustomerordersplusanaddト

ーional100casestorestoreinventorytothedesiredlevel,increaslngthesupplyline

ofunfilledordersto400units･Duetothedeliverydelay,lnVentOryremainsat300

inweek2.TheadjustmentforinventorylSagain100units.Thistime,eventhough

inventorylSStill100unitsshort,themanagerrealizesthatthetotalamountofin-

ventoryonhandandonorderisequaltothedesiredlevel,cutsordersbacktothe

replacementrate,andwaitspatientlyfortheextraunitsinthesupplylinetobede-

1ivered･Overthenext2weekstheextra100unitsmaketheirwaythroughthesup- plyline.Inweek5deliveriesare200units,inventorylSrestoredtothedesired

levelof400,andthesupplylinedropsfrom400backtoitsequilibriumlevelof

300.Theinventoryandsupplylineadjustmentsbothreturntozero.Equilibriumis

restoredafterjust4weeks,withnooscillation.

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Chapter17 SupplyChainsandtheOriginofOscillations 693

TounderstandtheroleofthesupplylineadjustmentintheorlglnOfoscilla-

tionsmoreformally,substitutethedefinitionsoftheadjustmentforthestockand

adjustmentforthesupplylineintotheequationfortheorderrate:

OR-MAX(0,IO)-MAXt0,EL+AS十ASL) -MAXt0,EL+(S真一S)/SAT+(SL不 -sL)/SLAT)

(17-13a)

NowdefinetheWeightontheSupplyLineastheratioofthetwoadjustmenttimes:

WSL-SAT/SLAr.SubstitutingWSLintoequation(17-13a)gives

OR-MAXIO,EL+(SF - S)/SAT+WSL*(SL*-SL)/SATI (17113b)

Combiningtens,

OR-MAXi0,EL+lS火+wsL*SL央 -(S十WSL*SL)]/SAT) (17-13C)

Nowdefinetheeffectivetotalstock,ETS,asthesumofcurrentinventoryandthe

fractionofthesupplylinethemanageraccountsfor,ETS-S+WSL*SL.The

desiredeffectivetotalstock,ETS'>-S*+WSL*SL*,representsthetotalstockon

handandonorderthemanagersbelievetheyneed･SubstitutingETSandETS*into

equation(17-13C)gives

OR-MAXi0,EL+(ETS*-ETS)/SAT) (17-lsd)

Theinterpretationisstraightforward.Equation(17-13d)definesafirst10rderneg-

ativefeedbacksysteminthestatevariableETS･IfWSL-1,managersgivethe supplylineasmuchweightasinventoryonhandandeffectivetotalstockequals

theactual,truetotalinventoryinthesystem.Fullyaccountingforthesupplyline

convertsthepotentiallyoscillatorynegativeloopwithadelayIntoaneffectively

first-ordernegativefeedbacksystem.Correctiveactions(orders)immediatelycor-

rectthediscrepancybetweenthedesiredandactualtotalstockonhandandon

order,andchangesinthetotalstockimmediatelyaffecttheorderdecision.Un-

anticipatedshocksinducenooscillationinthetotalstock,despltethedelaybe-

tweenplacingandreceivlngOrders･IfWSL-0,however,managerscompletely

Ignorethesupplyline･ThefailuretoconsiderthedelaylnreCelVlnggoodsthen

leadstooscillation.AsWSLapproches1,thegreaterthedamplngandthemore

stabletheresponseofthesystemtoshockswillbe.

TheanalystsaboveshowswhyitisimportanttorecognlZethetimedelaysin

negativeloopsandsupplylinesofcorrectiveactionsalreadytaken･Yetpeople oftenfailtodoso.InSterman(1989b)Iestimatedthedecisionruleshowninequa-

tion(17-13d)forasampleof44players.6overall,thedecisionruleworkedquite

well,explaining71%ofthevarianceintheorderdecisionsofthesubjects.Thees-

timatedI)arametersshowedthatmostwereusinggrosslysuboptjmalclleWeight_S;

TheaverageweightonthesupplylinewasonlyO134･Only25%ofthesubjects

consideredmorethanhalfthesupplylineandtheestimatedvalueofWSLwasnot

significantlydifferentfromzeroforfullyone-third.Figure17-13comparessimu-

latedandactualbehaviorforthefactorylnanactualgame.Theestimatedstock

6ToestimatethedecisionrulethetotaldesiredstockETS*wastreatedasaconstantandthe expectedlossrate(demandforecast)wasmodeledbyfirst10rderexponentialsmoothingof incomngorders.

694

FIGURE17-13 Estimatedvs, actualbehaviorin

thebeergame

Factoryordersfor anactua一p一ayer comparedto estimatedorders

fromequation (17-13C). Parameters:

Smoothingtime forforecastof

customerorders, 1.82weeks; desiredtotalstock onhandandon

order,9cases;

stockadjustment timeSAT,1.25

weeks;weight onsupplyllne WSL,0.

PartV InstabilityandOscillation

a a き

＼ S O S e 3

FactoryOrders Actual

'R2=0.87' 払ノSimuIated

/ 川も+++++.++ +++.++

0 5 10 15 20 25 30 35

Weeks

Source:Sterman(i989b).

adjustmenttimeSATisjust1.25weeks-theplayerreactedaggressivelytoinven-

toryshortfalls,orderingnearlytheentireinventoryshortfalleachweek.Atthe

sametime,theestimatedweightonthesupplylineWSLiszero.Asyouwould

expect,aggressivelyreactlngtOCurrentinventoryshortfallswhilecompletelyig-

noringthesupplylineleadstosevereinstabilityandhighcosts･Becauseittakes

3Weekstoreceiveproductionrequestedtoday,theplayereffectivelyorderedthree

timesmorethanneededtocorrectanyInventoryShortfall.

Otherexperiments(Sterman1989b;DiehlandStem an1995;Brehmer1992)

ShowthatthetendencytoIgnoretimedelaysandunderweightthesupplylineisro-

bust.Inseveraloftheseexperimentsthesupplylinewasprominentlydisplayedto

thesubjects,yettheyignoreditanyway.Asdiscussedinchapter1,theinformation

youuseindecisionmakingisconditionedbyyourmentalmodels.Ifyoudon'trec-

ognizethepresenceofatimedelayorunderestimateitslength,youareunlikelyto

accountforthesupplylineeveniftheinformationneededtodosoisavailable.

Manyplayersfindtheseresultsdisturbing.Theyarguethattheytookawide

rangeofinformationintoaccountwhenplacingordersandthattheirsubtleandso-

phisticatedreasonlngCannotbecapturedbyamodelassimpleasequation

(17113d).Afteral1,thedecisionruleforordersonlyconsidersthreecues(incom-

ingorders,inventory,andthesupplyline)-howcoulditpossiblycapturetheway

peopleplaceorders?Actually,players'behaviorishighlysystematicandisex-

plainedwellbythesimplestockmanagementhemi stic･Peopleareoftensurprised

howwellsimpledecisionrulescanmimictheirbehavior･

Infact,oneofthegamesshowninFigure17-10isasimulation,nottheactual

playofrealpeople.Isimulatedthebeergamewiththedecisionruleinequation

(171i3d).Theparametersoftherule,forailfourplayers,weresettotheaverage estimatedvalues.Asmallamountofrandomnoisewasaddedtotheorderrate.Can

youtellwhichisthesimulation?7

7simulatedordersweregeneratedbyORt-MAXt0,ELt+[ETSx -(St十WSL辛SLt)]/

SAT十 et)whereETS汝isthedesiredtotalstockandetisanormallydistributedrando聖variable withstandarddeviationequaltothemeanofthestandarderrorsoftheestimatedequatlOnOVerthe sample.TheforecastELtwasformedbyfirst-orderexponentialsmoothingoftheactualincomlng orderrate,ELt-(CORt_1- ELt-1)/TEO,whereTEO,thetimetoform expectedorders,isthe

smoothingtlmeconstant.ThemeanoftheestimatedparametersisTE0 -1.82weeks,ETS"- 17units,SAT-3.85weeks,andWSL-0.34.

Chapter17 SupplyChainsandtheOriginofOscillations 695

17.4.2 WhyDoWclgnoretheSupplyLine? ThebeergameclearlyshowsitisfollytoIgnorethetimedelaysincomplexsys- tems.ConsiderthefollowingSituation.Youareinvolvedinanautomobileacci-

dent.Thankfully,nooneishurt,butyourcarisatotalloss.Insurancesetdementin

hand,youvisitadealerandselectanewcar.YouagreeonaprlCe,butthemodel

youwantisnotinstock-deliverywilltake4weeks.Youpayyourdepositand

leave.Thenextmomlng,noticingthatyourdrivewaylSempty-Where'smy car!-yougodowntothedealerandbuyanotherone.Ridiculous,ofcourse.No

onewouldbesofoolishastoignorethesupplyline.Yetinmanyreallifesituations

peopledoexactlythat.Considerthefollowingexamples(Table1711Showshow

theymapintothestockmanagementstructure):

･Youcookonanelectricrange.TbgetdinnergolngaSSOOnaSpossible,you

settheburr)erunderyourpanto"high."Afterawhileyounoticethepanis

gettlngquitehot,soyouturntheheatdown･Butthesupplylineofheatin

theglowlngcoilcontinuestoheatthepanevenafterthecurrentiscut,and

yourdinnerisburnedanyway･

･Youaresurfingtheworldwideweb.Yourcomputerdidnotrespondtoyour

lastmouseclick.Youclickagain,thenagain.Growlngimpatient,youclick

onsomeotherbuttons-anybuttons-toseeifyoucangetaresponse.After

afewseconds,thesystemexecutesalltheclicksyoustackedupinthe

supplyline,andyouendupfarfromthepageyouwereseeking.

･Youarrivelateandtiredtoanunfamiliarhotel.Youtumontheshower,but

也ewateris丘eezlng.Youtumupthehotwater.Stillcold.Youtumthehot

upsomemore.Ahhh.Justright.Youstepin°AsecondlateryouJumpOut

screamlng,scaldedbythenowtoo-hotwater.Cursing,yourealizethatonce

agaln,yOu'velgnOredthetimedelayforthehotwatertoheatthecoldpipes

andgettoyourshower.

･Youaredrivingonabusyhighway.Thecarinfrontofyouslowsslightly.

Youtakeyourfootoffthegas,butthedistancetothecarinfrontkeeps

shrinking.Yourreactiontimeandthemomentumofyourcarcreateadelay

betweenachangein血espeedofthecaraheadandachangeinyourspeed.

Toavoidacollision,youhavetoslamonthebrakes.Thecarbehindyouis

forcedtobrakeevenharder.Youhearthescreechofrubberandprayyou woll'tberear-ended.

･Youareyoung,andexperimentlngWithalcoholforthefirsttime.Eagerto

showyourfriendsyoucanholdyourliquor,youquicklydrainyourglass.

Youfeelfine.Youdrinkanother.Stillfeelingfine.Youtakeanotherand

another.Asconsciousnessfadesandyoufalltothefloor,yourealize-too

late-thatyouignoredthesupplylineofalcoholinyourstomachanddrank fartoomuch.8

8TragiCally,youngpeopledieeveryyearfromalcoholpoISOnlnginducedbyaggressivedrinking (ashortstockadjustmenttime,SAT,andfailuretoaccountforthesupplylineofalcoholth ey've alreadyingested,WSL-0).

696 PartV InstabilityandOscillation

Howoftenhaveyoufallenvictimtooneofthesebehaviors?Wemaynotbuyanl

othercarwhenthefirstoneisn'tdeliveredimmediately,butfewofuscansay we'veneverburnedourdinnerorbeenscaldedintheshower,neverdrunktoo muchorbeenforcedtobrakehardtoavoidacollision.

RecognlZlngandaccountingfortimedelaysisnotinnate.Itisbehaviorwe mustlean.Whenweareborn,ourawarenessislimitedtoourimmediatesur-

roundings.Everythingweexperienceishe7:eandnow.Allourearlyexperiencesre-

inforcethebeliefthatcauseandeffectarecloselyrelatedintimeandspace:When

youcry,yougetfedorchanged.Youkeepcryinguntilmotherorfatherappears,

evenwhenyouhearyourparentssay,HWe'recomingH(i･e･,despiteknowledgethat

yourrequestforattentionisinthesupplyline).Asallparentsknow,ittakesyears

forchildrentolearntoaccountforsuchtimedelays.WhenInysonWastwohe

mightaskforacupofjuice:"Juiceplease,Daddy.''"Comingrightup,"I'dsay,

takingacupfromtheshelf.Thoughhecouldseemegettlngthecupandfillinglt

up,he'dcontinuetosay,HJuice,Daddy!門manytlmeS-evermoreinsistently-un-

tilthecupwasactuallyinhishand.

LearnlngtOreCOgnlZeandaccountfortimedelaysgoeshandinhandwith

learningtObepatient,todefergratification,andtotradeshort-runsacrificefor

long-term reward.Theseabilitiesdonotdevelopautomatically･Theyarepartofa

slowprocessofmaturation.Thelongerthetimedelaysandthegreatertheuncer-

taintyoverhowlongltWilltaketoseetheresultsofyourcorrectiveactions,the

harderitistoaccountforthesupplyline･9

Youmightarguethatbythetimewebecomeadultswehavedevelopedthe

requlSltepatienceandsensitivltytOtimedelays.Theremaybenocosttosaylng

"julCe"adozentimes,butsurelywhenthestakesarehighwewouldquicklylearn

toconsiderdelays.Youdon'tburnyourselfinyourownshowerathome-you've

learnedwheretosetthehotwaterfaucettogetthetemperatureyoulikeandtowait

longenoughfわrthewatertowarmup.Mostpeoplesoonleantopayattentionto

thesupplylineofalcoholintheirsystemandmoderatetheirdrinking.Thecondi-

tionsforlearninginthesesystemsareexcellent.Feedbackisswift,andtheconse-

quencesoferrorarehighlysalient(particularlythemorningafter).Thereisno

doubtineithercasethatitwasthewayyoumadedecisions-thewayyousetthe

faucetordranktoofast-thatcausedtheproblem.Theseconditionsare氏.equently

notmetinbusiness,economic,environmental,andotherrealworldsystems(see

chapter1fordiscussion).Causeandeffectareobscure,creatingambiguityandun-

certainty.Thedynamicsaremuchslower,andthetimerequiredforleamlngOften

exceedsthetenureofindividualdecisionmakers.Ignorlngtimedelaysisalso sometimesrationalfortheindividual.Inaworldofshorttimehorizons,ofannual,

quarterly,Orevenmonthlyperformancereviews,theincentivespeoplefaceoften

meanitisrationalforthemtobeaggressiveandignorethedelayedconsequences oftheiractions.

9Moresubtly,ourchildhoodexperiencesreinforcetheideathatthereisnocosttolgnOrlngthe supplyline.Thoughmysonmayhavesaid"Juice,Daddy"10timesbeforelcouldfillhis‖order,M Ibroughthimonly1cup.Hedidn'ttakethesupplylineintoaccotlnt,btltIdid.Inthatsituation, thereisnocosttooverordering,whilepatiencemightnotwork(dadmightgetdistractedandforget tobring血ejuice).Inmanyrealstockmanagementsituations,thereisnocentralauthoritytoac- countforthetimedelaysandpreventoverordering.

Chapter17 SupplyChainsandtheOriginofOscillations 697

TheFrencheconomistAlbertAftalionrecognizedintheearly1900showfail-

uretoaccountforthetimedelayscouldcausebusinesscycles.Usingthefamiliar

fireplaceasananalogy,hisdescrlPt10nexplicitlyfocusesonthefailureofdecision

makerstopayattentiontothesupplylineoffuel:

Ifonerekindlesthefireinthehearthinordertowarmuparoom,Onehastowaita whilebeforeonehasthedesiredtemperature.Asthecoldcontinues,andthether- mometercontinuestorecordit,onemightbeled,ifonehadnotthelessonsofex- perience,tothrowmorecoalonthefire.Onewouldcontinuetothrowcoal,even thoughthequantltyalreadyinthegrateissuchaswillglVeOfFanintolerableheat, whenonceitisallalight.Tballowoneselftobeguidedbythepresentsenseof coldandtheindicationsofthethermometertothateffectisfatallytooverheat theroom.10

WhileAftalionarguedthatHthelessonsofexperience"Wouldsoonteachpeople

nottoHcontinuetothrowcoal,Hhearguedthatbusinesscyclesintheeconomy

arosebecauseindividualentrepreneursfocusedonlyoncurrentprofitabilityand

failedtoaccountforthelagsbetweentheinitiationofnewinvestmentanditsreal-

ization,leadingtocollectiveoverproduction.

Yetevenifindividualscan'tleaneffectively,shouldn'tthedisciplineimposed

bythemarketquicklyweedoutpeoplewhousesuboptimaldecisionrules?Those

whoignorethesupplylineorusepoordecisionrulesshouldlosemoneyandgoout

ofbusinessorbefired,whilethosewhousesuperiordecisionrules,evenby

chance,shouldprosper.Theselectivepressuresofthemarketshouldquicklylead

totheevolutionofoptlmaldecisionrules･

Thepersistentcyclesinawiderangeofsupplychainspresentedatthestartof

thischaptersuggestAftalionwasright･Leamlngandevolutioninrealmarketsap-

peartobeslow,atbest,despitedecadesofexperienceandthehugesumsatstake.

Partoftheproblemislackofinformation.Individualfirmsusuallydonotignore

thesupplylinesofmaterialsonorderorcapitalunderconstmction.Theproblemis

oneofaggregation.Theindividualfirmtendstoviewitselfassmallrelativetothe

marketandtreatstheenvironmentasexogenous,therebyignorlngallfeedbacks

frompricestOSupplyanddemand.Theindividualfin maynotknoworglVeSuf-

ficientweighttothesupplylinesofallfirmsintheindustryorthetotalcapacityOf

allplantsunderconstruction.Firmstendtocontinuetoinvestandexpandaslong

asprofitsarehightoday,evenafterthesupplylineofnewcapacltyundercon-

structionismorethansufficienttocauseaglutanddestroyprofitability.Eachin-

vestortakesmarketconditionsasexogenous,1gnOrlngthereactionsofothers.

Whenallinvestorsreactsimilarlytocurrentprofitopportunitiestheresultisover- shootandinstability…

Thefinancialmarkets,seenbymanyasthemostefficientandfarsighted,

shouldrapidlyevolvetonear-optlmalityduetothehugestakesandenormous

talentbroughttobear.Yeteventhehighlysophisticatedhedgefundsbearthescars

ofself-inflictedwoundsfromopen-loopthinking.Thesefundsusecomplexmod-

elsdevelopedbyPhDsinfinance,mathematics,andphysicstoexploitsmall

10QuotedinHaberler,G.(1964)Py10SPerityandDepression.London:GeorgeAllenandUnwin, pp.135-136.

698 PartV instabilityandOscillation

departuresfromequilibriuminthemarkets.Inthefallof1998,Russiadefaultedon itsexternaldebt,throwlngStockandbondmarketsintoasharpcorrection.The

hugelysuccessfulhedgefundLongTermCapitalManagement(IJCM)collapsed asitshighlyleveragedbets,basedonmodelsassumlngCertainhistoricalregulari- tieswouldcontinue,failed.Forcedtosellmanyoftheirpositionsataloss,thecri-

sisrapidlycascadedbeyondIJCMtoshaketheentirefinancialworld,ultimately leadingtoamulti-billiondollarbailoutorchestratedbytheUSFederalReserve.

Kestenbaum(1999,p.1247)Commented:

SomecompetitorswatchedIJCM'sfiresalewithacertainglee."Itwashypnotic," Onerecalls,"thensickening."Sickeningbecauseitstartedtohappentoeveryone. HItwasn'tsupposedtobesohardtosell,Honetradersays.…Whatwemissedwas thatotherhedgefundsweredoingthesamething.Thatwasn'tanInputtOany- body'smodel.門

17.4.3 CaseStudy:BoomandBust jnRealEstateMarkets

Realestatemarketsareamongthemostunstableandcyclicassetmarkets,exhibiト

1nglargeamplitudecyclesof10-20years｡Realestateconstitutesalarge丘.action ofthetotalwealthinanyeconomy,generatesasignificantfractionofbanking activityanddebt,andstronglyaffectsthejobmarket.Consequently,realestate boomsareoftenaccompaniedbyperiodsofintensespeculationinvolvingexpan- sionofcreditandbankingactivlty,Stimulatingthelocalandevennationalecon- omy.Whenthebubblebursts,theresultingbadloans,defaults,andunemployment canthrowanentireregionintorecessionorevendepression･

Figure17-14showsaclassicexample,therealestatecycleinChicagofrom 1830to1932(Hoyt1933)AOverthisperiodChicagogrewfromasmalltownofa fewhundredpeoplewithpropertyvaluedatlessthan$100,000toaneconomic powerhousewithmorethan3millioninhabitantsandrealestatevaluedatmore than$3billion.Growth,however,wasanythingbutsmoothLandvaluesandde-

velopmentactlVltyWentthroughrepeatedcyclesofboomandbust･Landvalua- tionsfluctuateroughly±50%aroundthetrend,whileconstructionactivitySurges fromalowsome60%belowaverageduringdownturnstomorethandoublethe averageduringbooms.Theseamplitudesaremuchlargerandmuchlongerthan血e businesscycle-therealestatecyclecannotbeblamedonsomeextemalvaliation inthepaceofeconomicactivity.

RealestatecyclesarenotlimitedtoChicagonoraretheyanartifactofmerear-

chaeologlCalinterest.Thecyclecontinuestohavealargeamplitudeandlongpe- riod.Mostrecently,NorthAmericanandEuropeanpropertymarketsboomedin thelate1980S,onlytocrashresoundinglyintheearly1990S.Fromthe1980sbub-

bleeconomyofJapantothebuildingboomandbustinsoutheastAsiainthelate 1990S,instabilitylnpropertymarketsisaliveandwell･

Howdoesthecyclearise?Figure17-15shows仙ecausalstructureofthemar- ket.Thedemandforcommercialspacedependsoneconomicactivity･Thegreater theemploymentinthereg10n,themorespaceisneeded,andvacancyratesfalll Whenvacancyratesarelow,effectiverentsstarttorise(effectiverentsaregross rentsnetoftenantconcessionssuchasmovingandremodelingexpenses).Higher

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Chapter17 SupplyChainsandtheOriginofOscillations 701

rentsleadtosomereductionindemandasbusinessesmakedowithlessspaceper

worker,buttheelasticityofthenegativeDemandResponsefeedback(loopB1)is

lowandtheresponsetimeislong.Onthesupplyside,risingrentsboosttheprofit-

abilityandmarketvaluesofexistlngproperties.Whenpncesarehighandrising,

rentsandoperatlngProfitsarehighanddeveloperscanrealizesubstantialcapital

galnSaSWell｡Highprofitsattractnewdevelopers,whofindnoshortageoffinan-

cialbackerseagertocashinontheboom.ManynewprojectsareStarted,Swelling

thesupplylineofbuildingsunderdevelopment.Afteralongdelay(2-5years),the

stockofspacerises,vacancyratesrise,andrentsstarttofall,draggingdownmar-

ketvalues.Asprofitsfall,sodoesthedevelopmentrate.Themarketcreatesnega-

tiveloopsthatattempttobalancedemandandsupplythroughprice(thenegative

SupplyRespoIISeandSpeculationloopsB2andB3).

Inassesslngtheprofitabilityofapotentialnewdevelopment,developersand

theirinvestorsshouldforecastthefuturevacancyratebyprojectingthegrowthof

demandandsupply.Todosotheyshouldtakethefeedbackstructureofthemarket

intoaccount(theSupplyLineControlloopB4).Inparticular,developersshould

considerthesupplylineofbuildingsonorderandunderconstructionwhenesti-

matingfuturesupply.Iftheydid,therateatwhichnewprojectsareinitiatedwould

fallwellbeforepncespeak.Developerswouldrealizethattherewasenoughspace

inthepipelinetobalancedemandandsupplyeventhoughvacanciesremainlow

andprofitsarehightoday.Note,however,inFigure17-14thatconstruction

reachesitspeakatorafterthepeakinprices,thatis,afterthemarkethasalready

developedexcesssupply,vacancyratesarerislng,andrentsarefalling.Develop-

erscontinuetostartnewprojectsaSlongastheyperceiveprofitsarehighright

now,eventhoughittakes2-5yearstocompleteaproject.Failuretoaccountfor

thesupplylinecontributestooverbuildingduringbooms,andpreventsinvestment

fromrecoverlngearlyenoughtopreventatightmarketafterthebustends.Thesit-

uationhasnotimprovedoverthelasthundredyears.Reflectingontherealestate

bustofthelate1980S,Downs(1991,p.2)Commented:

Investorsarenotalwaysswayedbyobjectiveevidence-evenoverwhelming evidence-ifitleadstoconclusionsthatcontradicttheirimmediateinterestsas

perceivedbythe"herd."EvidenceofoverbuildinglnOfficeandothermarketswas overwhelmlngby1987,andprobablyevenearlier.By1987,thenationaloffice- spacevacancyrate-whichwasunder5%in1981-hadexceeded19%forthree yearsrunning.Yetbanksacceleratedtheirinvestmentsinnewconstructionloansin 1988and1989.Evenlong-terminvestorscontinuedtobuyrealestateatratherhigh prlCeS,althougheffectiverentswerefallingsharply.

HowcanitbethatrealestatedevelopersIgnorethesupplylineofbuildingsunder

development?Afterall,thefinancialstakesarehuge.Buildingsunderconstruction

arevisibletoall,andeventheprojectsOnthedrawingboardorawaitlngapproval

aregenerallyknowninthedevelopmentcommunity.

Inthelate'80sandearly'90sagroupofstudentsattheMITsystemdynamics

grouplnVeStlgatedthisquestionthroughaseriesoffieldstudiesandlaboratoryex-

periments.Hernandez(1990)andThornton(1992)interviewedarangeofdevel-

opers.TheintervieweeswereseniorexecutivesinleadingnationalorreglOnalreal

estatedevelopmentoradvisoryfirms,peoplewithbottomllineresponsibilityfor

702 PartV instabilityandOscillation

developmentandfinancingdecisions.Thegoalwastoidentifythementalmodels

theyusedtoguidedevelopmentdecisions.Inparticular,Wewereinterestedintheir

understandingofmarketdynamics.Didtheyaccountforthefeedbackstructureof

themarket?Didtheyviewthemarketascyclical,ordidtheyexpecttrendsinde-

mand,supply,andpricestocontinue?Mostimportant,didtheyaccountforthe

timedelaysandsupplylineofpendingprojects?

Elicitingthementalmodelsofdecisionmakersthroughinterviewsisdimcult.

Thereisadangerthattheinformantswilltellyouwhattheythinkyouwanttohear.

Thestudentsinitiallyaskedneutralquestionsencouraglngthedeveloperstotalk

abouthowtheymadedevelopmentdecisions,howtheyarrangedfinanclng,andso

on･If,withoutpromptlng,Peoplementionedcycles,thesupplyline,ordelaysit

wouldprovidestrongevidencethattheyunderstoodthefeedbackstructureinFig-

ure17-15andtookthetimedelaysintoaccount.Thedeveloperswereaskedex-

plicitlyaboutcyclesandthesupplyli王leOnlyiftheymadenomentionofthese

conceptsontheirown.

Amazlngly,almostnonespontaneouslymentionedcycles,timelags,thesup-

plyline,oranyrelateddynamicconcepts.Instead,theirdescnpt10nSfocusedheav-

ilyonthedetailcolnplexityofthedevelopmentsystem-howtoselectapromislng

site,howtosellaprojectandwinfinancialbacking,howtonavlgatethepermit-

tlngprocess,andsoon:

Locationisabiggerfactorthanthemacromarket.iknowit'sclichebutreally thekeytorealestateislocation,location,location‥.We‥.trytostaywithin SanFranciscobecauseweknowit.Weknowthepolitics.Weknowthearchitects, engineers,consultants,andsubcontractors.(DeveloperA)

Wedidourmarketanalysiskindofhaphazard[ly].[TheCEO]hadhisown feelingsaboutmarketsandsubmarkets.Hediditbygutfeel.Hisabilitywasamaz- ing･Hecouldwalkalongastreetandpointtoaretailcenter[inthecity].He'dsay, Hseethatcenter?It'sneverinthesun,nobodywillwalkonthatsideofthestreet,it willneverworkH-littlethingslikethat.‥mostofourmarketanalystsWasmicro, mainlylocational.(Developerち)

Ourbiggeststrengthisourknowledgeofthepoliticalapprovalprocess. (DeveloperD)

ThereisnodoubtthatsuccessfuldevelopersmustmasterthedetailcomplexltyOf

theprocess･Buttheinterviewsrevealedlittleappreciationforthedynamiccom-

plexltyOfthemarket.Whenaskedattheendoftheinterviewsaboutcycles,most

wereskeptlCal:

Wedon'tconsciouslypayattentiontocycles;moreintuitively｡Welookatthe moremicroaspectsofthemarket｡(DeveloperA)

Weneverlookedatcycles.Ouranalysisfiguredstable,positiveeconomic growth.(DeveloperB)

I'dsaywelookedatcyclesinaqualitative,subjectivekindofway.Wedidnot doanyemplricalanalysisofcyclesortrytomeasurethelengthoftherealestate cycles.(DeveloperC)

Wereallyhavenosenseforcycles.(DeveloperD) Quitefrankly,Iamlousywhenitcomestocycles.Ithinktheyexistbutdon't

payalotofattentiontothem.Therearetoomanyotherfactorsthataffectsupply

Chapter17 SupplyChaillSandtheOriginofOscillations 703

anddemand.Extemalfactorsmakeitdifficulttolookatcycles.Infact,Ithinkthey

probablynegatethem.(DeveloperE) Realestatecycles?C'mon.No,wedon'treallyanalyzethem;it'soutsideourarea

ofexpertise."I'llgototheseindustryforumswherepeoplewillpulloutnewspaper articlesthataretalkinggloomanddoom,andthenthey'lltellyouthesearticlesare

from1929,1974,and1981.Butevenwiththissupposedevidenceofrealestatecycles inhistory,lthey]won'tchangelpeople'S]minds!Thepressureofthesystemisvery strongandtheycan'tresistiteitherway.(AdvisorA)

LikeDeveloperB,manyexplicitlyacknowledgedthattheyfocusedoncurrent

marketconditions,extrapolatedrecenttrends,andmademinoradjustmentstotake otherfactorsintoaccount:

Inanalyzingmarketinformationwewouldmaketrendlineprq】ectionsto determineifgrowthwouldcontinueandthespace血atwewerecontemplatlng buildingwouldbeabsorbed.Thesameaslastyear'sbenchmark,greaterorless. Andthewayyouwoulddetemi nethat,istosaymostpeoplearebearish,rentsare comingdown,sowewon'tdoasmuch.Ortheconclusionwouldbethatmost

peoplearebullish,rentsarefirm,sowewilldoalittlemore･(DeveloperF) Wh atproblemsdowehaveintrackingthesupplysideeffects?Estimatinga

correlationbetweenvacancyratesandrentalratesistough･Youjustkindofwag yourfingerintheairtodeterminewhatitmightbe.(AdvisorA)

Weusedtouseaflat5%vacancyrateinourproformas.(DeveloperE)

Mostconfessedthattheydidn'tconsiderthesupplylineofprojectsunderdevell

opmentintheirinvestmentdecisions.Manyprojectedthatrentsandpriceswould

riseatconstantrates,independentofthevolumeofconstmctionactivity.Theydid

notrecognizethefeedbacksamongvacancies,rents,profits,construction,andthe

supplyofspace-anopenlloopmentalmodel:

It'sdifficulttoassessthesupplyside.Wedon'thaveaformalwayofdoinglt. Wordofmouthisusuallythebest.(DeveloperA)

Wedonothingformalaboutanalyzingprojectsthatareinthepipeline,nothing structured.Wejusttalktopeoplein血eindustry,leanourmarkets･(DeveloperB)

TrackingthesupplyinthepIPelineisarealdifficulttask.Nothingisdonefor一 mally.Willtheofficebuildingdownthestreetgo?Idon'tknow.Itisatotalguess and血ereisalotofbrokerlipservicethatyouhavetosiftthrough.(AdvisorA)

Therewasn'tanyrealsophisticatedanalysisofthesupplyside.(DeveloperC) Weneverdidaformalorthoroughanalysisofwhatsupplymaybeinlthe]works

incompetitionwithoneofourdevelopments.Inanalyzingfuturesupplyanddemand,

Ithinkit'StoounpredictabletoputalotofemphasisandtimeintrylngtOfigureitOUL PeveloperG)

Evenwhendevelopersclaimedtoaccountforthesupplyline,theyfailedtoclose thefeedbackstothemarket:

Wepaidstrongattentiontothesupplyside･Butwedidn'tconsiderthatadded supplywouldaffectrentalrates,Wefigureditwouldjustaffecttheamountoftime ittooktoleaseuptheproperty.(DeveloperC)

Butwhentheentiremarketisoverbuilt,eventhebestprojectsinthemostdesirable locationssuffer:

704 PartV InstabilityandOscillation

Problemwas,evenifyouwereasmartdeveloperyouhadotherguysadding

spaceandthereforeaffectingtherentsofyourproposedprojects.Itwouldeven

affectexistingProjectsfullyleasedup.Leaserenewalsbecamedifficultnegotia- tionsandmanytenantswouldwanttorenegotiatetheirleasesevenbeforethey

expired.(DeveloperD)

Wh enevidenceofoverbuildingeventuallybecameundeniabledevelopersoften

thoughtother,lessdesirableprojectsthantheirswouldbetheonestosuffer,slow-

1ngthereactiontoexcesscapaclty:

Developersarepromotersandmustmotivatepeople･It'sdifficulttoberealis-

tic.You'realwayssellingandafterawhileyoustartbelievlngyourOWndelusions

ofgrandeur.(DeveloperG)

Ofcoursedevelopers'egoshadsomethingtodowithit.Alldevelopersbelieve

thattheirbuildingisbetterthantheirneighbor'S.(DeveloperE)

Thesunkcostfallacy,lnWhichpeoplearereluctanttoabandonlosingStrategleS, furthersloweddevelopers'responsetoevidenceofoverbuilding:

Atthispolnt,Iamnotabouttowalkawayfromthisprq】ectglVenthetimeand

moneylhavealreadyinvestedinit…Iwillbeadevelopernomatterhowtoughit

mayget.It'sabigegothing.It'snotlikeyou'reproducingahomogeneous,mass-

merchandisedproduct.Developmentisamorepersonalthing,likecreatlnga

workofallBeingadeveloperlidentifywithdevelopergroupsandit'slike

beinglnafraternlty.It'SthemaJOrltyOfmyidentitythatIjustcan'twalkaway

from.(DeveloperG)

Nearlyallbuiltspreadsheetmodelstodocostn)enefitordiscountedcashflow

(DCF)analysis,However,financialanalysiswasusedprimarilytohelpsellproI

JeCtS,notaSatoolofinquirytOaidthedevelopers'understanding.Manydevelop-

ersbelievedmakinggooddecisionswaspnmarilyamatterofintuition:

Youcantailorthenumberstosayanythingyouwantthemtosay,butI'm

goingtotrustmygut.Myguthasbeenrarelywrong.(DeveloperA)

Allprofom afinancialmodelsrequireaSSumPtlOnSaboutfuturerents,expenses,

marketvalues,andinterestrates.TheseInputsaregenerallybasedonextrapolation

ofrecenttrends.Nofeedbacksareconsidered.TheinputsarethenmanlPulatedto

makeaprojectappeartObemoreprofitable:

In-depthmarketanalysiswasnotdonefordecisionmaking,1tWasdoneto

obtainfinancing...Frankly,duringthatperiodoftimeltheboomofthelate

1980S]youwereconcernedaboutgettingthedealdoneanddidn'treallycareabout

cycles-itwasallegoandpressuretodothedeal.(DeveloperB)

Insteadofcappingtoday'sincometheyldevelopers]trendrentsupwardperiod

byperiod.Forexample,theproformawouldshow4%annualrevenueincrease

anda3%annualexpenseincrease.Thinkaboutit-thoselinesneverintersect!

ThatproformaandacoupleofglossyplCmresandthebankgivesthemtheloan!

(DeveloperA)

Wewouldusefifteenpagespreadsheetsllargesheetswithsmallprint-which

wouldcomputenetpresentvaluesandinternalratesofretumofprojectsbyusing

costsoftheprojectingreatdetail...Rentswereassumedtoincreaseyearlybyfive

percentortheinflationrate.AtthetimeIthoughtthatwasaconservativeestimateand

Chapter17 SupplyChainsandtheOriginofOscillations 705

itwasn'treallyquestionedbylenders… Ispentmuchtimeandhumanresourcesin tweakingthenumbersonthesespreadsheetstogettheinternalrateofreturnwhichthe bankwantedtobewillingtofinancetheproject.(DeveloperG)

DevelopersassumedmarketvalueswouldkeeponrlSlng,leadingtocapitalgalnS

(theSpeculationloopB3inFigure17115).Projectsthatcouldn'tmakemoney

fromrentaloperationscanstillbemadetoseemprofitableduetothereversion

(capitalgain)anticipatedwhenthedevelopercashedoutafewyearslater:

InDCFanalysュs,Oneruleofthumbwasthatweneverwantedtogetina

positionwheretheresidualcomponentwas50%ofthevaluation･Unfortunately, webrokethisruleafewtimes.Youknowhowitis-themarketwasthemarketat

thattime-yougottahavethebuilding.(AdvisorA)

[Duringtheboominthe80S】therewassomuchcompetitiontododealsyoure- allybeganrelyingontheDCFmodel,andespeciallyrelyingtoomuchontherever-

sioncomponent.ThenweallstartedrunnlngIntoProblemswithcashflowbecauseof rentconcessions…Itgottobesocompetitive…thatyouwouldbe[showing日eveling

operatingexpenses,usea[low]lo啄IRR[internalrateofretum],andpushtheincome growthandreversioncomponentsoftheDCF…Wejustreliedonthemarketplace･ Mostlywebelievedthatthreeyearsdownthelinewewouldbenefitfromappreciation. (DeveloperB)

Asaboomgathersmomentum,thecapitalgalnSdominate,leadingtohugeprofits･

Formanydevelopers,greedoverwhelmsreasonandexperience:

Theguysmakingthedecisionsshouldhavebeensmartenoughtoknowbetter.

Theyshouldhaveseenit.Itwasn'tjusttheyoungerguyseither,whohadn'tbeen throughacycle.EveryonesittlngOnthecommitteehadgrayhairandwasintheir fortiesorfifties.Butweallgotgreedy.Whenweshouldhavesoldwewouldhold outforJustalittlebitmore.Theyweren'tgoodsellers.Theybelievedalltheirown

llies],allthel1ies]theytoldthepeoplefinancingtheprojects.(DeveloperB)

Thoughdeveloperscookthenumberstomaketheirprojectslookmoreattractive, theymuststillobtainfinanclng.Mostcommercialdevelopmentsrelyheavilyon

OPM (otherpeople'smoney)AThefinancialmarketsaresupposedtodampenthe

dreamsandschemesofdevelopers,Weedingouttheunprofitableprojects.But

whenrentsandmarketvaluesarehighandrising,developerscaneasilygetfi-

nanclngOnfavorabletermsasinvestorsscrambletogetinontheboom.Down

paymentanddebt/equltyStandardsfall,andnonrecoursefinanclngrisesasbanks

competeforthefeesgeneratedbythefranticrateofdevelopment･ll

lDuringtheboom]itwastooeasytogetmoney.Lookatitthisway.Youowna

pleCeOfproperty-youarethemanaglngpartner.AllyourequltylSinthatproperty･ Whoknowswhatyoupaidforit?Youprepareaprofomawhichincludesyour estimatedlandvalue,whichisundoubtedlygreaterthanwhatyoupaidforit.You can thenslgnaninterimnotebasedonthatestimatedlandvalue.Allofasudden you haveacheckinyourhandfわrthelandvalueoftheproforma.Ⅰ'mnotkidding!

(D eveloperD) Intheglorydayspercentagesarethrownawayalltogether,andryedoneprq】ects

in whichIcontributedpracticallynomoney.(DeveloperG)

llInnonrecoursefinanclngtheprojectitselfistheonlycollateral･Ifthedeveloperdefaultson theloan,thebankcannotrecoveritslossfromthedeveloper'sotherassets.

706 PartV InstabilityandOscillation

Easymoneyandtheerosionofcreditstandardsduringboomsincreasethedevel-

opmentrateandcontributetooverbuilding,butdevelopers'relianceonOPM only

begsthequestion,Whydon'ttheinvestorstakeaccountofthesupplylinewhen

evaluatlngWhethertoputtheirmoneyatrisk?Oneproblemisthecompetitionfor

up-frontfeesbylenders･Anotheristhelackofexperienceamongbanks,especially

duringaboomwhentheirrealestateoperationsgrowrapidly.Manyoftheloanof-

ficershiredduringboomsareyoungandhaveneverexperiencedamarketdown-

tum.Finally,withoutanappreciationforthestructureanddynamicsofthemarket,

thefinancialcommunltySuffersfromgroupthinkandtheherdmentality:

Thebanksaresupposedtobethelastlineofchecksandbalances,butthey wereJuSttheopposite･Theyweretooeasy-.Thebankshadnoconceptofthe market･Butnotonlywerethebankstooeasy,theyactuallyhelpedtodrivealotof deals.IrememberbecauseIworkedatabankforsomeofthattime.Loanofficers

wereglVengoalsthattheywerepressuredtomeet:Tbtalamountofloans,total amountoffees,totalamountofrenewalfees.Ifyouputabankeroutinthemiddle of[nowhere]‥.andyoutellhimheisgoingtobecompensated‥.bytheamount

ofloanshemakes,guesswhat?Hewillfindawaytomakeloans!Itgotsocom- petitive･Bankswerenotonlymakingill-advisedloans,theywereundercuttlng eachother'sfeestogetthedeal.(DeveloperA)

Theappraisers,whoweresupposedlyindependent,alsogotinvolved‥.and effectivelyrubber-Stampedanythingthatthelenderanddeveloperagreedwere reasonable‥.Itwasonebigcomplicitouscircle.Noonewantedtosaynoor theywouldlosebusiness.(DeveloperG)

Thereisatremendouspressuretofollowthecrowd.Ifyouarestandingonthe sidelinesandnotmakingInvestmentsandyourcompetitorsarecollectlngfeesfor placingfunds,whatareyougolngtOdo?Ifthepressureistheretoplacethemoney, youwillfindawaytobuy.(AdvisorA)

Willthebanksorthedeveloperslearn?Well,anumberoflendersarenowsaylng thattheywillneveragalnlendonrealestate.Ihaveananswerfわrthat.Allittakesis

JustOnegeneration･Agenerationofbankersanddeveloperstochurnthrough,Agener- ationthathasn'tbeenthroughthecycles.(DeveloperA)

Theinterviewsstronglysuggestdevelopersandinvestorsdonotunderstandthe

feedbackstructureofrealestatemarketsanddonotadequatelyaccountforthe

timedelaysorsupplylineofpendingspace.Theyareoverwhelminglyinfluenced

bycurrentconditionsandtendtoextrapolaterecenttrends.Butinterviewscanbe

misleading.Totesttheconclusionsfromtheinterviews,Bakken(1993)conducted

anexperimentwithamanagementflightsimulatorrepresentlngtherealestate

market･BasedonthestmctureshowninFigure17-15,playershadtomanagea

portfolioofpropertiesandcoulddevelopnewprojectsandbuyorsellexisting

properties･Professionaldevelopersworkingforwhatwasthenoneofthelargest

realestatedevelopmentfirmsintheUSdidnobetterthanMBAstudentsatMIT.

Averageperformancewasasmallfractionofthatachievedbyasimpleinvestment

rulethataccountedforthesupplyline.LearnlngWasSlowandtransferoflearnlng

todi飴rentmarketconditionswasweak･Whentheprofessionalswentbankruptln

thesimulationtheyoftencriticizedthemodel,ClaimingthatintherealworldprlCeS

couldneverdropsofarorsofast.Afewyearslater,mosthadlosteverything.

Chapterl7 SupplyChainsandtheOriginofOscillations 707

Expand妻ngtheRea!EstateModel ThecausaldiagraminFigure17115includesonlyafewofthefeedbacksdiscussed

insection17.4.3andsuggestedbytheinterviewswithrealestatedevelopers.Ex- pandthecausaldiagramtoincludetheseotherfeedbacks.Inparticular,consider

l･Theimpactofmarketconditionsoncreditstandards,lendingpractices,and theavailabilityoffinancingfornewprojects.

2･TheimpactofrealestatemarketandconstrtlCtionactivityOnthepaceof economicgrowthinthereglOn.

3.TheeffectofdevelopmentactivltyOntheavailabilityandcostof

architecturalandconstructionfirmsandhowtheavailabilityofthese resourcesaffectsplannlngandconstructiontimesandcosts.

41Theeffectofdevelopmentboomsandbustsontaxrates,zoningand permittlngregulations,andotherfactorsthatmayaffecttheattractiveness ofthereglOntOdevelopersandtobusinessingeneral,

5･Otherfeedbacksandeffectsyouthinkmightbeimportantinunderstanding thefullimpactofrealestatecyclesonacom unlty.

Foreachnewfeedbackprocess,assessitslikelylmPaCtOntheperiod,stability,and othercharacteristicsofthemarket.

17.5 SuMMARY

Supplychainsarefundamentaltoawiderangeofsystemsandmanyexhibitper-

sistentinstabilityandoscillatlon｡Everysupplychainconsistsofstocksandthe managementpoliciesusedtomanagethem.Thesemanagementpoliciesarede- Slgnedtokeepthestocksattheirtargetlevels,compensatingforusageorlossand

forunantlCIPateddisturbancesintheenvironment.Oftenthereareimportantdelays betweentheinitiationofacontrolactionandtheresult,CreatlngaSupplylineof unfilledorders.

Thischapterdevelopedagenericmodelofthestockmanagementstructureand showedhowitcanbecustomizedtovarioussituations.Themodelwasusedtoex-

plainthesourcesofoscillation,amplification,andphaselagobservedinsupply

chains･Thesepattemsofbehaviorarefundamentaltothebasicphysicalstructure ofstockmanagementsystemsandsupplychains.Oscillationarisesfromthecom- binationoftimedelaysinnegativefeedbacksandfailureofthedecisionmakerto

takethetimedelaysintoaccount･Fieldandexperimentalstudiesshowthatpeople oftenIgnorethetimedelaysinawiderangeofsystems.

Thebeergameandrealestateindustryarebuttwoexamplesofsituations wherecyclicalinstabilityarisesfromthefailureofdecisionmakerstoaccountfor timedelays.Thereisnoonesinglecauseforthefailuretoaccountfortimedelays

andthesupplyline.Arangeoffactors,frominformationavailabilitytoindividual

708 PartV InstabilityandOscillation

incentives,allcontribute.Butbehindtheseapparentcausesliesadeeperproblem. True,thesupplylineisofteninadequatelymeasured,butifpeopleunderstoodthe importanceofthesupplylinetheywouldinvestindatacollectionandmeasure一 mentsystemstoprovidetheneededinformation.True,Compensationincentives oftenencouragepeopletoignorethedelayedconsequencesoftoday'sactions,but ifinvestorsunderstoodthestructureanddynamicsofthemarkettheycouldre- designcompensationincentivesfortheiragentstofocusonlong-termperfor-

mance.Ourmentalmodelsaffectthedesignofourinstitutions,information systems,andincentiveschemes.These,inturn,feedbacktoourmentalmodels. Thefailuretoaccountforthesupplylinereflectsdeeperdefectsinourunder- standingofcomplexsystemsJgnorlngtlmedelaysisoneofthefundamentalmis- percept10nSOffeedbackthatleadstopoorperformanceinsystemswithhigh dynamiccomplexity(chapter1)･Failuretounderstandtheroleoftimedelays worsenstheinstabilitywefaceandleadstomoresurprises-usuallyunpleasant- reinforcingthebeliefthattheworldisinherentlycaprlCIOuSandunpredictableand strengtheningtheshorHerm focusstillmore.

Whatcanbedone?Thenextchapterstakeupthechallengeofmodelingsup- plychainsandoscillations,withspecialconsiderationtopoliciesfirmscanunder- taketoimproveperformance.

● The-_Pi呈aIi31iiiFae号'dr主張gSも旦Ppjiき1-∈虫EBi_!3_

ThecentralcoyleOfmanyindustrialcompaniesisthep710CeSSOfproductionand distribution.Arecurringproblemistomatchtheproductionratetotherateof finalconsumersales.Itiswellknownthatfactoryproductionrateoften jluctuatesmorewidelythandoestheactualconsumerpurchaserate.Ithas

oftenbeenobservedthatadistributionsystemofcascadedinventoriesand ofderingprocedwesseemstoamplljysmalldisturbancesthatoccuratthe

71etaillevel...Howdoesthesystemcreateampllficationofsmallretailsales changes?...lW]eshallseethattyPicalmanufacturinganddistribution practicescangeneratethetypesofbusinessdisturbanceswhichareoften blamedonconditionsoutsidethecompany.

lJayW.Forrester(IndustrialDynamics,p.22)

Thestockmanagementstructuredescribedinchapter17isqultegeneralandcan beusedtomodelsupplychainsforavarietyofresources･Thischaptershowshow thestockmanagementstructurecanbeadaptedtorepresentthesupplychainin manufacturingfirms.Locallyrationalpoliciesthatcreatesmoothandstablead- justmentOfindividualorganizationaltlnitsmay,throughinteractionswithother functionsandorganizations,causeoscillationandinstability.Instabilitycanfeed backtounderminetrustamongpartnersinasupplychain,leadingtobehaviorthat worsenstheinstability.

Themodelisdevelopedinstages.Simplifyingassumptionsarerelaxedoneat atimeandonlya洗erthebehaviorofeachversionisfullyanalyzed.Thisiterative processdeepensyourunderstandingoftheunderlyingrelationshipsbetweenthe structureandbehaviorofdynamicsystemsandinthelongrunspeedsthedevel- opmentofuseful,effectivemodels.

709

710 PartV InstabilityandOscillation

18.1 THEPoucySTRUCTUREOFiNVENTORYANDPRODUCTSON

Figure18-1showsthepolicystructwediagramforasimplemodelofamanufa(ン

turlngfirm･1Thefirmmaintainsastockoffinishedinventoryandfillsordersas

theyarrive.Ⅰnthisinitialmodel,assumethatcustomersaredeliverysensitive-

ordersthecompanycannotfillimmediatelyarelostascustomersseekother

sourcesofsupply(section18.1.7addsanexplicitbacklogofunfilledorders).In

仙isinitialmodel,customerordersareexogenous.Productiontakestime.Thestock

ofWIP(workinprocess)isincreasedbyproductionstartsanddecreasedbypro-

duction･Thekeyproductioncontrolandinventorymanagementdecisionsmadeby

thefin includeorderfulfillment(determiningtheabilitytofillcustomerorders

basedontheadequacyofinventory)andproductionscheduling(dete-iningthe

rateofproductionstartsbasedonthedemandforecastandinventorypositionof

thefirm,includingtheWIPinventory).Themodelincludesthreeimportantnega-

tivefeedbacks.TheStockoutloopregulatesshipmentsasinventoryvaries:Ifin-

ventorylSinadequate,someitemswillbeoutofstockandshipmentsfallbelow

ordersIIntheextreme,Shipmentsmustfalltozerowhenthereisnoinventory.The

lnventoryControlandWIPControlloopsadjustproductionstartstomovethelev-

elsofinventoryandWIPtowardtheirdesiredlevels.Inthisinitialmodelthereare

nostocksofmaterialsandnocapacityconstraints(either血.omlabororcapital). Theseextensionsaretreatedbelow.

FJGURE18-1 Thepolicystructureofinventorymanagement

lApolicystructurediagramshowsthestockandflowanddecisionstructureofamodelata highlevel(notattheleveloftheindividualequations)･Theroundedrectanglesdenoteorganiza- tionalsubunits,policies,ordecisionrulesandshowtheboundaryoforganizationalunits.Policy structurediagramsprovideanoveⅣiewofamodelhighlightingthefeedbackstructurewithout showingallthedetailsfoundinthemodeldiagram(Morecroft1982).

Chapter18TheManufacturingSupplyChain 711

18.1.1 0rderFult‖ment

Figure1812Showsthestructureoftheorderfulfillmentprocessandshipmentrate. Inventorycoverageisthenumberofweeksthe丘rmcouldshipatthecurrent

rateglVenitsinventory:

ⅠnventoryCoverage-Inventory/ShipmentRate (18-1)

Inventory=INTEGRAL(ProductionRate-ShipmentRate,Inventoryb) (18-2)

Theshipmentratenormallyequalsthedesiredshipmentrate,butifinventorylSin-

adequate,someoftheitemscustomersrequestwillbeoutofstock,reducingthe orderfu1fillmentratio(theratioofordersfilledtothedesiredfulfillmentrate):

ShipmentRate-DesiredShipmentRate*OrderFulfillmentRatio (18-3)

Theorderfulfillmentratioisafunctionoftheratioofthemaximumshipment

ratetothedesiredshipmentrate;thevaluesarespecifiedbytheTableforOrder Fulfillment:

Order Tablefor /MaximumShipment

FulfillmentRatio OrderFulfillment＼DesiredShipmentRate (18-4)

Themaximumshipmentratedependsonthefirm'scurrentinventorylevelandthe minimumorderfulfillmenttime:

MaximumShipmentRate-Inventory/MinimumOrderFulfillmentTime (1815)

Theminimumorderfulfillmenttimeisdeterminedbythefirm 'sorderfulfillment

process,thecomplexityOftheproduct,andtheproximltyOfcustomerstothe

FIGURE18-2 Structureoforderfulfi"ment

て■■■7 + Inventory -/ coverage ーー Inventory

∠_ゝ prOrFuI ∠_ゝ CuStoOrder

ProductionRate Shipment +gut Rafe. 7; psXeedn. .

+MaximShipmRaterl'IIment

Order Rate

Fu日fiHment頑針 -/琶 = .rdRea:io＼~鞄bleforprocesslng Order

712

FIGURE18-3 Orderfulf川ment asafunctionof

inventory

PartV instabilityandOscillation

firm'sdistributioncenters.Itrepresentstheminimumtimerequiredtoprocessand

shipanorder.

Inthissimplemodel,thereisnobacklogofunfilledorders,andallordersnot

immediatelyfilledarelostascustomersseekalternatesuppliers.Hence

DesiredShipmentRate-CustomerOrderRate (18-6)

wherethecustomerorderrateisexogenousfromthepolntOfviewoftheinventory

andorderfulfillmentsubsystem.

Amuchsimplerformulationforshipmentsis

ShipmentRate-MIN(DesiredShipmentRate,MaximumShipmentRate)(18-3a)

Whyusethefuzzyminimumfunctioninequations(1813)through(18-6)?Equa-

tion(1813a)saysthefirmshipswhatitwantstoshiporwhatitcanship,whichever

isless.ThissimpleloglCiscompellingforthecaseofaslngleproductorstock-

keepingunit(SKU).However,modelsoftenrepresentfirmsthatcarrymanydif- ferentSKUs,sometimestensofthousands.Usuallyltisnotnecessaryforthe

model'spurposetorepresenteachSKUseparately.Theinventorylevelinsuch

modelsrepresentstheaggregateofallSKUs･ThemixofSKUsrequestedbythe

customersvariesunpredictably,asdotheinventorylevelsofindividualitems･

Whenmanyitemsareaggregated,someindividualitemsarelikelytobeoutof

stockevenwhentheaggregatedesiredshipmentrateequalsthemaximumship- mentrate.Theorderfulfillmentratiowillthenbelessthan1.Figure1813showsa

typicalshapefortheorderfulfillmentratio･

Tointerpretthefigure,notethetworeferencelines･Combiningequations (18-3)and(18-4),

SR-DSR*OFR-DSR*f(MSR/DSR)

(ssal u O! Su a ∈ !P )

0 !tetJ lua Lu ≡ -一 n j Jla P JIO

(18-3b)

MaximumShipmentRate

DesiredShipmentRate (dimensionless)

SR-shipmentrate;DSR-desiredshipmentrate;MSR-maximumshlPment rate.

Chapter18 TheManufactunngSupplyChain 713

whereSR,DSR,andMSRaretheshipment,desiredshipment,andmaximumship一

mentrates,respectively,andOFRistheorderfulfillmentratio.Thehorizontalline OrderFulfillmentRatio-1representsthecasewhereshipmentsalwaysequalde- siredshipments.IftheshipmentrateSRfellalongthe450linepasslngthroughthe

orlgln,thenSR-MSR:Shipmentsalwaysequalthemaximumlevelinventory supports.TheactualrelationshipmustthereforeberestrictedtothereglOntOthe

rightandbelowbothreferencelines･Whenthefirmhasampleinventories,Sothat themaximumaggregateshipmentrateismuchgreaterthanthedesiredshipment rate,thenthechancethatanyindividualitemwillbeoutofstockisnegligibleand

theorderfulfillmentratioisl-Shipmentsequaldesiredshipments･Astheaggre- gatemaximumshipmentratefalls,thechancesthatsomeitemswillbeoutofstock increase,reducingtheorderfulfillmentratio.Theorderfulfillmentratiowillthere-

forebelessthanlatthepolntWheretheaggregatemaximumshipmentrateequals thedesiredshipmentrate.Furtherreductionsinavailabilityforcetheorderfu1-

fillmentratiodownuntilgoodsarebeingshippedatthemaximumrateinventory permits.Thegreaterthenumberofindividualitemsaggregatedtogether,Orthe greatertheunpredictabilityofdemandforindividualitems,thesmallertheorder

fulfillmentratiowillbeforanyratioofthemaximumtodesiredshipmentrate･The casewheretheorderfulflllmentratioequalsthe450linewhenMSR<DSRand lwhenMSR≧DSRcorrespondstothefomulationSR-MIN(DSR,MSR)and wouldrepresentasituationwhereeitherthereisonlyoneSKUorwherethede一

mandforeachtypeofinventorylSPerfectlycorrelatedandpredictable. Thediscussionsofarassumesthefirmwillshipanitemifitcan.Inpractice

firmswithinadequateinventoriesmaychoosenottofilltheordersofsomesmaller customerssoastomaintainareserveagalnStthechancethatafavoredcustomer

willplaceanorder.SuchstrateglCproductwithholdingreducestheorderful- fi11mentratiofurtherbelowthereferencelines,particularlyintheregionWhere MSRくDSR.

18.1.2 Production

Figure18-4Showsthepolicystructureoftheproductionrate･Typicallyproduction involvesmultiplestepsthatcreatesignificantinventoriesofworkinprocess

FJGURE18-4 ProductionandWIPinventory

714 PartV InstabilityandOscillation

(WIP).Chapter6providesexamplesofthestockandflownetworksformanufac-

tunngprocesses,Showinghowthevariousstagesofproductioncanberepresented.

Forthepurposeofthismodel,allstagesoftheprocessareaggregatedtogetherinto

theWIPinventory.

Athird-OrderdelaylSusedtomodeltheproductionprocess:

WorkinProcessInventory

-INTEGRAL(ProductionStartRate-ProductionRate,WIPt.)

ProductionRate

-DELAY3(ProductionStartRate,ManufacturingCycleTime)

ThemanufacturlngCycletimerepresentstheaveragetransittimeforallitemsag-

gregatedtogetherinthemodel.Thefeweritemsaggregatedtogether,thesmaller

thevarianceinindividualcycletimesandthehighertheorderofthedelaythatbest

characterizesproduction.

18.1.3 ProductionStarts

Figure18-5showsthestructureoftheproductionstartdecision.Fornow,noca-

pacltyCOnStraintsareconsidered:Productionstartsdonotdependonmaterials

availability,labor,orcapitalplantandequipment.

Theproductionstartsdecisionruleisformulatedusingthegenericstockman-

agementstructure.TheProductionStartRateisconstrainedtobenonnegativebut

otherwiseequalstheDesiredProductionStartRate(sincenoresourceconstraints

areyetconsidered).DesiredProductionStartsaredeteminedbytheDesiredPro-

ductionrateandtheAdjustmentforWIP(thesupplylineofpendingproduction):

ProductionStartRate-MAX(0,DesiredProductionStartRate) (18-9)

DesiredProductionStartRate-DesiredProduction+AdjustmentforWIP(18-10)

TheAdjustmentforWIPmodifiesproductionstartstokeeptheWIPinventoryln

linewiththedesiredlevel.DesiredWIPissettoprovidealevelofworkinprocess

sufficienttoyieldthedesiredrateofproductionglVenthecurrentmanufacturing

cycletime:

AdjustmentforWIP -(DesiredWIp-WorkinProcessInventory)/WIPAdjustmentTime

(1 8-ll)

DesiredWIp-ManufacturlngCycleTime*DesiredProduction (18-12)

DesiredproductionisdeterminedbytheExpectedOrderRate,modifiedbytheAd-

justmentforInventory.DesiredProductionisconstrainedtobenonnegative:

DesiredProduction

-MAX(0,ExpectedOrderRate+AdjustmentforInventory)

AdjustmentforInventory -(DesiredInventory-Inventory)仙lVentOryAdjustmentTime

DesiredInventoryCoverage -MinimumOrderProcessingTime+SafetyStockCoverage

ToprovideadequateinventoryasabufferagalnStunexpectedvariationsindemand

orproduction,the丘rmseekstomaintainacertaincoverageofexpecteddemand.

S 亡 t2tS u O l

.)Dn P O L

o a JnIU n JtS

S ･

eL u t Jn

715

716

FIGURE18-6 Demand

forecasting

PartV InstabilityandOscillation

Desiredinventorycoverageincludestwocomponents･First,thefirmmustmain-

tainenoughcoveragetoshipattheexpectedrate,requlrlngabasecoveragelevel equaltotheminimumorderprocesslngtlme.Second,toensureanadequatelevel

ofservice,thefirmmaintainsadditionalsafetystocks･Thehigherthecoverage providedbythesafetystock,thegreatertheservicelevel(fractionofordersfilled onaverage)willbe.

18.1.4 DemandForecasting

Thefirm isassumedtoforecastdemandusingfirst-orderexponentialsmoothingof theactualorderrate(Figure18-6).

ExpectedOrderRate -INTEGRAL(ChangeinExpOrders,ExpectedOrderRateb)

ChangeinExpOrders (CustomerOrderRate - ExpectedOrderRate)

TimetoAverageOrderRate

(18-16)

(18-17)

Asshowninchapterslland16,smoothingprovidesarealisticmodelofthe forecastlngProcessusedinmanyfirms.TheforecastingProcesscouldeasilybe augmentedtoincludeseasonaladjustmentsoranextrapolativecomponentto

antlClpatedemandgrowth･

18.1.5 ProcessPoint:

Pnitia!弓Zing昂Mode=11Equ=br∈um

ModeltestlngShouldbeaprocessofcontrolledexperimentation.Forthisreason, youshouldstrivetoinitializeyourmodelsinabalancedequilibrium.Equilibrium

meansthatallstocksinthesystemareunchanglng,requlrlngtheirinflowsand

outflowstobeequal.Abalancedequilibriumfurtherimpliesthatallstocksare equaltotheirdesiredvalues.Inthepresentmodel,equilibriumrequlreSproduction starts-production-shipments(theconditionsforWIPandinventorytobecon- stant);thechangeinexpectedordersmustalsobezero.haddition,abalanced

equilibriumrequiresthatInventory-DesiredInventory,WIP-DesiredWIP,and thatallflowsequaltheirtargetratesaswell:Shipments,desiredshipments,ex-

pectedorders,desiredproduction,desiredproductionstarts,productionstarts,and productionshouldallequalcustomerorders.(Notethatthemodeldoesnotinclude

Customer OrderRate

Chapter18TheManufacturingSupplyChain 717

scraprates;ifitdid,productionwouldhavetoexceedshipmentsbythescraprate toachieveabalancedequilibrium.)

Initializingyourmodelsinabalancedequilibriumfacilitatestheprocessof

modeltestingbecausethesystemremainsinequilibriumuntildisturbedbytestin- putsyouchoosetoimpose.Ifyourmodelbeginsoutofequilibriumitsbehavior

willconfoundtheresponsetoanytestInputWiththetransientbehaviorinducedby theinitialdisequilibrium.

Inthepresentmodel,abalancedequilibriumiseasilyachievedwiththefol-

lowingInitialconditions:

Inventoryb=DesiredInventory

WIPb-DesiredWIP

ExpectedOrderRateto= CustomerOrderRate

､了 .㌔㌔

/ _㌧

Undertheseconditions,theadjustmentsforinventoryandforWIPwillbezero,

sodesiredproductionstarts-desiredproduction-expectedorders-customer orders;further,wheninventory-desiredinventory,shipments-desiredship- ments-customerordersIPrOVideddesiredinventorycoverageissufficiently largethattheorderfulfillmentratiois1.

Notethattheinitialconditionsarespeci丘edintermsofothervariablesandpa- rameters,notasnumericalvalues.Byspecifyingtheinitialconditionsasexpres- sionsdependingonotherparametersinthemodel,thestockswillbeinitializedat theirequilibriumvaluesforanysetofparametersandinputs･Specifyinganumer- icalvaluewillthrowthemodeloutofequilibriumifyouchangetheparameters. Youshouldstriveto丘ndanalgebraicexpressionfわreachinitialconditionsothat yourmodelsalwaysbegininabalancedequilibrium.

Notallmodelspossessaunlquebalancedequilibriumoranybalancedequト libriumatall.Inthepresentmodel,thereisnobalancedequilibriumifdesiredin- ventorycoverageissetatalevelthatcausestheorderfulfillmentratiotobeless thanloo鞄.Forsomemodelsthereisnoequilibrium,balancedorotherwise.Many ofthemodelsofgrowthandproductdiffusiondevelopedinchapter9,forexam-

ple,havenonontrivialequilibriumconsistentwiththesituationnearthebeginnlng ofthedi軌ISionprocess･Themarketgrowthmodel(chapter15)hasnoequilibrium atallbecausethebasecaseparameterscausegrowthinanllnlimitedmarket.In

thesecasesitisstillusefultoinitializeeachsubsystemsothatitisinequilibrium relativetoitsInputsOrtOinitializethemodelinasteadystate,ifoneexists,even ifthatsteadystateisoneofgrowth.

Simu/taneouslnI'tiaIConditionEqualions

Sometimesyouwillfindthatthealgebraicexpressionsyouselectforinitialcondi- tionswillcreateasimultaneousequationsystem･Forexample,supposetheinitial valueofinventoryhadbeenspecifiedas

Inventoryb-DesiredInventoryCoverage*ShipmentRate (18-18a)

Thisformulationappearstobereasonable:Theinitialinventoryshouldprovide thb､desiredcoverageofinitialshipmentsforthesystemtobeinequilibrium.But

718 PartV ∫nstabilityandOscillation

specifyinginitialinventorylntermsOftheshipmentratecreatesasituationin

whichinitialinventorydependsonitself:

ShipmentRate-DesiredShipmentRate*OrderFulfillmentRatio -DesiredShipmentRate*f(_MaximumShipmentRate/DesiredShipmentRate)

DesiredShipmentRate*/ OrderFulfillment

DesiredShipmentRate (18-21)

Thereareseveralremediesforsituationswithsimultaneousinitialvalueequations･

Thebestsolutionistospecifytheinitialvalueintermsofotherparametersthat

donotparticipateintheloopcreatlngthesimultaneity.Initialinventorycouldbe expressedas

Inventoryh=DesiredInventoryCoverage*DesiredShipmentRate (18-22)

ThesimultaneltylSresolvedbecausethedesiredshipmentratedoesnotdependon

inventory･Thetwoformulationswilldifferonlytotheextentthatinitialshipments

fallshortofthedesiredrate.Anotherapproachistosolvethesystemofsimultane-

ousequationsandusethesolutionastheinitialvalue･Sometimessimplealgebra

willsufficetosolvetheequations;inothercasesthesolutionismorecomplexand requlreSlinearizationofthemodel'snonlinearfunctions.Asalastresort,simulta-

neousinitialvalueequationscanberesolvedbyuslnganumericalvalueforoneof

thestocksintheloop.

Simultaneous]nitjalConditions

ConsiderthesimplemacroeconomicmodelshowninFigure18-7(basedon

Samuelson1939;seealsoLow1980).Themodelprovidesasimpleexplanationof

theconsumptionmultiplier,animportantconceptinKeynesiananalysisofthe

economy.Inessence,thedemandforgoodsandservicesdependsonconsumers'

expectationsoftheirfutureincome.Incomeexpectations,inturn,dependontheto-

talincomeofallhotlSeholds,which,sincetheentirepopulationisincluded,isthe

totaloutputoftheeconomy(grossdomesticproduct[GDP]).Theresultisaposi-

tivefeedback,theconsumptionmultiplier,inwhichanincreaseinGDPboostsin-

comeandraisesconsumpt10n,furtherincreaslngaggregatedemandandGDP.In

thesimplemodelhere,inventoriesandthesupplychainintheactualeconomyare

omitted,soproductionadjuststoaggregatedemandwithashortlag.ConsumerexI

pectationsoffutureincomealsoadjusttoactualincome(GDP)Withadelay.

Thetotalproductionofgoodsandservices(GDP)adjustswithashortdelayto

therateofaggregatedemandintheeconomy.First-ordersmoothinglSassumed,a

commonassumptlOninmanymacroeconomicmodels.TheinitialvalueofGDPis

settoitsequilibriumvalue,aggregatedemandAD.WhenGDP-AD,thechange inGDPiszero:

GDP-INTEGRAL(ChangeinGDIIAD) (18-23)

ChangeinGDp-(AD-GDP)″imetoAdjustProduction (18-24)

Chapter18 TheManufacturlngSupplyChain

FIGURE18-7 Asimplemacroeconomicmodeloftheconsumptionmultiplier

719

AggregatedemandisthesumofconsumptionC,govemmentexpenditureG,and investmentI:

AD-C+I+G (18-25)

Consumersspendafractionoftheirexpectedincome,theMarginalPropensltytO ConsumeMPC:

C-MPC*Expectedlncome (18-26)

Expectedincomeadjuststoactualincome,whichintheaggregateistheGDP･

Manymodelsassumefirst10rderexponentialsmoothingfortheadjustment

process.TheinitialvalueofExpectedIncomeissettoGDP,itsequilibriumvalue:

Expectedlncome-INTEGRAL(ChangeinExpectedIncome,GDP) (18-27)

ChangeinExpectedIncome -(GDP-ExpectedIncome)偲XpectationFormationTime (18-28)

Inthissimplemodel,bothgovemmentexpenditureandinvestmentareexogenous.

Theinitialconditionsareindividuallysensible:Eachstockissetsothatitis

initiallyequaltoitsequilibriumvalue.Buttogethertheycreateasimultaneousini-

tialvalueequation:TheinitialGDPdependsonaggregatedemand,whichintu仙

dependsonexpectedincome,whichequalsGDP･

1. Resolvethesimultaneousinitialvalueprobleminthemultipliermodel.Be

sureyourinitialvalueswillstartthemodelinequilibriumforanysetofparame-

ters.Whichparametersdeterminetheequilibrium?Doestheequilibriumdepend

720 PartV InstabilityandOscillation

onthetimeconstants(thetimetoadjustproductionandthetimetoform expecta- tions)?Why/whynot?

2･ Simulatethemodelwithyourrevisedinitialvaluesandconfirmthatthesys- temdoesbegininequilibriumJnthismodelitmaybeobvious丘･ominspectionof yourequationsthatitwillbegininequilibrium.Youshouldstillnlnthetest.You mayhavemadeatypographicalerrorinanequation.Inmorecomplexmodels, simulatingtoconfirmthatyourmodeldoesindeedbegininabalancedequilibrium isanessentialcheckonyourcalculatedinitialconditions･

3.Typicalparametersfor也emacroeconomymightbeMPC-0.8,Production AdjustmentTime-1year,andExpectationFo-ationTime-2years･Setgov- ernmentexpendituret090andinvestmentto10.WhatistheequilibriumGDP? Nowsimulatethemodelassumlngthegovernmentstimulatestheeconomybyin- creasinggovernmentexpendituresby10units(yieldingalo啄increaseinaggre一 gatedemand)atthestartofyear1.Whatisthenewequilibrium?Howlongdoesit taketoreachit?Whatisthepattemofadjustment?Why?

18.1.6 BehavioroftheProductionModel

TobegintestingOfthemodel,Table18-lshowsillustrativeparametersforaman- ufacturlngfirm.Notethatwhiletheminimumorderprocessingtlmeis2weeks, thefirmdesiresasafetystockofanadditional2weeksofcoverage.GiventheasI sumedvaluesfortheorderfulfillmentfunction,inventorycoverageequaltothe minimumorderprocesslngtimewouldresultinaservicelevelofonly85%. Addingasafetystockequaltoanadditional2Weeksofexpecteddemandmeans themaximumshipmentratewouldbetwicethedesiredratewheninventoryequals itsdesiredvalue,enablingthefirmtofill100%oftheincomlngOrders.

Figure18-8showstheresponseofthe丘rmtoanunantlClpated20% step increaseincustomerorders.Theinitialcustomerorderrateis10,000widgets perweek.

Thedesiredshipmentraterisesimmediatelya氏erthestepincreaseindemand. Inventorycoverageimmediatelydropsfromitsinitialvalueof4weeksto3.33 weeks.Attheinstantthecustomerorderrateincreasesinventoryhasnotyet changed,SotheMaximum ShipmentRateremainsthesame(20,000widgets/ week).The20%increaseinordersreducestheratioofmaximumtodesiredship- mentsfrom2.00to1.67.Theorderfulfillmentratioatthatpolntisover99%,so thefirm isinitiallyabletofillnearlyalltheincomlngOrders,despltetheincrease. However,becauseproductioncontinuesattheinitialrateof10,000widgets/week, inventoryfalls.Asinventoryfalls,sotoodoesthefirm'sabilitytoship.Theorder fulfillmentratiodropstoaminimumofroughly95%about7weeksafterthede- mandshock,causingthefirmtolosebusiness(anditsreputationasareliable supplier).

Thegrowlnggapbetweendesiredandactualinventoryforcesdesiredpro- ductiontoriseaboveexpectedorders.AsitdoesthequantityOfworkinprocess

TABLE18-1 Basecase

parametersforthe productionmodel

Chapter18TheManufacturingSupplyChain

Parameter BaseCaseVane(Weeks)

MinimumOrderProcessfngTime

SafetyStockCoverage

ManufactunngCycleTime

hlVentOryAdjustmentTime

WIPAdjustmentTime

TimetoAverageOrderRate TableforOrderFulfillmentRatio:

(s s o lu O gS u a Lu EP )

0!l e

tuau l≡ I I

nJ JIa P JIO

0.0 0.4 0.8 1,2 1.6 2.0

MaximumShit)mentRate

Des(i;e}nhsiH.TLeensts)Rate

2 8

R o 2 4 6 8 0 2 4 6 8

Ds 0 .0 0 0 0 1 1 1 - 1 2

0 0 0 8 3 5 3 7 9 0 0

0 2 4 5 7 8 9 9 9 0 0

0 0 .0 .0 .0 .0 .0 .0 .0 .1 .1

721

requiredtomeetthehigherproductiongoalalsogrows,Openlngagapbetweenthe

desiredandactuallevelofWIP.Thusthedesiredproductionstartraterisesfurther

abovethedesiredproductionrate.

AstimepassesthefirmrecognlZeSthattheinitialincreaseindemandisnota

mererandomblipanditsforecastofdemandgraduallyrises.Giventhe8-week

smoothingtlmefortheforecast,ittakesabouty2yearfortheforecasttoadjust95%

ofthewaytotheneworderrate.Duringthistime,thesystemcannotachieveabal-

ancedequilibrium:IfinventoryandWIPinventorywereequaltotheirdesiredvaL

ues,productionwouldequalthedemandforecast,which,sinceitislessthan

orders,wouldcauseinventorytofall.

Asexpectedordersrise,sotoodoesdesiredinventory,addingtothegapbe-

tweendesiredandactualinventoryandboostlngdesiredproductionstillfurther.

Productionstartsreachapeakmorethan42%greaterthantheinitiallevelabout

4weeksaftertheshock,anamplificationratioof2.12.

TherapidincreaseinproductionstartssoonfillsthesupplylineofWIP,but

productionlagsbehindduetothe8-weekdelay.Productiondoesnotsurpassship-

mentsuntilmorethan6weekshavepassed;throughoutthisperiodinventorycon-

tinuestofallevenasthedesiredinventorylevelrises.Inventorystopsfallingwhen

productionfirstequalsshipments.Thesystemisnotyetinequilibrium,however,

sL a P LO u ! a S t2a JO u ! d a ts % o N 吋 0 〓 a P O ∈

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Chapter18 TheManufacturlngSupplyChain 723

becauseofthelargegapbetweendesiredandactualinventoryandbetweenorders

andexpectedorders.Productioneventuallyrisesaboveshipments,causlngInven- torytorise,untiliteventuallyreachesthenew,higherdesiredlevel.Notethatthe

peakofproductioncomesabouty4yearafterthechangeinorders,muchlonger thanthe8-weekproductiondelaysuggests.

Thesimulationrevealsseveralfundamentalaspectsofsupplychainbehavior.

First,theinitialresponseofthefirmtoanunanticIPatedincreaseindemandisade-

clineininventory.TheproductiondelaymeansaninitialdroplninventorylSin-

evitable-itisafundamentalconsequenceofthephysicalstructureofthesystem. Thereductionininventorycontrastssharplywiththefirm'sdesiretoholdmorein- ventorywhendemandincreases.

Second,amplificationofthedemandshockisunavoidable.Becauseinventory mustinitiallyfall,theonlywaytoincreaseitbacktoitsinitiallevelandthenraise ittothenew,higherdesiredlevelisforproductiontoexceedshipments.Produc-

tionmustovershoottheshipmentratelongenoughandbyalargeenoughmargln tobuildinventoryuptothenewdesiredlevel.Productionstartsmustovershootor- dersevenmoresothatthelevelofWIPcanbebuiltuptoalevelconsistentwith

thehigherthroughputrate. Third,thepeakproductionstartratemustlagthechangeincustomerorders.

Theadjustmenttoproductionfromtheinventorygapreachesitsmaximumabout whentheinventoryreachesitsminimum.Inventorybottomsoutonlyafterpro- ductionhasfinallyrisenenoughtoequalshipments,aneventthatmustlagthe

changeinorders.Likeamplification,thisphaselag,characteristicofmanyreal supplychains,isafundamentalandinevitableconsequenceofthephysicalstock andflowstructure,

Thestockmanagementstructurethusexplainswhysupplychainsgenerate amplificationandphaselag.Giventhestructureofthesystem(inparticular,pro- ductiondelaysandforecastadjustmentdelays),productionandproductionstarts

mustovershoot,amplify,andlagchangesindemand,nomatterhowsmartthe managersofthefirm maybe.

Thoughamplificationandphaselagareinevitable,oscillationisnot.There- sponseofthefirmtothedemandshockisintendedlyrationalinthesensedefined inchapter15.Theresponseofthefirm totheshockissmoothandstable(giventhe

basecaseparameters).Explainingoscillationrequirestheexpansionofthemodel toincludeadditionalstructure｡

18.1.7 EnrichingtheModel:AddingOrderBackbgs

Sofarthemodelassumesthatordersnotimmediatelyfilledarelostforever.While

thisassumptlOnisreasonableinsomesettings,Suchasretailsalesandsomedeliv- ery-sensitiveindustrialproducts,mostmanufacturingfirmscannotdeliverimme- diatelyandmaintainabacklogofunfilledordersthataccumulatesthedifference

betweenordersandshipments.Backlogsarisewheneverthereisadelaybetween thereceiptanddeliveryofanorder.Suchdelayscanbecausedbyadministrative

activitiessuchascreditapprovalandorderprocesslng,bytheneedtocustomizeor configuretheproducttotheneedsofparticularcustomers,andbydelaysinship- pingtOthecustomersite,amongothers.WhenthevalueandcarrylngcostsOf

724 PartV InstabilityandOscillation

FIGURE18-9 Structurefororderbacklog

inventoryareveryhigh,firmsprefertomaintainbacklogsofunfilledordersand

operatemake-t0-Ordersystemseveniftheytechnicallycouldstockfinishedprod-

uct･Boeingdoesnotmake777stostock･2Figure18-9showshowtheorderful-

fillmentsubsystemcanbemodifiedtoincludeanexplicitorderbacklog.

AnorderbacklogImpliesthatthereisadelaybetweentheplacementandre-

ceiptOforders.ByLittle'SLawtheratioofthebacklogtotheorderfulfillmentrate

measurestheaveragedeliverydelayatanymoment:

DeliveryDelay-Backlog/OrderFulfillmentRate (18129)

Backlog-INTEGRAL(OrderRate-OrderFulfillmentRate,Backlogb) (18-30)

Theorderfulfillmentrateisequaltotheshipmentrate.Everytimeawidgetis

shippedtoacustomer,thebacklogisdecrementedbyoneunitaswell･Notethat

whiletheshipmentrateandorderfulfillmentrateareassumedtobenumerically

equalandbotharemeasuredinthesameunits(widgets/week),theyaredistinct

2Moreprecisely,aircraftmanufacturersdonotintendtomakejetlinersforinventory.However, anunexpecteddownturnintheaircraftmarketleadstoordercancellationsandcancauseun- intendedinventoryaccumulation.Theexcessaircraftmustthenbemothballeduntilcustomers canbefound.UnsoldorsurplusjetsareOftenflOwntotheMojavedesertwheretheycanbestored cheaplyandsafelyuntiltheycanbesold.

Chapter18 TheManufacturlngSupplyChain 725

concepts.Theshipmentrateistheratephysicalproductleavesthefirm,whilethe orderfu1fillmentraterepresentsaninformationflow.

Intherevisedstructurethedesiredshipmentrateisnowtherateofshipments thatwillensureordersarefilledwithinthetargetdeliverydelay.Thetargetdeliv-

erydelayisthefirm'sgoalfortheintervalbetweenplacementandrecelPtOfor-

ders.Theactualdeliverydelaywillequalthetargetwhentheshipmentrateequals thedesiredshipmentrate｡

DesiredShipmentRate-BacklogrrargetDeliveryDelay (1816a)

Finally,thefirm'Sorderrateisnowsettothecustomerorderrate.Inmodelswith

multiplecustomers,theorderratewouldbethesumoftheindividualcustomeror- derrates.Toensurethatthemodelbeginsinabalancedequilibrium,theinitial

backlogmustequalthetargetdeliverydelay'sworthofincomlngOrders:

Backlogb-TargetDeliveryDelay*OrderRate (18-31)

18.1.8 Behavioro青theFirmwithOrderBack弓ogs Figure18-10showsasimulationofthemodelwiththetargetdeliverydelayset to2weeksandallotherparametersasinFigure18-8･Asbefore,thereisanun-

antlCIPated20%increaseincustomerordersfromaninitialbalancedequilibrium･ Thoughquitesimilartothemodelwithoutbacklog,therearesomesubtlediffer- ences.Ⅰmmediatelya触rtheincreaseinorders,shipmentscontinueattheinitial rate.Thebacklogthereforebuildsup,andasitrises,sotoodoesthedesiredship-

mentrate.Actualshipmentskeeppaceinitially,butasthefirm'sinventorylevel falls,theorderfulfillmentratiodropsbelow1O0%,causingShipmentstodropbel

lowdesiredshipments.Thedeliverydelaythenbeginstorise｡ Abackloghastwoeffects.First,becausethebacklogbuffersordersandship-

ments,desiredshipmentsrisemoregraduallythaninthecasewithoutbacklog.As aresult,thedeclineininventorylSmoregradual,reducingtheamplificationinpr o -

ductionstartsslightly,to1.97Comparedt02.12intheno-backlogcase.Thepeak

intheproductionstartratealsolagsthechangeinordersslightlymorethaninthe no-backlogcase.Second,ordersthatcannotbeshippedimmediatelyarenolonger lostbutremaininthebackloguntiltheycanbeshipped･Theshipmentratethere- foremustriseabovetheorderrateasthefirmworksoffitsexcessbacklogonce

sufficientinventorybecomesavailable.

18.1.9 AddingRawMがeria!sSntJen的ry Sofartheproductionstartratealwaysequalsthedesiredproductionstartrate,im-

plyingresourcessuchasmaterials,labor,andcapitalarealwaysample･Figure 18-llShowshowthestructureofthemodelcanberevisedtoincludeanexplicit

stockofrawmaterialsorcomponents.ThematerialsinventorylSmodeledasa stockmanagementstructureanalogoustotheinventoryoffinishedgoods.Produc-

tioncanonlybeginifthereisasufficientstockofmaterials,andthefirmmustor-

derenoughmaterialstokeepthepartsinventoryattheappropnatelevel･ TheProductionStartRateisreformulatedtoequalFeasibleProductionStarts

fromMaterials,therateatwhichproductioncanbebegunbasedontheMaterial

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FdGURE18-ll Addingamaterialsinventory

728 PartV InstabilityandOscillation

UsageRate(materials/week)andMaterialUsageperUnit(materials/widget),the

quantltyOfmaterialsrequiredperunitofoutput:

ProductionStartRate-FeasibleProductionStartsfromMaterials (18-32)

FeasibleProductionStartsfromMaterials

-MaterialUsageRate/MaterialUsageperUnit (18-33)

Thematerialusagerateisanalogoustotheshipmentrate.Theactualmaterial

usagerateisthedesiredmaterialusagerateunlessthestockofmaterialsisin-

adequate,1nWhichcaseusagefallsbelowthedesiredrate.TheMaterialUsage

Ratioisthefractionofthedesiredrateachievedbasedontheadequacyofthe

materialsinventories.Becausethemodelaggregatesmanytypesofmaterialsand

componentstogether,theusageratiograduallydropsbelowloo鞄asthemaximum

materialusageratefallsbelowthedesiredusagerate:

MaterialUsageRate -DesiredMaterialUsageRate*MaterialUsageRatio

MaterialUsageRatio -/(MaximumMaterialUsageRate/DesiredMaterialUsageRate)

(18-34)

(18-35)

Thefunctiondete-inlngtheMaterialUsageRatioisanalogoustothefomulation

fortheOrderFulfillmentRatio(seeFigure1813).

ThedesiredrateofmaterialuseisglVenbydesiredproductionstartsand

materialusageperunit:

DesiredMaterialUsageRate -DesiredProductionStartRate*MaterialUsageperUnit

(18-36)

Themaximumrateatwhichmaterialscanbeusedisdeteminedbythecurrentin-

ventoryandtheminimumtimerequiredtoprepareanddelivermaterialstothepro-

ductionline.Thisminimummaterialinventorycoveragedependsonthefirm's

materialshandlingsystemsandthetransportationtimebetweenthematerials

stocksandtheproductionline.

MaximumMaterialUsageRate -MaterialslnventoIY/MinimumMaterialInventoryCoverage

(18-37)

Thestockofmaterialsisincreasedbythematerialdeliveryrateanddecreasedby

thematerialusagerate:

Materialslnventory

-INTEGRAL(MaterialDeliveryRate-MaterialUsageRate,Materialsto) (18-38)

Fornow,immediatedeliverywithnosupplyconstraintisassumed:

MaterialDeliveryRate-MAX(0,DesiredMaterialDeliveryRate) (18-39)

Thedesiredmaterialdeliveryrateisformulatedusingthestockmanagementstruc-

ture,analogoustothemanagementoffinishedgoodsinventory:

DesiredMaterialDeliveryRate -DesiredMaterialUsageRate+AdjustmentforMaterialInventory

(18-40)

Chapter18 TbeManufacturlngStlpplyChain

Adjustmentfor (DesiredMaterialInventory-MaterialsInventory) MaterialInventory MaterialinventoryAdjustmentTime

729

(18-41)

Thedesiredmaterialinventoryisdeteminedbythedesiredusagerateanddesired

materialsinventorycoverage,which,likefinishedgoodsinventory,1SSettOthe sumoftheminimumcoveragerequiredandasafetystockcoveragetoensureparts stocksdonotconstrainproductionstartsundernormalcircumstances:

DesiredMaterialInventory -DesiredMaterialUsageRate*DesiredMaterialInventoryCoverage

(18-42)

DesiredMateriallnventoryCoverage -MinimumMaterialInventoryCoverage+MaterialSafetyStockCoverage

(18-43)

Tofacilitateanalysisofthemodel,andwithoutlossofgenerality,thesimulations belowassumeMaterialUsageperUnit-1materialunit/widget.MinimumMa- terialslnventoryCoverageis1week,andaトweeksafetystockcoverageisas- sumed.Thematerialsinventoryadjustmenttimeissetto2weeks.Thefunction determinlngthematerialsusageratioisassumedtobethesameasthatusedfor shipmentsfromfinalinventory.Figure18-12showstheresponseofthemodelto anunantlClpated20%stepincreaseincustomerorders･Giventheparametersand theassumedincreaseindemand,thematerialsinventoryneverconstrainsproduc- tionstarts.Thereforeproductionstartsalwaysequalthedesiredstartrateandthe behaviorofallmodelvariablesisthesameasshowninFigure18-10(thiswould

notbetrueforalargerdemandshock)･Thematerialsorderrateexhibitsadditional amplificationcausedbytheincreaseinthedesiredmaterialsstocktriggeredbythe surgeindesiredproductionstarts.Theamplificationratioofmaterialsordersrela- tivetocustomerordersis2.52(Comparedt01.97forproductionstarts).Adding additionaldelaysorstocksinasupplychainincreasestheamplificationofde- mandshocks.

18.2 ヨNTERACT10NSAMONGSuppLYCHAINPARTNERS

Sofarthestockmanagementstructurehasbeenappliedtoaslnglefirm.RealsuP- Plychainscouplemultipleorganizationstogether,andtheamplitudeoffluctua- tionsusuallyincreasesateverylink.Producersattheupstreamendofthesesupply chainsexperiencemuchmoreinstabilitylnOrdersandproductionthanthosenearer thefinalcustomer.

Themodeldevelopedsofarconstitutesagenericmodelofafirm'smanufac- turlngprocess.Anindustrysupplychaincanbemodeledbylinkingseveralofthe

slnglefirmmodelstogether.Eachmemberofthesupplychainisthenrepresented bythesamestructure,thoughofcoursetheparameterscandiffer.Thegeneric modulescanbelinkedinanarbitrarynetworktocapturethestructureofanindus-

tryoreconomy,lnCludingmultiplesuppliers,competitors,andcustomers. Toillustrate,considerasupplychainconsistingoftwofirms(Orsectors,such

astheautomobileindustryanditsprincipalsuppliers).Asbefore,thecustomeror-

derratereceivedbythedownstreamfirm(theproducer)willbeconsideredexoge- nous.Theorderratereceivedbytheupstreamfirm(thesupplier)willnowbe

730

FIGURE18-12 Responseof materials

inventorytoan unanticipated 20%increase jndemand

PartV instabilityandOscillation

0 10 20 Weeks30 40 50

28,000

26,000

B 24,0000ロ)11⊃ ]i 22,000

20,000

18,000

15,000

14,000

竜13,000 ≧i≡! 盟 12,000 dJ ロ〉

; ll,000

10,000

9,000

0 10 20 Weeks30 40 50

determinedbythedownstreamfirm.Intheslnglefin model,actualmaterialdel

liverieswereequaltothedesireddeliveryrate,implyingmaterialsorderswerede-

liveredinstantlyandfully.Lillkingthefirm toasuppliermeansthedeliveryrateof

materialstotheproducerwillnowdependonthesupplier'sabilitytoship.Delays intheresponseofthesuppliertochangesindemandmightnowlimitmaterialsin-

ventoriesandconstraintheoutputoftheproducerfirm.

Thestructureandequationsfortheupstreamsupplierareidenticaltothosefor

theproducerexceptthattheorderratereceivedbythesupplierisnowglVenbythe

producer'smaterialorderrate.Likewise,thesupplier'sforecastsarebasedon

theordersitreceives,Denotlngthesupplierbythesubscriptiandtheproducer bythesubscriptJ;

Backlog1

= INTEGRAL(OrderRateiIOrderFulfillmentRatei,Backlogib)

ChangeinExpOrdersi (OrderRatei-ExpectedOrderRatei)

TimetoAverageOrderRatei

OrderRatei-MaterialOrderRateJ

(18-44)

(18-45)

(18-46)

Figure18-13Showsthestructureoftheproducer'smaterialssupplyline.

Becauseittakestimeformaterialstobereceivedfromthesupplier,thepr o -

ducerkeepstrackofthesupplylineofmaterialsonorder.Thestockofmaterials

Chapter18 TheManufacturlngSupplyChain

FIGURE18-13 Addingasupplylineofmaterialstothemodel

731

Desired

Material

De一iveryRate

Onorderisincreasedbythematerialorderrateanddecreasedbythematerial arrivalrate:

MaterialsollOrderj

-INTEGRAL(MaterialOrderRatej-MaterialArrivalRatej,

MaterialsonOrderjt｡)

(18-47)

NotethatbecauseMaterialOrderRateJ-OrderRateiandMaterialArrivalRate

j-MaterialDeliveryRateJ-ShipmentRatei,thestockofMaterialonOrderj-

Backlogi･3Theorderrateformaterialsisformulatedusingthestockmanagement

structure.Materialordersaredeterminedbythedesiredmaterialdeliveryrate

modifiedbyanadjustmenttomaintainthesupplylineofmaterialsonorderatthe

approprlatelevel.Thedesiredstockofmaterialsonorderisdeterminedbythe

3providedBackloglb-MaterialonOrderjt｡,whichshouldalwaysbethecase.Theequilibrium Backlogib-TargetDeliveryDelayi*OrderRatei･

732 PartV InstabilityandOsciuation

desiredproductionstartrateandthe丘rm'sbeliefaboutthedeliverydelayfor

receiptofmaterials(theexpecteddeliverydelay):

｡rEearteiiaatlej-MAX(0,DDeeSlilrVeedry";taetrei;1IMa: rjiua芸m.ennbfodre,j) (18148,

Materials

Adjustmentlbr (D慧onOrderj .TBe,rdieaisj)

MaterialsonOrderj SupplyLineAdjustmentTimeA

DesiredMaterials ExpectedMaterials*DesiredMaterial onOrderj DeliveryDelayJ DeliveryRatej

TheadditionofamaterialsacquisitiondelayIntroducesanewfeedbackloop,the

MaterialsSupplyLineControlloop.Thisnegativeloopregulatesthesupplylineof

materialsonorderbyadjustingtheorderratesoastoachievethedeliveryratethe firmdesires.

Thelinkedmodelcapturesinteractionsbetweentwofirmsinasupplychain･

Customerdemandisstillexogenous,andthesupplierisassumedtoreceivethe

materialsitrequlreSinstantlyandfully･Laborandcapitalareagainimplicitlyas-

sumedtobeampleandneverconstrainproduction.

Fornow,assumetheexpectedmaterialsdeliverydelaylSaCOnStant,even

thoughtheactualdeliverydelaymayv∬yifthesupplier'sinventorybecomesin-

adequate｡Aconstantexpecteddeliverydelaymayariseifthecustomerdoesnot

monitordeliverydelaysoriftheinformationsystemusedtocontrolpurchasinglS

notupdatedfrequently.

Figure18-14showstheresponseofthelinkedmodeltoa20%steplnCreaSein

customerorders.Forthepurposesofexposition,theparametersofthetwofirms areassumedtobeidentical｡

ThetwoIStageSupplychainperformsmuchworsethanthecasewheremateri-

alscanbeacquiredfullyandwithoutdelay･Theproducer'smaterialsordersreach

apeakofabout18,000units/week,anamplificationratioof4.08(Comparedt0

2.52whenmaterialsareinstantlyavailable).Theincreaseinamplificationis

causedby血einabilityofthesuppliertodeliverontime,Causlngalargedroplnthe

producer'smaterialsinventoryandaconsequentincreaseinproducerorders(note

thebehaviorofinventorycoverage).

Whiletheproducer'sresponsetothedemandincreaseisstillcomparatively

stable,thesupplieriswhipsawedthroughlargeamplitude恥ctuations･Thesup-

pliermaterialdeliveryratereachesapeakofmorethan28,000units/week,anam-

plificationratioof2.22comparedtothesupplier'Sorderrate(thematerialorder

rateoftheproducer).Butbecausetheorderratereceivedbythesupplierisitself

alreadygreatlyamplifiedbytheinventory,WIP,materials,andsupplylineadjust-

mentsoftheproducer,theamplificationratioofsuppliermaterialdeliveriesrela-

tivetocustomerordersismorethanafactorofnine.Thesurgeinordersreceived

bythesuppliercausesasevereandprolongedshortageofinventoryatthesupplier,

causlngStOCkoutsofsomeitemsandboostingthesupplierleadtimetoapeakof

3.5weeks,75%greaterthannormal.NotetheHdoubledipHbehaviorofthesup-

pliershipmentrate.AsincomingOrderssurge,thesupplier'sdeliveryrateatfirst

keepspace,whileproductioncontinuesattheorlglnalrate･Supplierinventoryfalls

ose a LO u !P u e uJaP P

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733

734 PartV InstabilityandOscillation

sharply,limltlngShipments.Thebacklogswellsanddeliverydelayrises.Eventu-

ally,newproductionbeginstoarrive,andsuppliershipmentsriSetoanevenhigher

peakasthebacklogofunfilledordersisworkedoff･Eventually,theshipmentrate

stabilizesatthenewequilibriumof12,000units/week･4

Thetransientsurgeinproducerorderscompoundsthesupplier'sproblems.

Though thesuppliersmoothsincomingOrderstofilteroutshort-tem fluctuations,

thesupplier'sforecastofordersslgnificantlyovershootsthefinalequilibrium.The

supplierdoesnotknOwfinalsalesandcannottellwhichordersreflectanenduring

changeinconsumerdemandandwhichreflecttemporaryInventoryandsupply

lineadjustments.Consequently,thesupplierfirstfindsitselfwithfartoolittlein-

ventoryandmaterials,leadingtoaggressiveeffortstoboostproduction.ButJustaS

thetapbeginstoflow,ordersreceivedfromtheproducerfall,leavingthesupplier

withsignificantsurplusinventoryandforcingSupplierproductionstartsandpro-

ductiontofallfarbelowproducerorders.Thedelaysandstockadjustmentscause

supplierproductiontobenearlycompletelyoutofphasewithproducerorders.

SupplieroutputreachesitspeakjustaboutthetimeincomingOrdersfalltotheir

lowpoint.

Thesimulatedsupplychain,thoughitrepresentsonlytwolinks,exhibitsall

threephenomenaobservedinrealsupplychains:oscillation,amplification,and

phaselag･Mostimportant,theseattributesariseendogenously｡Thesupplierexpe-

riencesoscillationinoutputeventhoughtheextemalenvironmentdoesnotoscil-

lateatall.Thedynamicsemergefromtheinteractionofthephysicalstructureof

thesupplychainwiththedecisionrulesofthemanagers.

Ofcourse,thestepIncreaseincustomerdemandisnotrealistic.ThesteplS

analogoustohittingabellwithaslngletapoftheclapper･Asudden,permanent

changeindemandsuddenlyknocksthesystemoutofequilibrium,allowlngthe

modelertoobservehowthesystemrespondstoaslngleshock･Justasaslngle

strikeoftheclappercausesabelltoringformanyseconds,sotooaslnglechange

incustomerdemandcausesthesupplychaintooscillate,inthiscase,fornearly

ayear･

Intherealworld,ofcourse,supplychainsarenotstruckoncebutarecontinu-

ouslyperturbedbychangesincustomerorders(andrandomvariationsinotherkey

rates,includingproduction,materialsorders,andsoon)･Asdiscussedinchapter4,

theserandomshocksconstantlyknocksystemsoutofequilibrium,elicitingachar-

acteristicresponsedeterminedbytheirfeedbackstructure.Astreamofrandom

changesin,forexample,customerorders,canbethoughtofasacontinuoussuc-

cessionofsmallpulsesindemand,eachwitharandommagnitude.Figure18115

showstheresponseofthetwo-firmmodeltoarandomcustomerorderrate.For realism,therandomshocksarecorrelated.Successivevaluesofcustomerorders

dependtosomeextentonrecentorders.Suchpersistenceisrealisticbecauseall

4Thedouble-dipbehaviorofsuppliershipmentsillustrateshowadyna血csystemcangenerate hamonics(oscillationsatvariousmultiplesofasystem'sfundam entalfrequency).Theproduction ofsuchha-Onicsisfundamentallyanonlinearphenomenonandcouldnotariseiftheequations govemlngthesupplychainwerelinearJnthiscase,thenonlinearfunctiongovemlngStOCkouts, coupledwiththedelaylnproductionofnewunits,Causesaharmonicinshipmentsrotlghlydouble thefrequencyoftheunderlyingcycleinordersandproduction.

Chapter18 TheManufacturlngSupplyChain

FIGURE18-15 Responseofthe supplychainto randomvariations incustomerorders

20,000

15,000

.上亡 dJdJ 至 10,000的:=⊂=1

5,000

735

0 50 100 150 200

Weeks

realsystemshaveacertaindegreeofinertiaandcannotchangeinfinitelyfast(the

weather1hourfromnowisquitelikelytobesimilartotheweatherrightnow).5In

thesimulationthecorrelationtimeconstantis4weeks,meaningthatmostofthe

varianceincustomerordersarisesfromrapid,week-to-weekvariations.

Asexpected,randomshocksincustomerorderscausethesupplychaintorlng

likeabell.Thesupplier'smaterialdeliveryratefluctuateswithmuchlargerampli-

tudeandforamuchlongerperiodthanthechangesincustomerorders.Thestan- darddeviationofcustomerordersislessthan5%,butthestandarddeviationofthe

supplier'smaterialsdeliveryrateismorethanseventimesgreater(37%ofthe

averageorderrate).Andwhilemostoftherandomfluctuationincustomerorders

consistsofday-to-dayorweek-to-weekvariations,theresponseofthesupply

chainisacyclewithaperiodofabouty4yearinduration.

Thepurposeofinventoriesandbacklogsinasupplychainistobufferthesys-

temagainstunforeseenfluctuationsindemand.Thesupplychaindoesagoodjob

ofabsorbingtheveryrapidrandomfluctuationsincustomerorders･However,

typicalmanagementpoliciescansignificantlyamplifytheslowervariationsinde-

mand,leadingtopersistent,costlyfluctuations.Thesefluctuationsareprogres-

sivelyamplifiedbyeachstage.Thesystemselectivelyattenuateshigh-frequency

variationsindemandwhileamplifyinglowfrequencies･Smallperturbationsin

demandcanresultinhugeswlngSinproductionofrawmaterials･

18.2.1 lnstabHtyandTriJStinSupplyChains

ItisworthpausingtOconsidertheeffectofsuchsupplychaininstabilityonthe

beliefsandbehaviorsofmanagersinthedifferentfirms･Intheunstableworldill

lustratedbythesimulationsandtheindustrydatashowninchapter17,trustamong

partnersinasupplychaincanrapidlybreakdown･Downstreamfirmsfindtheir

supplierstobeunreliable.Deliveryquoteswilloftennotbemet,andproducerstoo

oftenfindthesuppliersplacetheirproductsonallocation(whereeachcustomer

receiveslessthantheirfullorderduetoashortageofsupply).Inturn,suppliers

findtheorderingpatternsoftheircustomerstobevolatileandcaprlCious.Inside

5Technical1y,therandomdisturbanceisfirst10rderpinknoise(seeappendixB).

736 PartV InstabilityandOscillation

eachfirm,managersfindtheirforecastsofincomlngOrdersarerarelycorrectand alwayschanglng.AsshowninFigure18-14,thesupplier'sforecastofincomlng orders(theexpectedorderrate)reachesitspeakjustasactualincomingordersfall belowtheirequilibriumlevelandbegintoapproachtheirminimum.Beforelong, theforecasts,whicharetyplCallyproducedbythesalesandmarketingorganiza- tion,loseallcredibilitywiththeproductionandoperationspeople.Themarketing organization,intum,Complainsthatunreliableproductionmakesforecastlng,not tomentionselling,difficult.Theendogenousinstabilitycausedbythestructureof asupplychain-inparticular,management'sownpolicies-Canbreedblameand mistrustwithinandbetween丘rmsinasupplychain.Theexampleofsemiconduc- tormakerSymbios,presentedinchapter11,illustratesthisphenomenon.Thefore- castsSymbiosprepared,basedonthecustomers'ownprqectionsoftheirfuture requlrementS,WereSystematicallyoutofstepwiththeactualsituation,degrading stability,ralSlngcosts,andslowlnggrowth,

Theconflictandmistrustcreatedbysupplychaininstabilityfeedbackto worsentheinstabilitylnaViciouscycle.Inthemodelsofar,theproducermanages itssupplylineofmaterialsordersontheassumptlOnthatthematerialsdeliveryde- laylSCOnStant.AsshowninFigure18114,however,fluctuationsinmaterials orderscancauselargeswingsinsupplierleadtimeJnmanysupplychains,down-

streamfirmshavelearnedtomonitorsupplierdeliveryquotesandleadtimes closelyandadjusttheirorderingaccordingly.Forexample,whensupplierlead timesincreaseandcustomersareplacedonallocation,thecustomersoftenrespond byincreaslngtheirdesiredinventorylevelsandorderingfartherahead,further swellingtheirsupplylineandstretchingdeliverydelaysoutstillmore.

Figure18-16Showsthestructureofthemodifiedmodel･Nowtheexpected materialsdeliverydelaytheproducerusestomanageitsmaterialssupplylineisa variable,respondingtochangesintheactualsupplierleadtime.

TheexpecteddeliverydelaylSnowanOnlinearfunctionofthefirm'sbelief aboutsupplierleadtimes(theperceivedmaterialsdeliverydelay).Thefunctionis alsonormalizedbythefirm'sReferenceDeliveryDelay,whichallowstheformu- lationtobeusedinsituationswithdifferentnormaldeliverydelays:

ExpectedMaterials Reference DeliveryDelay DeliveryDelay

MaterialsDelivery ReferenceDeliveryDelay

(18-51)

Theperceiveddeliverydelayadjustswithadelaytochangesintheactualsupplier leadtimeduetothetimerequiredtoreceiveandchecktheaccuracyofsupplier deliveryquotes,thetimerequiredtorevisebeliefs,andthelagintheresponseof thepurchasingandprocurementsystems.First-ordersmoothinglSassumed,With anaveragelagglVenbytheMaterialsDeliveryDelayPerceptionTime:

pe;ceeliiVvee:y",a芸an;ls-sMOOTH(,eliSvue:yplte:.ay,"atepr!芝sepDt:iinveTriym? elay) (18-52)

Figure18-17showsatyplCalnonlinearfunctionrelatingtheperceiveddeliveryde- laytotheexpecteddelay.

FIGURE18･16 Structurefor

dynamicleadtime expectations

FJGURE18･17

Relationship betweenthe

perceivedand expectedde‖very delay

Chapter18 TheManufacturlngSupplyChain

Suppljer DeJiveryDefay

LL)

(s s a 一u O !S u a ∈ !P )

^ t2[¢ 凸 h a 之一〇凸 a D u 巴 O la tJ

謝 la 凸 Xjo A !la 凸 P a IU a d X u

737

0 1 2 3 4 5 6 PerceivedDeljvervDelav ReferenceDe一iveryDe一ay

(dimensionFess)

ThefunctionisnormalizedbytheRefTerenceDeliveryDelay.ThelineEDD/ RDD-1representsthebasecaseinwhichthefirm usesaconstantdehverydelay tomanagethesupplylineofmaterialsorders･The450linerepresentsapolicyin whichtheexpecteddeliverydelayalwaysequalsthef:rm'scurrentbehefabout supplierleadtimes.Theassumedrelationshipsaturatesatamaximumforvery high deliverydelays'.Thepurchasingmanagersofthef+irm believeveryhigh

738 PartV instabilityandOscillation

deliverydelayswillnotpersistanddonotincreasethematerialssupplylinewith- outlimit.TheregionWheretherelationshiprlSeSabovethe450lineindicatesasit- uationinwhichthepurchasingmanagersdon'ttrustthedeliverydelayquotesthey receivefromthesupplierandhedgeevenfurtherbyincreaslngtheirestimateof leadtimesbeyondwhatrecentexperiencewouldindicate･SuchhedginglSpartic- ularlylikelyinsituationswherethesupplierservesmultiplecustomers.Suppose thesuppliermnsshortofproductandplacesthecustomersonallocation:Eachwill onlyreceive80%ofitsorder.Customersarelikelytorespondbyordering125% Orevenmoreofwhattheyactuallyrequire.Eachinflatesitsordertoseekalarger shareofthepieattheexpenseofitscompetitors･Firmsthatfailtoplaythisallo- cationgamewilllikelylosemarketsharetomoreaggressivecompetitors.Cus- tomersfacedwithlongdeliverydelaysfromtheirsuppliersalsofrequentlyplace orderswithmultiplesuppliers,thencancelthemwhentheleadtimefallsandprod- uctsbecomeavailable.

TheresponseofthemodifiedmodeltoanunanticIPated20%steplnCreaSein customerordersisshowninFigure18-18.ThedelaylnPerceivingSupplierlead timesisassumedtobe4weeks.¶)determinethatadeliveryquotewillnotbemet

requlreSWaltlngatleastuntilthepromiseddeliverydate,andfurthertimeisre- quiredtoreacttochangesinavailabilitybyalteringpurchaseorders.

Activemonitorlngandrevisionofsupplierleadtimes,whileintendedtoim- provetheflowofmaterialstotheproducer,actuallydestabilizethesystemfurther･ Supplierleadtimesrisetoapeakvalueabout23%greaterthanthecasewherethe expecteddeliverydelaylSCOnStant.Asproducermaterialsorderssurgeandthe supplierleadtimebeginstorise,theproducerreactsbygraduallyboostlngitseSti一 mateofthedeliverydelay,leadingtoalargeincreaseinthedesiredsupplylineof materials.Ordersincreasestillmore,pushingthedeliverydelayupstillhigher,in apositivefTeedback.Thesupplierisforcedtoexpandoutputevenmore.Asthe surgeofnewproductionbecomesavailableandthesupplier'sdeliverydelaybe-

glnStOfall,theproducerrespondsbycuttlngthedesiredsupplylineofmaterials, andproducermaterialsordersplummet･DuetothelaglnPerCeivlngandrespond- 1ngtOthesupplierleadtime,however,thedroplnOrderscomestoolatetoprevent theproducerfromaccumulatingamuchlargersurplusofunneededmaterialsIThe supplierishurtmuchmore.Whenproducerorderscollapse,thesupplierfindsit- selfwithsomuchexcessinventory,WIP,andmaterialsthatitcutsitsownmateri- alsprocurementtozerofornearlyamonth.Supplierinventorycoveragerisestoa peakofmorethan6weeks,50%morethanthedesiredlevelandmuchmorethan thebasecase.

Onthesurface,itappearsthatthesupplierbearsmostoftheexcesscostscre- atedbythepositiveleadtimefeedback･However,thesecostsmusteventuallybe passedontothedownstreamfirmsinthefom ofhigherpnces,poorcustomerser- vice,andunreliabledelivery.Producerfirmshaveastrongincentivetoimprovethe stabilityoftheirsuppliers.Nevertheless,theparochial,localincentivesfacingln- dividualfunctionsandfirmsoftenleadtoactionsthatdegradethestabilityofthe entiresupplychain.

Whywouldcustomersrevisetheirdeliverydelayestimateswhentheeffectis harmfultoboththeirsuppliersandthemselves?Flexibleexpectationsforsupplier leadtimesarelocallyrational.Toensureanapproprlatedeliveryrateofmaterials,

S と ¢ ¢ JVL

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740 PartV InstabilityandOscillation

thepurchasingdepartmentmustmaintainasupplylineproportionaltothedelivery delay.FromthepolntOfviewofthepurchasingmanagersinafirm,itiscritical thattheymonitorandrespondtochangesinsupplierleadtimes,eithermanuallyor byrevISlngtheassumedleadtimesintheirprocurementsystemsoftware.Failure torespondtochangesinleadtimescouldresultincostlyaccumulationofexcess partsinventories,or,worse,shortagesthatcouldshutdownproduction.

Thementalmodelsofthepurchasingmanagersindownstreamfirmstypically treatthesupplierleadtimeasexogenousandoutsidetheircontrolJnsomecases eachfirmreasonsthatitisresponsibleforonlyasmallpartofthesupplier'stotal demand,sochangesinitsorderswon'taffectsupplierleadtimes.Organizational routinessuchasupdatingthesupplierleadtimeassumptlOnSOfthematerialsre-

quirementplanning(MRP)systembasedonrecentdeliveryexperienceimplicitly presumethattheresultingchangesinmaterialsorderswon'taffectsupplierlead times.Butwhenallcustomersactinasimilarfashion,thepositivelooplSClosed. Themismatchbetweenthementalmodelsofthesupplier,inwhichleadtimesare exogenous,andtheactualsituation,inwhichleadtimesarestronglyaffectedby theorderingbehaviorofthedownstreamfirms,furtherdegradessupplychainper- formanceandreinforcestheviewofthedifferentorganizationsthattheirpartners areunpredictableanduntrustworthy.

18.2.2 FromFunctiona一Silosto

貞ntegratedSupplyChainManagement

Thesupplychainmodeldevelopedsofartreatseachfin asaseparateentity･The informationpassedbetweencustomerandsupplierislimitedtoorders,delivery delays,andshipments.OtherinformationiskeptprlVate.Indeed,downstream firmsarequitereluctanttoshareotherinformation,suchastheiractualsalesrate. Iftheirsuppliersknewtheactualcustomersalesrateitwouldbemoredifficult forthefirmtomanipulateorderstogetalargerallocationwhendeliverydelays werehigh.

Toaddresstheseissues,manyfirmshavemovedtointegratethesupplychain fromcustomertorawmaterialssupplier.Thesepoliciesgobynamessuchas EDI(electronicdatainterchange),ECR(efficientcustomerresponse),andVMI (vendor-managedinventory).Thesepolicieshaveenjoyedbroaddiffusioninthe 1990saspartofthegeneraltrendtowardleanmanufacturlngandjust-in-timepoli- cies.Eachattacksadifferentaspectofthesupplychain.EDIreducesthetime delaysandcostsofreplenishmentorderingsothatcustomerscanordersmaller batchesmorefrequently,smoothingthenowofmaterialsordersreceivedbysup- pliers.Otherpolicies,suchasECR,involveadditionalchangesinorderfulfillment, distribution,andtransportationpoliciestoreducedeliveryleadtimes.Thesepoli-

ciesincludethird-partywarehouslng,COntinuousreplenishment,useofmixed truckloadshipping,andsoon.Pointofsale(POS)datacanalsobeelectronically sharedwithsuppliers,eliminatingdelaysanddistortionsintheinfomationsuppli- ersneedtoplanproductionandcapacity.Vendor-managedinventorygoesfurther･

Chapter18 TheManufacturlngSupplyChain 741

UnderVMIthesuppliermanagestheentiredistributionchainanddetermineshow muchtoshiptoeachechelon,eliminatlngtheneedforcustomerstoplaceorders formaterials.6

ReengineeringtheSuppJyChain

Testtheeffectsofdifferentsupplychainintegrationpoliciesusingthetwo-Stage supplychainmodelshowninFigure18-18.Besuretoconsidertheeffectofeach policyonthefollowingVariables:

a.Thetotalamplificationofthesupplychain(theamplificationratioof suppliermaterialdeliveriesrelativetocustomerorders),ameasure ofinstabilityintheoverallsupplychain.

b.Thesupplier'sdeliverydelayandorderfulfillmentratio(measuresofthe supplier'sdeliveryreliability).

C.Theproducerfirm'sdeliverydelayandorderfulfillmentratio(measures oftheproducer'sabilitytoserviceitscustomers)･

d.Anyotherindicatorsyoufeelareimportant,suchasmaterials,WIP,and finishedinventorylevelsatthesupplierandproducer.

TestthefollowingPOlicies･First,testeachpolicylnisolation,keeplngallother policiesandparametersinplace.Ineachcase,explainwhythepolicyworks(or fails)intermsofthefeedbackstructureofthesystem.Whobenefits?Doesone

partnerinthesupplychainbenefitwhiletheothersuffers?Whatconflictsmight thepolicycreate?Youshouldtesttheresponseofeachpolicytoa20%stepIn- creaseincustomerordersandanyothertestInputsyoudesire.

1. SharingPOSdata:Assumethesupplierbasesitsforecastofordersontheac- tualcustomerorderrateiIISteadoftheincomlngmaterialsorderrate.Todoso,

modifytheinputtothesupplier'sforecastofdemandtobeCustomerOrders*Ma- terialsUsageperUnit.

2.EDIandquickresponse:AssumethatbymovlngtOelectronicdatainter- changeandmakingImprovementsintheorderfulfillmentprocessthesuppliercan reducethetimerequiredtoprocess,ship,anddeliverorders.Implementthispol- icybycuttingthesupplier'stargetdeliverydelayby50%.

3. Leanmanufacturing:LeanmanufacturlngPOliciesreducetheamountofin- ventoryafirmrequlreSWithoutcompromlSlngItsabilitytofillordersormeetpro- ductionschedules.Achievingawell-functionlngleanproductionsystemisfar

6simchi-Levi,Kam insky,andSimchi-Levi(1999)discusssupplychainmanagementindetail.

742 PartV InstabilityandOscillation

fromtrivialandrequiresChangesinmanyaspectsofoperations,Productionsched- uling,thelayoutofplantandequlPmentOnthefactorymoor,qualityImprovement andmaintenanceactivity,andothers(seeWomackand及oos1991).Thesupply chainmodeldoesnotindicatehowtoachievealeanproductionsystem.Other modelswouldbeneededforthat.Butitcanbeusedtoexplorehowaleansystem withdramaticallyshortercycletimesmightaffectsupplychainperformance･To modeltheeffectsofasuccessfultransitiontoleanmanufacturlng,considerreduc- tionsinthemanufacturingcycletime(thedelaybetweenproductionstartsand completion),minimum inventorycoverage,andminimummaterialsinventory coverage.Considerthesechangesindividuallyandfわrtheproduceralone,thesup-

plieralone,andforbothfirms.

4.Responsetoleanmanufacturlng:LeanmanufactunnglSmorethanareduction incycletimes.Inadditiontochangesinphysicaldelays,considerhowvarious managementpoliciessuchasthevariousinventoryadjustmenttimesandthesizes ofthesafetystocksmightchangeoncealeanproductionsystemisimplemented.

5.Phantomordersandleadtimegamlng:Supposetheproducerfirmreactstothe unreliabilityofthesupplierbyshortenlngthedelaylnupdatingltSperCeptlOnOf thesupplierdeliverydelay.Whatistheimpact?Why?Whatistheeffectofelimi- natlngleadtimegamlnglnWhichfirmsorderfartheraheadwhensupplierlead timesstretchout?implementthispolicybychangingtheresponseoftheexpected deliverydelaytotheperceiveddeliverydelay.

6.Vendor-managedinventory:Supposethesuppliermanagesthedistributionof materialscentrally.TherearemanyvariantsofVMI.Onesimpletreatmentistoas- sumethesuppliermonitorstheproducer'smaterialsinventoriesandshipsaccordl lngly.Thesupplieristhenresponsibleforensuringtheproduceralwayshasthe materialsneededtostartproductionatthedesiredrateandpaysapenaltyifitfalls short.Howwouldyoumodifythemodeltocapturesuchapolicy?Implementand testyourformulation｡

7.Tryanyotherpoliciesyouwish.Foreach,considerhowthepolicymightbe implementedintherealworldandhowthatchangecanbecapturedinthemodel.

Afterconsideringtheeffectsofeachpolicylnisolation,considertheirinteractions. Inparticular,implementthePo§andEDI/quickresponsepoliciestogetherand thenincombinationwiththeleanmanufacturingPOliciesyouprefer.Howdoesthe responseofthesystemtosharingPo§datachangewhenthesystemisleancom- paredtothebasecase?Why?

UnderwhatcircumstanceswilldifferentpoliciesforimprovingSupplychain performancework?Aretheresituationsinwhichsomeofthecommonlyrecoml mendedpoliciesarelikelytofail?W hy?

Finally,recom endacombinationofpoliciestostabilizethesupplychainand improvecustomerservice.Discussthechallenges丘rmsmightfaceinimplement- 1ngyourPreferredpolicies.Considerinparticularwhichfirmsbearthecostsof eachchangeandwhichreapthebenefits.Howmightthecostsandgainsbeshared amongthepartnersinasupplychain?

Chapter18 TheManufacturingSupplyChain 743

18.3 SysTEMDYNAMiCSINAcTlON:REENGENEERINGTHE SuppLYCHAINnAHJGH-VELOCITYiNDUSTRY7

ThecomputerandelectronicsindustrylSOneOfthemostdynamicanddemanding

industriesintheworldeconomytoday.Competitionisintense.Rapidgrow血,in-

CreaslngcomplexityOftechnology,globalization,andotherchangesposeenor-

mouschallengesforcorebusinessprocessessuchasthesupplychainandproduct

development,Pricesfallatatremendousratewhilespeedandfunctionalitygrow

witheachnewproductgeneration,Productlifecyclesofayearorlessmeancom-

panieshaveonlyafewmonthsinwhichtosellsufficientvolumeofanewproduct

athighenoughmarglnStOgeneratetheprofitsneededforproductdevelopmentand

growth.

"FastGrowthElectronics"(apseudonym;hereafterreferredtoasFGE),the

clientforthissystemdynamicsstudy,isoneofthemostsuccessfulfirmsinthein-

dustry.Inthe5yearspriortOthemodelingprojectthenumberofunitsshipped

grewabout50%/yearandrevenuegrewabout40%/year(revenuegrowthisslower

thanshipmentgrowthbecausecomputerpricesarecontinuallydeclining).During

thisperiodFGE'smarketsharegrewsteadily.Netincomegrewabout60%/year･

18.3.1 InitialProblemDefinition

OnfirstexaminationFGEwasdoingextremelywell･Butbeneaththesurfacestress

wasaccumulating｡RapidgrowthhadstrainedFGE'ssystemsfororderprocesslng,

forecastlng,Productionplannlng,materialsprocurement,andothercoreopera-

tions.Quoteddeliverydatesweretypicallyrevisedmanytimes･Toooftendelivery

commitmentsweremetthroughexpeditingandotherlast-minuteheroics.Asin

manyfirms,quarterlyrevenuetargetsledtoasevere"hockeystick"patternin

whichalargefractionofquarterlyshipmentsoccurredinthelastfewdaysofeach

quarteraspeoplescrambledtomeetthetarget,disruptingWOrkflowthroughoutthe

system.Thesupplychainandcustomerservicechallengewasbroughthomeforce-

fullyinameetingbetweenFGE'stopmanagementandtheCEOofoneofits

largestcustomersatthattime,alargeelectronicsretailchainwhosaid,"You'rethe

bestsupplierwedealwith,butyou'refirstinaraceofpigs."

FGE'sCEOsetaggressivegoalstoexceedworldclassbenchmarksforavar1-

etyofperformancemetrics.Whilethepotentialforimprovementwasgreat,the

challengewasdaunting.EvenasFGEgrewintoaformidableglobalcompany,bar-

rierstoentrywerelowandmanynimblecompetitorsarosetochallengethem｡

Internally,FGE'sgrowthhadoutstrippeditsownsystemsformanagingthe

supplychainandtheorganizationcouldnolongeradequatelycoordinateitsmany

incompatible,overlapplng,andundersizedsystemsandprocesses.Forexample,

7Iamindebtedto"FastGrowthElectronics"andtoMcKinsey&Companyfortheirpermission topresentthiscaseandhelpwithitspreparation.IparticularlythankDamonBeyer(Principalat McKinsey&Co.)andNathanielMass(formerlyaprincipalatMcKinsey&Co.;culTentlySenior VicePresidentatGenCorp)fortheirassistanceinthepreparationofthischapter･Ialsothankthe peopleIinterviewedatFGE.

744 PartV InstabilityandOscillation

productcomplexitywasgrowingexponentially:ThenumberofSKUs(stockkeep- ingumits)increasedbyafactorof35in5years.

Theexistingsupplychain(includingprocessesfororderprocessing,creditap- proval,productionscheduling,productallocation,shipmentsandreturns,demand forecasting,materialsrequirementsplanning(MRP),partsprocurement,expedit-

1ng,Supplierqualification,newproductlaunchplannlng,andproductdevelop- ment)hadnotbeendesignedsomuchasitevolved丘.omahostoflocalsolutions

tolocalproblemscausedbythegrowthandincreaslngCOmplexltyOfthebusiness･ Bytheearly1990S,thesystemwasclearlynolongeradequate･Productlifecycles were5to9months,yetacqulSitiontimesforsomekeycomponentsandmaterials wereover3months.Thedelayswereworsenedbyhightumoverinthesupplier

baseastechnologychanged.Compoundingtheprocurementdelayswerelongde- laysinFGE'sinternalplannlng,forecasting,andpurchasingsystems.Often2to

3monthswererequiredtoprepareandreviseproductionplansandorderthere- quiredcomponentsfromsuppliers.Productionplannersthereforehadtoforecast demandfornewproductswellinadvanceoftheirintroductiontothemarketand,

moreimportantly,hadtorampdownpartprocurementandproductionwellbefore theendoftheproduct'slife,oftenjuStaSSaleswereheatlnguP･Yet,asistypicalin suchhigh-velocltyindustries,theaccuracyofdemandforecastsovertherequired

planninghorizonwaslow,withtyplCalerrorsof50%tolOO%･Besidestheusual sourcesofuncertaintysuchasthestateoftheeconomy,forecastaccuracyislow becausethesuccessofaparticularproductdependsonitspriceandperformance

relativetotheprlCeandperformanceofcompetingPrOducts･Delaysofevenafew weeksintheintroductionofacompetitor'Slatestofferingwillsendcustomersyour

way,perhapsturnlngOneOfyourweaksellersintoanunexpectedsuccess,while introductionofcompetitorproductsearlierthanexpectedcantumyourstrongcon-

tenderintoanalso-ran.Predictlngthedatesofyourownproductintroductions 3monthsinadvanceisdimcultenough;anticIPatlngthemovesofthecompetition isevenharder.

Productdevelopmenttimesoftensignificantlyexceededthelifecyclesofthe

productsthemselves.Advanceddevelopmentteamswerealwaysdesignlngprod- uctsintendedtoreplaceproductsthathadn'tyetbeenintroducedtomarket･De-

laysinproductintroductioncouldleadtosituationswhereaproductwasphased outbeforeitssuccessorcouldbebuilt,leadingtogapsintheproductline.Though

productlinegapsweretoofrequent,OnaverageFGEwascaughtwithanunac-

ceptablelevelofexcessinventoryattheendoftheproductlifecycle･Becauseof thehighrateoftechnologlCalchange,oldproductshavelowsalvageorremain- deringvalue,forcingthesalesforcetofocusagreatdealofattentiononmovlng

oldproducttoavoidtheaccumulationofso-Calledsludgeinventoryandcostly write-downs.

UnanticIPatedinteractionsamongdifferentfunctionsandbetweenFGEandits customerscontributedtoforecasterrorandthebuildupofobsoleteinventory.The

retailchainsandcorporateresellersthatconstitutedFGE'smaindistributionchan- nelstyPicallyoperatedonverythinmargins.Oftenthefinancedepartmentwould

placecustomerordersoncredithold,delaylngtheproductionplannlngandpro- curementprocess.Astheendofthequarterapproached,however,financewould comeunderpressuretoliftthecreditholdssoproductgroupscouldmeettheir

Chapter18 TheManufacturlngSupplyChain 745

TABLE1812 Noc一earroot

causesorhigh leveragepolicies emergedfrom traditional

analysIS.

quarterlysalesobjectives.Distributionchannelpartnersquicklylearnedtowith-

holdtheirordersuntillateinthequarterinthehopeofreceivlngmorefavorable

pricesOrCreditterms･LaterecelptOfordersincreasedordervolatility,decreased forecastaccuracy,furtherstrainedtheprocurementsystem,anderodedtrustbe- tweenFGEanditscustomers.

SinceFGEprovidedfullprlCeprotectiontotheirchannelpartners,resellers

andretailershadstrongIncentivestoorderaggressivelyandcouldfreelycancelor-

dersaswell.Theresultingdemandvolatilitymadeithardertodeliverreliablyto

thechannel,Strengtheningbeliefsonbothsidesthattheotherwasunreliable｡

Therewasnolackofideastoaddresstheseproblems(Table18-2).Eachpol-

icyhaditsadvocates,wassupportedbyacertainlogic,andsuccessfulexamplesof

eachcouldbefoundinthebusinessliterature.Theproblemwasnotgeneratlng

ideasbutevaluatlngWhichideasmightwork,howtheymightinteract,which

wouldhavethehighestleverage,andwhichshouldbeimplementedfirst.Many

policiestrlggeredinternalconflict:Shrinkingprocurementleadtimesconflicted

withproceduresforsupplierqualificationandcomponentqualityassurance;cur-

tailingexpeditingdecreasedmarketingflexibility;freezingProductintroduction

datestopreventholesintheproductlinestressedtheproductdevelopmentorgani-

zation･MonthsoftraditionalanalysisbyFGEanditsconsultantsrevealednoob-

viouspolicyrecommendationsandmadeithardtomotivatetheneedforchange.

Afterall,thecompanywasundeniablysuccessRll.Someintheorganizationargued

awayanyparticularpastproblemwithstatementssuchas"WewereJustgrOWlng toofast,""Thatwasjustabadexample...lItwasthe]worstcase,"or"Wesolved

thatonealready."Paralysisthreatened.

KeyProb一ems

Longde一iverytimesandpoordeliveryreliability

Surplusinventory

Lowpredictabilityofdemand

Product=negaps

Quarterlyvolatility

SuggestedPolicies

oDramaticallycutrestaglngdelaysforlongleadtimematerials

oCutmonthlyplannlngCyc一ebyover80%

olmprovematerialpositionmgatnewproductintroduction

olmprovelaunchpredictab=ty

.fncreasecomponentcommonality ｡Getreaトtimedemand/salesinformation

olmprovedemandforecastaccuracy ･Buildtoorder

｡Resolvecreditholdsearlier

olnnovatewithmanufacturlngCeHs Source:McKinsey&Co.

746 PartV InstabilityandOscillation

18.3.2 ReferenceModeandDyr!amicHypothesis Atthispolnt,StimulatedbyseniormanagersatFGE,theMcKinseyteamworking toreenglneerFGE'ssupplychainturnedtosystemdynamics.Themodelwasde- velopedbyanexperiencedsystemdynamicspractitioner,NathanielMass,working inclosecollaborationwiththeMcKinseyandclientteams.Buildingonthedataal- readycollected,themodelingteamspentabout2weeksinterviewlngVarious membersoftheclientorganization,includingpurchasingmanagers,materials planners,andothersresponsibleforkeydecisionsinthesupplychain.Theteam alsoheldseverally21dayworkshopswithkeydecisionmakersfromthevarious supplychainfunctionstoelicitinformationneededtoformulatethemodel.These initialmeetlngSfocusedontheproblemcharacteristicsdiscussedabove:longand variabledeliverytimes,longdelaysinsupplychainresponse,quarterlyvolatility, financialpressuretoreduceobsoleteinventory,etc.Theteamfoundthatexcessin- ventoryattheendofproductlifewasasevereproblemwhethertheproductin questionwasaslowmoverorahotproductwhosesalesgreatlyexceededinitial expectations.Thislatterresultwasunexpectedandcounterintuitive.

Understandingthesourceofexcessinventoryforslow-movlngproductsis straightforward.Salesofsuchaproduct,forwhateverreason,fallshortofthefore-

castsusedtodetemineinitialbuildvolumesandmaterialscommitments.Anatural

reluctancetoreducetheforecastsevenassalesfellbelowexpectations,coupled withlonglagsintheresponseofthematerialsplanningandproductionsystem, causedexcessinventoriestoaccumulate.

Theaccumulationofsurplusinventoryforhotproducts,however,wasdifficult tounderstand.Howlsitpossibletoaccumulatesurplusinventoryforaproduct whosesalesgreatlyexceedexpectations,aproductwhichisflyingofftheshelves, aproductyoucan'tmakefastenough?Figure18-19ShowsthetyplCalbehavior observedforahotproduct,ShowinghowinitialbacklogsleadtorestaglngOfpro- ductionandthebuildupofexcessinventory.Figure18-20Showsacausaldiagram capturlngthedynamichypothesistheydevelopedtoexplaintheinventorybuildup.

Priortoproductintroduction,FGEdevelopsinitialsalesforecastsandreceives initialordersfortheproductfromthedistributionchannel.Thechannelpartners adjusttheirordersuntilthenumberofunitsonorderwiththemanufacturer(the channelbacklog)equalsthechannel'sdesiredorderbacklog,formingthebalanc- ingSupplyLineControlloopちl｡

Themanufacturerusestheinitialsalesforecastsandorderbacklogstocommit toaproductbuildscheduleandinitialstaglngOflongleadtimecomponents.When aproductturnsouttobeahotseller,customerpurchasesrapidlydepletechannel inventories.ThechannelpartnersmustthenordermorefromFGE.Theseunex- pectedlylargeorderssoondepleteFGE'sinventories,andshipmentsfallbelowre- quirements(thebalancingAvailabilityloopB2constrainsshipmentsbelowdesired levels).Theproductisputonallocationandthedeliverydelayexperiencedbythe channelincreases･Further,asshipmentsfallbelowrequlrementSthepredictability ofdeliveriesalsofalls-Channelbuyersandpurchasingagentsspendagreatdeal oftimetrylngtOgetmoreproductandaccurateestimatesofdeliveryquantitiesand timingfromtheiraccountmanager.Thechannelpartners,increaslnglydesperateto getmoreofthehotseller,reacttothelongleadtimebyOrderingAhead:When

Chapter18 TheManufacturlngSupplyChain

FIGURE18-19 Typicaldynamics ofahotproduct

Initialscarcity 一eadstophantom ordersasthedis- tributionchannel

reactstorislng leadtimes.The

productionsystem respondswitha Tagtothesurgein backorders.Asthe buildrateand

shipmentsrise, leadtimefa"S,

leadingtocancel- lationofphantom orders.Laggedre- sponseofthesup- plychaincauses excessinventory toaccumulateas

thebacklogof channe一orders

collapsesbefore thebuildratecan

berampeddown.

LJt u O M JS t!u n

747

deliverytlmeSStretchoutfrom,say,2to4weeks,血esupplylineofproductonor-

dermustgrow血.om2to4weeks'worthofexpectedsales･Thebacklogrisesstill more,furtherincreasingexpectedleadtimeandcauslngthechannelpartnerstoor-

derevenmore(reinforcingloopRl)･Further,asdeliveryreliabilityfalls,channel purchasingmanagersreactbyOrderingDefensively,increaslngtheirdesiredsafety stocksandboostlngthebacklogstillmore,whichfurtherreducesdeliveryreliabil-

1tyandclosesthereinforcingloopR2･Theeffectofthesetwopositivefeedbacks istocreateasurgeof"phantomorders"forhotproducts,ordersplacedinreaction tothegrowingSCarCltyOftheproduct.

FromtheperspectiveofFGE'schannelpartnersthisbehaviorisentirelyratio- nal.Whenahotproductbecomesscarce,eachresellerandretailermustcompete againsttheothersforalargerallocation.Wh enthemanufacturerinformsthemthat

ahotsellerisgolngOnallocationeachresellerrespondsbyorderingmore血anit reallyneedsinanattempttogetalargershareofthelimitedpieofproduction･The twopositivefeedbackscausedbyOrderingAheadandOrderingDefensivelymean

748 PartV InstabilityandOscillation

FIGURE18-20 CausaHoopdiagramshowinghowhotproductsgeneratesurplusinventory

+/w LeadTime

ま三二＼ ~＼一ミミ

Restaging ofRaw

AT･･ OrderAhead

Delivery Predictabilit

A亘･

Control Channel Orders

Channe一 Desired

Materials +

Source:AdaptedfromaMcKlnSeyandCo.dlagram.Usedwithpermission.

Backlog

が一//● +

普 -＼ customer Purchases

thatinthenearterm,reductionsinsupplyactuallyincreasedemand,worsenlngthe apparentshortage.

FGE,likemanysuppliers,Couldnotdistinguishrealordersfromthephantom ordersplacedinresponsetoproductscarclty｡Pointofsaleinformationonpur- chasesbyfinalcustomerswasnotwidelyavailableandresellersandretailerswere

reluctanttosharetheirsalesdataastheybelieveditwouldreducetheirabilityto controltheirinventoriesandhedgeagalnStVariabilitylnproductavailabilityby manlpulatingtheirorders.Assalesofahotproductledtoshortages,Channelorders

wouldrisefarabovefinaldemand,butthecustomers,ifasked,wouldinsistthey neededeveryunittheyordered,andmore,tomeettheballooningdemand.

Facedwithahugesurgeinorders,FGE'smaterialsplannlngandproduction systemwouldstraintorespond,reorderingcriticalcomponentsandexpeditingpro- duction.Despltetheseheroics,revislngProductiontargets,restaglngPartsandma-

terialsinventories,andassemblingtheproducttaketime(notethedelaysinthe linksbetweenchannelbacklogandthebuildrate).

Eventually,shipmentstochannelpartnersincreaseandthedeliverydelayex-

periencedbythechannelfalls.Retailersandresellersfindtheynolongerneedto ordersofaraheadandcanreducetheirorderbacklog.Soontheproductgoesoff

allocationandchannelpartnerscanreadilygeteverythingtheyorder. Assoonascustomersrealizethattheproductisnowfullyavailablewithshort

leadtimestheycanceltheremainlngphantom orders,shrinkingthebacklog. Further,oncetheycanquicklyandreliablyrestocktheirshelvesthereisnoneed

forthemtocarrydefensiveinventory,soordersfallevenfurtherastheyliquidate theirsafetystocks.ThereinforcingfeedbacksRlandR2nowreverse:Rising

Chapter18 TheManufacturlngSupplyChain 749

availabilityreduceschannelorders,shrinkingthebacklog,reducingleadtimesand increasingdeliveryreliability,andleadingtolowerandlowerorders.Theswitch fromtheviciouscycleofdeterioratlngOrderfulfillmentandstilllargerbacklogsto theself-reinforcingcollapseofthebacklogstartsataboutthepointWhereproduc- tionhasrisenenoughtomatchtherateatwhichnewordersa汀ive･Newproduc- tionplansandmaterialsordersareslashedasproductinventorybuilds,butthelong planningdelays,alongwithcommitmentstosuppliers氏)rmorecomponents,mean productioncontinuesforsometime.Thelaggedresponseofthesupplychain leavesthemanufacturerholdingamountainofexcessinventoryattheendofthe product'slifTe.

18.3.3 ModelFormu一ation

lnitialmodeldevelopmenttookabout2weeks.Theteampresentedtheinitial modeltoFGE'sseniormanagementteam,includingtheCEO,rightaway.The modelwaspresentedinaworkshopformat-Seniormanagerscouldsuggesttests andpoliciesthatwererunim ediatelyanddiscussedonthespot,helpingtobuild theirunderstandingofandconfidenceinthemodel･

Overthecourseofthenextmonththeyrevisedthemodelinresponsetothe crltlqueStheyreceived.Ateachstagetheyreviewedtheinterimresultsinwork- shopswiththeseniormanagementteam,oftenincludingtheCEO.Ineachthe modelwasrunlivewithFGE'sexecutivessuggestlngtestsandpolicies.Mostof thesecouldbesimulatedanddiscussedduringtheworkshop;Othersrequired changesinmodelstructureandwerereportedatthenextmeeting.

ThemodelfocusedonthedynamiccomplexityofFGE'ssupplychain,notthe detailcomplexity.TherewasnoattempttorepresenteverySKUintheproduct line.Instead,themodelfocusedontheinterdependenciesandfeedbackscreatedby thebehavioroftheactors,particularlyinteractionsbetweenthedistributionchan- nel,FGE,anditssuppliers.Thefinalmodeltrackedarepresentativeproduct throughitslifecycle.ThethOusandsofdifferentcomponentsandmaterialswere groupedintosevencategories,distinguishedbytheircosts,leadtimes,andother attributes.Themodeloftheproductionandassemblyprocesscapturedthecom- plexitycreatedbymultipleconfigurationoptlOnSbutdidnotrepresenteveryprod-

uctvariation.Themodelalsoincludedtheintroductionofthenextgeneration producttocapturethedynamicsofproducttransitions･Themodelcontained roughly500stocks,orstatevariables,renderingtherichdynamiccomplexityOf thesupplychainwithsufficientfidelityforthepurposewhileremainlngaman- ageablesize.

18.3.4 TestjngtheMode! Theteamtestedthemodel'sabilitytoreplicatethehistoryoftwoactualproducts, oneslowmoverandonehot.Thepurposeofthistestwasnotmerelytoexamine thestatisticalfitbetweenthemodelanddatanorwasittoevaluatetheforecasting performanceofthemodel.TheFGEmanagersweresophisticatedmodelusersand knewthatreplicationofhistoricalfitaloneisaweaktest.Themodelhadtobeable toreplicatethepatternsobservedforbothtypesofproductswithoutanychanges toitsstructureortheparameterscharacterizlngtheorderprocesslngSystem.Only

750

FlGURE1812l Simulationsof thefullmode一

comparedto historyforsLow-

movlngandhot products

Top:Simulation ofaslow-movlng product.Salesfall shortofinitialpro-

jections;backloglS rapidlydepleted andexcessinven-

toryaccumulates.

Bottom:Simu一ation

ofahotproduct. Strongsaleslead tohugeback一og, longdeliveryde-

一ays,andphantom ordersbydistri- butionchannel.

Whenrestaged productioneventu- allyshrinksdeiiv- erytimes,channel ordersarecan-

celed,leadingto excessinventory.

Timeperiodsand ve什icalscaJes

disguised.

PartV InstabilityandOscillation

theassumedpatternoffinaldemandcouldvary,fromthatofaweaksellertothat

ofastrongseller.Themodelhadtogeneratetherightbehaviorfortheright

reasons,withouttheuseoffudgefactors.Figure18-21showssimulationsofthe

fullmodelcomparedtotheactualdata(theverticalandtimescaleshavebeen

disguised).

Themodeltracksthebehavioroftheslow-movlngproductwell,showlngthe

depletionofthebacklogandtransitiontosludgeinventorylnthemiddleofthepro-

jectedproductlifecycle.Atthetimethesimulationwasmade,theslow-movlng

producthadalreadybeenwithdrawnfromthemarketandtheactualdatawere

available.Ⅰncontrast,thehotproductwasstillonthemarketatthetimeofthe

analysis.Indeed,atthetimethesimulationwasmade,therewasalargebacklogof

unfilledorders(netinventorywassignificantlynegative)andtheleadtimewas

100

0 -25

-50

･75

-100

1 2 3 4 5 6

Source:McKinsey&Co.

Chapter18 TheManufacttlrlngStlpplyChain 751

muchlongerthannormal.Themodeltrackedthebuildupofthebacklogreason-

ablywell.Moreimportantly,themodelsuggestedthatthebacklogwouldsoon shifttoalargeexcessinventory,CountertotheexpectationsofmanylnSidethe company.Shortlyafterward,thebacklogcollapsedandthefirmwasleftwitha largest叩lusinventory.Theabilityofthemodeltoreplicatethesetwoproducthis- torieswithoutextensiveparameteradjustmentshowedFGE'smanagementthatthe sourcesofthesurplusinventoryproblemweredeeplyembeddedinthestmctureof thesupplychainandwerenottheresultofbaddecisionsmadebyparticularman- agers.Themodelthusfocusedattentiononredesignlngthatstructureratherthan thedecisionsofthepeopleinthesystem.

Thereplicationofpastexperiencewasnottheonlytestofthemodel.Itisgen- erallyqulteeasytOtuneamodeltofitaglVenSetOfdata.Buildingconfidenceina modelinvolvesamuchbroaderseriesoftests,bothofthestructureanditsre-

sponsetoawiderangeofcircumstances,notonlythelimitedrangeofhistorical experience(Seechapter21)｡

18.3.5 PoEicyAnalysis

TobeginpolicyanalysistheteamfirstsimulatedeachmajorPOlicyInitiativeiniso-

lation,Calculatingthechangeinlifecycleprofitability.Contrarytotheexpecta- tionsofsome,improvlngforecastaccuracyorproductlaunchpredictabilityhad onlyaverageimpactandreducingtheseventyofthequarterlyhockeystickhada weakeffect.Thestand-aloneanalysisshowedthehighleveragepolnttObereducl lngthedelaysintheresponseofthesupplychaintochangesindemand.Buthow wouldthesepoliciesinteract?Mighttheynotinterferewithoneanotherorsuffer diminishingreturns?Simulationsshowedthatjointlyimplementlngmaterialslead timereduction,planningCycletimereductions,andabuild-t0-Orderpolicygener- atedasubstantialsynergy.Thetotalimpactexceededthesumofthebenefitsofthe individualpolicies.

ThesourcesofsynergycanbeseeninthecausaldiagramshowninFigure 18-22.Thecycletimereductionpolicies(showninboxes)createsynergybyre- ducingleadtimessothereinforcingfeedbackscreatingPhantomordersoperatenot asviciouscycles,astheyhadbeen,butasvirtuouscycles,progressivelyandcu一 mulativelyimprovlngSystemPerformanceandprofitability.Asfasterorderfulfi l l -

mentandsupplychainresponsereducetheincidenceofinitialshortages,phantom ordersfallandcustomersrequirelessdefensiveinventory,stabilizlngChannelor- ders.Thelessvolatilethechannelorders,themoreaccurateFGE'sdemandfore-

castsbecome,easingtheburdenonsuppliersandleadingtofewerinstancesoflate productrestaglng,fewerrawmaterialshortages,andmorereliabledeliveries-re- ducingphantomordersstillmore.Further,reductioninlaterestaglngOfmaterials andcomponentsleadstohighercomponentqualityandlowerrawmaterialsand expeditingcosts.Lessexpeditingandfirefightingtogetthecurrentproductoutin- creasethetimeavailabletoplantheintroductionofthenextgenerationproduct,re- ducinglaunchdelaysandtheriskofholesintheproductline.Moretimelynew productintroductionpreventsthebuildupofphantomordersatthestartofthenext product'slife,reducingdeliveryleadtimesfurther.Andsoon.

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FlGURE18-23 Buildupofsurplus inventorywas self-reinforclng.

Financialpressure toreduceinven-

torybuHdup一edto moreconservative initialmaterials

staglng,lnCreaSlng thechanceof

shortagesthat leadtophantom orders,aggressive laterestaglngOf materials,and buildupofeven moresurplus stock,ina viciouscycle.

Chapter18 TheManufacturingSupplyChain

Financial

/RePirnuevcseesnuf:erryiSu㌔ FnitiaIRaw Material

Commitments

去- Likelihood ol=Initial Shortages

耕一/

まき･

Surp一ushventory SupplyChain Overreaction

HiiZI Phantom

753

Ordering +

Overtime,effortstoreduceinventoryhadactuallymadetheproblemworse, throughthefeedbackshowninFigure18123･Asthebuildupofsludgeinventory worsenedfinancialperformance,managersthroughouttheorganizationcameun- derintensepressuretoreduceinventorycosts.TheyreactedbyreducingInitial staginglnVentOriesaseachnewproductwasplanned.CuttingInitialbuildcom- mitmentswasrationalfromtheirperspectivebecausetheyvieweddemandtobe exogenousandunpredictable.Fromthatperspective,smallerinitialbuildvolumes reducethelikelihoodanyglVenproductwillbeaslowmover.However,demandis notexogenousbutisstronglyshapedbyFGE'sownbehavior:Thelowertheini- tialmaterialscommitments,thegreaterthechanceofinitialshortages,trlggerlng phantomordersfromcustomersandforcingtheorganizationtoengageinexpen- sivelaterestaglngOfcriticalmaterials-culminatlnglnevenmoreSurplusinven- toryandstillmorefinancialpressure.Unchecked,thispositivefeedbackcouldact asadeathsplral.Akeyinsightemerglngfromthemodelwasthatlargerinitial staglngOfcriticalmaterialscouldactuallyreducethebuildupofsludgeandlower lifecycleinventorycosts.

18｡3｡6 8mp日emem竜a竜iom:Sequem地目Debo竜骨Eemeckjmg Themodelanalysisidentifiedanumberofhighleveragepoliciesandshowedhow theywouldgeneratesubstantialsynergyfromJOlntimplementation.Thepolicy recommendationswouldrequireCOmPleteredesignoftheentireorderprocessing, productionplannlng,loglStics,suppliermanagement,andproductionsystems-a hugeundertakingrequlrlngaPhasedapproach.Toputtheinsightsemergingfrom themodelintopractice,themodelingteamworkedwiththeclienttounderstand theoptlmalsequenclngOfpolicylnitiatives.Muchofthemanagementliterature suggeststhatimprovementactivitiesshouldfocusonfindingandrelaxingthecur- rentbottleneckinhibitingthethroughputofanyprocess(see,e･g･,Goldrattand Cox1986)AFocusingimprovementeffortonthecurrentbottleneckimmediately booststhroughp叫 whilee批)rttoimprovenonbottleneckactivitiesiswasted.The

754 PartV InstabilityandOscillation

modelingteamrealized,however,thatinthehigh-growthenvironmentofthecom-

pute〟electronicsindustry,relaxlngOnebottlenecksimplyenablesgrowthtocon-

tinueuntilanewpartoftheprocessbecomesthebottleneckandthreatensthe

healthoftheorganization.ThepaceofexpansionandtheintensltyOfcompetition

aresogreatthatwaltlngforeachbottlenecktoemergebeforeattackingltCOuld

slowthegrowthofthecompanyanderodeitscompetitiveness･

Theteamusedthemodeltoexploretheimpactofdi艶rentimplementationse-

quences.BysimulatingtheeffectofimplementlngOnePOlicy,saymaterialslead

timereduction,theteamcouldobservewhenandhowgrowthimproved,puttlng

evenmorestressontherestofthesystemandcreatlnganewbottleneck,saythe

MRPcycletime.Correctlngthatbottleneckwouldenablestillmoregrowth,until

thenextbottleneckemerged,saytheassemblyandbuildcycletime･Byuslngthe

modeltoanticIPatetheshiftingsequenceofbottlenecks,theteamwasabletode-

signanimplementationplantoredesigneachaspectofthesupplychainbefわreit

couldchokeoffthroughputandslowgrowth(Figure18-24)･

Thesequentialdebottleneckinganalysiswasacriticalinputtothedetailedim-

plementationplanforthesupplychainredesigneffort,amassiveprojectspanning

3yearsandinvolvingatitspeakover150full-time-equlValentFGEprofessionals

andanarmyofsystemsintegration,manufacturlng,andotherconsultants･

FIGURE18-24 SequentialdebottEenecking

ThebottomcurveshowshowtradlLlionaJmanagementpracticesfocusonsolvlngthecurrentproblem. Growthresumes,causlnganewbottlenecktoemerge.Growths一owsagain･Thetopcurveshows growthwhenthemodeHsusedtoanticIPatetheemergenceofbottleneckssoprocessredesrgnefforts caneliminatethembeforetheybecomebinding,enablingfastergrowth,lowervolatility,andgreater va一uecreation.

ln d LJ6 n oJ u ト

S S a 3 0J d

- iiiiiiiiiiiiiiiiiiiiiiIG

I- - ---- - -I l l-I-------

A=二･二二一:'i -__∴ . ∴ Time

Source:McKInSey&Co･

Chapter18 TheManufacturlngSupplyChain

TABLE18-3

Projectresu一ts

755

18.3.7 Results

Just3yearsafterthestartoftheprojecttheresultsweresubstantial･Asshownin nlble18-3,FGEdramaticallyreduceditssupplychaincycletime,slashedinven- torythroughoutthesupplychain,shorteneddeliveryleadtimes,andimprovedde-

liveryreliability.Theseeffortsgeneratedmorethan$3billionofbenefitby1997. Themodelingprocessalsochangedthethinkingofmanyofthepeoplein-

volved.Atthestartofthesystemdynamicsproject,manyOftheconsultantsen-

gagedinthereenglneerlngeffortwerehighlyskeptical･Bytheendoftheproject theyhadbecomeenthusiasticadvocatesfortheuseofsystemdynamicsinsuch

complexprojects.FGEitselfwentontodevelopothersystemdynamicsmodelsto considerissuessuchasproductdevelopmentandoverallgrowthstrategy･

Ordertoshipmentcycletimebytheendof1996was60%below1993Ql. Backorderswere60%be一ow1993Ql.

Majorproducttransitionsimprovedby$200millionmargin.

lnventorycarryingcostsfeHmorethan$600miHionbetween1995and1997

lnventorytumsincreasedfromabout4peryeartomorethan12peryearby 1997Q4andto16peryearby1999･

$3bi"ionincashwasgeneratedfromtheproject.

Source:FGEandMcKlnSey&Co.

18.4 SuMMARY

Supplychainsarefundamentaltoawiderangeofsystems･Thischaptershowed howsupplychainsarebuiltupfromlinkedinstancesofthestockmanagement structure.Themodelwasusedtoexplainwhysupplychainsinawiderangeofin-

dustriesexhibitoscillation,amplification,andphaselag･Thesefeaturesofsupply chainbehaviorariseevenwhenallactorsinthesupplychainarelocallyrational

andmanagetheirpieceOfthesystemwithdecisionrulesthat,inisolation,gener-

atesmoothandstableresponsestounantlClpatedshocks･ Intermsofthemodelingprocess,themodelwasdevelopedinstagessothat

thesourcesofamplification,phaselag,andinstabilitycouldbeidentified.Simpli-

fyingassumpt10nSWererelaxedoneatatime.Youshouldbuildyourmodelsinthis iterativefashion,beginnlngWithasimpleformulation,testlngitthoroughly,and addingadditionalstructureonlywhenyoufullyunderstandthemodel.

FF主詑IE_-･昌も｡FS嘩P呈ざ∈iliai訳孟訳d書鮎 ⑬訂畳g畳弧⑬官爵覗S畳neSSCye畳es

Theexternaltheoriesfindtherootofthebusinesscycleinthefluctuationsof somethingoutsidetheeconomicsystem-insunspotsorastrology,inwars, revolutions,andpoliticalevents,ingolddiscoveries,ratesofg710Wthofpopu-

lationandmigrations,discoveriesofnewlandsandresources,inscientlfic discoveriesandtechnologicalinnovations.

Theinternaltheorieslookformechanismswithintheeconomicsystem itselfwhichwillgiverisetoself-generatingbusinesscycles,sothateve77 expansionwillbreedrecessionandcontraction,andeve7Tcontractionwillin

turnbreedrevivalandexpansioninaquasi-regular:rePeatlng,never-ending chain.

-PaulA･Samuelson(1973,p.257).

Chapter18usedthestockmanagementstructuretomodeltheflOwofmaterial throughamanufacturlngSupplychain.Thischapterappliesthestockmanagement structuretothehumanresourcesupplychain.Thehumanresourcesupplychainis thenlinkedwithamanufacturlngSupplychain,showinghowproductionschedull lngandhiringpoliciescaninteracttogenerateinstabilityandoscillation.Chaト lengesinviteyoutoexplorepoliciestoenhancestabilityandresponsivenessand extendthestructuretoincludetrainlngandon-theJoblearnlng.Thechaptercloses byconsideringhowinteractionsofinventorymanagementandthelaborsupply chaincontributetobusinesscyclesintheeconomyasawhole.

757

758 PartV instabilityandOscillation

19.1 THE邑_ABORSuppLYCHAIN

ThemanufacturlngSupplychainmodelsinthepreviouschapteromittedlaborand

capital,implyingtheseresourceswerealwaysampleorinfinitelyflexible.Neither

assumptlOniscorrect.Thissectionadaptsthestockmanagementstructurede-

velopedinchapter17torepresenttheprovisionoflabor(Figure19-1showsthe structure)｡

19.1.1 StructureofLaborandH岳ring

Tobegin,aggregatethefirm'slaborforceintoasinglestock,whichisincreasedby

thehiringrateanddecreasedbytheattritionrate:

Labor=INTEGRAL(HiringRate-AttritionRate,Laborb) (19-1)

TheattritionrateincludesvoluntaryqultSandretirements.Fornow,excludethe

possibilityoflayoffs.Theattritionratecanbemodeledasafirst10rderprocessin

whichemployeesremainwiththe丘rmfortheAverageDurationofEmployment:

AttritionRate-Labor/AverageDurationofEmployment (1 9-2)

FIGURE19-1 Thestockmanagementstructureadaptedtohumanresources

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 759

Theaveragedurationofemploymentisstronglyaffectedbythestateofthejob

market･WhentheeconomylSrobustandunemploymentislow,workerscanread-

ilyfindbetteropportunities,sovoluntaryattritionrises.Duringrecessions,few

goodjobsareavailableandtherearemanymoreunemployedcompetingforthem.

Workersluckyenoughtohavejobstendtokeepthemandvoluntaryattritionfalls.

Inamodelofasinglefirm,thestateoftheeconomylSeXOgenOuSandtheaverage

durationofemploymentmightbeassumedconstant･lInamodelofareglOnalor nationaleconomy,however,theaveragedurationofemploymentandthelabor

marketmustbemodeledendogenously.

Thefirmcannotinstantlyhiretheworkersitneeds.Hiringtakestime:Posi-

tionsmustbeauthorizedandvacanciesmustbecreated.JobopenlngSmustbe

postedandadvertised,followedbyinterviews,backgroundchecks,trainlng,and

otherdelays･Inthesimplestmodelallthesedelaysareaggregatedintoaslngle stockofvacancies.Vacanciesareincreasedbythevacancycreationrateandde-

creasedbythevacancyclosurerate,whichisequaltothehiringrate.Thestockof

vacanciesisthesupplylineofordersforworkersthathavebeenplacedbutnotyet

filled･TheTimetoFillVacanciesrepresentstheaveragedelaybetweencreatlng

andfillingavacancy.

HiringRate-Vacancies/¶metoFillVacancies (19-3)

Vacancies

=INTEGRAL(VacancyCreationRate-VacancyClosureRate,Vacanciesb) (19-4)

VacancyClosureRate-HiringRate (19-5)

NotethatthereisnodirectphysicalflOwfromthestockofvacanciestothelabor

force･Thelaborforceisastockofpeople,whilethestockofvacancies,though

measuredinpeople,isinfomation.Inthissimplemodel,thesourceforthehiring flowisassumedtobeoutsidetheboundaryofthemodel(andhencenevercon-

strainsthehiringrate)･Inreality,thepoolofunemployedorpotentiallyavailable

workersoftenlimitshiring.Inthesecases,thedelayinfillingvacancieswillbe longerandvariable.

Becausethelabormarketisnotmodeled,thevacancycreationrateissetequal

tothedesiredvacancycreationratebutconstrainedtobenonnegative(vacancy

cancellationwillbeaddedlater).Thedesiredvacancycreationrateisformulated

uslngthestandardstockmanagementstructure:

VacancyCreationRate-MAX(0,DesiredVacancyCreationRate) (19-6)

DesiredVacancyCreationRate -DesiredHiringRate+AdjustmentforVacancies

(19-7)

lEvenwhenthestateoftheeconomylStakentobeexogenous,factorsinternaltothefirmsuch asmorale,compensation,andworkloadmaystillcausetheattritionratetovaryslgnificantlyand wouldhavetobemodeledendogenously.

760 PartV InstabilityandOscillation

Thefirmseekstoclosethegapbetweendesiredandactualvacanciesoverthe

nmetoAdjustVacancies:

AdjustmentforVacancies -(DesiredVacancies-Vacancies)/TimetoAdjustVacancies (1918)

Thedesiredlevelofvacanciesisthenumberthatwillyieldthedesiredhiringrate

giventhefirm'sbeliefabouthowlongittakestofillaposition.Desiredvacancies cannotbelessthanzero:

DesiredVacancies

-MAX(0,ExpectedTimetoFillVacancies*DesiredHiringRate) (1919)

Realistically,beliefsabouttheexpectedtimerequiredtofillpositionsadjustslowly

tochangesintheactualtimeaslabormarketconditionschange.Theexpectedtime

tofillvacanciescouldbemodeledusinganinformationdelay,similartothegrad-

ualadjustmentofperceiveddeliverydelaytoactualdeliverydelayinthemanu-

facturlngmodeldevelopedinsection18.2.Inthissimplemodel,theExpected

TimetoFillVacanciesisassumedtoequaltheactualtimetofillvacancies.

ExpectedTimetoFillVacancies-AverageTimetoFillVacancies (19-10)

ThefirmattemptstoreplacethoseemployeeswholeaveandeliminateanydisI

crepancybetweenthedesiredandactualnumberofworkers:

DesiredHiringRate-ExpectedAttritionRate+AdjustmentforLabor (19-ll)

ExpectedAttritionRate-AttritionRate (19-12)

AdjustmentforLabor-(DesiredLabor-Labor)/TimetoAdjustLabor (19113)

Inthissimplemodel,expectedattritionisassumedtoequalactualattrition.Like

theexpectedtimetofillvacancies,itislikelythatthereissomedelayinthere-

sponseoftheorganizationtochangesinthequitrate･Inamorecompletemodel

theexpectedattritionratewouldadjusttotheactualattritionratewithadelay.

19.1.2 Beh･3VhyoftheL抽orSupplyChain

Totestthemodel,thedesiredlaborforceisexogenous･Theparametersdepend

stronglyontheindustryandskilllevelofthejob.Forunskilledworkersinthefast

foodindustrythetimetofillvacanciesmightbeadayortwoandtheaverage

tenureofemployeesmaybeafewweekstomonths.Recruitinghighlyskilleden-

glneerSCantakemonths,andtherecruitlngCycleforMBAstudentsbeginsinthe

fallforjobsthatstartaftergraduationthefollowlngSPrlng.

Forillustration,theaveragedurationofemploymentisassumedtobe100

weeks(2years)andtheaveragetimetofillvacanciesisassumedtobe8weeks.

WithanarbitraryInitiallaborforceof1000people,theseparametersdefinean

equilibriumwithqultSOf10people/weekand80vacanciesatanyglVentime.The

firmisassumedtoadjustthenumberofvacanciestothedesiredlevelovera4-

Weekperiod,reflectlngdecision-makingandadministrativedelaysinthehuman

resourcesdepartment.Thelaboradjustmenttimeissetto13weeks,representing

thefirm'sreluctancetoalterthelaborforcetooquicklyduetothehighcostsof

adding(Orcutting)permanentemployees.

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 761

Figure19-2showstheresponseofthemodeltoa50%stepIncreaseindesired

laborinweek5丘.omaninitialbalancedequilibrium.Thevacancycreationrate

immediatelyrlSeS,bothtorespondtotheincreaseinthedesiredhiringrateandto increasethenumberofvacanciestothenewdesiredlevel.Soonthestockofva-

canciesrisesroughlytotheapproprlatelevel･Thehiringratelagsbehindthe

vacancycreationrate.Asthelaborforcegrows,theadjustmentforlaborfalls,

reducingthedesiredhiringrateand,gradually,theactualhiringrate.Thelabor

forceadjustsinasmoothandstablefashion,settlingwithin2%ofthenewtarget afterabout32weeks.

125

100

.3■

2: 75 ≧ i=さ dJ

g･ 50 4) EL.

.3<

冨 40 > i=! q)

oE1 20 d) EL

O ･20

FLGURE19-2 Responseto unantllcIPated lnC｢eaSeln

desiredlabor

0 10 20 Weeks30 40 50

762 PartV InstabilityandOscillation

Exceptforthedifferencesintimeconstants,theresponseisidenticaltothere-

sponseofthestockmanagementstructureadaptedforcapltalinvestmentinchap- ter17.Bothsituationsrepresentexamplesofthebasicstockmanagementsystem andhaveidenticalstructure.Notethecharacteristicamplificationgeneratedbythe

stockmanagementstructure:A50%increaseindesiredlaborcausesthevacancy

creationratetorisefrom 10people/weektoapeakof125people/week･Small changesinthedesiredworkforceinducelargeswlngSintheloadplacedonthehu一 manresourceorganization.Ofcourse,iftherequiredrateofactivltyexceedsthe

capacltyOfthehumanresourceorganization,thedelayinfillingvacancieswould increaseandthequalityofnewhiresmightfall.

Thebehaviorofthestockmanagementstructureasadaptedtolaborappearsto

bereasonable.However,whentestingaformulation,ltisimportanttoestablishits

robustnessbyexaminlngItsresponsetOaWiderangeofinputs･Figure19-3shows theresponseofthemodeltoa50%decreaseindesiredlabor･Nowthelaborforce doesnotreachitsdesiredlevelfornearly2years.TherearetwoprlnClpalreasons

fortheslowadjustment. First,血elargedropindesiredlabormeansdesiredhiringbecomesnegative･

Becausetherearenolayoffs,theworkforcecanfallatmostattherateofattrition･

Theno-layoffpolicyIntroducesanimportantnonlinearltythatcausestheresponse tolargeincreasesinthedesiredstocktodifferfromtheresponsetolargedecreases･

Second,notetheslowrateofdeclineofthehiringrate.Thelargedecreasein

desiredlaborcausesthedesiredvacancycreationratetobecomenegative(it

reachesaminimumofnegative48people/week).However,theactualvacancycre-

ationratefallsatmosttozero.Consequently,thestockofvacanciesalreadycre- atedcontinuestobefilled.Withan81Weekaveragetimetofillvacancies,80new

peoplearehiredoverthenextfewmonthseventhoughthefirmhasfartoomany

employees･ Whileafirmmaychoose,asamatterofpolicy,nottolayoffunneededwork-

ers,itisnotreasonabletocontinuetofillallexistingVacancieswhenthefirmhas farmoreemployeesthanitneeds.Theproblemcannotbecorrectedbyremoving theMAXfunctionthatconstrainsthevacancycreationratetobenonnegativein

equation(1916).Doingsocould,ifthesurplusworkforcewerelargeenough,drive thenumberofvacanciesnegative,aphysicalimpossibility.Thesolutionisto

modelthevacancycancellationprocessasaseparaterateflowlngOutOftheva-

cancystock(section13.3･3)･ ExistlngVacanciescannotbecanceledimmediately.Ittakestimeforthehu一

manresourceorganizationtocancelavacancy,andsomearesofaralonginthe processthattheycannotbecanceled(forexample,thosepositionsforwhichoffers have-beenmade).Theseconsiderationsdefineaminimumdelayincancelingva- cancies.Thecancellationrateistherefore the lesseroftheDesiredCancellation RateortheMaximumCancellationRate:

VacancyCancellationRate -MIN(DesiredVacancyCancellation Rate,MaximumⅥlCanCyCancellationRate)

(19-14)

MaximumVacancyCancellationRate -Vacancies/VacancyCancellationTime

(19-15)

Chapter19 TheLaborStlpplyChainandtheOriginofBusinessCycles 763

4) EL 3 40 【L

FlGURE19-3 Responseto unanticIPated decreasein desiredlabor

0 20 40 Weeks60 80 100

20 40 Weeks60 80 100

0 20 40 WeekS 60 80 100

Note･'Thesimulationshows100weeks･Compareto50weeksshowninFigure1912.

Theformulationforcancellationsensuresthatthestockofvacanciescannever

becomenegative.Ifthedesiredcancellationrateisverylarge,theactualcancella-

tionrateandstockofvacanciesapproachzeroexponentiallywithatimeconstant

detem inedbytheVacancyCancellationTime.

ThedesiredrateofcancellationsisglVenbythemagnitudeofthedesiredva-

cancycreationratewheneverthatrateisnegative:

DesiredVacancyCancellationRate -MAX(0,-DesiredVacancyCreationRate)

(19-16)

764 PartV InstabilltyandOscillation

Thesameformulationcanbeusedtomodellayoffs.Justasittakestimetocancel

avacancy,Sotooittakestimetoterminateemployees.

LayoffRate-MIN(DesiredLayoffRate,MaximumLayoffRate) (19117)

MaximumLayoffRate-Labor/AverageLayoffTime (19-18)

TheAverageLayoffTimeisthemeantimerequiredtoterminateemployees･The

desiredlayoffrateisthemagnitudeofthedesiredhiringratewheneverthatrateis

negative:

DesiredLayoffRate -WillingnesstoLayOff*MAX(0,-DesiredHiringRate)

(19-19)

TheparameterWillingnesstoLayOffrepresentsthefirm'slayoffpolicy･Ifthe

firmhasano-layoffpolicy,thenWillingnesstoLayOff-0･IfWillingnesstoLay

Off =1,thefirmlSJuStaSWillingtofirepeopleastohirepeople.

Figure19-4showstheresponseoftherevisedmodeltotheunantlClpated50%

decreaseindesiredlabor.TheAverageLayoffTimeissetto8weeks,withWilレ

1ngneSStOLayOff-1.TheVacancyCancellationTimeis2weeks.

Assoonasdesiredlaborfalls,thefirmstartstocancelexistingVacanciesand

layoffworkers･Vacanciesfalltozeroafterabout6weeks,comparedtomorethan

30weeksintheorlglnalmodel.Throughlayoffsthelaborforcecomesintobalance

a氏eraboutayear,comparedtonearly2yearsintheonglnalmodel. Includingexplicitvacancycancellationandlayoffsincreasestherealismand

flexibility ofthemodel･Themodelincludesimportantnonlinearitiescapturing

basicphysicalconstraints(vacanciesandthelaborforcecanneverbenegative).

Theformulationalsoenablesthemodelertorepresentimportantasymmetries

inthereactionofafirmtoexcesslaborcomparedtoasituationofinsufficient

labor･2Thestructureforlayoffsandvacancycancellationcanbeusedinotherap-

plicationsofthestockmanagementstructuresuchastheacqulSltionofplantand

equlPment,thereturnofpurchasesfromaconsumertoasupplier,orthetransferof

workersbetweendifferentjobswithinafirm(forexample,betweenproduction

andmarketing).

19.2 FNTERACT旧NSOFLABORANEHNVENTORYMAト姐GEMENT

Thissectionaugmentsthemodelsofproductionandinventorymanagementde-

velopedinchapter18byaddinglaborasanexplicitfactorofproduction,uslngthe

simplemodelofthelaborsupplychaindevelopedabove.

2Thespeedoflayoffsversushiringcanbefurtherdifferentiatedbyrevisingthemodelsothe laboradjustmenttimeLATdependsonwhetherthereisexcessorinsufficientlabor:

LaborAdjustmentTime LATHifDesiredLabor≧Labor LATLifDesiredLabor<Labor

whereLATHisthetimeconstantwhenthefirmseekstohireandLATListhetimeconstantwhen thefirmneedstofireexcessworkers.AfirmthatdislikeslayoffswillhaveLATH<LATL;afirm thatisquicktofirebutslowtohirewillhaveLATH>LATL.

Chapter19 TheLaborSllpplyChainandtheOriginofBllSinessCycles

T-

と

むa A

ld o ad

FIGURE19)4 Responseto unanticIPated decreasein desiredlabor

withlayo什s andvacancy cance"ations

0 10 20Weeks30 40 50

0 10 20 Weeks30 40 50

765

0 10 20 Weeks30 40 50

Note:ThissimulatIOnShows50WeeksCompareto100weeksshowninFlgure19-3.

Considerthefirstinventorymanagementmodeldescribedinsection18.1.The

modelrepresentsstocksofworkinprocessand血ishedinventory,alongwiththe

productionschedulingdecision.ThemodelincludessomestrongsimplifyingasI

sumptlOnS.Customerordersareexogenous.Orderbacklogsandmaterialsinven-

toriesareomitted,asareinteractionswithsuppliersandcustomers.Most

important,productionstartsalwaysequaldesiredproductionstarts.Inreality,pro-

ductionisdeterminedbytheavailabilityofmaterials,plantandequlpment,labor,

andotherinputs.Section18.2relaxedtheassumptlOnthatmaterialswerealways

766 PartV InstabilityandOscillation

available.Thissectionfocusesontheroleoflaborasadeteminantofproduction. Capitalplantandequlpmentareassumedtobeample.TheProductionStartRate thenbecomes

ProductionStartRate-Labor*Workweek*LaborProductivlty (19-20)

Productionstarts,inwidgetsperweek,aredeterminedbythelaborforce,theav-

eragenumberofhoursthesepeopleputinperweek,andtheirproductivity(mea- suredinwidgetsproducedperperson-hourofe放)rt).

TomeetproductionrequlrementSthefirmmustadjustitslaborforce.Desired laborisbasedonthedesiredproductionstartrate,thestandardworkweek,andex- pectedproductivlty:

DesiredLabor

-DesiredProductionStarts/(StandardWorkweek*ExpectedProductivity) (19-21)

Management'sestimateofproductivityCan,andoftenwill,differfromtruepro- ductivlty.Forthepurposesofthissimplemodel,however,assumethestandard workweekis40hoursandthatexpectedproductivltyequalsactualproductivlty.

Theseparametersaffectonlythenumberofworkersneededtoproduceawidget, notthedynamicsofthelaborsupplychain.Fortesting,Settheactualworkweek

equaltothestaildardworkweekandsetproductivitytOO･25widgetsperperson- hour｡

Figure19-5Showsthestructureoftheinventorymanagementandlaborsec- tors.Thelaborsectorincludesthestructurefbrlayoffsandvacancycancellation.

Mem竜aESimuFa骨岳on⑳mmvem竜⑳FyMaLmaLgemem菅 WithLabor

WhatistheresponseofthemodelshowninFigure19-5toanunanticlpated20%

stepIncreaseincustomerordersinweek5?Sketchthepatternofbehavioryouex- pectfordesiredandactualinventory,themowsoforders,shipments,production, productionstarts,vacanciesandlabor,andthelaborflows.Payattentiontothe

phaserelationshipsamongthevariables,thatis,theleadsandlagsofthevariables relativetooneanother.

19.2.i 買nvcntory-Workfot'f;e棚即aC的さ1STF:.!eh:.:tvior

Figure19-6showstheresponseofthefullsystemtoanunanticIPated20%stepIn-

creaseincustomerorders.Theparametersforthelaborsectorarethesameasin

section19.1.2.Theparametersoftheinventorysectorarethesameasusedinsec- tion18.1.6excepttheInventoryAdjustm entTimehasbeensetto12Weeksandthe WIPadjustmenttimehasbeensetto6weeks.

Addingthelaborsupplychainmeansproductionstartsadjusttodesiredstarts withadelay.Afterthedemandshock,inventorythereforefallsfartherthantheno-

laborcase,boostlngProductiontoahigherinitialpeakandincreaslngtheamplifi- cationratioofproductionstartsrelativetocustomerordersto2.07,comparedto

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 767

1.61forthemodelwithoutlabor.Mostimportant,thesystemnowoscillatesvlgOrl

ously,withaperiodofabout1year･Theoscillationisqultelightlydamped,re- qulrlngabout3.5yearsforproductionstartstosettlewithin2% ofthenew

equilibrium.

19.2.2 ProcessPoint:ExpbinさngModelBehavior Addingthelaborsupplychaintotheinventorymanagementmodelintroducesim- portantdelaysinthenegativefeedbacksthroughwhichthefirmregulatesitsin-

ventories.Thesedelayscausethesystemtooscillate,asyoushouldhavepredicted･ However,explainlngthebehaviorbysaying血atproductionoscillatesbecause

thesystemcontainsnegativeloopswithdelaysisnotsufficient･Goodmodelers muststriveforadeepunderstandingofthecausesforthebehaviorobservedin

血eirmodels(whe血eritisoscillatoryornot).

Itisseductivelysimpletodevelopexplanationsformodelbehaviorthatareflat outwrong.Anditisalltooeasytomakeerrorsinfb-ulations,parametervalues, andinitialconditions.ManytlmeSI'veobseⅣedpeopledevelopIntricatetheories

toexplainthebehavioroftheirmodel,oftensupportedbycomplicatedcausaldia- gramsandargumentation,onlytodiscoverthatthebehaviorwasanartifactofa

poorformulationorevenatypographicale汀Or.Failuretoanalyzethebehaviorof yourmodelindepthincreasesthechancestheseerrorswillgoundetected,Slowing yourlearningandreducingtheconfidenceyouandyourclientscanhaveinyour

analysis･Theantidotetosuchself-delusionistherigoroususeofsensitivltyanaly- sis,extremeconditionstestlng,andotherstandardtestsdesignedtouncoverflaws indynamicmodels(Seechapter21).

Understandingmodelbehaviorgoesbeyondtheinvocationofsimplearche- typessuchas"theoscillationiscausedbynegativeloopswithdelays"or "SIShapedgrowthresultsfromthelimitstogrowthonareinforcingfeedback." Whiletrue,thesestatementsdon'tprovidethedeepInsightintomodelstructure

andbehaviorrequiredtodevelopyourintuitionaboutdynamicsoryourabilityto identifyhighleveragepolicies.Youshouldbeabletoexplainwhyamodeldoes whatitdoesindetail,intermsyourclientcanunderstand,andwithoutcontradict- ingyourself.

E.xp6ainingOsc‖ations Beforecontinuing,Writeanexplanationforthebehaviorproducedbythestep increaseinordersshowninFigure19-6.Youmayfindtheexplanationemerges naturallyasyouanswerthefollowingquestions:

Whyisn'tthesysteminequilibriumwheninventoryfirstequalsdesired inventory?

Whyisn'tthesysteminequilibriumwhenproductionstartsfirstequal

orders?Wh enproductionfirstequalsorders?

Whydoesproductionovershootitsequilibriumvalue?

Whydoesitundershoot?

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Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 771

YouranalystsShouldproceedstepbystep,explainlngateachjuncturewhatis

occurrlngandwhy･Makeacausalloopdiagram showinghowtheproduction schedulingandhiringpoliciesinteractwiththestockandflowstructuretocreate

theimportantfeedbacksinthesystem.Itishelpfultoplotthebehaviorofevery

variableinthemodel･CheckthateachvariableisbehavingapproprlatelyglVen yourknowledgeoftherealsystemandthestmctureanddecisionrulesofthe

model･Makesurebasicstockandflowrelationshipsarecaptured･Ifproduction exceedsshipments,inventorymustberising.Striveforaninternallyconsistent historyofthefirm,expressedinmanageriallymeaningfultermsyourclientcan understand.

19.2.3 UndersiandingtheSourcesofOsc州ation

Beginbytracingtheeffectsofthedemandshockthroughthesystem(Figure19-6). Immediatelyaftertheincreaseindemandinweek5,thefirmtriestoboostship- mentstothenewrateof12,000widgets/week.Production,however,remainscon-

stantattheinitialrateof10,000･Inventorythereforefalls･Asinventoryfalls,and asthefirm'sdemandforecastgraduallyrlSeS,desiredproductionbeginstorise.As

itdoessotoodoesdesiredWIP･Desiredproductionstartsrisesharply･Intheorlg- inalmodelwithoutlaboractualproductionstartsequaldesiredstarts,soWIPin- ventorybeginstoriseimmediately.Now,however,theriseindesiredstartshasno immediateeffectonactualstarts.Instead,desiredlaborrisesaboveactuallabor.

Thefirm'Shumanresourcedepartmentstrugglestocreateadditionalvacancies. Thevacancycreationraterisessharplytoapeaknearly7timesgreaterthanthe

initialequilibriumrate.Thesevacanciesbegintobefilledafteradelay,gradually liftingthelaborforce･Byaboutweek15,enoughnewpeoplehavebeenhiredto boostproductionstartstothecustomerorderrate.Inventory,however,continuesto falluntilproductioniscompleted.

Byweek20,expectedordershavenearlyadjustedtothenewrateofcustomer orders.ProductionfinallyrlSeStOmatchcustomerordersinaboutweek23.Inven-

toryactuallyreachesitsminimumandbeginstoriseafewweeksearlier,sincethe lowlevelofillVentOryhasconstrainedshipmentsbeloworders.Theinventorygap stopsgrowlng,SOdesiredproductionpeaksandstartstodecline.Asitdoes,thede-

siredlevelofWIPinventoryalsofalls.ActualWIPcontinuestorisesinceproduc- tionstartsstillexceedproduction.Consequently,desiredproductionstarts,and desiredlabor,fallsharply.Byweek24,desiredandactuallabormeet.Actuallabor

continuestolagbehindthedesiredlevel,peakingbyweek27evenasdesiredla- borcontinuestofall.Laborthenfalls,butremainsabovetheequilibriumlevel,so

productionstartscontinuetoexceedproduction,whichinturnexceedsshipments. ThereforeWIPandfinishedinventorykeeprlSlng･Byweek29,inventorylevels haverisenenoughfordesiredproductionstartstofallbacktocustomerorders.De- siredlaborthereforefallsbacktoitsnewequilibriumlevelof1200workers.Ac-

tuallaborstilllagsbehind･Productionstartscontinuetoexceedshipments.By week36inventoryreachesthedesiredlevelforthefirsttimesincethedemand shockJnventorydoesnotreachequilibrium,however.Laborandproductionare

772

FIGURE19-7 Phasep一otfor theinventory- workforcemodel

Flowiscounter- clockwise.The 450lineindicates

pointswhere ProductionStart Rate-Desired ProductionStart

Rate.Thesystem beglnSattheinitial equilibriumof 10,000widgets/ weekandendsat

thenewequilib-

riumof12,000 widgets/week.

PartV InstabilityandOscillation

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10 12 14 16

DesiredProductionStartRate (thousandwidgets/week)

nowneartheirpeakvalues｡Goodscontinuetoaccumulate,andinventoryover- shootsthedesiredlevel.

Excessinventorynowcausesdesiredproductionstartstodropbelowcustomer orders,forcingdesiredlaborbelowtheequilibrium level･Actuallabor,while falling,stilllagsbehind.Productionstartsdonotdropbacktocustomerordersun-

tilweek39,Withproductionfallingtocustomerordersonlyinweek48･Through- outthisperiodexcessinventorycontinuestoaccumulate,forcingdesired productionstartsanddesiredlaboreverlower.Thehumanresourcedepartment

findsitselfwithsomanyworkersthatitnowscramblestocancelunfilledvacan- cies.Layoffsbeginaroundweek28.

Afterweek39,withlaborbelowequilibrium,shipmentsexceedproduction

starts.Aggregateinventoryfalls.Desiredproductionstartstorise･Asbefore,the laginadjustlngtheworkfTorcemeanslaborcontinuestofall,reachingItsminimum

inweek53.Desiredproductionstartsonceagalnreachcustomerordersinweek 55,butactualstartslagbehind,Soinventoryfallsfartherthandesired.Byweek63, inventorylSagainbelowthedesiredlevelandfallingrapidly,thelaborforceistoo

small,andthenextcyclebegins. Addingthelaborsupplychaintotheinventorymanagementmodeldoesnot

changetheessentialfeedbackstructureofthesystem.Productionstartsstillre-

spondtothegapbetweendesiredandactualinventories･Butthehiringprocessin- troducesdelaysinthenegativeinventorycontrolloop,Causlngthekeystateofthe system-inventory-tooscillatearoundthedesiredlevel.Theimpactofthedelay

inadjustlngProductionstartsisillustratedinFigure1917,aphaseplotshowing productionstartsversusdesiredstarts.

Ifthefirmwereabletomatchactualstartsperfectlywithdesiredstarts,then

thesystem'Strajectorywouldalwaysliealongthe45oline･Instead,thesystemspi- ralsaroundtheequilibrium.Withtheparametersusedherethesystemislightly

damped.Startlngattheinitialequilibriumof10,000widgetsperweek,thedemand shockrapidlyincreasesthedesiredstartrate.Whendesiredstarts丘rstreachthe newequilibriumof12,000widgets/week,actualstartslagfarbehind･Bythetime

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 773

actualstartshavereachedthenewequilibrium,InventorylSSOlowthatdesired startsareneartheirpeak.Whendesiredstartsfallbacktotheequilibrium,actual startsareneartheirpeak,forcingInventorytOovershootandpushingdesiredstarts down.Andsoitgoes-thelaglntheadjustmentofactualtodesiredproduction startsforcesthesystemtochaseitstail,Spiralingaroundtheequilibriuminsteadof adjustlngSmoothlytoit･

Asdiscussedinchapter17,OscillationrequlreSbothdelaysinthenegative feedbackscontrollingastockandthatthemanagers'decisionrulesIgnorethesup- plylineofcorrectiveactionsinprocess.Thesupplylineofunfilledordersand workinprocessinventorylnamanufacturlngSupplychainareeasilymeasured andtakenintoaccount(thoughexperimentsshowpeopleoftenfailtodoso).The decisionrulesofthemodelfullyaccountforthesupplylineofWIP.However,the supplylineofcorrectiveactionsinprocesscreatedbythedelaysinthehiring processisnotsoobvious.Vacanciesandthestockoflaboritselfrepresentthepo- tentialtoproduceatacertainrate,notaparticularquantltyOfgoodsonorderorin production.Theyarenotmeasuredinwldgetsandcannotbecomparedeasilytoin- ventorylntheproductionschedulingdecision.

PolicyDesigntoEnhanceStability

Nowyoucanbegintousethemodeltoexplorepoliciestostabilizethefirm. Beforepolicyanalysisismeanlngful,however,youmustbeclearaboutyour objectives.

1.Instabilitysuchasillustratedbytheinventory-workforcemodelisundesir- able.Thegoalofpolicyanalysishereistoidentifyhighleveragepoliciesthatcan improvestabilitywithoutdegradingotheraspectsofsystemperformance,particu- larlytheabilityofthefirmtoprovidegoodcustomerservice(tofill100%ofin- comingorders),eveninthefaceofunpredictablechangesindemand.Providea briefexplanationofwhatstabilitymeansinthiscontext.

2.Toimprovetheperformanceofthesystemasyoudefineitin(i),Shouldthe InventoryAdjustmentTimeandWIPAdjustmentTimebeincreasedordecreased? Writedownyouranswerbeforesimulatlngthemodel.

3.TestyourintuitionbysimulatingthemodelwithInventoryAdjustmentTime andWIPAdjustmentTimeeachlengthenedorshortenedby50%,accordingto yourpredictionin(2).Isyourintuitionconfirmed?Tryothervaluesforthesepa- rametersuntilyouaresatisfiedyouunderstandtheireffectsonthebehavior･ExI plaintheeffectofthechangeonstabilitylntermsOfthefeedbackstructureofthe SyStem･

4.Repeattheanalysisin(3)fortheotherimportanttimeconstantsinthemodel,

includingthebehavioralparameters(e.g.,theLaborAdjustmentTimeandVacancy AdjustmentTime)andthephysicaldelays(e.g.,theManufacturingCycleTime andAverageTimetoFillVacancies).Writedownyourpredictionforeachpara一 meterbeforesimulating.Brieflyexplainhoweachparameteraffectsthemodeland why･Doalltheparametershavethesameeffectonstability?Whyorwhynot?

774 PartV InstabilityandOscillation

5.Whatpolicieswouldyourecommendatthispoint?Youcanconsidercombi-

nationpolicies.Givespecifiesregardinghoweachpolicymightbeimplementedin

reality.

19.2.4 AddingOver!ime

Sofar,theworkweekhasbeenconstant-workersalwaysproduce,whethertheir

outputisneededornot･TheassumptlOnOfconstantlaborutilizationisnotabad

approximationformanytraditionalmanufacturlngenvironments,particularly thosewhereperformanceisevaluatedonthebasisofoverheadabsorptlOn,labor

utilization,andothermetricsdesignedtomaximizegrossthroughputorthosenor一

mallyoperatlngaroundtheclock.However,inmanysettlngS,theworkweekvaries

inresponsetotheneedtoincreaseordecreaseproduction.

Tbintroducethepossibilityofover-undertime,theworkweekbecomesafunc-

tionofschedulepressure,asinsection14.2:

Workweek -StandardWorkweek*EffectofSchedulePressureonWorkweek (19-22)

EffectofSchedulePressureonWorkweek-f(SchedulePressure) (19123)

SchedulepressureistheratioofDesiredProductionStartstoStandardProduction Starts:

SchedulePressure-DesiredProductionStar[S/StandardProductionStarts(19-24)

Standardstartsistherateofstartsthefirmwouldattainwhenthecurrentlabor

forceputsinthestandardworkweek,giventhefirm'sestimateofproductivlty:

StandardProductionStarts

-Labor*StandardWorkweek*ExpectedProductivlty (19-25)

Highschedulepressuremeansthefirmneedstoproducemorethanthestandard

ratepermits;lowschedulepressuremeansthereisexcesscapaclty.Nowcon-

sidertheshapeofthenonlinearrelationshipbetweenschedulepressureandthe workweek.

Tospecifytheworkweekasafunctionofschedulepressure,notethattheref- erencelineEffectofSchedulePressureonWorkweek-1meanstheworkweek

nevervaries.The450referenceline,incontrast,representsasituationwherethe

firmalwaysproducesatthedesiredrate.The45olineentails:

EffectofSchedulePressureonWorkweek

-i(SchedulePressure)-SchedulePressure

Substitutingthisexpressionintheequationfortheworkweek,

Workweek-StandardWorkweek*SchedulePressure

SchedulePressureistheratioofdesiredtostandardproductionstarts:

Workweek-StandardWorkweek*DesiredProductionStarts

StandardProduction

(19-23a)

(1 9-22a)

(19-22b)

Substitutlngthedefinitionofstandardstartsintotheequationforworkweekyields

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles

FIGURE19-8 Effectofschedule

PressureOn workweek (

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0.00 0.50 1.00 1.50 2.00

SchedulePressure (dimensionless)

Workweek-DesiredProductionStarts/(Labor*ExpectedProductivity) (19-22C)

Substitutingequation(19-22C)intotheequationforproductionstarts(19-20)

yields

ProductionStartRate Labor*Productivlty*DesiredProductionStarts

Labor*ExpectedProductivlty (19-20a)

Assumingthefirmhasanaccurateestimateofproductivity,equation(19-20a)re- ducesto

ProductionStartRate-DesiredProductionStartRate (19-ユob)

Henceanovertimepolicylyingalongthe450linewouldenablethefirmtohitits

productiontargetsatalltimes,independentoftheworkforce. Theworkweekfunctionmustlieintheareabetweenthetworeferencelinesin

Figure1918･IntheregionSchedulePressure>1,indicatingInsufficientcapaclty, itisnotreasonabletoassumethattheworkweekwouldrisemorethanneededto

liftproductionstartsbeyondthedesiredrate.Likewise,intheregionSchedule Pressureく 1,itisnotreasonablefortheworkweektobecutbacksomuchthat

productionstartsfallbelowthedesiredrate.Similarly,excesscapacltyShould

nevercauseafirmtoscheduleovertimeandinsufficientcapacityShouldneverlead toundertime.

Theworkweekcannotincreaseindefinitely.Therelationshipmustsaturateata

maximumvalue.Areasonablemaximumworkweekfortheentireworkforcemight

be50or60hoursperweek･Figure19-8Showsworkweekrisingtoamaximum

25%greaterthanthestandard,ortoanaverageof50hoursperweekfortheentire

workforcewhenthestandardis40hours/week.Thisfigurerepresentsanaverage

overtheentirelaborforce:Someworkerswouldbeputtlnginlongerhoursand some,shorter.3

3Notethatthemaximumeffectofschedulepressureonworkweekandthestandardworkweek arenotindependent.Givenamaximumworkweekof50hours,theeffectsaturatesatavalueof 1.25whenthestandardworkweekis40hoursbutat1.43whenthestandardworkweekis35hours.

776 PartV InstabilityandOscillation

Whathappenswhenthereisexcesscapacity?Manyfirmsareunwillingtore-

ducetheworkweekbelownormal(especiallywhentheyarecontractuallyoblig- atedtopayforafullweek).Facedwithexcesscapacity,manyprefertostockpile additionalunitsforfuturesale,waitlngforattritionandlayoffstoreducethelabor forceandeliminatetheneedforundertime.Firmsmayalsochoosetomaintain

productioninthefaceoflowschedulepressuretokeepworkerskillsfromeroding･ ThefunctionshowninFigure19-8capturesapolicylnWhichtheworkweeknever fallsbelow75%ofnormal,or30hours/week.Theslopeofthefunctionisless

than1inthenormaloperatingregion(whereschedulepressureisnearone),corre- spondingtoacompromisebetweenthepressuretomaintainfulllaborutilization andtheneedtoadjustproductionstartstothedesiredrate.

Otherworkweekpoliciesarepossible,includingthepolicyofnoundertime

(thefunctionisonewhenschedulepressureislessthanone)andapolicyinwhich productionstartsfalltozeroasschedulepressurefallstozero.Underthelatterpol-

1Cy,thefirmiswillingtosacrificelaborproductivltytOavoidthebuildupofexcess

inventory･Insuchafirm,theworkersmayusetheirextratimeintraining,mainte- nance,Orprocessimprovementactivities.

19.2.5 Respomse官oF日ex岳b萱eWorkweeks

Figure19-9showstheresponseofthemodelwiththeover/undertimepolicytothe 20%stepIncreaseinorders.Theresponseisdramaticallysmootherandmoresta-

ble.Productionstarts,ofcourse,stillovershootcustomerorders,buttheoscillation

isnearlyeliminated(thesystemisalmostcriticallydamped).Theamplificationof productionstartsrelativetocustomerordersfallsfrom2.07withoutworkweek

flexibilityto1.52.Theneedtorebuildinventorystillforcesthelaborforcetoover- shootitsnewequilibrium,butthefirmisabletopreventtheaccumulationofex-

cessinventorybycuttlngtheworkweekwhiledownsIZlngthroughattrition.There isnoneedforlayoffs.Customerserviceimprovesaswell.Orderfulfillmentdrops

onlytoalowof93%,Comparedt088%intheconstantworkweekcase,andtheto-

talnumberoflostordersisreduced.

Theimprovementinstabilityarisesbecausethev∬iableworkweekallows productionstartstotrackdesiredstartsbetterthanbefore.Productionstartsstill

fallshortofdesiredstartsbecausetheassumedovertimepolicyhasaslope lessthan1(notethesmallervariationoftheworkweekcomparedtoschedule

pressure)･ Figure19-10Showsthephaseplotforproductionstartsagainstdesiredstarts.

Workweekflexibilitymeansthefirmcanalignactualstartstonearlymatchdesired starts,and,comparedtoFigure19-7,thetrajectoryOfthesystemdoesliemuch closertothe45oline.Consequently,damplnglSincreased,andthesystemsplrals intothenewequilibriummuchfaster.

Figure1911lshowsacausaldiagramillustratlngthefeedbackstructureofthe

system.ThesystemoscillatesbecausethenegativeWorkforceAdjustmentloopIn-

volveslongdelayscausedbythehiringprocess･Workweekflexibilitycreatesa newfeedback,thebalancingOver-Undertimeloop.Theovertimeandworkforce

adjustmentloopshavethesamegoal:tobringaggregateinventory(finishedin- ventoryplusWIP)inlinewiththedesiredvalue･However,theovertimeloop

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FIGURE19-10 Phasep一otfor theinventory- workforcemode一 withflexibBe workweek

Compareto Figure19-7･ FIowiscounter- clockwise.The

systembeglnSat theinitialequilib- riumof10,000 widgets/week andendsatthe

newequilibrium of12,000 widgets/week･

PartV InstabilityandOscillation

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DesiredProductionStartRate (thousandwidgets/week)

operateswithnodelay,allowlngthesystemtorecoverfromshockswithoutgener-

atingthecyclesseenintheconstantworkweekcase.

Themoreaggressivelythefirmusesovertime,thecloserproductionstarts

trackdesiredstartsandthegreatertheabilitytobalanceinventorieswithoutforc-

1nglaboraboveitsequilibriumvalue.Themoreflexibletheworkweek,themore

dominantthefirst-orderovertimeloopbecomes,andthelessthesystemmustrely

ontheoscillatoryworkforceadjustmentprocesstorestoreinventoriestotheirde-

siredlevels.InthelimltlngCaseOfperfectlyflexibleworkweeks,theinventorysec-

torreducestotheorlglnalmodelinwhichproductionstartsalwaysequaldesired

startsandoscillationdoesnotoccurbecausethenegativefeedbackscontrollingag-

gregateinventorybecomeeffectivelyfirst10rder.

TheeffectofworkweekflexibilityillustratesageneralprlnCiple:Thestability

ofoscillatorysystemscanalwaysbeenhancedbyaddingorstrengtheningfirstl

ordernegativefeedbacksthathelpthesystemreachitsgoalswithoutslgnificantde-

lays.Asintuitionmightsuggest,addingfirst10rderpositiveloopstoanoscillatory

systemisdestabilizlng.Asanexampleofsuchapositivefeedback,considertheef-

fectofschedulepressureonfatigueanderrorrates(section14.4.3).Ifhighsched-

ulepressureandlongworkweeksleadtostressandfatigue,errorsmayIncrease,

reducingthroughputandcausingafurtherincreaseinschedulepressure.Thepos-

itivefeedbackisdestabilizlngbecauseltPushesthestateofthesystemfartherfrom

itsgoal,forclnglargerexcursionsintheoscillatoryworkforceadjustmentloop.4

Recngineeriぎ1g<'8%ManufacturingFir門｢

forE.nhancedSt壬柚iEity

Usingthemodelwithovertime,designanensembleofpoliciestoenhancethesta-

bilityofthefirmwhilealsoimprovlngCustomerService.Drawonthepoliciesyou

4seeGraham(1977)foragoodnontechnicaldiscussionofthedeterminantsofstabilityin oscillatorysystems.

Chapter19 TheLaborSupplyChainandtheOriginofBllSinessCycles

FlGURE19-ll Causalstructureofinventory-workforceinteractions

779

exploredinthepreviouschallengebutconsidernowhowthesepoliciesmayInter-

actwithaflexibleworkweek.Onceyouhavearrivedatasetofpoliciesyoube-

lievecanenhancestabilityandperformance,consideragaintheresponseofthe

systemtoshorterinventoryandWIPadjustmenttimes.Tbboostperformancein

thereenglneeredsystem,Shouldthesetimeconstantsbeincreasedordecreased?

Writedownyouranswerbeforetestlngthemodel･Next,Carryouttheexperiment

byalteringboththeseparametersby50%inthedirectionyousuggested.Wasyour

intuitioncorrect?Whyorwhynot?Comparetheimpactofshorterinventoryand

WIPadjustmenttimesintheconstantworkweekcasetotheirimpactinthereengl-

neeredmodelwithyourfullsuiteofpolicies.Istheeffectthesame?Explain.

19,2.6 TheCostsoflnstabih-ty

Theinventory-workforcemodeldevelopedsofarfocusesonthecoreprocessesof

inventorymanagementandthelaborsupplychain.Tokeepitsimplethemodel

doesnotincludeanyaccountlngOrfinancialvariablesIWhileyoucanexaminethe

impactofvariouspoliciesonthestabilityofthesystem,itsperiod,damplng,and

soon,youcannotassesstheimpactofyourpoliciesonprofitabilityorcashflow.

780 PartV InstabilityandOscillation

Dothebenefitsofeachpolicy(enhanceduseofovertime,acceleratedhiringand

training,orreducedmanufacturingcycletime)outweighthecosts?Withoutthe

abilitytoassesshowyourpoliciesaffectthebottomline,yourmodelwillbeoflit-

tleusetoyourclient.

Youcaneasilyexpandthemodeltoincludeafullsetoffinancialaccounts,in-

cludingtheflowoffunds,incomestatement,andbalancesheet.Youcanalsoeas-

ilymodelafirm'smanagerialaccountingSystem,generatlngVariablessuchasunit

directcosts,overheadabsorption,andlaborutilizationvariances･5However,the

modelisthenlikelytounderestimatethebenefitsofenhancedstability.CostacI

countlngSystemsdonotcontainalineitemfor"CostsofInstability.HThereisno

entryintheincomestatementforchargesagalnStnetincomeduetoself-inflicted

fluctuations.Yetthereisnodoubtthatinstabilityandoscillationarecostly.Mod-

elingthestandardaccountingSystem,Whilenecessarytobuildclientconfidencein

yourmodel,isnotsufficient.Indeed,thestandardaccountingSystemWillbebiased

agalnStpoliciesthatenhancestability,becausethecostsofimplementlngthepol-

icyWillbeaccountedforwhilethebenefitswillnot.Toproperlyassesstheimpact

ofyourpoliciesyouneedtoidentifythecostsofinstabilityandincludetheminthe

analysis.

TheeosモS⑳mnsせab冊y

Listasmanycostsofinstabilityasyoucan.Considertheimpactoffluctuationsin

production,inventories,employment,andothervariablesonallaspectsoftheper-

formanceofafirm.Donotlimityourselftofactorsthatareexplicitinthemode1-

considerallpossibleareas,includingoperations,Suppliers,humanresources,

customers,management,thefinancialmarkets,andothers.

Foreachcostyouidentify,indicatehowyoumightestimatetheimpactofim-

provlngStabilityonthatcost.Thatis,howcanthecostsofinstabilitybemeasured?

Forexample,anunstablefirmexperienclnglargeswingsindemandwillperiodi-

callyfinditselfshortofmaterialsandproduct,requlrlngexpeditingandtheuseof

premiumfreight.YoumightestimatethesavlngSarisingfromreduceduseofthese

expensivemeasures.

AddingT柑inimgandExpeF岳emee

ThemodeldevelopedaboveassumesproductivitylSCOnStant.Inreality,many

feedbackscauseproductivitytOVary.Theseincludechangesinworkerexperience,

fatigue,andmoraleeffects.Themodelofthelaborsupplychaindevelopedsofar

doesnotdistinguishbetweennewandexperiencedemployees.InmostsettlngS,

however,newrecruitsaresubstantiallylessproductivethanexperiencedworkers,

asdescribedinsection12.i.Firmsthatsufferfromchronicbusinesscyclesgo

5Foranexample,seeLyneis(1980).Sterman,Repenning,andKofman(1997)alsodevelopa modelwithfullfinancialandcostaccountlngSectors.

Chapter19 TheLaborSupplyChainandtheOriginofBtlSinessCycles 781

throughperiodsofrapidhiringwheretheaverageexperienceoftheworkforce

falls,cuttingPrOductivlty･ Modifythelaborsectoroftheinventory-workforcemodeltoincludetheeffect

ofemployeeexperienceonproductivlty.UsetheaglngChainstructuredeveloped insection12.1inwhichnewemployeesaredistinguishedfromexperiencedem-

ployees･Includethestructurefortheimpactofmentoringandon-the-job(OTJ) trainlngOnthetimeexperiencedworkershaveavailableforproduction.

YouwillneedtomodifytheaglngChaintoincludethepossibilityoflayoffs

frombothcategoriesofworkers･Tokeepthemodelsimpleassumetheprobability oflayoffisthesameforrookieandexperiencedemployees.(Howwouldyoufor- mulatelayoffsifthefirmfollowsastrictpolicyofreverseseniority,firingexperi-

encedpeopleonlyafterallnewemployeeshavebeen丘red?) Besuretherevisedfわrmulationforhiringtakesboththerookieandexperi-

encedworkersintoaccountwhenassesslngtheadjustmentforlabor.

Basedonyourexperienceandjudgment,selectparametersforthetimere- quiredtobecomeexperienced,therookieattritionrate,andtherelativeproductiv- 1tyOfnewemployees.Tobegin,assumerookiesdonotreducethetimethat

experiencedemployeescandevotetoproduction･ Next,youwillneedtomodifytheformulationforexpectedproductivity.Be-

causetherewillbesomerookieemployeesinequilibrium(tocompensateforthose experiencedemployeesleavingthefirm),averageproductivityWillbelessthanthe

productivltyOfexperiencedworkersIReferringtosection12･1,deriveanalgebraic expressionforequilibriumproductivity.Setexpectedproductivltyequaltothatex- pression.

Beforerunningthefullmodel,conductpartialmodeltestsofyourrevisedla- borsupplychain.Inyourtests,makedesiredlaborexogenous.Makesurethelabor

supplychainbeginsinequilibrium.Thentestitsresponsetovariousshockstode-

siredlabor,includingastepupandastepdown,bothsmallandlarge.Examinethe responsesofthelaborforceandofproductivlty,Checkingforanyanomaliesorun-

realisticresponses.Correctanyflawsyoufind.

OnceyouaresatisfiedtherevisedlaborsupplychainisfunctionlngProperly, runthefullmodel.Togenerateabaselineforcomparison,assumerookiesareJust asproductiveasexperiencedemployees.Inthiscase,themodelshouldbehave

nearlythesamea§血eonglnalmodelwithouttrainlng･Next,settheparametersto

reflectlowerrookieproductivlty･Howdoestheinclusionofworkertrainingaffect thebehaviorofthemodel?Considertheeffectsontheperiodandstabilityofany oscillation.Examinetheamplificationgeneratedontheproductionsideandinthe

laborsupplychain. Next,addtheeffectofmentorlngandOTJtrainlng.Selectareasonablevalue

fortheimpactofrookiesonthetimeexperiencedworkershaveavailableforpro- duction.Whatnewfeedbackloopdoestheeffectcreate?Howdoesitalterthebe- haviorofthesystem?

ExplorethesensitivltyOfthemodeltovariationsintheparametersofthere- visedlaborsupplychain.

Whataretheimplicationsofyouranalysisforfirmswithlongtrainingdelays andsignificantOTJmentorlng?TrainlngdelaysandOTJlearningareParticu- larlyimportantinindustriesheavilydependentonskilledtradesandenglneerlng

782 PartV InstabilityandOscillation

know-how,includingaerospace,construction,andmachinetools.Interestlngly,

theseindustriesareallfarupstreamintheirsupplychainsandexperienceagreat

dealofinstabilityindemand.HowdoesextremedemandvolatilityInteractWith

longtrainlngandmentorlngtlmeStOaffectstabilityandcosts?Whatpoliciesmight

helpsuch丘m smltlgatetheproblemscausedbyinstability?

19.3 JNVENTORY-WoRKFORCE]NTERACTJONS ANDTHEBusINESSCYcLE

Howrealisticisthebehaviorofthemodel?Withtheillustrativeparametersused

here,thenaturalperiodofthecycleisabout1year.Inreality,suchacyclewould

beentrainedwith,andprobablyblamedon,Seasonalvariationsindemandorma-

terialsavailability.Indeed,manyfirmsexperienceannualdemandcyclesandbe-

1ievetheserepresentexternallylmpOSedseasonalvariations.Thereisnodoubtthat

suchseasonalfluctuationsexist,fromtherhythmsofagriculturetothewinterlull

inconstructiontotheDecemberspikeinthedemandforconsumergoods.How-

ever,firmsoftenamplifythenaturalvariationsindemand,destabilizingoperations

evenastheyseektorespondtotheseasonalvariations.Forrester(1961,appendix

N)showedthatafirmcanmistakenly"learn"thatitsdemandisseasonalandbe-

glntOgenerateStrongSelf-sustainlngannualcyclesinproduction,employment,in-

ventories,profit,andorders,evenwhenconsumptionOftheproductisperfectly

randomandhasnoseasonalcycleatall･6

Theeconomyalsoexhibitscycleswithlongerperiods,includingthebusiness

cycle,theconstructioncycle,andtheso-calledeconomiclongwave(seeForrester

1979andSterman1986).Thebusinesscyclehasanaverageperiodofabout3to

5years;theconstructioncyclehasaperiodintherangeof10to20years,andthe

longwaveperiodisroughly50to70years.ThebusinesscycleisalsohighlyvarL

able,rangingintheUSfromaslittleas19monthsto8yearsormore(seeMoore

1983andCordon1986fordetails).7

Whatistheroleofinventory-workforceinteractionsincreatlngOramplifying

businesscycles?Economistshavedebatedtheorlginofbusinesscyclesformore

thanacenturyandthereisnoagreementyet(forasurveyseeZarnowitz1992).

Theoriesemphasizlngtheroleoflaggedresponsestodemandshocksand,in

6ForrestelJs1961modelofself-generatedseasonalcyclesconstitutesoneoftheearliestformal modelsofleamlngandtemporalself-organization.

7Emplricalassessmentofbusinesscyclesisdifficult･TheNationalBureauofEconomicRe- search,theofficialarbiterofbusinesscyclesintheUS,definesarecessionroughlyastwocon-

secutive.quartersofdeclineinaggregateeconomicactivity(fallingGDP)･Thisdefinition underestlmateSthenumberofcyclicaldownturnsintheeconomybecauseitfocusesonabsolute declineineconomicactivlty.SincetheUSeconomygrowsatanaveragerateof3.4%/year,adown- turninthet)usinesscyclemaynotcauseeconomicactivltytOfalllongenoughtomeetthedefini- tionforafull-fledgedrecession,eventhoughactivltyClearlyfallsagainsttrend.Such"growth cycles"punctuatedthelongboomsofthe1960S,1980S,and1990S.Whenthelong-tengrowth trendintheeconomylSremovedfromthedata,theremainlngCyCllCalfluctuationshaveanaverage periodofabout3years(seeMoore1983).

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 783

particular,theroleofinventory-workforceinteractionshavelongbeencentralto

manybusinesscycletheories.

Themodeldevelopedinthischapterrepresentsasinglefirm andomitsmany

importantstructures,includingthefullsupplychain,plantandequlpment,back-

1ogs,consumerdemand,labormarkets,prlCeS,Capitalmarkets,andsoon･Hence,

theperiodanddamplngOfthecycleltgeneratesarenottypicaloftheentireecon-

omy.Systemdynamicsmodelsincorporatlngtheinventory-workforcestructure

andotherimportantfeedbacksoperatingattheaggregatelevelhavebeendevel-

opedandcalibratedforvariousindustriesandfortheeconomyasawhole(e･g･,

Mass1975;N.Forrester1982;Senge1978;Sterman1986).Figure19-12Shows

thebehaviorofthemodeldevelopedinthischapterwhenparameterizedwithval-

uestypicallyestimatedinmacroeconomicmodels･8customerdemandisrandom,

Varylngaroundaconstantlevelwitha5%standarddeviation･Thebehaviorofthe

system isstronglyoscillatory.Theperiodofthecycleisnowapproximately3

years,quiteClosetotheperiodoftheactualbusinesscycle･

Thephaselagsinthesimulationcloselyapproximatetheobservedleadsand

lagsintheeconomy.Intheactualeconomy,vacancies,hiring,andtheworkweek

∬eleadingindicators,peakingbeforeaggregateoutput(grossdomesticproduct)･

Employmentisacoincidentindicator(inphasewithproduction)andinventoryis

alaggingindicator(peakingafterproduction)･Asseeninthefigure,themodelex-

hibitsallthesephaserelationships.Ofcourse,thecorrespondencebetweenthe

modelandactualbusinesscyclebehaviorisnotperfect,asexpected,giventheex-

tremesimplicltyOfthemodel｡Addingadditionalstructuretocapturetheimportant

omittedfeedbacksinthemacroeconomyfurtherenhancesthecorrespondenceof

themodeltotheactualbusinesscycle.

Theinventory-workforceinteractionliesatthecoreoftheshort-termbusiness

cycle.Businesscyclesarenotcausedbytheactionsofcentralbanks,changesin

governmentfiscalpolicy,Orrandomshockssuchasoilcrises,wars,ortechnolog-

icalbreakthroughs.Rather,thebusinesscyclearisesfromthefundamentalstruc-

tureofanindustrialeconomy-fromtheinteractionofinventorymanagementand

hiringpolicieswiththestockandflOwstructureofproductionandemployment･

Thenaturalperiodoftheinventory-workforceinteractionissimilartotheob-

servedperiodofthebusinesscyclebutthecycleishighlydisslpative-the

8Theparameters,roughlyconsistentwithSenge(1978)andN.Forrester(1982),areTimeto AverageOrderRate-26,ManufacturlngCycleTime-40,hventoryAdjllStmentTime-26, WIPAdjustmentTime -40,MinimumOrderProcesslngTime-8,SafetyStockCoverage-8, AverageLayoffTime -16,AverageTimetoFillVacancies-26,LaborAdjustmentTime-16, VacancyAdjustmentTime-16,VacancyCancellationTime-16,AverageDurationofEmploy- ment-150.TheEffectofSchedulePressureonWorkweekis(0,0.83),(0.25,0.86),(0.5,0.9), (0.75,0.95),(1,1),(1.25,1.05),(1.5,1.10),(1.75,1.14),(2,1.17)･Notethatparameterchanges

alonecannotconvertthemodelintoagoodrepresentationofthemacroeconomy･Thelevelof aggregationcapturedinamodelaffectsthedetailsoftheformulationsused･Forexample,inthe modelthefirmeitherhiresorlaysoffworkersbutdoesnotdobothatthesametime･Intheecon- omy,anindustry,oreveninalargefirm,however,laborneedsarenotperfectlycorrelatedacross allfirmsorsites,sosomedivisions,firms,andregionsarehiringwhileothersarelaylngWOrkers off.Inaggregatemodelsthelayoffratemightbeformulatedastheproductofthelaborforceand afractionallayoffrate,whichinturnwouldequalanormalfractionalratemodifiedbyvarious pressuresarisingfrom,e.g.,schedulepressureandprofitability･See,erg"Mass(1975).

784

FtGURE19-12

Simulatingthe businesscyc一e

Responseof theinventory- workforcemodel calibratedwith

parameterstypICa】 ofmacroeconomic modelsand

stimuJatedby randomvariations incustomerorders

(first-Order autocorre】ated noisewitha 4-weekcorrelation timeand5%

standarddevia-

tion).AHvariables normalizedso

theirequHibrium value-100. Seenote8for

Parameters.

PartV InstabilityandOscillation

o o L

nEê Lun !Jq![!nb 山

iii

o o L E a n lê ∈ n!L q!l!nb u

0 0

ー

1･

ooL = ¢n苛 > uJn!Jq≡ n b u

01 2 3 4 5 6 7 8 9 10ll12131415

54320 6 7 8 9 10ll12131415

A Li/-蜘ingRate Eど八

0 1 2 3 4 5 6 7 8 9 10ll12131415 Year

responseoftheeconomytoaslngleshockishighlydamped･Thebusinesscycle

persistsbecausetheeconomylSCOnStantlyperturbedbyrandomshocks,asseenin

Figure19-12.Theseshocksarenotthecauseofthecyclebutthetrlggerlngevents

thatelicitthelatentpatternofbehaviorgeneratedbytheunderlyingfeedback structure.9

9EconomistshavedebatedsinceatleastFrisch(1933/1965)whetherthebusinesscycleisa dampedoscillationkeptalivebyrandomshocksorase一f-sustaimngcyclerequlrlngnOrandom shocks.Researchinthesystemdynamicstraditionsuggeststheshort-termbusinesscycleis damped,whiletheeconomiclongwaveorKondratievcycleappearstobeaself-sustainlnglimit

Chapter19 TheLaborSllpplyChainandtheOriginofBusinessCycles 785

Theobservationthatthebusinesscycleisahighlydampedmodeofbehavior

excitedbyrandomshocksexplainsthevariabilitylnthedurationanddetailsofin-

dividualcycles.Bothintheeconomyandinthesimulationsofthemodel,theran-

domshockscauseeachcycletohaveauniqueCharacter･Somearelongerthan

average,someareshorter.Theamplitudeofthenuctuationvariesfromcycleto

cycle.Theextenttowhichtheleadingandlagglngindicatorsleadandlagvaries

fromcycletocycle.

19.3.1 lstheBusinessCycleDead?

Thehypothesisthatthebusinesscyclearisesfrom inventory-workforceinter-

actionsandrelatedfeedbackshasimportantimplications.Itmeansthebusiness

cycleorlglnateSintheprlVateSeCtOr丘.omtheordinary,everydaydecision一making

processesofmillionsoffirmsandindividuals.Italsomeansstabilizationofthe

businesscyclethrough governmentmonetaryandfiscalpolicyisdifficuh

Policyleverssuchastaxandinterestratesdonotaltertheunderlyingfeed-

backsorparametersoftheinventory-workforcestructureandthusareunlikelyto

alteritsinherentoscillatorybehavior.Changesintaxandinterestratescreate

shocksthatperturbthesystemandmaythemselvesexciteratherthandampoutthe

cycle.Economists acrossthe politicalspectrum,from Milton Friedman

(1956/1973)toA.W.Phillips(1954),havelongarguedthatmonetaryandfiscal

policiesintendedtostabilizethebusinesscyclemayactuallybedestabilizlng.Poli-

ciessuchasralSlngInterestratesWhentheeconomyoverheatsandloweringthem

whenrecessionthreatensaredesignedtocreatenegativefeedbackswhosegoalis

tocounteractvariationsinunemployment,inflation,oroutput.However,thereare

longdelaysinthemeasurementandreportlngOfthedata,inthedecisiontoalter

monetaryandfiscalpolicies,andinthetimerequiredforanychangesininterest

rates,transferpayments,ortaxratestohavetheireffects.Thesedelaysarelongrel-

ativetotheperiodofthebusinesscycleandmayactuallydestabilizeit,Counterto

theintentionofpolicymakers.

Underrationalexpectations,Welllinformedrationalagentsandcentralbankers

understandthestructureoftheeconomyandperfectlyaccountfortimedelaysand

feedbackeffects.Intherealworld,theydon't.AlanBlinder(1997,pp.9-10),re- flectlngOnhisexperienceasViceChairmanoftheUSFederalReserve,described

withrefreshingcandorhoweasyltisevenforexperiencedpolicymakerstounder-

estimatedelaysuslngthefamiliarthermostat-with-time-delayanalogy:10

cycle(Seechapter4forthedistinctionandSter竺an1986fordiscussion)･Thoughbeyondthescope ofthischapter,theanalysishereraisesthequestionOfentrainment.Evenifindividualfirmsoscil- lateinresponsetorandomshocks,whydotheseoscillationsoccurinphase?Thatis,whyistherea businesscycleatthelevelofthemacroeconomyratherthanahostofindivldualcyclesthatcallCel outattheaggregatelevel?Entrainmentofindividualcyclesiscommoninthenaturalworld,from theentrainmentoftheorbitalandrotationalperiodofthemoon(accountingforitsdarkside)tothe beatingofyourheart(life-threateningfibrillationoccurswhenthisentrainmentbreaksdown)tothe

synchronizedflowe.ringofcertainspeciesofbamboo･Haxholdtetall(1995)discussentrainmentof economic.Cyclesusln_gaSimplemodel･Strogatz(1994)providesanexcellentintroductiontothe mathematlCSOfentralnment.

10compareBlinder'sthermostatsystemtoAftalion'scoal-thermostatanalogyandthediscussion ofsystemsinwhichpeopleignorethesupplylineofcoITeCtiveactionsdiscussedinchapter17･

786 PartV InstabilityandOscillation

Lagsinmonetarypolicy-･tendtobetrivializedorIgnoredinacademia‥.But theyposeahugepracticalproblemforpolicymakers.Failuretotakeproper accountoflagsIS,Ibelieve,oneofthemainsourcesofcentralbankerror.

Onereasonissimple-･Allcentralbankersunderstandthattherearelong lagsinmonetarypolicy.Butwhenpolicyisbeingeithertightenedoreased,policy makerstypicallyhavenousablequantitativeestimateofwhatareoftencalled "pipelineeffects,"thatis,thelaggedeffectsofpreviousmonetarypolicyactions thathavenotyetshownthroughinthedata.

Thesecondproblemwithlagsrunsmuchdeeperandis,atleastinpart,psy- ChologlCal.Putplainly,humanbeingshaveahardtimedoingwhathomoeconomi-

cusdoessoeasily:waltlngPatientlyforthelaggedeffectsofpastactionstobefelt Ihaveoftenillustratedthisproblemwiththeparableofthethermostat.Thefollow- 1nghasprobablyhappenedtoeachofyou;ithascertainlyhappenedtome.You checkintoahotelwhereyouareunfamiliarwiththeroomthermostat.Theroom

ismuchtoohot,soyoutumdownthethermostatandtakeashower.Emerglng 15minuteslater,youfindtheroomstilltoohot.Soyouturnthethermostatdown anothernotch,removethewoolblanket,andgotosleep.Atabout3A.M.,you awal(eshiveringlnaroomthatisfreezingCOld.

ThecorrespondingerrorinmonetarypolicyleadstoastrategythatIcallHlook- lngOutthewindow.=Ateachdecisionpolnt,thecentralbanktakestheeconomy's temperatureand,ifitisstilltoohot(Ortoocold),proceedstotighten(ortoease) monetarypolicyanothernotch･Withlonglags,youcaneasilyseehowsuchmy- opicdecisionmakingcanleadacentralbanktooverstayItspolicystance,thatis, tocontinuetightenlngOreasingfortoolong.

‥icannottellyouhowmanytlmeS,bothattheFederalReserveandat meetlngSWithforeigncentralbankers,discussionsoffuturepolicywerecutshort withphraseslikeHlet'sseewhathappensHorHwe'llhavetowaituntilnextmonth (ornextmeeting)."

IfactivistgovemmentpolicylSn'tlikelytostabilizetheeconomy,perhapstechn0-

10glCalinnovationsandlearningWill.InformationtechnologyandsoICalledlean

manufacturlngtechniquesshouldenablefirmstointegratetheirentiresupply

chain,reduceinventories,anticipatethedelaysinadjustlngresources,andstabilize

thecycle.

Changeslnproductionschedulingandhiringpoliciesand c h angesinthe

lengthsofhiringandproductiondelayscanalterthecharacteristic so f thecycle.As

seeninthesimulationsandpolicyanalysis,greaterflexibilityln W O rk weeksand

capacltyutilization,bystrengtheningthefirst10rdernegativefeed b ac k sregulating

inventories,arestabilizing･Cuttlngthedelaysinadjustlngpr o d u c tio n capaclty,

employment,andtrainlngisalsostabilizlng.Reducing in v en to ry coverage

throughoutthesupplychaincanalsoreducetheperiodandincreaseth estabilityof

thecycle･Overthepasttwodecadestheleanmanufactunngrev o lu tio n h asbegun

toreduceinventorycoveragethroughouttheeconomy.Inform atio n tec h nologylS

helpingtolinkpartnersinarangeofsupplychains,shortening in fo rm atio nreport-

1nganddecision-makingdelays.

ThesechangesshouldhelptostabilizethebusinesscycleJ n d eed , th eevidence

suggeststhebusinesscyclewasslightlylessviolentinthelate2 0 th c en tu ry thanin

thelワth,atleastinthedevelopedeconomies.However,theim p ac t o f th esewel-

comechangesshouldnotbeoverestimated.Theymayarisesim p ly fro m thenat-

uralevolutiontowardaservice-basedeconomy.

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 787

InthelワthcenturyagrlCultureandmanufacturlngdominatedtheeconomy.

Bothsectorsinvolvesignificantinventories,longsupplychains,andlongdelaysin

adjustlngproductiontochangesindemand.Overthepastcentury,theshareof

GDPandemploymentarisingfromthesesectorshasfallen,whilethesharearising

fromservicesandgovemmenthassteadilyrisen.Serviceindustriesinvolvemuch

smallerinventoriesthanmanufacturlng.Asshowninthesimulationsandpolicy

analys上sabove,reducinglnVentOryCOVerageinthesupplychainshortensthepe-

riodandincreasesthedamplngOfthecycle.Thusthetransitiontoaserviceecon-

omymayreducethedurationandseverltyOfbusinesscycles,independentofany

technologlCalprogressorlearningbyfirms.

Thetransitiontoservices,however,isunlikelytoeliminatebusinesscyclesal-

together･Thoughmanyserviceindustriesdonotinvolvesignificantphysicalin-

ventories,theservicedeliverysupplychainofteninvolveslongdelays.For

example,theinsuranceindustrycarriesnoinventoriesofphysicalproductandno

rawmaterialsstocks.YetthedelaysbetweenwrltlngInsurancePOliciesandthere- alizationoflosses,andbetweenlossesandtheresolutionofclaims,contributeto

thepersistentunderwritingCyclethathasplaguedtheindustryforatleastacentury (Figure19-13).

Eveninmanufacturing,therearelimitstolean･Inventoryreductionsgenerated

byjust-in-time(JIT)andleanmanufacturingpoliciesimplementedbyonefirmare

oftenoffsetbyincreasesininventoriesheldbysuppliersorcustomers.Wh ena

manufacturermovestoJITmaterialsdelivery,itssuppliersmustdelivermore

frequentlyandwithmuchhigherreliability.Tomeetthesemorestrlngentrequire-

mentssuppliersoftencarryadditionalinventory.Largefirmsoftencuttheinven-

toriescarriedontheirbalancesheetsthroughthird-partywarehouslnglnWhich

materialsinventoriesremainattheproducer'ssitebutarestillownedbythesup-

plieruntiltheyareused.Suchpoliciesreducetheinventorylevelsofindividual

firmsbutdon'tappreciablychangeinventorylevelsfortheeconomyasawhole.

Figure19114ShowsaggregateinventorycoverageintheUSmanufacturlngSector.

Asinthemodelhere,inventorycoveragefluctuatesstronglyoverthebusiness

cycle.Fromthe1950sthroughabout1990coverageoscillatedaroundarela-

tivelyconstantlevelofaboutl･7months･Since1990,asleanproductionpractices

FIGURE19-13 Theinsurance

underwritingcycle

Underwriting profitsf一uctuate sharplythough thereare

nophysical inventoriesor rawmaterialsin theinsurance

supp一ychain･

(

Lun !u aJd pa u

t=3

叫

% )

芸0 Jd 6u !)!)Nu

1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

Source:191011970,Stockinsurancefirms,HistoricalStatistlrCSOftheUS,Series X-956,1974-1996,propertyandcasualty/Iiab‖ltyf‖'ms,StatI'stl'ca/AbstrlaCtOftheUS, Varl0uSyearS･

788

FIGURE19-14 Inventory coverage,US manufacturJng

Inventoriesrelative

toshipmentsin USmanufacturlng industry.Doesnot includefinished

inventoriesheldby retailersandother distributorsoutside

themanufacturlng sector.

PartV instabilityandOscillation

2.0

1.8切 .!= ･l･･J l= ○

≡ 1.6

1.4

1950 1960 1970 1980 1990 2000

Source.PUSCensusBureau,M3Survey,

diffusedthroughtheeconomy,Coveragehasgraduallydeclinedtoanaverageof about1.4bythelate1990S,adropoflessthan20%.

Nodoubtfurtheradoptionofleanmanufacturlngandfurtherdevelopments ininformationtechnologywillenableinventorycoveragetodeclinestillmore.

Nevertheless,itwouldbeunwisetopredictthattechnologicalprogressspellsthe deathofthebusinesscycle.Overthepastcentury,thebusinesscyclehasbeenpro- nounceddeadmanytimes,usuallyafterlongperiodsofexpansionsuchasthe 1920S,1960S,and1990S.Eachtime,thecycleemergedagain,Oftenwithrenewed

vlgOr,BusinesscycleshaveexistedsincethebeginnlngOftheindustrialage,con- tinulngOVermorethantwocenturies,desplteunimaginablechangesintheprod-

ucts,technologleS,markets,transportationandcommunicationtechnologleS, economicinstitutions,governmentpolicies,anddominantnationsintheworld eCOnOmy･

Thepersistenceofbusinesscyclesdespltethecompletetransformationof everyaspectoftheglobaleconomytestifiestotheenduringandfundamentalchar- acterofthestructureunderlyingthecycle.Thoughmanyoftheproductsandtech-

nologleSusedtodaywouldbeunrecognizabletoAdamSmith,manufacturingfirms stillmaintaininventoriesandstillrequlrelabor.Itstilltakestimetoalterproduc- tion,acqulrematerials,andbuynewequlpment.Itstilltakestimetobi一eandtrain

workers.AnunantlClpatedincreaseindemandstillcausesadroplninventory,and theonlywaytorebuilditistoboostproductionaboveshipments.BoostlngprO- ductionstillrequlreSmoreresources,includinglabor.Mostofthechangesintech-

nology,marketstructure,products,andsoonoverthepast200years,despitetheir undoubtedimpactonourlives,Canbewellrepresentedinthemodelbymodest changesinparameters.

19.噂 SuMMARY

Thischaptershowedhowthestockmanagementstructurecanbeappliedtothela- borsupplychain.AsimplemodeloflaboracqulSitionwasdeveloped,including vacancycreation,hiring,andlayoffs.Themodelwasthenlinkedtothemanu-

facturlngSupplychainmodel.Theresultingmodelofinventory-workforceinter- actionsoscillateswithcharacteristicscloselyresemblingthebusinesscycle.The

Chapter19 TheLaborSupplyChainandtheOriginofBusinessCycles 789

cyclearisesfromthenegativefeedbacksthroughwhichfirmsseektomaintainin-

ventoriesatapproprlatelevels.Delaysinthesefeedbackscausedbythehiring

processmeanproductioncannotbeadjustedinstantlytodesiredlevels.Thedelays

inthesenegativeloopscausetheoscillation,

Thechapteralsoshowedhowflexibilitylntheworkweekandcapacltyutiliza-

tioncanhelpstabilizesuchoscillations.Ⅰngeneral,youcanstabilizeanoscillatory

systembycreatingfirst-ordernegativeloopsthatshort-circuitthedelaysinexist-

1ngloopsthatcreateinstability.

IntermsofmodelingskillS,thechapterprovidedexamplesoffomulatingro-

bustdecisionrulesandnonlinearbehavioralrelationships.Guidelinesforanalyz-

1ngandexplainlngmodelbehaviorwerealsodeveloped.

T馳e五mvisibleHandSomet毒m es

S艶盛eS…f=¢_!ltii3i3_串貞呈年章二ざ∈_!ieS

Correctivefeedbackfwcesweprovidedincompetitiveeconomiesbychanging profitpossibilitiesthathavetendedtodirectcapital..into"approprlate" channels.Theimpliedfeedbackhasbeencomplicatedbytwohuman characteristics:thetendencytoenvisagethefutweonthebasisoflinear

projectionsoftherecentpast,andafollow-the-leadertendencyamongthose whomakeinvestmentdecisions.Thesecharacteristicsdecreedthatthe

economiessystematicallyundershotandovershot.. ,lurchingtheirway throughhistofTlnPerpetualdisequilibrium.

-W W.Rostow(1993,pp.14-15)

Uptonowthefocushasbeenmodelsofindividualfirms･Marketforces-thefeed- backsbetweenprlCeanddemandandsupply-wereomitted.Thesesupplychain modelstendtooscillateinresponsetoshocks.Domarketforcesattenuateoram- plifysuchoscillations?Manyindustriesexperiencechroniccyclicalinstability･ Mostcommodities,whetheranimal,vegetable,Ormineral,experiencecyclesin prlCeSandproductionwithcharacteristicperiods,amplitudes,andphases.Indus- trieswithlongCOnStruCtiondelaysandlongassetlifetimessuchasshipbuilding, paper,chemicals,andrealestatelikewiseexhibitstrongcyclicaldynamics.Even serviceindustriessuchasinsuranceexhibitcharacteristiccyclesinprlCe,prof- itability,andinvestment.ThediversltyOfthesecyclessuggeststheyariseendoge- nouslywithineachindustry.Inthesemarketsthenegativefeedbacksthrough whichpriceseekstoequilibratesupplyanddemandofteninvolvelongtlmedelays, leadingtooscillation.

791

792 PartV InstabilityandOscillation

Thischapterdevelopsagenericcommoditymarketmodel･WhereprlOrChap-

tersfocusedontheresponseofafirmtochangesinorders,thischapteraddsthe

roleandresponseofprlCeSandprofitability.AformulationforprlCeSettinguseful

inawiderangeofmarketsettlngSisdevelopedandtested･Thechapterdevelops

yourformulationskills,includingprlnCIPlesforformulatlngdecisionrulesthat

representanaggregateindustryratherthanaslnglefirm,whilestillgroundingthe

formulationsinknowledgeoftheindividualdecisionmakers.Challengesinvite

youtoelaboratethemodelandtodesignandtestpoliciestoimproveperformance･

20月 GoMMODITYCYcLES:FROMAIRCRAFTTOZぎNC

Commoditiesincludemineralproductssuchascopper,iron,andmercury;forest

productssuchaslumber,pulp,andpaper;andagriculturalproductssuchascoffee,

cocoa,andcattle･1Manycommoditiessufferfrompersistentcyclicalinstabilityln

prlCeS,Production,profitability,andinvestment.InstabilitylScostlyfortheaf- fectedindustriesandtheircustomers.Fromthecostofyourmorningcoffeeand

newspapertothepriceOfsteel,commodityprlCeSaffectyouincountlessways･

Manydeveloplngnationsdependoncommodityexportsforthebulkoftheirhard

currency.FluctuationsinprlCeSanddemandhaveforceddevaluations,plunged

wholenationsintodepression,andtriggeredpoliticalunrest･

Acommonexplanationforcommoditycyclesisthatdemandiscyclical.Itis

ofcoursetruethattheoveralleconomyrisesandfallswiththebusinesscycle,and

thesemovementsinducesomecorrespondingfluctuationincommoditymarkets･

Yetmanycommoditymarketsfluctuatefarmorethantheeconomyasawhole,ex-

hibitcycleswithdifferentperiods,andarenotentrainedtothebusinesscycle,sug-

gestlngthatafeedbackstructureendogenoustotheparticularcommodity lS

responsible･

Figures20-1through20-6showsometypicalexamples･HogprlCeSandpro-

duction(Figure2011)fluctuatewithroughlya4-yearperiod,whilethecattlecycle

averagesabout10-12years(Figure20-2)･Cyclesincopperpricesarewelldocu-

mentedbacktoatleast1840(Figure20-3).Thedatashowratherregular,largeam-

plitudecyclesofabout8-10yearsaroundthelong-termtrend･Thetrendexhibits theeffectsofpostwarinflationbutalsoshowsalongcycleassociatedwiththeeco-

nomiclongwave.

CommoditycyclesnotonlyariseinrawmaterialsandagrlCulturalproductsbut

alsoinhigh-techandhighlydifferentiatedproducts.Asanexample,Figure20-4 showsthatcommercialaircraftordersandproductionfluctuatewithalargeampli-

tudecycleofroughly10years.Figure19-13presentedtheinsuranceunderwrltlng

cycleラ ShowingthatcyclicalinstabilitylSnotlimitedtocommoditiesbutalso

plagueshighlydiftTerentiatedserviceindustries.

iThenotionofacommodityImpliesanundifferentiatedproduct,oftensuppliedbymanysmall, independentproducerssothatthemarketisapproximatelycompetitive･However,chroniccyclical instabilityarisesalsoinindustriesdominatedbyasmallnumberoflargeproducersandinindus- triesofferinghighlydifferentiatedproducts,includingcommercialaircraft,realestate,shipbuilding, semiconductors,andinstlranCe.

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796 PartV InstabilityandOscillation

FIGURE20-4 Worldwideaircraftorders

Annualgrowthratein ordersforcommercialair-

craft(jetswith≧50seats), commerciaJairtravel(rev-

enuepassengerkm/year), andGDPweightedby eachreg10n'sshareof worldairtraveldemand. Demandforaircraftex-

hibitsalargeamplitude cycleofroughly10years.

FIGURE20-5

USelectricutHity capabifitymargFn

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1950 1960 1970 1980 1990 2000

Source:Statl'sticalAbstractoftheUS,EdisonElectnclnstltute.

Asyoushouldexpect,thesecyclesarenotperfectlyregularandtheinfluence

ofeventsexternaltothemarkets,suchasbusinesscycles,wars,andweather,is

clearlydiscernible(e･g･,thepricecc･ntrolsoncopperduringWorldWarII).

Manyindustriesgenerateatleasttwodistinctcycleperiods･AsshowninFig-

ure20-18,thepaperindustryexperiencesaroughly4-yearcyclemostprominent

ininventories,production,andprice,andalsoalonger,10-15yearcyclemostap-

parentincapacity･Likewisetheoiltankerindustry(Figure20-6)exhibitshigh-

frequencycyclesOfafewyearsinpricebutalsoalargeamplitudecapacltyCycle

ofroughly20years･Theamplitudeoftheshort-ten cycleinpricedependsonthe

phaseofthe20-yearcapacityCycle:PricesarehighandvolatilewhenworldBeet

utilizationishigh;whenthereisexcesscapaclty,prlCeSandpricevariabilityare low.Realestatemarkets(Section17.4.3;Figure17-14)∬esimilar:Pricesandcon-

Stmctionactivityrespondtothepulseoftheshort-termbusinesscyclebutaredom-

inatedbya10-20-yearcycleofmuchlargeramplitude･Sla°e(1982),using

spectralanalysis,foundcyclesof10-14yearsintheprlCeSOfmetalsincludingalu-

minum,copper,iron,lead,silver,tin,andzinc,alongwithmorerapidfluctuations

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correspondingtotheshort-term businesscycle.A goodmodelofcommodity

industriesmustexplaintheorlginofboththeshort-term inventorycycleandthe

slowercapacltyCyclesobservedinthesemarkets･2

20.2 AGENERICCoMMOlJ汀YMARKETMoDEL

Theunderlyingfeedbackstructureresponsibleforcommoditycyclesisshownin

Figure20-7･3Buildingonthebasicfeedbackstructureofmarketsintroducedin

section5.5,Figure20-7showsthestockandnowstructureofcommodityproduc-

tionandtheperceptualandadministrativedelaysinthemainbehavioraldecision

processes.ThestockandflOw structureforproductionandinventoryatthetopof

thediagramrepresentsthesupplychainforthecommodity(suchasinventoriesof

copperoreandrefinedmetal);thestockandflOwstructurefTorproductioncapacity

(suchasmines,orecrushers,andsmelters)appearsattheleft.

ConsiderfirstthestockandflOw structureforproductioncapacltyandpro-

duction.ProductioncapacltylSincreasedbycapacltyaCqulSitionanddecreasesas

capacitydepreciatesandisdiscarded.Capacityacquisitionofteninvolveslong

delays,CreatlngaSupplylineofcapacltyOnOrderandunderconstruction.Capaclty

andcapacltyutilizationdeterminetheproductionstartrate.Productionusually

takestime,creatlngaSignificantsupplylineofinventorylnProcess.Avai1-

ableinventoryofthecommoditylSincreasedbyproductionanddecreasedby

COnSumptlOn･

2TheclassicaleconomictheoryofcommoditycyclesIStheso-Calledcobwebmodelwhich positsthatdemand(D)respondstoprice(P)immediatelybutsllpply(S)respondswithalag:

Dl-j:D(Pt);St=j:S(P卜1)･Youcan?asilyshowthatthecobwebmodeloscillates,withaperiod equaltotwicetheintervalbetweentlmePeriods.First,linearizethesupplyanddemandcurves aroundtheequilibriumpolnt:Dt-do+dlPt;St-So+sIP卜1;Sl>0,dl<0.Next,assumethe

marketclearseveryperiodandequatedemandandsupplytoyleldasinglefirst10rderlineardiffer- enceequation:Pt-(so-do)/dl+(sl/dl)Pt【1.ThesolutionisPt-P｡+[Po-P｡](sl/dl)t,WherePo istheinitialpriceandP｡ -(so-do)/(dl-Sl)istheequilibriumprice.Whilecobwebmodelsdo capturethecorestructureunderlyingcommoditycycles-thetimedelayinthenegativefeedback fortheresponseofsupplytoprlCe-theyareunsuitableforseriousmodelingofmarketdynamics.

First,theydonotrepresentthestockandnowstructureofrealmarkets(includinginventorieヲ,work inprocess,andproductionヲapacity)･Second,theyarefomulatedindiscretetime･Discretetlme modelsoftengeneratespuriousdynamics,akintotheintegrationerrorthatariseswhendifferential equationmodelsaresimulatedwithtoolargeatimestep(soICalledDTerrorlAppendixA]).Third, theintervalbetweenperiodsisassumedtocorrespondtothetimerequiredtoproducethecom- modity,suchasthegestationandmaturationtimeforlivestock.However,theobservedperiods ofcommoditycyclesaremuchgreaterthantwicetheproductiondelays･Thegestation一maturation delayforhogsisllmonths,buttheperiodofthehogcycleis4years;theconstructiontimefor commercialbuildingsisabout3years,buttherealestatecyclerangesfrom10to20years.Fourth, theydonotdistinguishbetweenproductioncapacltyandcapacltyutilizationandsocannotexplain themtlltipleoscillatoryperiodsobservedinmanylndustries･Propercommoditycyclemodels,like alldynamicmodels,shouldrepresentthestockandflowstructure,timedelays,andbehavioral decisionprocessesofthemarket.Thedelaysshouldbesettotheiractualvalues,notmultiples ofsomearbitrarytimePeriod,andthemodelsshouldbeformulatedincontinuoustime.

ヨThemodelsdevelopedinthischapterwereinspiredbyMeadows(1970)whodevelopedan earlysystemdynamicsmodelofcommoditycyclesandappliedittolivestock.SeealsoW eymar (1968).Gtivenen,Labys,andLesourd(1991)provideagoodoverviewofmoderncommodity models.

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800 PartV InstabilityandOscillation

Figure2017showsthethreeprlnCipalfeedbackshelpingtoequilibratesupply anddemand.Onthedemandside,thedemandforanycommoditydependsonits prlCerelativetosubstitutes,thenumberandpurchasingpowerofconsumers,and

socialandtechnicalfactorsunrelatedtoprice(suchasatrendtowardlow-fatdiets thatmightreducebeefconsumption).Highpricesreducetherelativevalueofthe commodity,CausingdemandtofallthroughtheSubstitutionloopB1.Substitution ofteninvolvessubstantialdelays:Whileconsumerscanrapidlyswitchfrombeef

toporkwhenporkpricesfall,theresponseofoildemandtoprlCeisveryslowdue tothelonglifetimesofoil-consumingcapitalstockssuchascarsandbuildings(see Figure5-ll).

Onthesupplyside,higherprlCeSleadtohigherutilizationofexistlngCapaClty (thebalancingCapacityUtilizationloopB2),Ⅰfhighpricespersist,capacitywill expand,boostingProductionthroughtheCapacityAcquisitionloopB3.Whileboth utilizationandcapacityaCqulSitionrespondtoprlCe,thesedecisionsdifferinim-

portantways.Theutilizationdecisionrespondstotheexpectedprofitabilityofcur- rentoperations.ExpectedoperatingProfitability,lnturn,dependsonthevariable

costsofoperationsandtheprlCeproducersexpecttorealizewhenproduction startedtodayisavailableforsale.Theexpectedprofitabilityofnewinvestmentin contrastdependsonthetotalcostsofnewcapaclty,bothfixedandvariable,andon

investors'forecastsofwhatprlCeSWillbeoverthelongterm･Thesemaydiffer fromtheshort-runpriceexpectationsusedtodriveutilization.

ThecurrentorspotprlCeOfacommoditydependsonthebalanceofsupplyand demand･Thecurrentsupplyistheavailableinventory,beitlngOtSOfcopperor frozenporkbellies.Demandisthecurrentorderrateororderbacklog.Pricestend

torisewheninventorycoverage(theratioofinventorytoconsumption)falls. Pricesarealsoinfluencedbyotherfactors,suchasthecostofinventorycompared

tothecostsofstorageandriskofspoilageorobsolescence,thedegreeofcompet- itivenessinthemarket,beliefsaboutthecostsofsubstitutes,andsoon.

NotealsothebalancingAvailabilityloop(BO),whichlimitsconsumption wheneverinventorylSinadequate｡Inmanymarkets,prlCeS,demand,andproduc-

tionusuallyadjustquicklyenoughtopreventshortages.Butmarketsdonotalways clearbyprlCealone,AvailabilityoftenplaysalargeroleinbalanclngCOnSumptlOn

withproduction･Shortagesareexperiencedaslengtheningdeliverydelays,prod- uctsplacedonallocation,orsimplystockouts.Availabilityalsoplaysakeyrolein marketsfordifferentiatedproductswherepricesadjustslowly(suchasrealestate

orcommercialaircraft)orwheresocialnormsforfairnesslimitpriceincreases whensuppliesareshort(Thaler1991).Evenincommoditymarketswhereprices normallyadjustrapidly,extremeconditionssuchaspricecontrolsorarunofPanic buyingcanoverwhelmthepricefeedbacksandforceshipmentsbeloworders.

TheSubstitution,Utilization,andCapacityAcqulSitionloopsallinvolvede- laysofvarioustypesandmaythereforecauseinstabilityandoscillation.Ifthepro- ductiondelaysarelongenough,oscillationsmayariseascapacityutilization

adjustsinresponsetochangesinprlCe･ThedelaysinthecapacltyaCqulSltionfeed-

backaremuchlongerandmayproduceevenlongercycles･Bothsupplysideloops includephysicaldelays(thecapacityacquisitionandproductionlags)andinfor- mation/perception/decision-makingdelays(thedelaysinformingpriceexpecta- tions,assessingexpectedprofitability,andmakinginvestmentplans).

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 801

20.2.1 Productionand!nventory TomovefromtheconceptualmodelinFigure2017toaformalmodel,beginwith

thesupplychainforproduction(Figure2018)･Thesupplychainiscapturedvery

simplyasatwo-stockchainwithWIPandfinishedgoodsinventories.Backlogs

andotherstagesofprocesslngandstorage,bothupstream anddownstream,are

omitted.Ofcourse,itisasimplemattertoreplacethetwo-Stocksupplychainused

herewithoneofthemoresophisticatedversionsdevelopedinearlierchaptersor

withoneofyourowndesign.Thestockandflowchainisformulatedas

Inventory=INTEGRAL(ProductionRate-ShipmentRate,Inventoryb) (20-1)

WIP∫nventory

-INTEGRAL(ProductionStartRate-ProductionRate,WIPt｡)

FIGURE20-8 Manufacturingsupplychainandcapacityutilizationsectors

PrlDductionand

Inventory

+production StartRate

Work in

Process Rnventory

MinimumOrder ProcessJngTime

Tablefor

/ --宣 { Fu冨㌶ rent Maximum

Shipment Rate

FulfilJment

】nventory

Order Fulf‖ment

2 tio もDesired

Shipment Shipment Rate

Rate サー一一/

(20-2)

Pr10duction

Capacity

Manufacturing CycleTime

鼻_+

nventory------へ､一､ -㌔ Coverage

Capacity UtiHzation

･トト

ム卓･ Capacity UtihLzation

Utilization ､hdicated Adjustment Capacity

Time Utjlization

F上慧望;kCLepd TabreforEffect ofMarkupon Utilization

CapacityUtilizelion

TimetoAdjust Short-RunPrice Expectations

TimetoAdjust Expected

VariableCosts

Customer Orders

Unit Variable Cost

802 PartV InstabilityandOscillation

ShipmentsaredeterminedbycustomerordersandtheOrderFulfillmentRatio:

ShipmentRate-DesiredShipmentRate*OrderFulfillmentRatio (2013)

OrderFulfillmentRatio

-i(MaximumShipmentRate/DesiredShipmentRate) (20-4)

MaximumShipmentRate-Inventory/MinimumOrderProcessingTime (20-5)

DesiredShipmentRate-CustomerOrders (20-6)

Theorderfulfillmentratioisthefractionofordersfilledandisafunctionofthe

MaximumShipmentRaterelativetotheDesiredShipmentRate.Themaximum shipmentrateisdeterminedbyinventoryandtheminimum timerequiredto processandfillanorder.Themeanlngandderivationoftheorderfulfillmentfunc- tionaredescribedinsection18.1.1.Desiredshipmentshereequalcustomerorders (backlogsareomitted).

Productionismodeledasadelay.Athird-orderdelayprovidesareasonable distributionofcompletionsaroundtheaverageManufacturingCycleTime:

ProductionRate

-DELAYS(ProductionStartRate,ManufacturingCycleTime) (20-7)

Capacltyandcapacltyutilizationdetermineproductionstarts:

ProductionStartRate-ProductionCapaclty*CapacityUtilization (20-8)

CapacltyutilizationcapturesvariationsintheintensltyOfproductionaboveorbe-

lowtheno-alrate･Utilizationmayvaryduetodeliberatemanagementdecisions torespondtocurrentprofitabilityorproductionpressureorduetoundesiredfac- torssuchasequipmentbreakdowns,materialsshortages,Orshortagesofstorage capacityforotltput･Laborisnotmodeledexplicitlybutisinsteadimplicitinthe delayinadjustlngutilizationtotheindicatedlevel.

20.2.2 CapacityUtHZation

Utilizationdependsonproducers'expectationsregardingthecurrentprofitability ofoperations(Figure20-9).Inreality,utilizationalsorespondstoinventoryand

backloglevels･Forexample,productionofmanycommoditiesisconstrainedby theavailablestoragecapaclty-WhenstoragecapacltylSapproached,production mustbecutback,evenifprofitabilityremainshigh(seeHomer1996foranexam- pleinthechemicalsindustry).Likewise,shortageswillleadtoincrea-Sedutiliza-

tionatanygivenlevelofprofitability･Thedecisionstructurefortheseeffectsis consideredinchapters17-19･Fornow,theimpactoftheseinventoryadjustments onutilizationisomitted;thechallengeinsection20.3invitesyoutoaddthemto

themodelandexploretheirimpactonmarketstability. Utilizationcannotgenerallybechangedimmediately.Ittakestimeforproduc-

erstogatherdataoncostsandprofitability.Evenwhendataareavailablefre-

quently,lttakestimetofilteroutnoiseanddetectchangesinthetrend.Evenafter, say,adroplnOPeratlngProfitisrecognized,producersarereluctanttoshutdown alineorplant,waltlnginthehopethatprofitabilitywillrebound.Oncethedeci-

siontoadjustutilizationismade,ittakesfurthertimetoimplement(forexample,

Chapter20 TbelnvislbleHandSometimesShakes:CommodityCycles

F】GURE20･9

Dependenceof

indicatedcapacity utHzationonthe

expectedmarkup (s s a lu O !S u a Lu !P )

u o E[te N ≡ l⊃ ^ lP e d t23

P a t申 Ul.P U つ

1.0

0.8

0.6

0.4

1.0 2.0 3,0 4.0

ExpectedMarkupRatio (dimensionless)

803

tochangethelaborforce).Forsimplicitythedelayintheadjustmentofutilization

tothedesiredlevelisform ulatedasfirst-orderexponentialsmoothing:

CapacityUtilization

-SMOOTH(IndicatedCapacityUtilization,UtilizationAdjustmentTime)(20-9)

wheretheUtilizationAdjustmentTimeaggregatesthedatacollection,decision-

making,andimplementationdelaysJndicatedutilizationdependsontheexpected

profitabilityofoperations,indicatedbytheExpectedMarkupRatio,theratioofex-

pectedpricetoexpectedunitvariablecosts.

IndicatedCapacityUtilization-f(ExpectedMarkupRatio) (20110)

ExpectedMarkupRatio -Short-RunExpectedPrice侶ⅩpectedVariableCosts

(20-11)

UtilizationdependsonlyonvariablecostsbecausethedecisiontorunexistingCa-

pacitydependsonlyonmarginalrevenue(theprice)comparedtothemarginalcost

ofanincreaseinutilization.Forthepurposeoftheutilizationdecision,CapacltylS asunkcostandshouldnotmatter.4

Theeffectofexpectedmarkuponutilizationcapturestheshort-runsupply

curvefortheaggregateindustry-howmuchadditionaloutputisgeneratedbyan

increaseinprice,glVeneXistlngCapacity.Specifyingtheshapeandlikelyvaluesof

thefunctionrequlreSfirstconsideringtheutilizationdecisionforanindividual

plantorpleCeOfequlpmentandthenaggregatingOverthepopulationoffacilities

intheindustry.

4Inpractice,peopleoftenfallvictimtothesunkcostfallacy'continulngtOinvestinlosingposi-

tionsinanattempttorecovertheirpriorinvestment(throwinggoodmoneyafterbad).Inthecon- textofcapacltyutilizat10n,thesunkcostfallacymeansproducerswouldcontinuetooperateeven whenprlCefallsbelowunitvariablecostsinanattempttorecovertheirfixedcosts.Costaccountlng systemsthatpenalizeoperatorsforunderrecoveryofoverheadreinforcethetendencytooperateat aloss･Totheextentthesunkcostfallacyoccurs,capacltyutilizat10nWillbegreaterthanzeroeven whentheaverageexpectedmarkupratioislessthan1･

804 PartV InstabilityandOscillation

Economictheorysuggestsfirmsshouldoperateanyequipmentforwhichthe

markupratioisgreaterthan1,thatis,aslongasprlCeexceedsthevariablecostsof

producinganotherunitwiththatequlpment.TheequlpmentShouldbeshutdown

whenprlCefallsbelowunitvariablecosts･5whilethetheoreticalutilizationfunc-

tionforasingleunitofcapacityissharplydiscontinuous(reflectingthedecisionto

operateorshutdown),theaggregateutilizationfunctionforanentireindustrywill

beasmoothcurve,rislnggraduallyastheexpectedmarkupincreases.Why?There

isadistributionofproductivitiesandcosts-SomeequlPmentCanoperatemore

cheaplythanothers.Further,expectedpricesandexpectedvariablecostsrepresent

theaveragebeliefsofallproducers.Atanymomentsomewillbemoreoptlmistic

andotherswillbemorepessimisticthanaverage.Thus,asshowninFigure20-9,

utilizationisgreaterthanzeroevenwhentheaverageexpectedmarkupratioisless

than1.Wh enthemarkupislow,onlythemostefficientplants,andtheproducers

withthemostoptimisticexpectations,finditworthwhiletooperate･Astheex-

pectedmarkuprlSeS,moreandmoreproducersbelievetheircapacityCanbeoper-

atedprofitablyandutilizationrisesrapidly.Oncemostofthefacilitieshavebeen

recruitedintoproduction,furtherincreasesinexpectedmarkupyielddiminishing

returns,untilutilizationsaturatesatlO0%.Thegreaterthedispersioninproductiv-

1tyacrossProducers,orthegreaterthedifferencesofopinionaboutexpectedprlCeS

andvariablecosts,thesmoothertheaggregateutilizationcurvewillbe･6

EquilibriummarkupandutilizationwilldependonthecapitalintensltyOfthe

particularindustry.Incapitalintensiveindustrieswheremostcostsarefixed,in-

cludingsemiconductors,paper,andchemicals,theequilibrium markupratiois

high,fin swillnormallyoperateathigh-utilizationlevels,andutilizationwillbe

relativelyunresponsivetovariationsinthemarkupratioJnindustrieswheremost

costsarevariable(e.g.,someagriculturalcommodities),equilibriumutilization

willbelowerandthesensitivltyOfutilizationtomarkupvariationswillbe

greater-theindustrywillnormallyoperateonthesteepershoulderoftheutiliza-

tioncurverepresentedbyFigure20-9.

Theexpectedmarkupdependsonproducers'expectationsforprlCe･These

short-runprlCeexpectationsmaydifferfromthelong-termpriceexpectationsused

inthedecisiontoinvestinnewcapacity.Asdiscussedinchapter16,prlCeexpec-

tationsincommoditymarketsandmanyothersettlngSareCharacterizedwellby

adaptiveexpectations(possibly withsometrendextrapolationaswell)･First-order

exponentialsmoothinglS assumedfortheexpectationfわrmationprocess:

Short-RunExpectedPrice -SMOOTH(Price,¶metoAdjustShort-RunPriceExpectations)

(20-12)

50ftenitispossibletoincreasetheoutputofamachineabovenormal(e.g.,throughovertime

orbyspeedinguptheproductionprocess),butthesesteps.usuallyraisethemarginalcostofproduc- tionandarethereforeundertakenonlywhenthemarkupnsesabovenomal･Suchflexibilityfurther spreadsouttheaggregateshort-runsupplycurve･

6Theutilizationfunctioncanbeestimatedeconometricallyifutilization,prlCe,andcostdata seriesareavailable.However,evenwhendataareavailable,themarkuprarelyspansthefullrange overwhichthefunctionmustbespecified,soextremeconditionsconsiderationswillbeimportant inspecifyingthefunction(seechap.14).

Chapter20 ThelnvlsibleHandSometimesShakes:CommodityCycles 805

Thetimeconstantfortheformationofshort-runprlCeexpectationsshouldberel

latedtothelengthofthemanufacturlngSupplylineandthevolatilityofdemand.

ThelongerthedelaylnalterlngProduction,thelongerproducerswillwaitbefore

theydecideachangeinpriceisenduringenoughtojustifyachangeinutilization.

Likewise,thenoisiertheprlCe,thelongerittakesforproducerstodiscernanen-

duringchangeinprlCeSamidthetemporaryvariations.

20.2.3 ProductionCapacity ProductioncapacltylStherateofoutputgeneratedatfullutilizationbyexistlng

plantandequlpment･Inthepaperindustry,Capacltycorrespondstothenumberand

productivityofpulpandpapermills.Inthecopperindustryitdependsonmine,

crusher,andsmeltercapacity.TheacqulSltlOnandlossofcapacltyaremodeledby

usingthestandardstockmanagementstmctureadaptedforcapitalinvestment(de-

velopedanddocumentedinchapter17)･Figure20-10showsthecapacitysectorfor

血egenericmodel.

Withoutlossofgenerality,capaclty1Smeasuredinarbitrarycapacltyunits,and

theproductivltyofcapacityisdefinedtobeone.Henceeachcapacityunitcorre-

spondstotheamountofplantandequlpmentneededtoproduceoneunitofoutput

peryear･TheproductivityOfcapacltyis,fornow,constant･7

ProductionCapaclty-CapitalStock*CapitalProductivlty (20-13)

Thesupplychainforcapacltyassumesafirst-orderdiscardprocessandthird-order

capacltyaCqulSitiondelay.TheCapacityAcqulSltionDelayandAverageLifeof

Capacltyareassumedconstant.Thestocksareinitializedtotheirequilibrium values.

CapitalStock

-INTEGRAL(AcquisitionRate-DiscardRate,CapitalStockb)

CapitalStockt｡

-(ReferenceDemand/CapacityUtilizationto)/CapitalProductivity

DiscardRate-CapitalStock/AverageLifeofCapaclty

AcquisitionRate-DELAYS(OrderRate,CapacityAcquisitionDelay)

CapitalonOrder

-INTEGRAL(OrderRate-AcquisitionRate,CapitalonOrderto)

(20-14)

(20-15)

(20-16)

(20-17)

(20-18)

CapitalonOrdert｡-DiscardRate*CapacityAcqulSitionDelay (20-19)

Theorderrateisformulatedwiththestandardstockmanagementstructure.Orders

areconstrainedtobenonnegative(fornownoordercancellationsareallowed)'･

OrderRate-MAX(0,IndicatedOrderRate) (20-20)

7Inreality,theproductivltyOfcapltaldependsontheleveloftechnologyembeddedin山ecapl- talstock,cumulativelearningeffects,scaleeconomies,andotherfeedbacks.Structurestomodel 血eseprocesseshavebeendescribedinearlierchapters.Forexample,embeddedtechnicalprogress canbemodeledwithacoflOwstructurethatkeepstrackoftheleveloftechnologyandotherinput requirementsassociatedwitheachunitofcapltalfromthetimeitisorderedthroughconstruction, startup,aging,andfinallydiscard(Seesection1212)･

806 PartV InstabilityandOscillation

FlGURE20-10 Productioncapacitysector

Theindicatedorderrateisthedesiredacquisitionrateadjustedbytheadequacyof

thesupplyline.Producersseektocorrectthegapbetweenthedesiredandactual

supplylineovertheSupplyLineAdjustmentTime.

ⅠndicatedOrderRate

-DesiredAcqulSitionRate+AdjustmentforSupplyLine

AdjustmentfわrSupplyLine (DesiredSupplyLine-CapitalonOrder)

SupplyLineAdjustmentTime

(20-21)

(20-22)

Thedesiredsupplylineistheamountofcapitalfirmsmusthaveonorderandun-

derconstructiontoyieldthedesiredacqulSitionrate･ByLittle'sLaw,producers

mustthereforemaintainasupplylineequaltotheexpectedacquisitiondelaytlmeS

thedesiredacquisitionrate.Forsimplicity,theexpectedacqulSltiondelaylSas-

sumedtoequaltheactualdelay.Amorerealisticmodelwouldcapturethedelays

intheadjustmentofproducerbeliefsaboutthetimerequiredtoacqulreCapaClty.

DesiredSupplyLine -ExpectedAcqulSitionDelay*DesiredAcqulSitionRate

(20-23)

ExpectedAcqulSitionDelay-CapacityAcqulSitionDelay (20-24)

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 807

Thedesiredacquisitionrate,inturn,consistsofthereplacementofexpecteddis-

cards,adjustedinresponsetothegapbetweendesiredandactualcapitalstocks. Expecteddiscards,forsimplicity,areassumedtoequaltheactualdiscardrate･

DesiredAcqulSitionRate -ExpectedDiscardRate+AdjustmentforCapacity

AdjustmentforCapaclty (DesiredCapacity-Capacity) CapacityAdjustmentTime

ExpectedDiscardRate-DiscardRate (20-27)

TheresponseofthecapacityaCqulSitionsectortotestInputsisdescribedinsec- tion17.3.

20.2.4 Des舶dCapaci!y

lncommoditymarketswhereindividualproducersaresmallrelativetoindustry demand,profitabilityisthechiefdeterminantofinvestmentinnewcapacity･Ex- istlngproducerswillexpandandnewplayerswillenterthemarketwhentheex- pectedprofitabilityofnewinvestmentishigh;sustainedlowprofitabilityleadsto contractionandexit.Ofcourse,JustaSproductionpressuressuchasillVentOries, backlogs,andorderratesmayaffectutilization,Sotoothesedirectindicatorsof demandmayaffectthedecisiontoinvest,particularlyinconcentratedindustries withonlyafewmajorProducers.Addingthesefeedbacksisleftasanexercise.In thegenericmodelindividualproducersareassumedtoexpandorcontracttheir productioncapacltySOlelyinresponsetotheirbeliefsaboutthelong-runprof- itabilityofnewcapacity(Figure20-1I).

HowmuchcapacltyShouldeachproducerhave?Manyecono血cmodelscal- culateoptlmalcapacitybasedonexpectedpricesandcostsandthenadjustactual capacltytOthatlevel.Theseformulationsimplicitlyassumeproducerscansolve foroptlmalcapacityand,actingindependently,choosetargetsthat,somehow,yield exactlytheproperaggregatelevelofcapacity.SuchmodelsviolatetheBakerCri- terion(chapter13).Nooneknowsthelong-runequilibriumstockofproductive capitalinacommoditymarket.Theoptimalcapitalstockdependsonhighlyun- certainfactorssuchasfutureeconomicgrowth,consumerpreferencesforthe

commodity,theprlCeelasticityOfdemand,thedevelopmentandcostsofsubsti- tutes,theproductivityofcapital,andsoon･Behavioraldecisiontheorysuggests suchuncertainfactorswillhavelittleweightinthecapacltydecision･Incontrast,

eachproducercanestimate,albeitimperfectly,whetheranewinvestmentisprof- itable.Aslongasproducersbelievenewcapacitywillbeprofitable,eachwould liketohavemorethanheorshecurrentlydoesandnewproducerswillenterthe

market.WhentheindustrylSexpectedtobeunprofitable,producersseektoreduce theircapacltyandsomewillexit.

Theformulationusedhereisbasedontheanchoringandadjustmentheuristic commonlyusedindecisionmaking.Desiredcapitalisanchoredtothecurrentlevel

thenadjustedupordownbasedontheexpectedprofitabilityofnewinvestment･

808 PartV InstabilityandOscillation

FIGURE20111 Desiredcapacitysector

ProductionCapacity

隼 CapacityGoal Adjustment

capital.i

DesiredCapacity

Etfectof

ExpectedProfit onDesired l司トー___I._I._

cap(city ' TableforEffectof

ExpectedProfiton DesiredCapacity

Expected Profitabilityof New】nvestment+

Expected Production

Costs

TimetoAdjust

Long-RunPric e

Expectation s

1トー一･.･.･.･.._･...

㌔+ TimetoAdjust ExpectedCosts

UnitCosts

Unit Variab□e Cost

AsshowninFigure20111,thisformulationcreatesapositivefeedbackloop,the

CapacltyGoalAdjustmentloop.Producersincreasedesiredcapitalabovecurrent

levelswhentheybelievenewinvestmentisprofitable.Eventually,capitalstock

rises,and,aslongasnewinvestmentisstillexpectedtobeprofitable,producers

thenresettheiraspirationsandraisetheircapitalstockgoalfurther･TheflOating

goalforcapitalstockfunctionsasahill-Climbingheuristicinwhichcapacitygrows

aslongasprofitsarehigherthannormalandfallsaslongasreturnoninvestment

fallsshort(section13.2.12).Thus,

DesiredCapital-Capital*EffectofExpectedProfitonDesiredCapacity(20128)

EffectofExpectedProfitonDesiredCapaclty -f(ExpectedProfitabilityofNewInvestment)

ExpectedProfitabilityofNewInvestment _(ExpectedLong-RunPrice-ExpectedProductionCosts)

ExpectedLong-RunPrice

(20-29)

(20-30)

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles

FJGURE20112

Effectofexpected profitabilityon desiredcapacity 5

(S s a lu O !S u a E

苛 )

^ )!u tEd t23 P 巴

!S ¢ G

u o

だ IO Jd P¢ 1 9 ad x u

i O

I 3 9 若山

-1.0 -0.5 0.0 0.5 lJO

ExpectedProflLtabilityofNewlnvestment (dimensionless)

809

Expectedprofitabilityfornewinvestmentisthedifferencebetweenthelong-run expectedpriceandexpectedcostsofnewcapacity(includingbothfixedandvari- ablecosts).Expectedcostsincludethenormalreturntocapitalinvestorsrequire, Sothatwhenexpectedpriceequalsexpectedcost,producersareearnlngthenormal profitandareJustcontentWiththecapitaltheycurrentlyhave･Expectedprofit- abilitylSnormalizedbytheexpectedpricetoprovidea血mensionlessratio.

TheeffectofexpectedprofitondesiredcapacltylSupwardsloplng･Likethe effectofoperatingmarglnSOnutilization,thereisadistributionofcostandprice expectationsinthemarket.Thereforethefunctioniszeroonlywhenprofitability issufficientlynegativethateventhemostefficientproducers,withthemostopt1- misticexpectationsaboutfutureprlCeandcosts,believetheindustrywillbesoun- profitableinthefuturethattheyseektoabandonitaltogether･Asexpected profitabilityrlSeS,thefunctionrises.Theeffecteventuallysaturatesatamaximum representinglimitsonthefinancingandabsorptionofnewcapacity(Figure20112)A

ThesteepertheEffectofExpectedProfitonDesiredCapacitythemorere-

sponsivedesiredcapitalistoaglVenChangeinexpectedprofit･Theresponsiveness ofdesiredcapitaltoexpectedprofitaroundtheequilibriumpointdependsontwo mainfactors.First,itdependsontheresponsivenessofindividualproducersand

potentialproducerstoexpectedpro臥 Second,itdependsonthedistributionof costs,prices,andexpectationsamongthepopulationofproducersandpotential

prodlLiCerS.Asdiscussedforthecaseofcapacltyutilization,thegreaterthedisper- sionincostsandbeliefsacrossthepopulation,血esmootherandmoregradualthe aggregaterelationshipwillbecomparedtothetypicalcurveforanindividual･The responsivenessofdesiredcapitaltoexpectedprofitforindividualproducersand potentialproducersalsodependsonavarietyoffactors.Theseincludetheavail- abilityandreliabilityoftheinformationaboutcostsandpricesneededtoassessthe

profitabilityofanewinvestment･Psychologicalfactorsplayanimportantrole,in- cludingthewillingnessofproducersandentrepreneurstoundertakerisk,their

810 PartV InstabilityandOscillation

eagernesstoexpandwhenprofitbeckonsandtheirwillingnesstocontractinthe faceoflosses,andtheextenttowhichtheyderivenonmonetarysatisfactionfrom

particIPatlnglntheindustry.Institutionalandstructuralfeaturesofthemarketcan

affecttheirresponseaswell,includingaccesstofinanclng,thescaleoftheinvest-

mentrequired,barrierstoentryandexit,andadjustmentcostssuchasstartupand decommissionlngcosts.Tbexpandorenterthemarket,producersandpotential producersmustbeabletomarshalthevariousresourcesneededtoinvest.Thesere-

sourcesincludefinancialbacking,ofcourse,butalsotechnicalknow-how,theabil-

1ty toassembleaqualifiedteam tooverseetheproject,and,often,political connectionsandsocialcapltaltogreasetheskidsofsiteselection,lineupsuppli- ers,andwincommitmentsfromcustomers.

Theformulationfordesiredcapacltyrepresentstheaggregateactionsofall producersandpotentialproducersinthemarket,Inequilibrium,desiredcapltal equalscapitalandinvestmentJustreplacesthelossofoldfacilities.Itisadynamic equilibrium.Newplayers,withmoreoptlmisticexpectationsthanaverage,willal- waysbeenterlngthemarketevenwhentherearenoexcessprofits,buttheseare balancedinequilibriumbytheexitofotherswhoseexpectationsaremorepes- simistic,

Long-runpriceforecastsareformedbyfirst-orderadaptlVeexpectations.The timeconstantgovemngtheprlCeexpectationsdrivinglnVeStmentdecisionsis longerthanthatusedintheutilizationdecision.Producersmustbeconfidenta changeinprlCeWillpersistlongenoughforinvestmentundertakentodaytobe profitablewhenitcomesonline.

ExpectedLong-RunPrice -SMOOTH(Price,TimetoAdjustLong-RunPriceExpectations)

(20-31)

Similarly,producersandinvestorsmustformexpectationsregardingthecostsof newinvestment･Duetothelongdelaysincapacltyacquisitionandlongcapaclty lifeandtouncertaintyaboutfutureinterestrates,capitalcosts,andoperatingcosts,

theseexpectationsarelikelytochangeonlyslowly.

ExpectedProductionCosts -SMOOTH(UnitCosts,TimetoAdjustExpectedCosts)

UnitCosts-UnitVariableCosts+UnitFixedCosts

IntendedRationa批yo官的e;llVeStmen号Pr9CeSS

DesignandexecutepartialmodeltestsofthedesiredcapacityandcapacityaCqu1- sltionsectorstodemonstratewhethertheformulationfordesiredcapacitylSin- tendedlyrational.Chapter15describespartialmodeltestlngandprovides

examples.Forthepurposeofyourtests,linkthecapacitysector(section20.2.3)

anddesiredcapacitysector(section20.2.4).Treatpriceandcostsasexogenousin- puts.Initializeyourmodelinequilibriumwiththecapltalstocksettoanarbitrary levelof100unitsandwithPrice-UnitCostssothatinitialexpectedprofitiszero･ Confirm thatCapital-DesiredCapitalandthatinvestmentJustOffsetsdiscards.

Chapter20 TheinvisibleHandSometimesShakes:CommodityCycles 811

Next,testtheresponseofthesystemtovarioustestInputsinprlCeand/orcost.

Whathappenswhenpricerisespe-anendyaboveunitcosts?Whathappenswhen pricefallspermanentlybelowunitcosts?Considertheeffectofsmallandlarge

changesinprofitability･Explorethesensitivityoftheresponsetothekeyparame- ters,includingtheEffectofExpectedProfitonDesiredCapacityandthetimecon-

StantsinthestockmanagementstructureforcapitalacqulSltion.Isthebehavior consistentwiththeintendedrationalityofthedecisionprocessassumedforthein-

dividualproducersinthemarket?Howdotheresponsivenessandstabilityofca- pacitydependontheparameters?

Asdiscussedabove,theresponsivenessofdesiredcapitaltoprofitabilityde- pendsonavarietyoffactors,includingtheavailabilityofinformation,investoraト titudes,barrierstoentryandexit,andaccesstofinanclngandotherresources.In lightoftheseconsiderations,evaluatethelikelyresponseofdesiredcapltaltoex- pectedprofitforthefollowingindustries:Coffee,commercialrealestate,copper,

hogfarming,Oil,pulpandpaper,andshipbuilding･Rankthemfromstrongestto weakest,thatis,fromthesteepestslopetothesmallest.Explainbriefly.

Howmightyouestimatetheslopeoftheeffectofexpectedprofitabilityonde- siredcapltalfわrtheseindustriestotestyourjudgmentalestimates?Considerboth statisticalandfield-basedapproaches.

20.2.5 Demand

Thedemand(orderrate)forcommoditiescanbemodeledatvariouslevelsof

detail.Asimpledemandsectorissufficientforthepurposesofthegenericmodel developedhere(Figure20-13).

Inmodelingparticularcommoditiesorindustries,ltWilloftenbeessentialto capturetheinventoriesofproductinthedownstreamsupplychainandtomodel thesubstitutionprocessinmoredetail.Forthepurposeofthegenericmodel,how- ever,theessentialdynamicfeatureisthatdemandfallswhenpricesrise,though possiblywithalag.Theadjustmentdelayaggregatesthetimerequiredforcus- tomerstoformpriceexpectationswiththedelaysintheirresponse(findingsubsti-

tutes,redesignlngproductstousesubstitutes,retrofittingorreplacingcapital stocksdependentonthecommodity,etc.).

Customerordersaremodeledastheproductofanunderlyingindustrydemand andtheeffectofotherfactorsondemand,anexogenousInputCapturingnoiseand othershorトーermvariationsindemandsuchasthebusinesscycle.

CustomerOrders-IndustryDemand*OtherFactorsAffectingDemand (20134)

IndustrydemandadjustswithalagtothedemandindicatedbytheprlCeOfthe

commodity.Ingeneral,thedelaymaybeofhighorder,butforsimplicity,afirstl orderresponseisassumed:

IndustryDemand -SMOOTH(IndicatedindustryDemand,DemandAdjustmentDelay)

(20-35)

812

FIGURE20-13 Demandsector

PartV InstabilityandOscillatioll

OtherFactors

IndicatedIndustryDemandrespondstoprlCerelativetoareferencepricerePre-

sentlngthepriceOfsubstitutes.Forsimplicity,alineardemandcurveisassumed.

ThedemandcurveisnormalizedtogeneratetheReferenceIndustryDemandatthe ReferencePrice:

InduIsnt:;cAteeEand=MIN[C."n霊mp71:n,

InduRs芸erBnec:and*MAX(0,1+CUD,:TST.d,e*

Price-ReferencePrice

(20-36)

TheMAX functionensuresthatdemanddoesnotfallbelow zeronomatter

howhightheprlCe.TheMINfunctionensuresthatdemandremainslessthana

specifiedmaximumnomatterhowlowtheprlCe.Betweentheselimits,thede-

mandcurveislinear.Theslot)eOfthedemandcurveischosenbythemodelerby⊥

settlngtheelasticltyOfdemandattheinitialequilibrium:8

DemandCurveSlope _(-ReferenceIndustryDemand*ReferenceIndustryDemand

ReferencePrice

8ThedemandelasticityeisthefractionalchangeindemandDforaglVenfractionalchangein

priceP:e-(∂D/D)/(∂P/P).Sincethedemandcurveslopesis∂D/∂P,theslopewherepriceand demandequaltheirreferencevaluesPRandDR,respectively,lSgivenbys- eRDR/PR,WhereeRIS

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 813

Thedynamicsofthedemandsectorinisolationarestraightforward･Apermanent

changeinprlCeinducesapermanentchangeinindicatedindustrydemand.Actual

demandadjuststothatlevelwithsomedelay･ApproprlateChoiceofthelengthand

orderofthedelayoffersreasonableflexibilitylnmOdelingtheresponseofdemand

toprlCe.Ifthepurposeofthemodelwarrantstheextradetail,thedemandmodel

canbeelaboratedtoincludeadditionalstructure,includingthedistributionchan-

nelandconsumerstocksofproduct,Crosselasticitieswithsubstituteproducts,and

investmentinthedevelopmentofsubstitutes.Thedemandadjustmentdelaycanbe

modeledinmoredetail･Short-runchangesindesiredinventorylevelscanbesep-

aratedfromlong-runchangesintheinputrequirementsOftheconsumingSector.

Asanexample,Figure5-llprovidesacausaldiagramillustratlngthemultiple

feedbacksaffectingthedemandforgasoline.

20.2.6 ThePr毒ce･SettingProcess

PricesettingOffersoneofthemostdifficultformulationchallengesineconomic

modeling･TheprlCeSOfsomegoodsandservicesareverystable,whileothers

changefrommomenttomoment･Thereareaswellmanydifferentprice-Settingln-

Stitutions･Onecommonformistheposted-pricesystem,whereoneparty(usually

theseller)postsnonnegotiableprices(pricetags)Oneachitem.Seller-postedprice

isthedominantpricinginstitutioninretailsales(someintemetbrokersusebuyer-

postedpnces,wherebuyersstatetheprlCetheyarewillingtopayforanitemand

suppliersrespondyeaornay)･Avariantofpostedpricesisone-on-onehaggling,

whereanindividualbuyernegotiateswithanindividualseller,usuallystartlng

fromapostedaskingprice(asystemcommoninrealestateandretailautosales).

Attheotherendofthespectrum,varioustypesofauctionsbringmultiplebuyers

and/orsellerstogetheratonce.Perhapsthemostdramaticistheopenoutcrydou-

bleauction,inwhichmultiplebuyersandsellerscalloutbidsandofferssimulta-

neously,Strikingdealswhenevertheyhearabidoroffertheylike.Doubleoral

auctionsareusedinmanycommoditytradingpitsandstockmarketsaroundthe world.

ThedifferentprlCeinstitutionsprovidedifferentinformationtothebuyersand

sellersandinvolvedifferentdecisionrules.Forexample,inanEnglishauction,all biddersknowthebids,andoftentheidentities,oftheirrivals,whileinasealedbid

auctiontheydonot･Likewise,prlCeSformanyretailandindustrialproductsareset

bymarkupprlClng,Wherethedirectcostsperitemaremarkedupbyastandardra-

tiotoyieldthelistprlCe.Storeorproductlinemanagershavelimiteddiscretionto

adjustpricesinresponsetosupplyanddemandorcompetitorprices.

Thegoalofthissectionistocreateasimpleandrobustmodelofpricesettlng

consistentwiththebehavioraldecisionprocessesofandinformationavailableto

thedemandelasticltyatthereferencepnce.NotethattheelasticltyatOtherpricesdiffersfromeR:

AsprlCerisesabovethereferencelevel,theelasticityOfdemandincreases,andaspricefallsbelow thereferencelevel,theelasticltyOfdemanddecreases･Thelineardemandcurveisobviouslyasim- plificationbutismorerobustthantheconstantelasticitydemandcurveD-DR(P/PR)C,Whichgen- eratesinfinitedemandwhenprlCeiszeroandgivesfinitedemandforveryhighprices.

814 PartV InstabilityandOsci一lation

themarketmakers.Themodelisgeneric;detailcaneasilybeaddedtocustomize

ittoparticularprlClngInstitutionsasthepurposeofthemodelwarrants･9

Ⅰnmanyeconomicmodels,pricePisformulatedasanequilibriumpriceP*,

adjustedbyafunctionofthecurrentdemand/supplybalance:

P-P不*f(Demand/supply) (20-38)

wherethefunctionf()isupwardsloping.Theequilibriumpriceisconstantandis

usuallytheaveragepriceovertherangeofavailabledata.Whileattractiveforits

simplicity,amoment'sreflectionshowstheequilibriumpriceCannotbeconstant.

ImaglneapermanentChangeinthecostsofproduction.TheequilibriumprlCeWill

permanentlychange,butsincetheexpectedequilibriumpriceisfixed,themarket

isforcedintopermanentdisequilibrium.Inaninflationaryenvironmenttheequ1-

11briumprlCeWillberisingcontinuously,Somethingtheformulationcannotgeneト

atewithoutanever一growlngimbalancebetweendemandandsupply.Evenmore

fundamentally,assumlngmarketparticipantsknowtheequilibriumprlCeViolates

theBakerCriterion.Itisnecessarytomodeltheprocessofpricediscovery-the

processbywhichmarketparticlpantSformexpectationsaboutthelevelofprice

thatwouldbalancedemandandsupplyandclearthemarket(Seesection13.2.12). Justasinvestorsdonotknowtheequilibriumlevelofcapacitythatwouldclear

themarket,Sotoonooneknowsthetrueequilibriumpricelevel.Ifpricesrose

abovecurrentbeliefsabouttheequilibrium prlCeandremainedthere,traders

wouldgraduallybegintorevisetheirestimateoftheequilibriumpriceuntilitulti一

matelyreachedtheactuallevelofprices.Inotherwords,traders'expectedprice-

thelevelofpricetheybelievewillclearthemarket-adjustsgraduallytotheactual

levelofprices.TheevidencesuggestsexpectationsaboutprlCeSareStronglycon-

ditionedbypastprlCeSandcanoftenbemodeledwellbysomeformofadaptlVe

expectations,suchasexponentialsmoothing(seechapter16):

Pk= SMOOTH(Price,ExpectationAdjustmentTime) (20-39)

Giventraders'expectedprlCe,howthenareactualprlCeSdetermined?Short-term

pressuresarisingfromimbalancesofsupplyanddemandorchangesincostsor

competitorprlCeSWillCausetraderstobidpricesupOrdownrelativetotheirbelief

abouttheequilibriumprice.Thatis,Pncesaresetbyananchoringandadjustment

process(section13.2.10)inwhichvariouscuesmovethepriceawayfromthe anchor:

P-Pf*fl(Cuel)*f2(Cue2)*-･*fn(Cuen) (20-40)

wherethecuesrepresentfactorssuchasdemand/supplybalance,unitcosts,

competitorprice,anCLPerhapsotherstlnatmaycausetraderstoacLJuStPrices.The

9DifferencesininformationavailabilityandprocedurescanaffectoptlmalStrategyforbuyers andsellersindi恥rentprlCeinstitutions,andexperimentalstudiesshowthatactualbehavior oftendiffersfromoptimalbehavior.Forexample,experimentalpostedpricemarketsconverge moreslowlythandoubleauctionmarkets;biddersinexperimentalsealedbidmarketsoftenpay toomuchforitemswithuncertainvalue(thewinner'scurse);anddoubleauctionsoftenleadto speculativebubbles(seeHogarthandReder1987,Thaler1992,andSmith,SuchaI-ek,andWilliams 1988).Thesefeaturesofspecificpricinginstitutionscanbemodeledexplicitlyiftheyareimportant tothemodelpurpose.

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 815

anchor,theexpectedequilibriumprlCe,itselfadjuststopastexperience.Pricesare

anchoredtoexpectedprlCeS,andtheanchorinturngraduallyadjuststotheactual

levelofprices,closlngapositivefeedbackloop･LikethecapacltyaCqulSltion

processdescribedabove,suchaprice-SettlngProcessformsahill-climbingsearch

procedureinwhichpricesriseaslongasdemandexceedssupplyandfallaslong

asthereisexcesscapacity(withinlimitsdescribedbelow)･Thehi lトClimbingpro-

cedureenablesmarketmakerstodiscoverthemarketclearingprlCeWithouthav-

1ngtOknowthepreferencesofconsumersorthecoststructureofproducers;that

is,withouthavingtoknOwthesupplyanddemandcurvesfortheproductandall

potentialoractualsubstitutes.

Thefomulationforpricedevelopedhereincorporatesadditionalstructureto

ensurerobustnessandbehavioralrealism.AsshowninFigure20-14prlCeisan-

choredontheTraders'Expectedprice,representingtraders'beliefsaboutthemar-

ket-clearingPrice.10Actualpriceisadjustedupordownfrom theanchorin

responsetovariouspressures.Inthissimplemodel,adjustmentsarisefromthede-

mand/supplybalanceandtraders'beliefsabouttheunderlyingcostsofproduction.

Price-¶aders'ExpectedPrice *EffectofInventoryCoverageonPrice*EffectofCostsonPrice (20-41)

OtherfactorsmayalsocausepricetOadjustawayfromtheequilibriumlevel,such

asnewsaboutnew technologies,Substituteproducts,changesinthemacro-

economy,andsoon.Inthismodeltheseareomitted,thoughtheyareeasilymod-

eledeitherasnoiseoraspartofthefeedbackstructure(substitutedevelopmentwill

beaffectedbypricesand,inturn,theavailabilityandcostofsubstitutesmayaffect

prices).ll

Traders'beliefsabouttheunderlyingequilibriumprlCeadjusttopastprlCeS.

First-orderadaptiveexpectationsareassumed,withatimeconstantglVenbythe

mmetoAdjustTraders'ExpectedPrice.

Traders'ExpectedPrice

=INTEGRAL(ChangeinTraders'ExpectedPrice,Pricet｡)

ChangeinTraders'ExpectedPrice (IndicatedPrice-Traders'ExpectedPrice)

TimetoAdjustTraders'ExpectedPrice

(20-42)

(20-43)

IndicatedPrice-MAX(Price,MinimumPrice) (20-44)

NotethattheexpectedpriceadjuststothelndicatedPrice,nottheactualprlCe.

MarketmakersknowthatequilibriumprlCeSCannotfallbelowtheminimumcosts

ofbringlngproducttomarket.HeretheminimumprlCeissettotheexpectedunit

variablecostofproduction:Pricemayfalltemporarilybelowvariablecostsbut

10Inthecontextofaposted-pricesystemsuchasretailsales,theTraders'ExpectedPricemight

representthelistpriceormanufacturer'ssuggestedretailprice(MSRP),withtheactualselling pnceofthegoodsadjustedaboveorbelowlistinresponsetosupplyanddemand,costs,and possiblyotherpressures.

llThemodelisdevelopedhereasamodeloftheaggregateprlCeOfacommodity･Whenusedto representtheprlClngdecisionofanindividualfirm,Otheradjustmentsmayberelevant,particularly theprlCeOfcompetitorproducts.

816 PartV InstabilltyandOscillation

FIGURE20-14 Pricesetting

ComparetoFigure1317.

overthelongrun,productionwillceaseifproducerscannotcovertheiroperatlng costs.

MinimumPrice-ExpectedV∬iableCosts (20-45)

Inthediscussionthusfar,pricesareassumedtorespondtothebalanceofdemand

andsupply,withoutspecifyinghowsupplyanddemandareperceivedbymarket

partlClpantS.Thereareseveralpossibilities.Ⅰncommoditymarkets,producersare

mostconcernedaboutthelevelofinventorytheymuststoreandfinance_Onthe

demandside,consumersareconcernedabouttheabilityofsellerstomakedeliv-

eriesinfullandontime･Inventorycoverage(theratioofavailableinventoryto

shipments)isanexcellentmeasureofbothinventorycarryingcostsforproducers

andtheabilityofbuyerstoreceivereliable,timelydeliveries.Consistentwith

manycommoditymodelsandsubstantialempiricalevidence,prlCeisadjusted

above(below)theexpectedequilibriumlevelasinventorycoveragefalls(rises) relativetoanormal,orreference,level.

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles

EffectofInventory _,lPerceivedInventoryCoverage＼

CoverageonPrice '＼ReferenceInventory

817

(20-46)

Severalfunctionalformsfortheeffectareplausible.Asimpleandflexiblefunction

isglVenbythepowerfunctiony-Ⅹawheretheexponenta,theSensitivltyOf

PricetoInventoryCoverage,mustbenegative(higherinventorycoverageleadsto

lowerprices):

EffectofInventory /PerceivedInventory

CoverageonPrice ＼ReferenceInventory (20-47)

Pricedependsonperceivedcoverage,notinstantaneouscoverage,becausethein-

stantaneousshipmentrateisnotknown･Ittakestimetogatherandreportdataon

inventoryandshipments.Forsimplicity,perceivedcoverageismodeledwithfirsト

ordersmoothing.TheCoveragePerceptionTimewouldbeshortinmarketswith

verygooddataorhighsensitivltyOfstoragecoststoinventorylevelsandlongerin

marketswithpoorqualitydataorlesssensitivltytOStoragecosts.

PerceivedInventoryCoverage

-SMOOTH(InventoryCoverage,CoveragePerceptionTime)

InventoryCoverage-Inventory/Shipments

Inothercontextsthedemand/supplybalancemaybeindicatedbyothervariables.

Inmodelinganindividualmanufacturingfirmthedemand/supplybalanceiscap-

turedwellbytheratioofdesiredproductiontocapacity(schedulepressure),where

desiredproductionrespondstoimbalancesininventoriesandbacklogs.Inaser-

vicesettlngWheretherearenoinventories,desiredproductiondependsprlmarily

onthebacklogofordersorqueueofcustomers,andthedemand/supplybalance

wouldstillbewellrepresentedbytheratioofdesiredtopotentialoutput･12 Pricesarealsoassumedtorespondtochangesintraders'beliefsaboutthe

costsofproductionrelativetotheexpectedequilibriumprlCe.Thestrengthofthe

effectisdeterminedbytheSensitivityOfPricetoCosts.

EffectofCosts-1･pS,ei::1ttl.VIE.sot:*onPrice

ProductionCosts

Trader'sExpectedPrice (20-50)

12Novicemodelersoftenusecapacltyutilizationordelivervdelayasmeasuresofthe demand/supplybalance.Thesevariablesarenotrobust,however,andshouldnotbeused.Consider utilization･When･desiredproductionishighrelativetocapaclty,utilizationsaturatesatitsmaxi- mumandthereforecannotindicatethemagnitudeofexcessdemandfacedbythefirmorindustry. Iiighutilizationdoesnotindicatewhetherdemandis5%or500%greaterthancapaclty,yetClearly prlCeSwouldrisefartherandfasterinthelattercase･Similarly,deliverydelayscannotfallbelow theminimumtimerequiredtoprocessandshipanorder,nomatterhowlargeinventoriesare･ ThereforewhendeliverydelaylSatitsminimumvalueitisnotpossibletotellwhetherinventory coverageis20r10timesthedesiredlevel,thoughthedownwardpressureonprlCeisgreaterin thelattercase.

818 PartV instabilityandOscillation

lftheSensitlvltyOfPricetoCosts-0,thencostinformationisIgnoredinprlCe

settlng.IfSensitivltyOfPricetoCosts-1,thentraders'beliefsabouttheequl-

1ibriumpriceareIgnoredandpricesareanchoredonexpectedcostsinstead･Inan aggregatecommoditymarket,unitcostsdifferfromproducertoproducer･Inglobal marketsfluctuatlngexchangeratesfurthercomplicatecostassessment.Informa- tionaboutproductioncostsevenforaslngleproducerisuncertainandunreliable. Behavioraldecisiontheorysuggestssuchunreliablecuesarelikelytohaveless

weightindecisionsthanmorecertainandreliablecues･Thusincommoditymar-

ketstheresponseofpricetocostsislikelytobeweak(SensitivityofPriceto Costs<i)andexpectedproductioncoststhemselvesarelikelytoadjustslowlyto newinformation(equation(20132)).

ThebehavioroftheproposedformulationforpriceCanbequitesubtle.Con-

siderfirsttheresponseofpricetOaChangeinexpectedproductioncosts,assuming

demandandsupplyflemaininbalance.Thesystemwillalwaysmoveexponentially toanewequilibriuminwhichPrice-Traders'ExpectedPrice-ExpectedPro- ductionCost.Theadjustmenttimewilldependontheadjustmenttimefor thetrader'sexpectedprice,ofcourse,butalsodependsonthesensitivltyOfprice tocosts.

Toseewhy,notethataslongasexpectedcostremainsgreaterthanthemini- mumprice,therateofchangeinexpectedprlCereducesto

ChangeinTraders'ExpectedPrice-dP弓/dt-(P-Pネ)rre (20-43a)

wherePdenotestheprice,PSdenotestheTrader'sExpectedPrice,andTedenotes theTimetoAdjustTraders'ExpectedPrice･AssumingInventoryCOVerageisatthe normalvalueanddenotingtheEffectofCostsonPriceasfcglVeS

ChangeinTraders'ExpectedPrice -dP*/dt-(P"fcIP*)/Te-P"(fcI1)Ire

(20-43b)

NowsubstituteintothisexpressiontheequationfortheEffectofCostsonPrice, fc-I+Sc*[(C*/P*)I1],whereScistheSensitivityofPricetoCostsandC*is

ExpectedProductionCost,andcollectterms:

ChangeinTraders'ExpectedPrice-dPx/dt -Px(1+Sc*[(C不仲*)-1]-1)/Te -Sc*(C串-p*)/Te -(C* -Px)/(Te/Sc)

(20-43C)

Youshouldrecognizeequation(20143C)astheformulationforafirst10rderlinear negativefeedbacklooplnWhichtheTraders'ExpectedPriceadjustsexponentially tot1XPeCtedCostswithatimeconstantequalto(Te/Sc)･AslongasSc>0,the positivePriceAdjustmentfeedbackisdominatedbythenegativeCostPressure loopandthesystemconvergestotheproperequilibriumwithPrice-Expected Price-ExpectedProductionCosts.Theweakertheimpactofpriceoncosts,the longertheadjustmentwilltake.Figure20-15confirmstheresultsIThefigure

showsapaHialmodeltestinwhichexpectedcostssuddenlydoubletInventory coverageremainsconstantatthereferencevalue.Theadjustmenttimeforex-

pectedprlCeis1year,andthesensitivltyOfpricetocostsis0.50.Priceimmedi- atelyrlSeSby50%ofthechangeincosts.InresponsetothegapbetweenprlCeand

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles

FIGURE20-15

Responseof prlCetOaChange incosts

Partialmodel

test.Expected ProductionCosts

doubleinyear1. TimetoAdjust Traders'Expected Price-1year; SensitivityofPrice toCosts-0.50.

200

180

.t 160 ≦= =l 誌 140

120

100

S S a

JuO ]Su a u ]! 凸

ExpectedProductionCosts

price./-･･-'-/Jl

TradersrExpectedPrice

1 2 3 4 5 6 7 8 9

EffectofCostsonPrice

819

1 2 3 4 5 6 7 8 9 Year

expectedprlCe,theexpectedpricestartstorise･Asitdoes,sotoodoesprlCe,but

becausetheratioofcoststoexpectedpricefallsasexpectedpricerises,prlCein-

creasesataslowerratethanexpectedprice,untiltheyconvergeatthenewequl-

1ibrium.Asexpected,thetimeconstantfortheadjustmentisTe/Sc-2years(it

takes2yearsforexpectedpricetomove63%ofthewaytothenewequilibrium).

Theresponsetoadecreaseinexpectedcostsissymmetric･

NowconsidertheresponseofprlCetOimbalancesbetweendemandandsup-

ply,First,considerthecasewherethesensitivltyOfprlCetOcostiszero.Thenthe

equationforthechangeintheexpectedequilibriumprlCebecomes

ChangeinTraders'ExpectedPrice -dP串/dt-(P帯*fI-P不)/Te-P祥*(fI-1)/Te

(20-43d)

wherefIdenotestheEffectoflnventoryonPrice.Youshouldrecognizethisex-

pressionastheequationforallinearfirst-orderfeedbacksystem.Ifthereisinsuffi-

cientinventory,then(fII1)>0andthesystemisdominatedbythepositivePrice

Adjustmentloop.TheexpectedequilibriumpriceP kwillgrowexponentiallyat

fractionalrate(fII1)/Te.Ifthereisexcessinventory,then(fII1)<0andthe

systemisdominatedbythenegativeExpectationAdjustmentloop.Theexpected

equilibriumpricewilldecayexponentiallyatfractionalrate(fI-1)rTe,untilprice fallstotheminimumlevel.

Figure20-16presentspartialmodeltestsforthesecases.Beforeyear1,the

systemisinequilibrium.Inyear1,relativeinventorycoveragefallsto0.8.The

820

FIGURE20･16 Responseof pncetochanges ininventory coverage

PartiaJmodeJtest.

SensitivityofPrice toCosts-0(no responseofprlCe toexpectedcosts). Relativelnventory CoveragefaHsto 0.8fromyear1 to3,returnsto normalfromyear3 to5,thenrisesto 1.4.TimetoAdjust Traders'Expected Price-1year, Sensitivityof PricetoInventory Coverage--1.

PartV InstabilityandOscillation

1 2 3 4 5 6 7 8 9

S S aluO !Su a

∈ !CI

1 2 3 4 5 6 7 8 9

Year

assumedsensitivltyOfpricetoinventorycoverageis-1,soprlCeimmediately

rises25%.Tradersgraduallybegintorevisetheirexpectationsabouttheunderly-

1ngequilibriumpriceinthebeliefthathigherprlCeSWillclearthemarketandre-

storeinventorycoveragetonormal.Instead,theinventoryshortagepersists,the

actualprlCeremainsabovetheexpectedequilibriumprlCeandtraderscontinueto

revisetheirbeliefsaboutthelevelofpricethatwillclearthemarket･Theexpected

equilibriumpriceChasesitsowntailinapositivefeedback･As longasinventory

coverageremainslessthannormal,prlCeSCOntinuetoriseexponentially.Inyear3

relativeinventorycoveragesuddenlyreturnstonormal･Priceimmediatelydropsto

theexpectedlevel.Note,however,thattheexpectedequilibriumprlCehasnow

risentomorethan160.Inthistest,wherecostshavenoimpactonprice,PnCewill

remainatthenew,higherequilibriumuntilthereisanotherimbalanceininventory.

Inparticular,priceCannotfallbacktowardtheinitiallevelunlessthereisasurplus

ofinventory.TradershavelearnedthatthenigherprlCeisneededtoclearthemar-

ketandwillonlyrevisetheirbeliefsifthereisnewevidenceofdisequilibriumat

thatprlCe.

Inventorycoveragerises40%abovenormalatthestartofyear5･Responding totheimbalance,tradersimmediatelyadjustprlCeSdownwardby29%.Themarket

doesnotimmediatelyclear,SotheirbeliefsabouttheequilibriumprlCenowbegin

todrop.Sinceinventorycoverageremainsexcessive,prlCeremainslowerthanthe

expectedequilibriumlevelandtradersreducetheirestimateofthemarkeトclearlng

prlCeStillmore.Priceandtheexpectedequilibriumpricedecayexponentially.

Chapter20 ThelnvisibleHandSometimesShakes:CommodityCycles 821

FIGURE20･17

Responseof

fullprlCeSector

tochanges

ininventory

COVerage

Partia一modeHest.

RelativehlVentOry

Coveragefallsto 0.75att'me1, returnstolattime

7,andfallsto 0.48attime12.

SensitJrVityofPrice toCosts-0.50.

TimetoAdjust

Traders'Expected

Price-lyear, Sensitivityof

Pricetolnventory

Coverage- -1･

S Sa F u O

!S ua uJ!凸

1.50

1.00

0.50

0.00

0 1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15

0 1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15 Year

PricecontinuestofalluntiltheexpectedprlCedropstothelimitimposedbyunit

variablecosts(assumedtobe$60/unit).13

WhathappenswhenprlCeSrespondtobothinventorycoverageandexpected

costs?Supposeinventorycoverageislessthannormal･Priceswillstarttorise･But

astheexpectedpricerisesabovecosts,theeffectofcostonpriceWillbegintooff-

settheeffectofinventory.Whathappensthendependsonthefunctionschosenfor

theeffectsofeachpressureonprlCeandthemagnitudeoftheassumedinventory

shortage･Giventheequationsandparametersabove,smallinventoryimbalances

willeventuallybebalancedbythecosteffectandpricewillreachequilibrium

whenithasrisenjusthighenoughthatthecosteffectoffsetstheinventoryeffect.

TheCostPressureloopdominates･However,iftheeffectofinventoryonpriceis

largeenough,thecosteffectwillneverovercomeit･ThepositivePriceAdjustment

loopdominates,aridpficeriSesexponentiaiiyuntiltheinventorylmbaianceisre-

solved･Figure20-17illustratestheshiftinloopdominanceJnventorycoverage

13Readersfamiliarwithcontroltheorywillrecognizethattheresponseofexpectedpriceto thedemand/supplybalanceisanexampleofintegralcontrolbecauseexpectedpricecontinues tochangeaslongasthereisanimbalancebetweendemandandsupply･Theresponseofexpected prlCetOcosts,incontrast,isanexampleofaproportionalcontroller.Theintegralresponsetothe demand/supplybalanceallowsprlCetOadjusttowhateverlevelbalancesdemandandsupply･How- ever,illtegralcontrolcanleadtoinstabilitybecausethecontrolactionisstrongestJustWhenthegap betweenthedesiredandactualstateofthesystemiseliminated.See,e.g"Ogata(1997).

822 PartV instabilityandOscillation

fallsto75%ofnormalinyearl.Pricesrisebutthecosteffectslowstheincrease.

Giventheparameters,thesystemreturnstoequilibriumwhenprlCeSdouble.By

year7theexpectedequilibriumpricehasnearlyreachedthatlevel.Inyear7,in-

ventorycoveragereturnstonormal.Priceandexpectedpricenowregresstoward

traders'beliefsaboutthelong-rununitcosts･Byyear12theadjustmentisnearly complete.Inyear12,however,relativeinventorycoveragefallsto48%ofnormal.

NowtheeffectofinventorycoverageonpriceissogreatthateveninfiniteprlCe

cannotgenerateenoughcostpressuretoovercomeit,andprlCerisesexponentially

withoutbound.Intherealworld,ofcourse,pricecouldnotcontinuetoriseforever

sinceveryhighprlCeSWOuldtriggerproductionincreasesanddemandreductions

thatwouldeventuallybringInventoryCOVeragebackdown･14

ThericharrayofbehaviorsgeneratedbytheprlCeformulation,eveninpartial

modeltests,arisesfromshiftsinthedominantfeedbackloopsgoverningPricead-

JuStmentS.Forsmallinventoryimbalancesthenegativeloopsdominateandex-

pectationsareregressive,tendingtoreturntotraders'beliefsaboutthelong-run

fundamentalvalueofthecommodity.Largerimbalancescauseloopdominanceto

shifttothepositivePriceAdjustmentloop,andthestabilizlngImpactOfbeliefs

aboutthefundamentalvalueofthegoodisoverwhelmed.Suchbehaviormayseem unreasonable,butinmarketswherefundamentalvalueisdifficulttoassess-or

viewedasirrelevant-pricesOftenrisebymanyordersofmagnitude,evenafter

yearsofcomparativecalm.Asanexample,Figure4-13showedthebubbleinsil-

verpricesinthelate1970sISilverrosebyafactorof700%injuSt2years,before

collapslngevenfaster.Clearly,anynotionspeoplemayhavehadaboutsilver's

fundamentalvalueorlong-runproductioncostshadlittleifanyimpactduringthe

speculativefrenzy.

ThepricefomulationdevelopedaboveisquitegeneralJtcanrepresentprlCe

settingatthelevelofanindustryormarket,asdevelopedhere,ormodifiedtorep-

resenttheprlCeSetbyindividualfirms.Inthatcase,theexpectedpricemayrepre-

sentthelistprlCeandpricemayrespondtootherfactorsbesidescostandthe

demand/supplybalance,suchastheprlCeOfcompetitors'products.Withsuitable

parameters,itcanrepresentmarketswhereprlCeexpectationsandpriceschange

quickly(suchasthestockmarket)ormarketswherepricesaresluggish(e.g.,real

estateorretailgoods).Theprocessbywhichexpectedpricesarefomedcanbeen-

riched,forexample,byincludingatermfortheexpectedrateofinflation.Youare

freetochoosedifferentfunctionalformsfortheeffectsofvariouspressureson

priceaSthecase-specificdatasuggest.

ThemodelprovidesaformulationfortheprlCediscoveryprocessthatisro-

bust,generatesaricharrayofbehaviors,andisconsistentwiththeprlnCiplesof

boundedrationality.Thetwokeyformulations,priceSettlngaSananchoringand

adjustmentprocessandtheadaptationoftheanchortopastprices,arealsosup- portedbyanumberofstudies.Econometricstudiesroutinely showthatcommod-

1tyPrlCeSrespondtoinventorycoverageandunitcosts･Topickatypicalexample,

14Asachallenge,deriveananalyticexpressionfortheequilibriumpriceaSafunctionofrelative inventorycoverageandidentifythepolntatWhichtheequilibriumceasestoexist.Explorehowthe existenceandcharacterofequilibriumdependontheshapeofthefunctiondefiningtheeffectof inventorycoverageonprlCe.

Chapter20 TheInvisibleHandSometimesShakes'.CommodityCyc一es 823

Gerlow,Irwin,andLiu(1993)Show thathogpricesrespondbothtothe demand/supplybalanceandtotheso-calledhog/comratio(thepriceofhogsrela- tivetothepriceOfcorn;cornistheprimaryVariableInputtOhogfarmingand muchmorevariableinpricethanotherinputs)･Althoughhedidnotestimatethe fullpricesettingmodel,Williams(1987)foundinexperimentaldoubleauction marketsthattraders'prlCeexpectationswerebestmodeledasadaptingtopast prlCeS.Thedatastronglyrejectedtherationalexpectationshypothesisthattraders optimallyandimmediatelyIncorporateallrelevantinformationsothattheirex- pectationsare,onaverage,co汀eCt.

Outsidethelaboratory,prlCeexpectationsinmanycommoditymarketshave beenshowntoadjustgraduallytopastprlCeSandotherinformationsuchascosts. Chapter16presentedevidencethatexpectationsforawiderangeofvariables,in- cludingprices,areOftenformedadaptively,thoughinsomecasessuchascattle prlCeSthereisevidenceofanextrapolativecomponentaswell.FrankelandFroot (1987)foundthatexpectationsoffuturecurrencyexchangeratesamongcentral bankers,traders,andotherpartlCIPantSinforeignexchangemarketsincludedboth adaptiveandregressivecomponents.Expectationsadjustedgraduallytorecent spotexchangerates(justastraders'expectedpriceadjuststotheactualpriceinthe model)butalsotendedtoregressslowlytopurchasingpowerparity(analogousto thegradualadjustmentofexpectedpricestolong-runexpectedunitcosts).Typical ofmanysuchstudies,thedatastronglyrejectrationalexpectations.

TheprlClngmodelhasalsobeenappliedinanumberofcases,withgenerally goodresults.Taylor(1999)analyzedthepaperindustrywithamodelsimilartothe onedescribedhere.Homer(1996),inmodelingacommoditychemicalmarket,no- ticedthatprlCeStendedtorisewheninventorieswerelowandfallwheninvento- rieswerehighandshowedthataprlClngformulationsimilartothatproposedhere workedquitewell.Hines(1987)appliedtheformulationtointerestrates･The Traders'ExpectedPricerepresented血ebeliefsofbondtradersabouttheunder- lyingequilibriuminterestratethatwouldbalancethesupplyanddemandforfunds. Tradersthenadjusttheactualinterestrateaboveorbelowtheexpectedequilibrium levelinresponsetovariationsindemandandsupply,measuredbythefreereserves ofthebankingsystem.Freereservesarereserveaccountsheldbybanksandother financialinstitutionsinexcessoftheirdesiredlevelandrepresentunexploited lendingcapaclty.Hinesestimatedthemodelparameterseconometricallyfrom 1959to1980,OneofthemostturbulentperiodsinUSbondmarkethistory.The modelexplainedasubstantialfractionofthevariationininterestrates.Theesti- matedsensitivityofinterestratestofreereserveswasabout-4(a1%dropinfree reservescausedinterestratestoriseabout4%abovetheunderlyingequilibrium expectation).Theestimatedtimeconstantfortheexpectedequilibriuminterestrate was1.4years.Theadjustmenttimemayseemlong,butbehavioraldecisiontheory suggeststhatexpectationsadjustslowerwhentheinformationcauslngthead- justmentsisuncertain.Asinthecaseofinflationexpectations(chapter16),thefac- torsaffectingInterestratesarenumerous,poorlyunderstood,difficulttomeasure, andhardtoforecast.Thusexpectationsabouttheunderlyingrateenvironment formedduringaperson'Scareerasatraderorbankerarelikelytobedurable,ad- justlngSlowlyandfilterlngOutShort-termmovementsininterestratescausedby temporaryswlngSinliquidityorunpredictableeconomicandpoliticalevents･The

824 PartV InstabilityandOscillation

estimatedtimeconstantisapproximatelythesameasthedelaylnupdatinginfla-

tionexpectationsestimatedinchapter16.

20.3 AppL!CAT!ON:CYcLESINTHEPuLPANDPAPER隻NDUSTRY

ThepulpandpaperindustryprovidesatyplCalexampleofacommodity.Asshown

inFigure20-18,theindustryishighlycyclical,Production,inventories,capaclty

utilization,prlCeS,andinvestmentallexhibitalargeamplitudecycleofabout3-5

years.TheamplitudeofthecycleisverylargeinprlCe,Whichtypicallymoves

from40%aboveitsaveragevalueto40%belowit(thereisalong-termdeclining

trendinrealprlCeSduetoeconomiesofscale,1earnlng,andtechnicalprogressin

theindustry).Inventorycoveragefluctuatesabout±20% arounditsaverage･

Capacltyutilizationaveragesabout90%andmovescomparativelylittleoverthe

cycle,typicallyvaryingbetween85%and95%.Capacltyexhibitsalmostnovari-

ationsinthe315yearrangebutdoesexhibitlonger,slowermovements.Theca-

paclty,production,andinvestmentdatainFigure20-18havebeendetrendedby

plottlngtheratioofoutputandcapacitytOthelong-runexponentialgrowthtrend･

Capacity(andproduction)bothroserelativetotheaveragegrowthtrendbetween

thelate1940sandabout1973.After1973,thegrowthratefellsharply,withca-

pacltyandproductiondecliningrelativetotrend.Theroughly601yearriseandfall

ofpaperdemandandcapacityreflectstheimpactoftheeconomiclongwave(See

section19.3).Acloselookatthecapacitydataalsorevealsanintermediatecycle

incapacity.ThecycleismosteasilyseeninthegraphofdetrendedCanadianpulp

capaclty.Relativetothelong-runtrend,capacltypeakedin1975andagalnin1992

(17years).TheintermediatecycleisalsoweaklyvisibleintheUScapacitydata.

CapacltyCyclesinthe12-20yearrangehavebeennotedinawiderangeofindus-

triessincethe1800sandarealsoknownasconstructionorKuznetscycles,after

theeconomistSimonKuznets,aplOneerOfnationalincomeaccountlngWhowas

amongthefirsttostudythem(SeeKuznets1953).

Thegenericmodelcanbeappliedtothepulpandpaperindustrywithoutany

structuralchanges.Onthedemandside,Taylor(1999)foundademandelasticity

ofroughly-0.5witha6-monthadjustmentdelay.Onthesupplyside,thepaper

supplychainislong,progressingfromloggingthroughpulping(debarking,chip-

ping,digestion,bleaching,andfiltration),papermaking(impregnationofpulp

withadditivesandcolorants,runningpulpthroughthepapermachine),thenfin-

ishing(coating,drying,rolling,cutting,andpacking),andfinallyinto d istribution

channels.Thepapersupplychaininvolvesslgnificantinventories o f workin

processand丘nishedinventories･15

15Thereareidiosyncraciesspecifictothepaperindustry,asinmostmarkets,whichwouldre- qulremodificationstothestockandflowstructureinamoredetailedmodel･Theseincludethe abilitytodry,store,andtradepulpandthegrowingimportanceofrecycledfiber･Taylor(1999) developsadetailedmodelofthepulpandpaperindustrythatconsiderstheseissues･Similarly,

paperisnotapurecommodity(fewgoodsare),ComiTginahugevarietyofgradesandtypes･ Paperproductsarehighlydifferentiatedalongdimens10nSlnCludingcolor,weight,acidity,fiber

composition,deliverytimes,andothers･Risch,Troyano-Bermddez,andSter望an(1995)analyze thestrateglCimplicationsofdifferentiationforamajorPaperSuPPlier･TheseIssuesarebeyond thescopeofthischapter.

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826

TABLE20-l Parametersforthe

paperindustry model

Theeffectof

expectedmarkup onutilizationand

effectofexpected profitabiJityon investmentare

specifiedas showninFigures 2019and20-12L Themodelis initializedwith referencedemand

andpncesetto loo,representing 100%oftheir

long-runvafues.

PartV InstabilityandOscillatioIl

Parameter Value Units

CapitalProductivity

AverageLifeofCapacity

CapacityAcqulSitionDelay

CapacityAdjustmentTime

SupplyLineAdjustmentTime

l Units/year/capitalunit 20 Years

4 Years

3 Years

1 Year

TimetoAdjustLong-RunPriceExpectations 2 Years

TimetoAdjustExpectedCosts 2 Years

ReferenceInventoryCoverage 0.2

MinimumOrderProcesslngTime 0.1

ManufactunngCyc一eTime 0.5

UtilizationAdjustmentTime 0.5

TimetoAdjustShort-RunPriceExpectations 1

TimetoAdjustExpectedVariableCosts 1 lnitialVariab一eCostFraction 0.4

ReferencelndustryDemandElasticity 0.5

DemandAdjustmentDelay 0.5

MaximumConsumption ∞ SensitivityofPricetoinventoryCoverage -1

CoveragePerceptionTime 0.167

SensitivityofPricetoCosts 0.5

TimetoAdjustTraders'ExpectedPrice l

Years

Year

Dimensionless

Years

Units/year Dimensionless

Years

Dimensionless

Year

Capacltyacquisitiondelaysareevenlonger.ThecapacltyaCqulSltlondelayfor

pulpandpapermillsisroughly4years(includingsiteselection,financing,per-

mitting,andcontractorselection,aswellasthedesignandconstructionprocess).

TheaveragelifetimeoftheplantandequlPmentinpulpandpapermillsisabout 20years.

Table201lsummarizestheparametersusedtoadaptthegenericmodeltothe

pulpandpaperindustry.Thenonlinearfunctionsusedforutilizationandtheeffect

ofexpectedprofitondesiredcapitalarethesameasshowninFigures2019and 20-12.

Sincethefocusofthisanalystsisthecyclicalbehavioroftheindustrythe

modelisinitializedwithdemandequalto100units/yearatthereferenceprlCe,rep-

resentlngloo鞄ofthelong-runtrend.Likewise,theprlCeissetto100(represent-

ingloo鞄ofitsinitialequilibrium).Whiletheabsolutelevelofinitialpriceand

productionareunimportanttothedynamics,themixofcostsandthenormalca-

pacityutilizationleveldomatter.Paperproductioninvolvesrelativelyhighfixed

costs,roughly60%oftotalcosts.Duetothehighfixedcosts,firmsseektorun

theirpapermachinescontinuously.Accountlngfornormalmaintenancedowntime,

nomalutilizationisabout90%(asseeninFigure20-18).

Figure20-19showsasimulationofthesystemwiththeapproximatepaperin-

dustryparameters.Themodelisinitializedinequilibrium･Atthestartofyear1,a

Chapter20ThelnvisibleHandSometimesShakes:CommodityCycles

FEGURE20･19

Pulseresponseof fullmodelwith

pulpandpaper parameters

Thesystemisper- turbedbya25% pulseincreasein customerordersat

thestartofyear1.

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Note:Timescaleoftoptwopanelsis10yearstoshowthe3.6-yearcyclecausedbythe Utllizatl0nAdjustmentloop･Timesca一eofbottompanelis40yearstoshowthe14-year cyclecausedbytheCapacityAcquisitionloop.

pulseequalto25%ofequilibriumdemandisaddedtocustomerorders,causlngan immediatedroplninventory.Theresponseofthesystemshowstwodistinctoscil- 1atorymodes.First,inventory,prlCe,utilization,andproductionoscillatewitha periodalittlelessthan4years.Second,capacltyOSCillateswithaperiodofabout

14years･TheshortperiodisgeneratedbythedelaysinthenegativeCapacityUti- lizationloop(Figure20-7)andthe141yearPeriodisgeneratedbythelongerdelays inthenegativeCapacityAcqulSltlOnloop.Notethephaselagbetweeninventory

828 PartV InstabilityandOscillation

coverageandprlCe:Priceisnotsimplythemirrorimageofinventorycoverage.

Rather,prlCeisrlSlngWhencoverageisatitsminimumandcontinuestorisefora

littlewhileevenaftercoveragebeginstorecover.ThephaselaglSPartlyaconse-

quenceofthe(quiteshort)timerequiredfortraderstoperceivechangesincover-

ageandlargelyaconsequenceofthepricediscoveryprocess,inwhichpricestend

toriseaslongasinventorycoverageisinadequate･16

Figure20-20ShowsamorerealistictestinwhichdemandbeglnStOV∬yran-

domlyatthestartofyear1,simulatingtheunpredictableshort-termvariationsin customerorders,Therandomnoisehasastandarddeviationof5%andanauto-

correlationtimeconstantof1year(thenoiseisintroducedthroughequation (20-34),OtherFactorsAffectingDemand.

Thesimulationexhibitsthetwocyclicalmodesbutwiththeirregularityyou

shouldexpectglVentherandomshocksperturbingthesystem･Thecapacltyuti-

lizationloopgeneratesa3-5yearcyclemostapparentinprice,utilization,pro-

duction,andinventorycoverage･ThecapacityaCqulSltionloop,withitslonger

delays,generatesacyclerangingfromabout12120years･Theseperiodsarecon-

sistentwiththedataforthepulpandpaperindustryshowninFigure20-18.The

relativeamplitudesofthekeyvariablesarealsoconsistentwiththedata.Capaclty

andcapacityutilizationvarytheleast.Utilizationgenerallyremainsinthe85-95%

rangeandcapacltyVariesroughly±lo啄∬ounditsequilibrium.inventoryand

pnceshavemuchlargeramplitudes,fluctuatlngbetweenabout60%and150%of

theirequilibriumvalues.Finally,thecapacltyacquisitionrate,whichservesasa

proxyfわrcapitalexpenditures,hasthelargestamplitude,fromabout30%tonearly

200%ofitsequilibriumvalue･Thephaserelationshipsamongthevariablesare alsosimilartothoseobservedinthedata.

Themodelisnotperfectandnogreatattempthasbeenmadetocalibratethe modelparameters(mostofwhicharesettoroundnumbers)｡Thesimulatedindus-

trylSSmootherthantheactualdatabecauseonlyonesourceofrandomvariation

wasincludedJnreality,notonlydemandbutalsoutilization,production,invest- ment,costs,andothervariablesalsoexperiencerandomshocks.Econometricesti一

nationoftheparametersandfurtherdisaggregationwouldnodoubtimprovethe

correspondenceofthemodeltothedata.Nevertheless,themodelcapturesthe

phaserelationshipsandrelativeamplitudesofthetwodifferentcyclicalmodes

seenintheindustryqulteWell.

Sensit毒V柁yモoUncert'lintyinParameters

ImaglneyouhavejustPresentedtheresultsofyotlrPaperindustrymodeltomem-

bersofyourclientteam.Theyfindyourexplanationforthecyclesintheindustry

intrlgulngbutwonderhowsensitiveyourresultsaretoyourassumptlOnS.Your

clientsknowthattheparameterestimatesyouusedareapproximateandmanyare

likelytobewrong.Forexample,howdotheperiods,relativeamplitudes,and

16closeexaminationshowsthatprlCePeaksandbeginstofallbeforecoveragereturnstonormal duetotheeffectofcostsonprlCe,Whichtendstopullpricebacktoitsequilibriumlevel.

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830 PartV InstabilityandOscillation

stabilityoftheinventoryandcapacitycycles(the3-5yearand12-20yearcycles) dependontheparameters?WherearethehighleveragepolntSforaction?

Sensitivltyanalysュsisimportantforseveralreasons.First,ithelpsdevelop yourintuitionregardingtherelationshipbetweenthestructureandbehaviorof complexdynamicsystems.Second,Sensitivltyanalysishelpsyouandyourclient testtherobustnessofyourconclusionswithrespecttouncertaintyintheestimated parameters.Third,Sensitivltyanalysisguidesyourdatacollectionefforts.Allpa- rametersareuncertain.Most,glVenenoughtimeandmoney,canbeestimated moreaccurately.However,youcanneverestimateparametersperfectlyandmust alwaysdecidewhichtofocusonandwhentostop.Aparameterthatstrongly affectsthebehaviormaybeagoodcandidateforadditionaldatacollectionlead-

ingtOabetterandmorereliableestimate.Conversely,forthosewithbutlittleef- fectyoucanbeconfidentthatyourresultsarerobustevenwithanapproximate estimate,savingtimeandeffort.Modelersoftenspendtoomuchtimerefining estimatesforparametersthatsimplydonotmatter.Finally,parametersthat stronglyaffectthebehaviorofthemodelmaybehighleveragepolntSforpolicy intervention.

Befbrerunnlngthetests,writedownyourexpectations.Whatdoyoupredict theimpactofeachchangeinparameterswillbe,andwhy?Recordingyourpredic- tionsinadvance-andtherationaleforthem-providesagreatopportunityforyou toimproveyourintuition.Afterrunnlngthetests,gobackandcomparetheout- cometoyourexpectations.Reformulateyourexplanationfortheeffectofeach change,andtestyournewtheorywithadditionalexperiments.Thisiterative processoftestlngWillsoondevelopyourabilitytounderstand,explain,andantic- 1patethebehaviorofcomplexsystems.

Howmuchshouldyouvaryeachparameter?Oneruleofthumbistoestimate thelikelyrangeofuncertaintyineachparameterandthenvaryitbymore(because peopleareoftenoverconfidentandunderestimatetheuncertaintyintheiresti- mates,whetherthesearejudgmentalorstatistical.Ifyouthoughttheuncertaintyln aparameterwas±20%,youmightvaryit±50%ormore.Analternativeandoften highlyeffectivestrategylStOtryextremeChanges.Whathappenswhenyouzero outaneffect,effectivelyeliminatingafeedbackfromthemodel?Tobuildyourin- tuitionaboutparametersensitivityltisimportanttoconductcontrolledexperi一 meれtsinwhichyouvaryeachparameterinisolation,oneatatime,soyoucanbe sureanychangesinbehaviorareduetothechangeintheparameter.Acaveat:In complexnonlinearsystems,theresultsofsuchunivariatesensitivltyanalysismay providelimitedguidancetotheresponseofthesystemtomultipleparameter changes.Becauserealsystems(andrealisticmodelsofthem)arehighlynonlinear, theimpactofmultipleparameterchangesisingeneralnotthesumoftheimpactof theindividualchanges,andtheimpactofa50%changeinaparameterisnotnec- essarilytwicetheimpactofthe25%change.Ingeneral,youmustalsoconduct multivariatesensitivityanalysistounderstandthefullrangeofresponsesofthe system.Forthepurposeofthischallenge,though,itissufficienttoconductuni- variatetests.Chapter21takesupmodeltestlngandsensitivltyanalysisinmore detail.

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 831

ConsiderparameterchangesinthefollowlngSectorsOfthemodel:

Capacityutilizationandproduction

l･VarythetimedelaysintheCapacityUtilizationloop.Considerboththe physicaldelayssuchasthemanufacturingCycletimeandthedecision一making

delayssuchasthetimerequiredtoformprlCeexpectationsoralterutilization･

2･ Varytheslopeoftheeffectofexpectedmarkuponutilization.Isthestability ofthe3-5yearinventorycycleenhancedifutilizationismoreresponsiveto markuporlessresponsive?Whatistheimpactofincreasedresponsivenessof

utilizationontheperiod,stability,andamplitudeofthecapacltyaCqulSition cycle?Wh y?Toanswerthisquestion,youmaywanttoreviewtheimpactofthe

Over/Undertimeloopintheinventory-workforcemodeldevelopedinchapter19.

Productioncapacity

3･VarythetimedelaysintheCapacityAcquisitionloop･Considerboththe physicaldelayssuchasthecapacltyaCqulSitiontimeandthedecision一making

delayssuchasthetimerequiredtoformpriceeXPeCtations･

4･Varytheslopeoftheeffectofexpectedprofitabilityondesiredcapltal.Is stabilityenhancedifdesiredcapitalismoreorlessresponsivetoexpectedprofit?

Demand

5･Varythedemandelasticltyanddemandadjustmenttime.Giventhecompara- tivelyshortdemandadjustmenttimeassumedinTable2011,isthenegativeSub-

stitutionfeedbackstabilizlngOrdestabilizing,andwhy?

Pricesetting

6.VarytheparametersintheprlCe-Settlngprocess.WhathappensifprlCeS

aremoreresponsivetoinventorycoverage?Iftradersupdatetheirbeliefsabout theunderlyingequilibriumpricefasterorslower?Ifcostsaremoreinfluential orless?

Ineachcase,explaintheresultsintermsofthefeedbackstructureofthemodel. Howwellwereyouabletoanticlpatetheimpactoftheparameterchanges?What

∬ethehighleverageparameters,theparametersthathavealargeimpactonthepe- riod,amplitude,andstabilityofthesystem?Howcouldtheseparametersbealtered intherealworld?Thatis,whatpoliciescouldbeimplemented,eitherbyindivid-

ualproducersorbylargerinstitutionssuchasgovernments,tostabilizecommod- 1tymarkets?

SensitivitytoStructurafChanges

Sensitivltyanalystsinvolvesmorethanv∬ylngmodelparameters.Allmodelsare approximations-tobuildamodel,everymodelermustomitsomefeedback processes,aggregatedifferentactorsandentities,andassumethesourcesandsinks forthestockandflOwstructureshaveunlimitedcapacity.Itisnotsufficientto

832 PartV InstabilityandOscillation

considerthesensitivltyOfyourresultstouncertaintylntheparameterswithinthe model.YoumustalsoexaminethesensitivltyOfyourresultstoplausiblealtema-

tivestructuralassumptlOnS,includingchangesinthemodelboundaryandlevelof

aggregation(chapter21). Aftersatisfyingyourclientregardingthesensitivltyofyourmodeltouncer-

taintylnparameters,Skepticalmembersoftheclientteamthenchallengeyourre- sultsbecauseyouhaveomittedsomefeedbackstheythinkmightbeimportant･For eachofthefollowing,modifythemodeltoincorporatethehypothesizedeffect･ Useyourbestjudgmenttoestimatethenewparameters.Tounderstandthelikely effectsofthenewstructuresitishelpfultomodifyyourcausaldiagramofthemar- kettoincludethenewfeedbacks.Aswithparametricsensitivityanalysis,write

downyourexpectationsregardingtheeffectsofthenewfeedbacksontheperiod,

stability,andotherfeature.sofmodelbehaviorbeforeru.nningthemodel･After-

ward,ChecktoseeifyourIntuitionwascorrect,andcontlnuetOtestuntilyouun- derstandwhythenewstructuredoeswhatitdoes･Youmayneedtoexperiment withdifferentparametersforthestrengthsofthenewfeedbacks･Youcanaddthese effectsinisolationtothebasecasemodeloraddthemcumulatively.Ineithercase,

besureyouunderstandtheimpactofeachnewstructurefullybeforemakingaddi- tionalchanges.

1.VariablecapacityliJTetime:TheclientspolntOutthatinyourmodelthe usefullifeofcapacltyisfixed.Inreality,theysay,theusefullifeof capacltyVarieswitheconomicconditionsintheindustry･Producerscan decommissionexistlngfacilitieswhenprofitabilityislow,andtheycankeep oldplantsrunnlnglongerwhenthereisashortageofcapacityandprofitsare expectedtobehigh.

Modifythemodeltoincludeavariablelifetimeofcapltal･Makethe averagelifTetimeofcapltalequaltoanormallifetimemodifiedbyafunction oflong-runexpectedprofitability(theexpectedprofitabilityofnew investment).Specifythefunctionsothatthelifetimeofcapitalequalsthe normallifetimeinequilibrium.Estimatevaluesforthefunctionuslngyour bestjudgmentandfollowlngtheguidelinesinchapter14･Explainyour choice.Whichfactorswouldaffectthewillingnessofproducerstoaccelerate

orpostponethedecommissionlngOfexistingCapacity?Identifyanynew feedbackloopscreatedbythenewstructure･Whateffectswillthenew structurehaveonthebehaviorofthesystem?

Next,testyourhypothesesbycomparlngthebehavioroftherevised modeltothebasecase.Consideravarietyoftestconditions･Wereyour

expectationsabouttheimpactofthenewstructurecorrect?

2.Cancelingordersfornewcapacity:Anothermemberoftheclientteam

polntSOutthatthemodeldoesnotallowordersfornewcapacltytObe canceled.Addthepossibilityofcancelingordersforcapltalinthesupply line.Rememberthatthesupplylineofcapitalonorderincludesbothorders

fornewcapacityintheplanningStageandthestockofcapitalunder construction.Ordersmaysometimesbecanceled,butprq】ectsunder

Chapter20 ThelnvisibleHandSometimesShakes:CommodityCycles 833

constmctionrarelyare･Youmaywishtoadaptthestructuredevelopedin

section19.Itomodellayoffsandvacancycancellation.Selectappropriate

parametersandjustifyyourchoices.

Asabove,identifyanynewfeedbackscreatedbyordercancellations,and

predicttheirimpactonthebehaviorofthemodel.Thentestyourintuitionby

runnlngthemodel.

3.Extrapolativeexpectations:Membersof血eclientteampolntOutthat

you'veassumedprlCeeXPeCtationsareformedadaptlVely,bysmoothing.

Onesays,

Duringmarketboomsakindofeuphoriaspreadsthroughouttheindustry. Prettysoon,industryanalystsandtradepublicationsbegintoprq】ectcontinued prlCeincreases.Weneversuccumbtotheseple-in-the-skyforecasts,butmany ofourcompetitorsaretakenin.Thisleadstooverinvestmentandworsens thenextslump･Theneveryonebecomesexcessivelypessimistic,delaylng血e reCOVery･

Recallingchapter16,youmodifytheformulationforthelong-termexpected

pncetocapturetheclients'hypothesisthatprlCeexpectationsrespondtothe

recenttrendinprlCe:

ExpectedLong-RunPrice -RecentPrice*EffectofTrendonExpectedPrice

RecentPrice

-SMOOTH(Price,TimetoAdjustLong-RunPriceExpectations)

EffectofTrendonExpectedPrice -i(ExpectedTrendinPrice,ForecastHorizon)

(20-31a)

(20-51)

(20-52)

TheEffectofTrendonExpectedPricecapturestheimpactofperceivedprice

trendsonthefTorecastofpriceusedininvestmentdecisions.Presumably,the

highertheexpectedinflationrateinprlCeOrthelongertheforecasthorizon

(thefartherinthefuturethepricetrendisprojected),thegreatertheeffect. Theforecasthorizonshouldberelatedtothetimebetweeninitiatingand

realizingInvestmentinnewcapacity:ThelongerthecapacltyaCqulSition

delay,thelongertheforecasthorizonmustbe.Theexpectedrateofinflation

canbemodeledwiththeTRENDfunctiondefinedinchapter16:

ExpectedTrendinPrice-TREND(Price,PricePerceptionTime, HistoricalHorizonforPriceTrend,nmetoPerceivePriceTrend)

(20-53)

HerethePricePerceptionTimeisthetimerequiredtoperceiveprlCeand

smoothouthigh-frequencynoise,theHistoricalHorizonforPriceTrend

representshowfarbackinhistorylnVeStOrSlookinassesslngPnCetrends,

andtheTimetoPerceivePriceTrendrepresentsthetimerequiredtoupdate

beliefsaboutprlCetrends.

TherearemanyplausiblefunctionsfortheEffectofTrendonExpected

Price･AsimplestartlngpOlntistheassumptlOnthatinvestorsexpectthe

834 PartV InstabilityandOscillation

currentinflationrateinpricetOremainconstantovertheforecasthorizon. Inthatcase,

EffectofTrendonExpectedPrice - exp(ExpectedTrendinPrice*ForecastHorizon)

(20-52a)

Ifthefわrecasthorizoniszero,therevisedformulationreducestotheorlglnal

modelinwhichlong-termexpectedprlCeSareformedbysmoothingactual

prlCe･17

Implementtheformulationforextrapolativeexpectations.Useyourbest

judgmenttoselectreasonableparameters.

WhatistheimpactofextrapolativeprlCeexpectationsonthestability

andothercharacteristicsofthecycle?Youmaywanttostartbynlnnlngthe

modelwithasingledemandshocktogetafeelforthebehaviorofthe

forecastandthephaserelationshipsoftheforecastandactualprlCe,butbe

suretoconsidertheresponsetorandomdemandaswell.Experimentwith

differentparametersfortheformationoftheexpectedtrendinpriceandfor

theforecasthorizon･Whataretheimplicationsforproducersandinvestors?

4･Thelong･runsupplyCurve:Thecostsofnewcapacltyinthemodelare

constantandindependentofthescaleoftheindustry.Ineconomictens,the

long-runsupplycurveisflat:Capacitycoulddoublewithoutanychangein

marglnalcosts.Insomeindustries,thisisareasonableassumptlOn.Inothers,

suchasmanymineralandagriculturalcommodities,themarginalcostofnew

capacltyrisesasindustrycapacltygrows.Expandingcopperproduction

meansoresoflowerqualitymustbemined;expandingoilproduction

capacltymeansdrillingdeeperandinmoreremotelocations;expanding

cocoaproductionmeanscultivatlnglandthatislessproductiveormore distant血･omthemarket.

Modifythemodeltoaccountforthefeedbackfromproductioncapacity

tothemarglnalcostofnewcapaclty.Forsimplicity,assumebothunitfixed

costsandunitvariablecostsrisebythesameproportionascapacltygrows.

Normalizethefunctionyouselectsothatcostsequaltheirreferencelevels

whencapacltyequalsitsreferencelevel.Setthereferenceleveltotheinitial

equilibrium･SelectanapproprlateShapeforthedependenceofmarginal

costsonproductioncapacity.Typically,costsriseslowlyatfirstbutat

progressivelysteeperratesascapacitygrows.

Identifythenewfeedbacksintroducedbythelong-runsupplycurveand

predicttheimpactofthenewfeedbackstructureonthebehavior.Designand

iirlPlemerltteststOexaminetheimpactofthelong-ruriSupplycurve.

5.Separatingaverageandmarginalcost:Addingthefeedbackfromcapacity

tocostscapturesthelong-runsupplycurve,buttheclientsthenpolntOutthat

17Theassumptionthatinvestorsbelievecurrenttrendswillcontinueovertheforecasthorizonis notlikelytoholdfわrveryhighillnationratesorverylongfわrecasthorizons.Amorerealisticmodel wouldreplacetheexponentialfunctionwithafunctionthatapproximatestheexponentialforsmall inflationratesbutsaturatesatamaximumandminimumvalueattheextremesofveryhighorlow lnPutS･Thesaturationnonlinearitiescapturetheideathatinvestorsexpectextremeratesofprice changetomoderateovertime.

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 835

themodeldoesnotdistinguishbetweenthemarglnalcostofnewinvestment

andtheaveragecostsofoperatingeXistlngCapitalJnvestorsdevelopthe

leastexpensivesourcesofsupplyfirst,turningtOmoreexpensivesitesonly asrlSlngPnCeSjustifytheaddedcost･Thenextcopperminetobeopened willhavelowergradeorethantheaverageofexistlngmines,andnewpaper

machlnesaremuchmoreproductivethanthemachinesavailablethree decadesago.Thedecisiontoinvestinanewfacilitywilldependonthefixed

andvariablecostsofnewcapital,buteachproducers'decisiontooperate dependsonthevariablecostsofexistingfacilities.

Modifythemodeltodistinguishbetweentheunitcostsofnew investmentandtheaverageunitcostsofexistlngCaPltal.Todosoyoumust

introducecoflOwstokeeptrackofthefixedandvariablecostsassociated witheachnewunitofcapitalfromthetimeitisordereduntilitisdiscarded. Section12.2describestherelevantstructure.UtilizationofexistlngCapaClty

willnowdependonaverageunitvariablecostsoverthestockofexisting

capaclty,nottheunitvariablecostsassociatedwithnewinvestment･ TesttherevisedmodelbyassumlnganeXOgenOuSrateOftechnical

progressthatlowersthemarglnalcostsperunitofnewcapacltyatSOmerate, say5%/year.Howdoessuchtechnicalprogressaffectthedynamicsofthe market?

TheclientsalsopolntOutthatthedecommissionlngdecisiondependson

theprofitabilityofoldcapltalcomparedtonewcapltal･Olderfacilitiesare lessproductiveandhavehigheroperatlngcoststhannewones.During

marketupswlngS,WhenprlCeSarehigh,evenold,unproductiveplantscan operateatapro臥 DuringdownswlngS,theleastproductiveplantsare shutdownfirstaspricesfall.Eventually,aplantbecomessocostlythat

managementisforcedtoscrapit(orinvestinexpensiveretrofittingtoboost productivity).Thedecommissioningdecisiontherefわredependsonthe profitabilityofexistingCapital,whichdiffersfromtheexpectedprofitability ofnewfacilities.Whenoldcapitalismuchmorecostlytooperate, decommissionlngandretrofittingareaccelerated.Reviseyourformulation

forthevariablelifetimeofcapltalsothelifeofcapltaldependsonthe expectedprofitabilityofexistingCapitalratherthantheprofitabilityofnew

investment.Whatistheimpactonthefeedbackstructureandbehaviorofthe model?

6.FeedbackofinventorytoCapacityutilization:TheclientspolntOutthat

capacltyutilizationinthemodeldependsonlyontheexpectedmarkul)ratio,⊥

Theyargueinsteadthatutilizationisaffecteddirectlybytheinventory positionoftheproducers･Thedecisiontoshutdownafacilitybecauseitis unprofitableistypicallymadeatcorporateheadquarters,notbytheplant

managers･Theyarguethatproductionschedulesatanyplantrespond prlmarilytotheorderandinventorypositionoftheplant.Indeed,as discussedabove,Shortagesofproductwillstimulateutilizationand

limitsonphysicalstoragecapacltyCanforceproductiontofallwhen

inventoriesgrowtoolarge,nomatterhowprofitabletheindustrymay appeartobe.

836 PartV InstabilityandOscillation

Takingyourhigh-levelcausaldiagramofthemarket(Figure20-7),they

redrawittocapturethefeedbacksfrominventorytoutilization(Figure 20121).Themodifieddiagramshowsanewfeedbackfrominventoryto utilization,thelnventoryControlloop(shownwithheavylines)Jndicated

capacltyutilizationintherevisedmodelnowrespondstobothexpected markupsandSchedulePressure,definedastheratioofthedesired

productionstartratetoproductioncapaclty. Youdecidetomodifythemodeltoincorporatethedirectfeedbackfrom

inventorytocapacityutilization｡Youdecidetousethestructurefordesired

productionstartsdevelopedinchapter18.Ⅰnthatstructure,showninFigure 1815,desiredproductionstartsdependontheforecastofcustomerorders modifiedbyanadjustmenttobringinventorylnlinewithdesiredinventory andasimilaradjustmentfortheworkinprocessinventory.Thisstructure generatestherateofoutputproducerswouldliketoattainbasedontheir aggregateinventoryposition,includingWIP,andtakingtheirforecastof ordersintoaccount.ChooseappropriateValuesfortheparameterssuchasthe inventory,WIP,andforecastadjustmenttimes.Youwillhavetomodifythe formulationforcapacityutilizationandindicatedutilizationtoincorporate boththeeffectsofprofitability(expectedmarkup)andschedulepressure. Considerwhetherthedelaysintheeffectsofmarkupandschedulepressure maydiffer.Yourrevisedformulationshouldallowtherelativeimportance ofthesetwofactorstobevariedinsensitivltytests,fromtheorlglnal formulationwithmarkupastheonlyinputtoutilizationtotheotherextreme whereschedulepressureistheonlyinput.Besureyourrevisedmodelbegins inequilibrium.

Implementandtesttherevisedformulation.Howdoesthebehavior changewhenbothschedulepressureandmarkupaffectutilization?Alsotest theextremeconditioninwhichschedulepressureistheonlydeteminantof utilization.WhatistheeffectoftheInventoryControlloopontheperiod, stability,andotherpropertiesoftheshort-termcycleandthecapaclty acqulSitioncycle?Explainintermsofthefeedbackstructureoftherevised systemshowninFigure20-21.

Finally,Cntlqueyournewutilizationformulation.Whatdefectsdoyou see?Howcouldyoureformulatethemodeltoimprovetherepresentation ofutilization?Underwhatcircumstanceswouldsuchelaborationbe

appropriate?

Emp始ment如gS加ut3tu!̀a_!Char一駅5-

ModeEirtgLit.restockMarkets

AsillustratedinFigures20-1and20-2,thehogandcattleindustriesexperience

persistentoscillations.Theperiodofthehogcycleisabout4years,whilethecaト tlecycleisabout10-12years.

Adaptthegenericcommoditymodeltothelivestockindustry.InnonagrlCuL

turalmarketsproductioncapacitylSindependentofthemanufacturlngSupply

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838 PartV InstabilityandOscillation

chain:Pulpmillsandpulparen'tthesamething.Inlivestockmarkets,however,

productioncannottakeplacewithoutabreedingstock.Producersmustchoose whethertosendtheirstocktomarketnowortokeepanimalsonthefarmtoin-

creasethefuturesupply.Inplainterms,ittakeshogstomakehogs.Thisfunda一

mentalbiologlCalfactrequiresthestockandflOwstructureofproductiontobe altered,asshowninFigure20-22.

Theproductionsupplychainisdisaggregatedintothreecategories:thegesta- tiondelay,1mmatureStock,andmaturestock.Forcattleandhogs,matureanimals

aretypicallykeptoncornfeedlotsuntiltheyreachtheoptimalweightandwill

fetchthebestprlCe･Thekeydifferencebetweenthelivestockproductionprocess andothercommodities,however,isthatproductionstartsarenotdirectlycon- trolledbytheproducer.Productionstartscorrespondtothebreedingrate,which dependsonthesizeofthebreedingstock(alongwiththenumberoflittersperyear andtheaveragelittersize)･Producerscontrolthesizeofthebreedingstock.The breedingstockisincreasedwhenproducerswithholdmatureanimalsfrommarket.

Inadaptingthemodeltolivestockyouwillneedtospecifytheorderofeachdelay inthegestation-maturationprocess,rememberingthatyourmodelaggregatesall producers(seechapter11forguidelines).

Thedecisiontoincreasethebreedingstock,showninFigure20-22astheln- dicatedBreedingStockIncreaseRate,Canbemodeledwithavariantofthestan-

dardstockmanagementstructure｡Producersneedtoreplaceolderbreedingstock senttomarketandadjusttheactualbreedingstocktowardthedesiredbreeding stock･Youshouldmodelthedesiredbreedingstockastheproductofproduction capacityandindicatedcapacityutilization.Thatis,producerswillincreasetheir desiredbreedingstock(toincreasefuturesupply)whentheexpectedmarkupratio ishighandwillreducetheirbreedingstockswhenitislow.Thetotalsizeofthe breedingstockislimitedbyproductioncapacity,representingthecapacltyof ranches,farms,andfeedlotsintheindustry.

Takecarethatyourreformulatedmodelisrobustunderextremeconditions:

Thestocksofanimalsmustremainnonnegativeandtotalbreedingstockmustre- mainwithinthecapacltyoftheindustry.TheprlnCIPalparametersforbothhogs andcattleareshowninTable20-2.Useyourbestjudgmentandotheravailable informationtoestimatetheotherparametersandbehavioralrelationshipsinthe model.

Parameter

AverageLitterSize

LittersperYear GestationPeriod

MaturationTime

MatureStockFeedingPeriod

AverageBreedingPeriod

8.0 1.0 Animals/litter

2.0 1.0 Litters/animal/year 0.31 0.83 Years

0.42 1.67 Years

0.17 1.0 Years

2.5 2.5 Years

Sources:Meadows(i970),CommodityResearchBureau,CommodI'fyYearbook,vanousyears

FJGURE20-22 Modifyingthemodeltorepresentlivestockmarkets

IndicatedBreeding StockIncreaseRate

Customer Orders

840 PartV InstabilityandOscillation

Runthemodelforthecaseofbothhogsandcattleandcontrastitsbehavior

agalnStthedata.Doesthemodelreproducetheperiodandothercharacteristicsof

thehogandcattlecycles?ExplorethesensitivltyOfyourresultstoparameters･ Becausetheonlywaytoincreasethesupplyofhogsorcattleinthelongrunis

towithholdsomematureanimalsfrommarket,theshort-runresponseofanin-

creaseintheexpectedmarkupISareductioninsupply.Whattypeoffeedback processiscreatedbythisbiologlCalreality?Whateffectdoesthisloophaveonthe stabilityofthemarket?DesignandexecutesensitivltyteststOexploretheimpor-

tanceofthisfeedbackIstheeffectstrongestforthehogorcattlemarket,andwhy? Assumethat,fromequilibrium,thepnceofcornsuddenlyandpermanentlyin-

creases.Designandimplementthistestinthemodel.Whatisthelong-runbehav- iorofthemarket(price,production,breedingstock,etc.)?Whatistheshort-run response?Howdoestheresponseofthedesiredbreedingstocktothecostincrease affectproducerprofitabilitylntheshortrun?Whataretheimplicationsforpro- ducersinthelivestockmarkets?18

PolicyAnalysis

Commoditycyclesresult丘･omtheinteractionoflongdelaysintheresponseof supplytopncewiththeboundedrationalityofproducers.Producersandinvestors form expectationsofprofitabilityandprlCeadaptivelyanddonotappeartoacI countadequatelyforthetimedelaysinthesystemortheimpactofotherpro- ducers'decisionsonfutureinvestment,production,andprices.

CanyoudesignpoliciesthatimproveperformanceandprofitabilitylnCyClical markets?Suchpoliciesmightinvolvechangesintheinformationusedtoform priceexpectationsormakeinvestmentdecisionsorotherchangesintheinvest- ment,utilization,andpriceexpectationformationdecisions.Designandtestyour policiesinthemodel(eitherthebasecasemodel,theenhancedmodelincluding thestructuralchangesdescribedinthechallengesabove,orthelivestockversion

ofthemodel).Contrasttheperformanceofyourpoliciesagainsttheoriginalmodel foravarietyofcases,includingvariousone-timedemandandcostshocksand randomvariationsindemand.Howcouldthesepoliciesbeimplementedinreality?

Economistsoftenarguethatoscillationsincommoditymarketscannotlong endurebecausetheyprovidearbitrageopportunities･Iftherewereacycle,savvy investorscouldmakeextraordinaryprofitsbytimlngtheirinvestmentstobuyat

cycletroughsandsellatcyclepeaks.Asmorepeoplepursuedsuchcountercyclical strategleS,theiractionswouldcausethecycletovanish.Evenifpeoplecan'tlearn

atall,markets,bytransferringwealthfromthoseuslngpoofdecisionrulestothose withsuperiorrules,wouldquicklycausethepopulationofproducerstoevolveun- tilallwereusing(nearly)optimalstrategies.Whilethelogicoftheargument soundscompelling,thepersistenceofcyclicalmovementsinsomanycommodity marketsoververylongperiods(morethanacenturyformanyindustries)suggests

18Rosen,etal.(1994),MundlakandHuang(1996),andHayesandSchmitz(1987)offer contrastlngmodelsandemplricalallalysesofthelivestockmarkets.

Chapter20 TheInvisibleHandSometimesShakes:CommodityCycles 841

learnlngandarbitragearen'tqultethatsimple.CritiquethearbitrageargumenL Whichfeaturesofcommoditymarketsfavorlearnlngandsuggestpersistentcycles woulddisappear?WhichfTeaturesworkagalnStlearnlng?Considerphysical featuressuchastimelagsincapacityacquisition,institutionalfeaturessuchasthe degreeofconcentrationinthemarketandtheincentivesfacingindividualin- vestors,CognitiveandinformationalfeaturessuchasthecomplexityOfthemarket andnumberofrelevantcuesrequiredforgoodperformance,andsociologlCalfac- torssuchasthebackgroundsandtrainlngOftypicalmarketplayersJnwhichmar- ketswouldlearningbemostrapid?Leastrapid?Howmighttherateoflearnlngbe measured?

20.4 SL棚 MARY

Thischapterdevelopedmodelsofmarketsinwhichpricefunctionstobalance supplyanddemand.Thegenericindustrymodelintroducedseveralimportantand usefulformulations,includingprlCeSettlngandtheresponseofinvestmenttoex- pectedprofitability･Theseformulationsareusefulacrossmultiplelevelsofaggre- gation,fromindividualfirmstotheeconomyasawhole.Themodelexplainsthe orlglnOfthechronicfluctuationsobservedinawiderangeofcommodityindus- tries.Commoditycyclesarise丘.omtheinteractionofthephysicaldelaysinpro- ductionandcapacltyaCqulSitionwithboundedlyrationaldecisionmakingby individualproducersandinvestors.Thepersistenceofcyclesinindustriesfrom coppertocattleandrubbertorealestatesuggestslearnlngandmarketforcesthat mightstabilizethecyclesareweak.InmarketeconomiesprlCeliesinthecenterof anetworkofnegativefeedbackswhichacttoeliminateimbalancesbetweende- mandandsupply,thuspromotlngtheefficientallocationofresources:theinvisible hand.YetinmanymarketsthereactionsofdemandandsupplytoprlCeareVery slow.Negativefeedbackswithtimedelaysarepronetooscillationandinstability: Theinvisiblehandsometimesshakes.

-Timi醸a罷畠鮎表裏ざ; 寺恵呈呈由盲言草ミミ-;3_筆fl二き_iI串鹿妻:-_fTes転写

Amodelisaworkoffiction.

-NancyCartwright(1983,p.153)

WilliamJamesusedtopreachthe"willtobelieve."Formypart,Ishouldwish

topTleaChthe"willtodoubt."‥.Whatiswantedisnotthewilltobelieve,but

thewishtofindout,whichistheexactopposite･ -BertrandRussell(1928/1961,pp.1041106)l

NoIain'tgotawitnessandIcan'tproveit

Butthat'smystofTandI'mstickin'toit. ILeeRoyParnellandTonyHaselden, HThat'smyStory,HsungbyCollinRaye

Whatmakesagoodmodel?Asamodeler,howdoyouknowtheresultscanbe

trusted?Asamodelconsumer,whenshouldyouacceptamodelasthebasisforac-

tion?Whatquestionsshouldyouask,whatevidenceshouldbeused,andwhat

standardsshouldbeapplied?Whodecides?Thischapterdescribesmodeltesting

andfocusesontheprocessbywhichyouandyourclientscanbuildconfidencethat

amodelisapproprlateforthepurpose･Unfortunately,testlngisoftendesigned

to"prove"themodelis"right,"anapproachthatmakeslearningdifficultand

IscepticalEssays,1928･1961edition,London:UnwinBooks･

845

846 PartVI ModelTesting

ultimatelyerodestheutilityofthemodelandthecredibilityofthemodeler.Worse,

manylmpOrtanttestsareSimplyneverdone.Manymodelersfocusexcessivelyon replicationofhistoricaldatawithoutregardtotheappropriatenessOfunderlying assumptlOnS,robustness,andthesensitivityOfresultstoassumptlOnSaboutthe modelboundaryandfeedbackstructure.Modelersoftenfailtodocumenttheir

work,preventlngOthersfromreplicatlngandextendingit･Modelersandclientsof- tensufferfromconfirmationbias,Selectivelypresentlngdatafavorabletotheirpre-

conceptlOnS,andthenstickin'totheirstorydespltetheevidence.Modeltestlng shouldinsteadbedesignedtouncovererrorssoyouandyourclientscanunder- standthemodel'slimitations,improveit,andultimatelyusethebestavailable modeltoassistinimportantdecisions.Thechapteralsodescribesspecifictestsand proceduresyoushouldfollowtotestthesuitabilityofamodelforyourpurpose,

uncoverflaws,andimprovethechancesyourmodelwillbeusedanduseful.The testscanbeappliedbymodelersandmodelconsumersandrangefromexamina- tionofmodelboundaryassumptlOnStOquantitativeassessmentofthemodel'shis- toricalfit.Examplesillustratehowthetestscanbeappliedandhowfailuretodo sooftenresultsinabsurdityorprojectfailure.

21.1 VAL旧AT10NANDVERIFICAT10NAREIMPOSS旧しE

Manymodelersspeakofmodel"validation"orclaimtohave"verified"amodel. Infact,validationandverificationofmodelsisimpossible.Theword"verify"de- rivesfromtheLatinverus-truth;Webster'sdefines"verify"as"toestablishthe truth,accuracy,orrealityof,""Valid"isdefinedas"havingaconclusioncorrectly derivedfrompremises...Validimpliesbeingsupportedbyobjectivetruth"

Bythesedefinitions,nomodelcaneverbeverifiedorvalidated,Why?Be- causeallmodelsarewrong.Asdescribedinchapter1,allmodels,mentalorfor- mal,arelimited,simplifiedrepresentationsoftherealworld･Theydifferfrom realitylnWayslargeandsmall,infiniteinnumber.Theonlystatementsthatcanbe validated-showntobetrue-arepureanalyticstatements,propositionsderived fromtheaxiomsofaclosedlogicalsystem,because,asstatedbythephilosopher A.∫.Ayer(1952,p.31),HTheydonotmakeanyassertionabouttheempirical world,butsimplyrecordourdeterminationtousesymbolsinacertainfashion."

Somemodelershavelongrecognizedtheimpossibilityofvalidationinthe

senseofestablishingtruth.Forrester(1961,p.123)wrote:

Any"objective"model-validationprocedurerestseventuallyatsomelowerlevel onajudgmentorfaiththateithertheprocedureoritsgoalsareacceptablewithout objectiveproof.

Forrester'sview,controversialatthetime,isnowmorewidelysharedamongmod- elers.Inaninfluentialassessmentofthestateofpolicymodelinglnthemid1970S, Greenberger,Crenson,andCrissey(1976,p｡70-71)concludedthat

Nomodelhaseverbeenoreverwillbethoroughlyvalidated-･"Useful,=Hillumi- natlng,""convincing,"or"insplrlngconfidence"aremoreaptdescrlPtOrSapplying tomodelsthan"valid."

Chapter21TruthandBeauty:ValidationandModelTesting 847

Morerecently,Oreskes,Shrader-Frechette,andBelitz(1994,p.644)wrote,"Mod-

elsarerepresentations,usefulforguidingfurtherstudybutnotsusceptibleto

proof."

Theimpossibilityofvalidationandverificationisnotlimitedtocomputer

models.Anytheorythatreferstotheworldreliesonimperfectlymeasureddata,

abstractions,aggregations,andsimplifications,whetherthetheorylSembodiedin

alarge-scalecomputermodel,consistsofthesimplestequations,orisentirelylit-

erary.Thedifferencesbetweenanalytictheoriesandcomputersimulationsaredif-

ferencesofdegreeonly,

Manyarguethatwhilethetruthofamodelcannotbeestablished,surelyitsfal-

sitycan.ThelateSirKarlPopper'Sphilosophyofrefutationismorfalslficationism

remainspopularamongmanyscientists,modelers,andeconomists(C｡g.,Belland

Senge1980;Redman1994;McCloskey1994).Whilethetruthofanyempirical

statementcanneverbeestablished,Popperfamouslyarguedthatitispossibleto

showatheorytobefalse.EmpiricalstatementssuchasHallswansarewhite"can

neverbeverified.Nomatterhowmanyswanswefindtobewhite,wecannever besurewe'Vetestedthemallorthatthenextswantohatchwillbewhite.How-

ever,Observationofaslngleblackswanshowsthestatementtobefalse･Popper

arguedthattobescientificatheoryhadtobesubjecttorefutation,thatis,ithadto

bepossibletofalsifyitbyexperimentorotheremplricaltest.OnceatheoryisfaL

sifiedempiricallyithastobediscardedandreplacedbysomenew,moreaccurate

theory.Onlythosetheoriesthathavenotyetbeenrefutedshouldbeacceptedand

thatacceptanceisalwaysconditional.

ThewidelytaughtstoryofGalileo'sexperimentattheleanlngtowerOfPisa

providesaclassicexample･Galileoreportedlydroppedcannonballsofdifferent

weightsfromthetower,showingthattheyhitthegroundatthesametime.Theold

theorythatheavyobjectsfallfasterthanlightoneswasfalsifiedandreplacedwith

thenewtheorythatgravltyCausesallobjectstoaccelerateearthwardataconstant

rate,independentofmass･2

PoppercalledonscientiststoseektheHcrucialexperiment"that,likeGalileo'S,

couldfalsifytheirtheories･Iftheproponentsofatheorycannotdescribeanexper-

imentorevidencethatwouldpersuadethemtoabandontheirtheory,then,Popper

argued,itcannotbeconsideredscientific,butmustberecognizedasadogmano

differentinprinciplefromanymatteroffaith･Hepointedtotheclaimsofpsycho-

analysis,Marxism,andastrology,amongothers,asprlmeOffenders.

Thisna-I-veversionofPopper'sapproachenjoysCOntinuedpopularityduetoits

simplicityandintuitiveappeal･Thereareindeedmanycaseswheresuperstition

andideologycloakthemselvesintheauthorityofscience.Popper'scriterionof

falsifiabilityshowstheemperorsofthesepseudosciencestobenaked.

Unfortunately,manypeoplearetaughtthesound-biteversionofrefutationism

inintroductoryclasses,neverdiggingmoredeeplyIntothephilosophyofscience

2Actually,Galileomeasuredtherateatwhichballsrolleddowninclinedplanes(toslowtheir accelerationandimprovetheacPuracyofhismeasurements),andthestoryoftheleaningtower maybeapocryphal･SimonStevlnOfBrugeswaslikelythefirsttocarryoutthedropped-weight experiment,pub一ishingtheresultsin1587,priortoGalileo'swork(Boyer1991).

848 PartVI ModelTesting

todiscoveritssubtletiesandlimitations･3Mostobviously,sinceallmodelsare

wrong,allcanbefalsifiedbysometestorother.Arockfallsfasterthanafeather,

andevenGalileo'Sweightsdidnotallfalltoearthatexactlythesametime-dense

objectsconsistentlyfallfasterthanlessdenseones,refutingthetheoryofconstant acceleration.Sinceallmodelsarefalseandrefutable,whicharewetouse?

Paradoxlcally,atthesametimethatallmodelsarewrong,anyparticulartheo-

reticalpropositioncanalwaysberescuedfromapparentfalsification.Accurate

measurementshowsthatobjectsofdifferentmassesandshapesdofallatdifferent

rates.Doesthisfalsifythetheory?No.Asallgradeschoolstudentsaretaught,ob-

jectswouldfallatthesameratelftherewerenoairfriction.Thetheoryissavedby InvokinganauxiliafThypothesis.Duringa1971Apollo15moonwalk,astronaut

DavidScottfamouslydemonstratedtheroleofairfrictionbysimultaneouslydrop-

pingahammerandafeather･Bothfelltothesurfaceatthesametime.Butsuppose

thefeatherhadn'tfallenasquicklyasthehammer･Wouldphysicistsaroundthe

worldhaveshouted,"Thetheoryhasbeenfalsified!"andabandonedtheideathat

gravitationalaccelerationisindependentofmass?Ofcoursenot･Theywouldhave

invokedauxiliaryhypothesestoexplainthediscrepancy･PerhapsstaticelectrlClty

inScott'sgloveslowedthefeather'sdescent.IfstaticelectrlCltyWereruledoutby

subsequenttests,scientistswouldstillnothaverewrittenthetextbooks･Perhaps

magnetiteinthelunarsurfaceacceleratedthehammer'sfall･Ifthiswereruledout,

Wewouldhavepostulatedsomeother,unknownforce･Afavoredhypothesiscan

alwaysbesavedbyinvokingother,auxiliaryhypotheses･

Testsofanytheorytakeplaceataparticulartimeandplace,withparticular

equlpmentandinstruments･Experimentscannevertestthetheoryalone,butonly

thejointhypothesisconsistlngOfthetheoryandtheauxiliaryassumptlOnSthatthe

equlpmentisproperlysetup,thattheinstrumentsworkasexpected,andthatthere arenosourcesofuncontrolledvariation.Nomatterhowcarefullyanexperimentis

doneaninfinitenumberofpossiblesourcesofuncontrolledvariationalwaysexist;

therefore,thereisalwaysaninfinitenumberofauxiliaryhypothesesthatcanbein-

vokedtosaveanytheoryfromdisconfirmation･Thisrealization,knownasthe Quine-Duhemthesis,meansalltheoriescanalwaysbeadjustedtoaccordwithany

datawhatsoeverwithoutdiscardingthecorepropositions･

TheintroductionofauxiliaryhypothesestosaveafavoredtheorylSSOmetimes

arewardingpathtoknowledge.AfterthediscoveryofUranus,observationsre-

vealedthatitsorbitdidnotfollowthepathpredictedbyNewton'slaws.Insteadof

discardingormodifyingtheinversesquarelawofgravitation,astronomersin-

vokedtheauxiliaryhypo血esisthatamoredistantplanetwasperturbingItsOrbit.

AssumlngNewtonwasright,astronomerscalculatedwherethenewplanetshould

beandNeptunewasindeedfoundnearbyin1846･Inthiscase,holdingfastto

Newton'Slawsdespiteevidencecontradictingthetheorywasagoodstrategy･

Mostoften,however,auxiliaryhypothesesservetoinsulateatheory丘.om

confrontation withunfavorabledata.Pre-Copernicanastronomersreconciled

3Lakatos(1976)providesamoresophisticateddevelopmentoffalsificationism.

Chapter21 TruthandBeauty:ValidationandModelTesting 849

discrepanciesbetweenthePtolemaicsystemandobservationbyinvokingever

morecomplexeplCyCles.TheeplCyClespreservedthefavoredhypothesisthatthe

earthreignedsupremeatthecenteroftheuniverse.PostulatingyetanothereplCy-

clecouldalwayseliminateanydiscrepanciesrevealedbymoreaccurateobserva-

tions.Copernicus,workingwithessentiallythesameevidence,abandonedthe

geocentrictheoryandarguedthattheplanetscircledthesun.Theevidencedidnot

determinethechoice.Indeed,foralongtlme,thePtolemaicsystemprovidedmore

accuratepredictionsthantheCopernican.

Invokingauxiliaryhypothesestosaveafavoredtheoryremainsacentraltac-

ticinbattlesbetweencontendingworldviewstothisday.Themostpopulartheory

ofthebigbang,knownasinflation,initiallyrequiredthetotalmassoftheuniverse

tobemuchlargerthanobservationsuggested.Ratherthanabandoninflationinthe

faceofthisapparentdisconfirmation,physicistshypothesizedthattheuniverse

containsHmissingmatter"intheformofbrowndwarves(unignitedstarstoodim

tosee),WIMPS(Weaklyinteractingmassiveparticlesundetectablebyourinstru-

ments),andeventhepresenceofa"cosmologicalconstant"-amysteriousforce

hypothesizedtopushallmatterapart.OnlytlmeWilltellwhetheranyoftheseaux-

iliaryhypotheseswillbesupportedbynewdataandbecometheneworthodoxyor

whetherfuturephysicistswilllookbackonthemasfoolisherrors.Physicistsare

notaloneintheirmasteryoftheauxiliaryhypothesis.Inthefaceoflaboratory

experimentsandfielddatashowingthatpeopleviolatetheaxiomsofrationality

andthatmarketsarenotperfectlyefficient,Someeconomistsinvokeauxiliaryas-

sumptlOnS,eplCyClesoneplCyCles,topreservethecoreaxiomsofrationalityand

equilibrium.Typicalmovestosavehomoeconomicusfromextinctionincludein-

vocationofinfわrmationasymmetries,transactioncosts,searchanddeliberation

costs,limitationsontherepertoireofactionsavailabletotheagents,unusualutil-

ityfunctions,andsoon(seeSimon1984).Rationalityandequilibriumarenotem-

plricalfactsbutthecentraltenetsofadeeplyfeltfaith･4

Theoriesbuiltonsuchnonfalsifiablefoundationsconstituteparadigmsinthe

senseofthelateThomasKuhn(1970).Paradigmsareself-consistentcommunities

oflike-mindedscientists,SharingaworldviewencompasslngnotOnlyabodyof

theoryandevidencebutalsomethodsofinqulry,Standardsofproof,textbookex-

amples,andheroes.Kuhnarguedthatdifferentparadigmsarefundamentallyin-

commensurable,meanlngthatrationalchoicebetweenparadigmsbasedon

evidenceisnotpossibleanddoesnotdrivechangesinthedominantscientificthel oriesofanera.

TherealsignificanceofKuhn'sparadigmsandtheQuine-Duhemthesisisthis:

ThedecisiontoabandonatheorylSneverforceduponusbyrealitybutisalways

andessentiallyahumanchoice.Whentheoryanddataclash,wenecessarily

4ThisdiscussionisnotmeanttosingleouteconomicsIAllseriousscientifictheoriesinclude acoreoffavoredbeliefsthatarenotsubjecttorefutation･Trytoimaglneanexperimentorem- piricalresultthatcouldpersuadeasystemdynamicsmodelerthatfeedbackloopsdon'texist･ SeeMeadows(1980).

850 PartVI ModelTesting

choosebetweenthemuslngnOneVidentialcriteria,suchasparsimony,elegance,or

conformancetoreligious,POlitica1,0raestheticbeliefs･ Validationisalsointrinsicallysocial.Thegoalofmodeling,andofscientific

endeavormoregenerally,istobuildsharedunderstandingthatprovidesin-

sightintotheworldandhelpssolveimportantproblems･ModelinglStherefore

inevitablyaprocessofcommunicationandpersuasionamongmodelers,clients, andotheraffectedparties.Eachpersonultimatelyjudgesthequalityandappropr1 -

atenessofanymodelusinghisorherowncriteria.ThephysicistturnedsociologlSt

ofscienceJohnZimannotes,"TheobjectiveofScienceI.･isaconsensusofra-

tionalopinionoverthewidestpossiblefield"(1968,p･9)･C･WestChurchman,a pioneerinthemanagementsciences,goesfurther(1973,p･12):

ApolntOfview,oramodel,isrealistictotheextentthatitcanbeadequatelylnter- preted,understood,andacceptedbyotherpolntSOfview･

RecognlZlngthefundamentallysubjectiveandsocialnatureofmodelevaluation doesnotmeanmodeltestinglSunSCientificorthatinpracticeanytestorcriterion isjustasgoodasanyother･Likewise,theQuine-Duhemthesisisnotajustification foravoidingempiricaltests,Ignoringevidence,orstonewallingcritics･Forthose whobelievetheUSgovernmentcoveredupthealleged1947crashofanalien spacecraftinRoswell,NewMexico,anygovernmentdenialsaresimplyfurtherev- idenceoftheconsplraCy.Thesebelieversareextremelycreativeininvokingauxil- iaryhypothesestointerpretanyinformation,nomatterhownegative,asconsistent withthetruthastheyseeit･Whetherusedintheserviceofacultorascientificthe- ory,suchbehaviorresultsinaninternallyconsistentworldviewsealedofffrom surprlSeandimmunetoevidence.Modelersshouldfocusonteststhatcanreveal thelimitationsofourcurrentmodels,mentalandformal.Oreskesetal.(1994) write:

Wemustadmit也atamodelmayconfirmourbiasesandsupportincorrectintu- itions.Therefore,modelsaremostusefulwhentheyareusedtochallengeexisting formulations,ratherthantovalidateorverifythem.Anyscientistwhoisaskedto useamodeltoverifyorvalidateapredeterminedresultshouldbesuspICious･

Ifvalidationisimpossibleandallmodelsarewrong,whythendowebotherto buildthem?AsaleaderyoumustrecognlZethatyouwillbeuslngamOdel一men-

talorformal-tomakeimportantdecisions.Yourchoiceisneverwhethertousea modelbutonlywhichmodeltouse.YourresponsibilitylStOusethebestmodel availableforthepurposeathanddesplteitsinevitablelimitations.Thedecisionto

delayactioninthevainquestforaperfectmodelisitselfadecision,withitsown setofconsequences.Experiencedmodelerslikewiserecognizethatthegoalisto helptheirclientsmakebetterdecisions,decisionsinformedbythebestavailable

model.Insteadofseekingaslngletestofvaliditymodelseitherpassorfail,good modelersseekmultiplepolntSOfcontactbetweenthemodelandrealitybydraw- 1ngOnmanySOurCeSOfdataandawiderangeoftests･InsteadofviewlngValida- tionasatestingStepa氏eramodeliscompleted,theyrecognizethattheory buildingandtheorytestlngareintimatelylntertWinedinaniterativeloopJnstead ofpresentlngevidencethatthemodelisvalid,goodmodelersfocustheclienton thelimitationsofthemodelsoitcanbeimprovedandsoclientswillnotmisuseit.

Chapter21 TruthandBeauty:ValidationandModelTesting 851

21.2 QuESTIONSMoDELUsERSSHOULDAsK-

BuTUsuALLYDoN'T

Inmostdebatesoverparticularmodelsphilosophicalconsiderationsarelikethe officialideologyanarmyfightsfor･.greatinprinciplebutforgottenintheheatof battle.Inpractice,modelsfallonthefieldoforganizationalconflictformore mundaneandavoidablereasons.MeadowsandRobinson(1985)reviewednine

modelsdesignedtoaddressvariouspublicpolicyquestionsintheareasofecO- nomicdevelopment,resources,andtheenvironmenLThemodelsusedmethodsin-

cludingeconometrics,linearprogrammlng,andinput/outputanalys上s,aSWellas systemdynamics.Thoughthemodelswere"identifiedas'betterthanaverage"by theauthorsandby‖othermodelers,clients,andsponsors,"MeadowsandRobin- son(p.104)found"mismatchesofmethodswithpurposes,sloppydocumentation, absurdassumptlOnSburiedinovercomplexstructures,conclusionsthatdonoteven followfrommodeloutput,andprojectmanagementStrategleSthatdestroytheposI sibilityofinfluenclngactualpolicy."Therecordintheworldofbusinessmodelsis atleastasdismal.

Asanantidote,Table21-1listsavarietyofquestionsmodelers,andespecially modelusers,shouldaskbutusuallydon't.Thesequestionsaredesignedtoassess theoverallsuitabilityofthemodeltoyourpurpose,itsconformancetofundamen-

talformulationprlnCiples,thesensitivltyOfresultstouncertaintylnaSSumptlOnS, andtheintegrltyOfthemodelingprocess.

21.3 PRAGMATtCSANDPoL汀ICSOFMoDELUsE

OncewerecognlZethatallmodelsarewrongandabandontheblackandwhite dualismoftruthandfalsification,wecanfocusontheimportantquestions:Isthe modeluseful?DoitsshortcomlngSmatter?Toanswerthesequestionsyoumust firstask:Usefulforwhatpurpose?Mattertowhom?

Modelusersmustcriticallyassessthemodel'sboundary,timehorizon,and levelofaggregationinlightoftheirpurpose.Themodelboundarydetermines whlchvariablesaretreatedendogenously,whicharetreatedexogenously,and whichareexcludedaltogether.Factorsrelevanttothepurposemustbecaptured endogenously.TreatingaCOnCePtaSeXOgenOuS,OrOmittinglt,Cutsallfeedbacks involvingthatvariable.Modelswithnarrowboundariesdonフtcapturethesystem's responsestopolicies,1eavlngtheclientstodiscoverthem asunforeseenside effectsintherealworld.Narrowmodelboundariesaretheslnglegreatestsource ofpolicyresistanceinsystems(chapter1).

Section21.4discussesteststohelpanswerquestionsaboutmodelpurposeand boundary,physicalanddecision-makingstructure,andsensitivltyanalysis.This sectionfocusesonthepracticalandpoliticalissuesofmodeling.Thereareno value-freetheoriesandnovaluejreemodels.Modelusersmustaskaboutthemod-

elers'biases(andtheirown).Howdothesebiases,especiallythosewewerenot awareof,colortheassumptlOnS,methods,andresults?

Thecostandeffortrequiredtorunthemodelalsoaffectthereliabilityofthe results.Largemodelsposeformidabledataqualitychallenges.Simplyensurlng thattherearenotypographicalerrorsinalargemodelisadauntlngtask.Ifitis

852

TABLE21-1 Questionsmodel usersshould

ask-but

usua‖ydon't

PartVI ModelTesting

Purpose.Suitabi/ity,andBoundary

oWhatisthepurposeofthemodel?

oWhatistheboundaryofthemodel?Aretheissuesimportanttothe purposetreatedendogenously?Whatimportantvariablesandissuesare exogenous,orexcluded?Areimportantvariablesexcludedbecausethere arenonumericaldatatoquantifythem?

.Whatisthetimehorizonrelevanttotheproblem?Doesthemodelinclude thefactorsthatmaychangeslgnificantlyoverthetimehorizonas endogenouse一ements?

orstheleve;ofaggregationconsistentwiththepurpose? PhysI-carandDecision･MakI'ngStructure

@DoesthemodelconformtobasicphysicaHawssuchasconservationof matter?Areallequationsdimensionallyconsistentwithouttheuseof fudgefactors?

oisthestockandflowstructureexp‖Citandconsistentwiththemodel purpose?

oDoesthemodelrepresentdisequiHbriumdynamicsordoesitassumethe systemisinornearequilibriumaHthetime?

oAreappropriatetimedelays,constraints,andpossiblebottleneckstaken intoaccount?

oArepeop-eassumedtoactrationallyandtooptimizetheirperformance? Doesthemodelaccountforcognitivelimitations,organizationalrealities, noneconomicmotives,andpoliticalfactors?

oArethesimulateddecisionsbasedoninformationtherealdecision

makersactua‖yhave?Doesthemodelaccountfordelays,distonions, andnoiseininformationfFows?

F70bustnessandSensitivitytoAlternativeAssumptions

oJsthemodelrobustinthefaceofextremevariationsinInputconditionsor policies?

｡ArethepollCyrecommendationssensjtjvetoplausiblevarjatjonsin assumptions,includingassumptionsaboutparameters,aggregation,and modelboundary?

PragmaticsandPolitI'csofModelUse

｡Isthemodeldocumented?lsthedocumentationpubliclyavaiFable?Can yourunthemodelonyourowncomputer?

◎Whattypesofdatawereusedtodevelopandte.Stthemodel(e･g･, aggregatestatisticscollectedbythirdpanies,prlmarydatasources, observationandfield-basedqualitativedata,archivaFmaterials, jnterviews)?

◎Howdothemodelersdescribetheprocesstheyusedtotestandbuild confidenceintheirmodel?Didcriticsandindependentthirdpartiesreview themodel?

oAretheresultsofthemodelreproducible?Aretheresu一ts"add-factored" orotherwisefudgedbythemodele｢?

｡Howmuchdoesitcosttorunthemodel?Doesthebudgetpermit adequatesensitivitytesting?

oHowlongdoesittaketoreviseandupdatethemodel?

olsthemode一beingoperatedbyitsdesignersorbythirdparties?

oWhatarethebiases,ideologleSandpoliticalagendasofthemodelersand clients?HowmightthesebiasesaffecHheresults,bothdeliberatelyand inadvertently?

Chapter21 TruthandBeauty:ValidationandModelTesting 853

veryexpensiveortime-consumlngtOrunthemodel,itisasurebetthatadequate

sensitivityanalysishasnotbeendone,erodingtheconfidenceyoucanhaveinthe reliabilityoftheresults.Moreinsidious,whenamodelcannotberevisedandrun quickly,themodelerstendtoresistpressurestochangeit.Often,themodelerwill becomedefensive,argulngthatsuggestedrevisionsorpotentialflawsarenotim-

portant.Theconsequenceofdefensivenessislossofclientconfidencethatthe modelcanbeuseful,leadingtoimplementationfailure.

Youshouldalsodeterminewhetherthemodelisbeingoperatedbyitsdesign-

ersorbythirdparties･Thedevelopersofmodelsareoftenpromotedormoveinto otherresponsibilities,leavlngtheirmodeltobemaintainedandrunbyotherswho maynotunderstanditsassumptlOnSOrbeabletomodifyitasconditionschange.

21.3.1 TypesofData

Forrester(1980)identifiesthreetypesofdataneededtodevelopthestructureand decisionruleslnmodels:numerical,written,andmentaldata.Numericaldataare thefamiliartimeseriesandcross-Sectionalrecordsinvariousdatabases.Written

dataincluderecordssuchasoperatlngprocedures,organizationalcharts,mediare- ports,emails,andanyotherarchivalmaterials･Mentaldataspanalltheinforma- tioninpeople'smentalmodels,includingtheirimpressions,storiestheytell,their understandingofthesystemandhowdecisionsareactuallymade(asopposedto whatiswritteninproceduresmanuals),howexceptionsarehandled,etc.Mental datacannotbeaccesseddirectlybutmustbeelicitedthroughinterviews,observa- tion,andothermethods.

Thenumericaldatacontainonlyatinyfractionoftheinfomationinthewrit-

tendatabase,whichinturnisminisculecomparedtotheinformationavailableonly inpeople'smentalmodels.MostofwhatweknowabouttheworldisdescrlptlVe, impressionistic,andhasneverbeenrecorded.Suchinformationiscrucialforun- derstandingandmodelingcomplexsystems.ImaglnetrylngtOmanageaSChool, factory,OrcltyusingOnlytheavailablenumericaldataoreventhewrittendata.

WithouttheexpertiseoftheparticlpantS,theresultwouldbechaos. Thoseconstructsforwhichquantitativemetricsandnumericaldataareavail-

ablearesometimestermed"harddata"or"hardvariables.''"Softvariables,"in

contrast,arethoseforwhichnumericalmetricsanddataarenotavailable,includ-

1ngfactorssuchasgoals,perceptlOnS,andexpectations･ThetermHhard"isin- tendedtoshowthatnumericaldataaremoreaccurateandrealthanqualitativedata,

Seenbymanyasinsllbstantialandunreliable.Inreality,Disraeliwasright:There are"lies,damnlies,andstatistics"-bothhardandsoftdatacanbebiased,dis-

torted,andunreliable.Further,nonumericaldataareavailableformanyofthe variablesknowntobecriticaltodecisionmaking.Thesemightincludecustomers'

perceptlOnSOfproductquality,theleveloftnlStbetweenamanagerandsubordi- nates,apurchasingmanager'sbeliefaboutthereliabilityofasupplier,employee morale,andinvestoroptimism.

Despitethecriticalimportanceofqualitativeinformationsomemodelersre- stricttheconstnlCtSandvariablesintheirmodelstothoseforwhichnumericaldata

areavailableandincludeonlythoseparametersthatcanbeestimatedstatistically･ Thesemodelersdefendtherejectionofsoftvariablesasbeingmorescientificthan

854 PartVI ModelTesting

"makingup"thevaluesofparametersandrelationships.How,theyask,cantheac-

curacyofestimatesaboutsoftvariablesbetested?Howcanstatisticaltestsbeper- formedwithoutnumericaldata?

OmittlngStructuresOrVariablesknowntobeimportantbecausenumericaldata

areunavailableisactuallylessscientificandlessaccuratethanusingyourbest

judgmenttoestimatetheirvalues."Toomitsuchvariablesisequivalenttosaying

theyhavezeroeffect-probablytheonlyvaluethatisknowntobewrong!"(For-

rester1961,p.57).Ofcourse,youmustevaluatethesensitivityofyourresultsto

theuncertaintylnyouraSSumptlOnS-Whetheryouestimatedyourparameters

judgmentallyorbystatisticalmeans.

Thatsaid,itisimportanttouseproperstatisticalmethodstoestimateparame-

tersandassesstheabilityofthemodeltoreplicatehistoricaldatawhennumerical

dataareavailable.Manyapparentlysoftvariablessuchascustomerpercept10nSOf

quality,employeemorale,investoroptlmism,andpoliticalvaluesareroutinely

quantifiedwithtoolssuchascontentanalysis,surveys,andfocusgroups.The

quantificationofsoftvariablesoftenyieldsimportantinsightintothedynamicsof

asystem｡5

Atthesametime,thedatayouneedtobuildandtestyourmodelarerarely

availablewithoutsignificantcostandeffort.Modelersmustconstantlymakejudg-

mentsaboutwhetherthetimeandcostofadditionaldatagatheringareJustified.In

theearliestphaseofmodelingltiso洗enworthwhiletouseexperientialdataandes-

timateparametersjudgmentallysoyoucangettheinitialmodelrunnlngaSSOOnaS

possible.SensitivltyanalysisOftheinitialmodelcanthenidentifythoseparame-

tersandrelationshipstowhichthebehaviorandpolicyrecommendationsaresen-

sitive.Parametersthatdonotsignificantlyaffecttheresultsneednotbeestimated

withhighaccuracy,allowingyoutOfocusyourlimitedresourcesonthosefactors

thatdomattersotheycanbemodeledandestimatedmoreaccurately.

Somemodelersgototheotherextremeanddiscounttheroleofstatisticalpa-

rameterestimationandnumericaldataingeneral.Theyarguethatqualitativein-

sightsaremoreimportantthannumericalprecisionandthatmodelbehavioris

insensitivetovariationsinmostparametervalues.Thisisaseriouserror,even

whenthepurposeofamodelisinsightandwhenbehaviorisinsensitivetop lausi-

bleparametervahes.Ignorlngnumericaldataorfailingtousestatistic a l tools

whenapproprlateissloppyandlazy.Itincreasesthechancethatthein sig h ts you

derivefromyourmodelwillbewrongorharmfultotheclient･Rigorou sly defin-

ingCOnStruCtS,attemptingtOmeasurethem,andusingthemostapprop rla tem ethl

odstoestimatetheirmagnitudesareimportantantidotestocasualem p lrlC ism,

muddledformulations,andtheerroneousinsightsweoftendrawfrom ou rm en tal

models･Fo汀eSter(1961,p･59),whilestressingtheimportanceofexperientialdata,

so氏variables,andjudgmentalparameterestimates,cautions:

Thesecommentsarenottodiscouragetheproperuseofthedatathatareavailable northemakingofmeasurementsthatareshowntobejustified･-LordKelvin'S

5ofcourse,therearesubtlemeasurementissuesinsurveyandrelatedmethodologleSIWording andquestionordercanmakelargedifferencestoresponses,and,asobservedinthecaseofthe drugusesurveysdescribedinsection7.3,self-reportsareoftensystematicallybiased･

Chapter21 TruthandBeauty:ValidationandModelTesting 855

famedquotation,thatwedonotreallyunderstanduntilwecanmeasure,stillstands. Butbeforewemeasure,weshouldnamethequantlty,Selectascaleofmeasure一 ment,andintheinterestsofefficiencyweshouldhaveareasonforwantlngtO know.

21.3.2 Documentation

Perhapsthemostimportantpragmaticissueformodelersisdocumentation.Docu一

mentationisanintegralpartofthemodelingprocess,atonceoneofthemostim-

portantandmostoftenneglectedactivities.

Documentationisrequiredtoensurethatyourresultscanbeunderstood,repli-

cated,Criticized,andextendedbyothers.Withoutproperdocumentation,your workisneitherscientificnoruseful.

Mostimportant,documentationisessentialforyou･FewthingsaremorefruS-

tratlngthantryingtOreconstructthemeaningOforrationaleforyourownmodel

becauseyoudidn'ttakethetimetodocumentyourworkatthetime.Documentas

youbuildthemodelthefirsttime.Don'twaituntilyouarefinishedwiththe"more

importantMworkofbuildingthemodel-bythenyoumayhaveforgottenwhyyou

didwhatyoudid.DocumentlngaSyougOhelpsuncovererrorsthatotherwise

mightnotbedetecteduntilmuchlater,preventlngCOStlyrework.Oneofthesad-

destsightsIknowisthelookofpaniconathesisstudent'sfacewhen,ontheeve

ofgraduation,Wediscoveranerrorinthemodelthatearlydocumentationwould

haverevealed.Table21-2presentsguidelinesfordocumentation.Followthemrlgl

orously.

2i J 5.3 ReF,≒'!結納弓き糖

Replicationallowsotherstobuildonyourwork,providesanimportantcheckthat

revealserrors,improvesthetransparencyandutilityofmodelingwork,andalso uncoverstheoccasionalfraud.

Unfortunately,replicationisrarelydoneinthesocialandmanagementsci-

ences.6HubbardandVetter(1991,1992)examinedmorethan2700empirical

papersineconomicsandfinance.Theyfoundonlyonepurereplication.Only

about4%ofjoumalpagesweredevotedtoreplicationswithextensionsoftheorlg- inalwork.

Theneedforreplicationisgreat･Inap10neerlngStudy,Dewald,Thursby,and

Anderson(1986)workedwiththeJournalofMoney,CreditandBankingtorepli-

cateemplrlCalstudiesreceivedforconsideration.Disturbingly,theyfoundone-

thirdoftheauthorsofpreviouslypublishedpapersdidnotrespondtorepeated

requeststosupplytheirdataSets.Halftheremainderchosenottosubmittheirdata

orcouldnotlocatethem.Responseratesweremuchhigherforthosewhosepapers

6Therearemanysensesoftheterm"replication"includingcheckingforerrors,repeatlnganex- perimentorstudywithexactlythesamemethodsanddata,repeatlngthestudywithsimilarexperi一 mentalconditionsorwithanewsampleofdatadrawn丘'omthesamepopulation,conductinganew studyaimedattestingthesamehypothesesastheorlglnal,andothers.Forthenuancesanddifferent viewsonreplication,seethereferencescitedaboveandalsoCollins(1991)andCartwright(1991); Wulwick(1996)providesacompellingexampleoftheimportanceofreplication.

856

TABLE21-2 GuideHFneS formodel

documentation

PartVI ModelTesting

YourEleSultsmustbefullyreplicable.

.Ensurethatindependentthirdpartiescanreplicatea"yourresultsusFng onryyourwrittendocumentation.

｡MakeyourmodelanditsdocumentationpubliclyavaiFabfe(foracademic

researchandpublicpolicymodels).CreateawebsitethataHowsanyone todownloadandrunyourmode一.

｡MakeyourmodelavailabletoaHmembersofthecfientteam(forbusiness modelswheretheremaybeproprietarydata),lncludea"thosewhowiH

beinvolvedinoraffectedbyimpFementation,evenyourcritics.

Rememberthatyouarewritingtot'anaudience.

.Besurethatyourdocumentation,simulationoutput,andtextconformto highstandardsforprofessionalcommunicationinthereJevantfield.

.Describetheassumptionsofthemodel:itsstructure,boundary,parameter values,datasources,andoverallrationale.Documentationisnotmerefya printoutofmodelequations.

.Organizeyourdocumentationbymodelsubsystem.

.PresentastructuraldiagramfoHowedbyanequat-rondescriptionforeach subsystemorkeydecision.

oPresentanddescribeyourequationsinaloglCaEsequence,by subsystem,Sothatreadersdonothavetorefertoanalphabetical equationlisting.

oUsedescriptivenamesorphrasesforvariablenames,notacronymsor symbols."ProductionStarts-Labor*Workweek'Productivity"isbetter than"Ps-L★W ★P".

olncFudeforeachequationthefu川nameofthevariable(ifitwas abbreviated),theunitsofmeasure,adescriptionoftherationaleand functionoftheformulation,andthesourcesforanyparametervalues ordata.

oSpecifytheunitsofmeasureforeveryvariableandparameter,andmake sureallequationsaredJlmenSionaHyconsistent.

｡Prepareasuccessionplan.Documentthemodelsootherscan

understand,run,andmodifyitwithouthavingtoaskyoualotof questions.Recruitandtrainotherswhounderstandandcanusethe

modeI.Onceyougetpromotedyouwon'twanttogetemaiHromyour successoraskinghowtousethemodel,

wereunderconsiderationorJustpublished.Amongthosewhodidrespond,

Dewaldetal.found69instancesoferrorinorinabilitytoreplicateresultsin54

datasets.Theyconclude,HInadvertenterrorsinpublishedemplrlCalarticlesarea

commonplaceratherthanarareoccurrence"andcautionedthat"Thefrequency

andmagnitudeoferrorsinemplricalarticlesraiseseriousquestionsregardingthe

integrityoftherefereelngProcessOfprofessionaljournals."Inafollow-uparticle,

AndersonandDewald(1994)weredisappointedtofindthat"Adecadeafterthe

JMCBproject,thereplicationofpreviousstudiesasapartofnewresearchseems

aninfrequentoccurrence."

Chapter21 TruthandBeauty..ValidationandModelTesting 857

Whyistheresolittlereplication?Replicatingandextendingsomeoneelse's

studyisviewedasuncreativedrudgeworkbymostresearchers.Ofthosefewrepli-

cationsthatareattempted,joumalsarefarmorelikelytopublishthosethatcontra-

dicttheorlglnalfindings,creatingIncentivesforresearcherstowithholdtheirdata

fromothers.HubbardandVetter(1991,1992)foundonly20%ofthefewrepli-

cationsandextensionsintheirsampleprovidedfullconfirmationoftheorlglnal

findings･7

Demandingthatallmodelsbefullydocumentedandallresultsbefullyreplic-

ablealsodefendsagalnStadd-factorlng-thepracticeofaddingafudgefactorto

theoutputofamodelsothatitsquareswiththemodeler'sintuition(Sterman

1988C;chap.16).Add-factoringallowsmodelerstogenerateresultstheylikewhile

avoidingthetroublesomebotherofactuallyuslngthemodeltoreachconclusions

fromwe111documentedassumpt10nS.

InoneinfamousstudytheJointEconomicCommitteeoftheUSCongress

(throughthepoliticallyneutralGeneralAccountingOffice)askedthethreeleading

econometricforecastlngfirmstoruntheirmodelsunderdifferentassumptions

aboutmonetarypolicy.Eachfirmsuppliedtheirforecastsandanalysisofthedif- ferentscenarios.Inaddition,theGAOrepeatedthesimulationsuslngthesame

models,providinganindependentreplicationtest.Inascenariowherethemoney

supplywasheldconstant,Onefirmprojectedinterestratesafteradecadetobe

7%/year.However,thisapparentlyreasonablevaluewasnottheresultofthe model.TheGAO'ssimulationofthesamemodelyieldedaninterestrateof

34%/year,aresulttotallycontrarytobotheconomictheoryandhistoricalexperi-

ence.Whathadhappened?Facedwiththisridiculousresult,themodelmanagers

atthatfirmhadnotbotheredtocorrecttheflawsinthemodelbutsimplyadd-

factoredtheinterestratedownbythemodestamountof79%.Theothermodels

faredlittlebetter(JointEconomicCommittee1982).TheGAO'sreplicationtest

revealedboththeinabilityofthemodelstoyieldmeaningfulresultsandtheex-

tensiveadhoeadjustmentsmadebytheforecasterstocoveruptheflawsintheir models.

Add-factorlngisfraudulentanddeceptlVeevenWhenthemodelerdoesnot

keepltSecret.Add-factorlngallowsunethicalmodelerstoselltheirmentalmodels,

withalltheirambigulty,hiddenassumptlOnS,andlimitations,whileatthesame

timecloakingthemintheauthorityofscience.Add-factorlngremovesallcon-

straintsthatmightprovideacheckonthemodelers'biasesandhubris･Thelate

OttoEckstein,founderofthehighlysuccessfuleconometricforecastlngfirmData Resources,Inc.,whocoinedtheterm"addfactor,"admittedina1983interview

thatDRI'sforecastswere60%modeland40%judgment･Heconcededthathis

forecastssometimesreflectedanoptlmisticview,modestlycommentlngthat"Data

Resourcesisthe mostinfluentialforecastingfirminthecountry...Ifitwereinthe

handsofadoom -and-gloomer,itwouldbebadforthecountry"(TheWallStreet

Journal,17February1983).

7ThelowincidenceofreplicationandhighrateofnonreplicabilityarenotunlquetOeCOnOmics･ Indeed,theseresearchersandjournalsshouldbecommendedfortheirwillingnesstoundertakeand publishstudieshighlightingtheproblem.

858 PartVI ModelTesting

Despltethecontinulngneed,replicationremainsrareinthesocialsciences.

Thesituationinpublicpolicydebatesandcorporatemodeling,wherefeedback frompeerreviewandrefereelngareOftenabsentandwheremodelsarekeptsecret toprotecttheirproprietarycontent,isfarworse.Thelackofreplicationandqual- 1tycontrolundercutstheeffectivenessofallmodeling.Youshouldnotacceptany

resultgeneratedbyamodelyoucan'treplicate･

21.3.4 ProtecがveversusReflectiveMode!ing

Table21-3summarizestwopolarapproachestomodeltestlngandthemodeling process.Modelerscanusetheirmodelsinaprotectivefashion,coverlnguPlm-

portantassumptions,uSlngdataselectivelytosupporttheirprejudices,andactlng likeanoracle.TheprotectivemodeofmodelinglSSelf-defeatlng･Itsealsthemod-

elerofffromlearnlng,Weakeningthemodelandreducingthechancesofdiscover- 1ngerrors.Itundercutsthecredibilityofthemodelandmodelers,ultimately destroylngthepossibilityofsuccessfulimplementation.Alternatively,modelers

canusetheirmodelinginチrej7ectivemodeinwhichtestingisdesignedtounc?ver flawsandhiddenassumpt10nS,Challengepreconcept10nS,andexposeassumpt10nS forcritiqueandimprovement.Paradoxically,areflectivetestlngProcessdesigned

touncovererrorshelpsbuildconfidenceinthemodelandultimatelyincreasesthe chancesforsustainedsuccess.

21.4 MoDELTESTINGINPRACTICE

Systemdynamicsmodelershavedevelopedawidevarietyofspecificteststoun-

coverflawsandimprovemodels(e.g"Forrester1973;ForresterandSenge1980; Barlas1989,1990,1996).Thesetestshelpyouanswerthebig-picturequestions discussedaboveandsummarizedinTable2111.Table2114summarizesthemain

tests,thepurposeofeach,andtheprlnClpaltoolsandmethodsusedineach,

TABLE2113 Protectiveand reflectiveusesof models

Protective:Modelsusedto Reflective:Modelsusedto

Proveapoint

Keepassumptionshidden

Usedataselectively

Supportpreconceptionsand buttresspreselectedanswers

H.andcoverupthep｢eselection

Promotetheauthorityofthe modele｢

Promotelnqulry

Exposehiddenassumptions

MotivatewidestrangeofemplrlCaFtests

ChaHengepreconceptionsand supportmultip一eviewpoints

..andinvolvethewidestcommunity

Promotetheempowermentofthe clients

Source:AdaptedandrevisedfromlsaacsandSenge(1992,p.191)

Chapter21 TruthandBeauty:ValidationandModelTesting

TABLE21-4 Testsforassessmentofdynamicmodels

859

Test PurposeofTest ToolsandProcedures

1.Boundary

Adequacy Aretheimportantconceptsfor

addresslngtheproblem endogenoustothemode一?

Doesthebehaviorofthemodel

changeslgnificantlywhen

boundaryassumptionsare relaxed?

Dothepolrcyrecommendations

changewhenthemodelboundary isextended?

2.Structure lsthemodelstructureconsistent

Assessment withrelevantdescriptive

knowledgeoHhesystem?

lsthelevelofaggregation approprlate?

Doesthemodelconformtobasic

physicaHawssuchas conservationlaws?

Dothedecisionrulescapturethe behavioroftheactorsinthe

system?

31DimensionaR Iseachequationdimensionally Consistency consistentwI'thouttheuseof

parametershavingnorealworld

meanlng?

4･Parameter Aretheparametervalues Assessment consistentwithrelevant

descriptiveandnumerical

knowledgeoHhesystem?

Doallparametershaverealworld

counterparts?

Usemodelboundarycha｢【S,subsystem

diagrams,causaldiagrams,stockandflow maps,anddirectinspectionofmodel

equations･

Useinterviews,workshopstosolicitexpert

oplnion,archivaFmaterials,reviewof

literature,directinspection/particIPationin

systemprocesses,etc･

Modifymodeltoincludeplausibleadditional

structure;makeconstantsandexogenous

variabresendogenous,thenrepeatsensitivity andpollCyanalysIS.

UsepollCyStructurediagrams,causal

diagrams,stockandflowmapsanddirect

inspectionofmodelequations.

Useintervllews,workshopstosohlcitexpert

oplnion,archivalmaterials,directinspection

orparticipationinsystemprocesses,asin

(l)above.

Conductpartialmodeltestsoftheintended

rationaHtyofdecisionrules.

Conductlaboratoryexperimentstoelicit

mentalmodelsanddecisionrulesofsystem

participantsI

Developdisaggregatesubmodelsand

comparebehaviortoaggregateformulations,

Disaggregatesuspectstructures,thenrepeat sensitivityandpollCyanalysIS.

UsedimensionalanalysISSOftware.

Inspectmode一equationsforsuspect

parameters.

Usestatisticalmethodstoestimate

parameters(widerangeofmethods available),

Usepartia!modelteststoca‖brate

subsystems･

Usejudgmentalmethodsbasedon

interviews,expertoplnion,focusgroups, archivalmaterials,directexperience,etc.

(asabove)

Developdisaggregatesubmodelstoestimate

relationshipsforuseinmoreaggregate models.

(Continued)

860 PartVI Model¶∋stiIlg

TABLE21-4 (Continued)

Test PurposeofTest ToolsandProcedures

5･Extreme Doeseachequationmakesense Conditions evenwhenitsJnPutStakeon

extremevalues?

Doesthemodelrespondplausibly whensubjectedtoextreme

poricies,shocks,andparameters?

6.ntegration Aretheresultssensitivetothe

Error choiceoftimestepornumerical integrationmethod?

7･Behavior Doesthemode一reproducethe

Reproductionbehaviorofinterestinthesystem (qualitativelyandquantitatively)?

Doesitendogenouslygenerate thesymptomsofdifficulty motivatingthestudy?

Doesthemode一generatethe variousmodesofbehavior

observedintherealsystem?

Dothefrequenciesandphase relationshipsamongthevariables matchthedata?

8.Behavior

Anomady

9.Family Member

10.Surprlse Behavior

Doanomalousbehaviorsresult

whenassumptionsofthemode一 arechangedordeleted?

Canthemodelgeneratethe behaviorobservedinother

instancesofthesamesystem?

Doesthemode一generate

previouslyunobservedor unrecognizedbehavior?

Doesthemode一successfully anticJPatetheresponseofthe systemtonovelconditions?

Inspecteachequation.

Testresponsetoextremevaduesofeach

Input,aloneandincombination.

SubjectmodeHolargeshocksandextreme conditions.Implementteststhatexamine

conformancetobasicphysicaHaws(e.g., noinventory,noshipments;nolabor,no production).

Cutthetimestepinhalfandtestforchanges inbehavior.Usedifferentintegrationmethods

andtestforchangesinbehavior.

Computestatisticalmeasuresof correspondencebetweenmode一anddata:

descriptivestatistics(e.g.,R2,MAE);time domainmethods(e.g"autocorrelation

functions);frequencydomainmethods(e.g., spectralanalysis);manyothersl

Comparemodeloutputanddataqualitatively, includingmodesofbehavior,shapeof

variables,asymmetries,relativeamplitudes andphasing,unusualevents.

Examineresponseofmodeltotestinputs, shocks,andnoise.

Zerooutkeyeffects(loopknockoutanalysis).

Replaceequilibriumassumptionswith disequilibriumstructures･

Calibratethemodeltothewidestpossible

rangeofre一atedsystems･

Keepaccurate,complete,anddatedrecords ofmodelsimu一ations.Usemodeltosimulate

likelyfuturebehaviorofsystem.

ResolveaHdiscrepanciesbetweenmodel

behaviorandyourunderstandingofthereal SyStem･

Documentparticipantandclientmentai modelsprl0rtOthestartofthemodeling effort.

(Continued)

Chapter21 TruthandBeauty:ValidationandModelTesting

TABLE21･4 (Conc/uded)

861

Test PurposeofTest Too一sandProcedures

llrSensitivity NumericalsensitivI'ty.'Dothe AnalysdS numerica一valueschange

slgnificantly-･

Behavioralsensitivity:Dothe modesofbehaviorgeneratedby themode一changeslgnificantly.

PolicysensitivI'ty:Dothe pollCyJmPllcationschange slgnificantly- I

Hwhenassumptionsabout parameters,boundary,and aggregationarevariedoverthe plausiblerangeofuncertainty?

12.System Didthemodelingprocesshelp 日mprovemenモchangethesystemforthebetter?

Performunivariateandmultivariate

sensitivityanalysIS.

Useanalyticmethods(linearization,local andg一obalstabilityanalysis,etc.).

Conductmodelboundaryandaggregation testsHstedin(1)and(2)above.

Useoptimizationmethodstofindthebest parametersandpolicies.

Useoptimizationmethodstofindparameter combinationsthatgenerateimplausible resultsorreversepoITCyOutcomes,

Designinstrumentsinadvancetoassess theimpactofthemodeHngprocesson mentalmodels,behavior,andoutcomes.

DesigncontroFledexperimentswith treatmentandcontro一groups,random asslgnment,Pre-interventionandpost-

interventionassessment,etc.

Source:AdaptedandextendedfromForresterandSenge(i980)

2l.4∴i BoundaryAdequacyTesモs

BoundaryadequacytestsassesstheapproprlateneSSOfthemodelboundaryforthe

purposeathand.ThefirststepIStOdeterminewhattheboundaryis.Helpfultools

forthispurposeincludemodelboundarychartsandsubsystemdiagrams(chapter

3).Ifthemodelerdoesnotsupplytheseyoushouldconstructyourownbydirect

inspectionofthemodelequations.Searchthemodelequationsforexogenousin-

Putstoconfirmthatthelistofexogenousvariablesiscomplete.Rememberthatall

constantsareexogenousbutmayinfactbevariableoverthetimehorizonofinter-

est.Youshouldinspectmodeldiagrams,ifprovided,orconstructcausaldiagrams

fromthemodelequationstoidentifyconstantsthatmightproperlybeconsidered variable.

OncethemodelboundarylSestablished,considerwhethertherearepotentially

importantfeedbacksomittedfromthemodel.Ofcoursethelistofomittedconcepts

andvariablesisinfinite.Yourconcerniswhetheranyfeedbacksomittedfromthe

model,ifincluded,mightbeimportantglVenthepurposeofthemodel.Interviews

862 PartVI ModelTesting

withkeypartlClpantSandoutsideexperts,reviewoftherelevantliteratureand archivalmaterials,anddirectexperiencewiththesystem maysuggestsome

processesthatperhapsshouldbemadeendogenous.Constructadynamichypoth- esissuggestinghowtheinclusionofthecandidatefeedbackmightalterthedy-

namicsorpolicyImplicationsofthemodel.Ifreviewofthedatasuggeststhenew structuremightmatter,youshouldaddittothemodelandexamineitseffectson thebehavior(notonlyforthebasecasebutalsoforawiderangeofsensitivity tests).

IfanadditionalstructurehasasignificantimpactonthebehaviororpolicyIm-

plicationsofthemodelthenitmustbeincluded.Ⅰfithasnoimpact,youcan choosetoomititsoyourmodelissmallerandeasiertoexplainorretainitifit buildsclientconfidenceinthemodel.

Example:ModelBoundaryAssumptionsintheDebateoverNAFTA

DuringthecongressionaldebateovertheNorthAmericanFreeTradeAgreement (NAFTA)intheearly1990S,proponentsofNAFTAarguedthatfreetradewould boosttheincomesandstandardoflivlngOfalltradingpartners.Thetraditional economictheoryofcomparativeadvantagesuggeststradebenefitsbothpartiesbe- causeeachcanproducemoreofwhatitisbestatandtradefわrtherest,insteadof producingallthegoodsandservicesitconsumeswithlowerefficiency.NAFTA opponents,however,arguedthatcompanieswoulddivertcapitalinvestmentfrom theUS,withitshighwagesandcomparativelystrictenvironmentalregulations,to Mexico,destroyingUSjobsandharmlngtheenvironment･Theyarguedthatcapトーalmobilitywouldleadtoa‖racetothebottomHthatwoulddragdownwages, safetystandards,andenvironmentalqualityasdifferentcountriescompetedfor factoriesandjobs.

DozensofeconometricmodelswereusedtopredicttheeffectsofNAFTAon thehealthoftheUS,Canadian,andMexicaneconomiesandtheirresultswere

usedtobuttresstheargumentsinthedebate.ThevastmaJOrltyofthesemodels suggestedNAFTAwouldbeaboontoallthreeeconomies,withlittleornoshorト runcosts.Themodelswereusedtoarguethatconcemsovercapitalflightfromthe

USweremlSplaced. TheCongressionalBudgetOffice(1993)examined19modelsusedtomake

forecastsoftheimpactofNAFTA･Ofthe19models,14didnotconsiderinvest- mentflowsatall.Ofthefivethatdid,fourassumedtherewouldbenoimpacton

USinvestment.Implicitly,theyassumedallNAFTA-inducedinvestmentinMex- icowouldcomefromnationsotherthantheUS.Theonestudythattreatedinvest-

mentendogenouslyconcludedthatNAFTAwouldtransfer$2.5billionperyearin investmentfromUStoMexico,resultinglnalossofabout375,000USjobsover

5years. FollowlngStandardpracticesincethedaysofSmithandRicardo,most

NAFTAmodelersassumedthatcapitalandlaborwerefixedandimmobile.Goods flowedbetweennationsintradebutcapitalandlaborcouldnot.Thetheoryof

comparativeadvantageworksundertheseconditions･Butwhencapitalismobile,

comparativeadvantagenolongeroperatesbecausebusinesseswilllocateinthere- gionWiththegreatestabsoluteadvantage｡AssumlngImmobilecapitaleliminated

Chapter21 TruthandBeauty:ValidationandModelTesting 863

importantfeedbacksfromthemodelboundary,feedbacksthatchangedtheour comeofthepolicyanalysュs.

ThisdiscussionisnottoarguethatNAFTAwasamistake.Rather,thepointis thattheresultsofthemodelsdependedonboundaryassumptlOnSthatwereatthe veryleastquestionableandthatwerecertainlynotmadeexplicitbythemodelers. NoneofthemodelsendogenouslytreatedNAFTA'seffectonillegalandlegalim- mlgration,theeffectsofborderdevelopmentonenvironmentalquality,waterde- mand,demographicpatterns,andsoon.Partisans(onbothsides)Selectedmodels consistentwiththeirpoliticalviewsanddidnotmaketheirassumptlOnSavailable forreview.InthedebateoverNAFTA,assoofteninpublicpolicy,modelswere notusedhonestlyastoolsofinqulrytObuildsharedunderstandingbutasclubsto beatdowntheotherside.

21.4.2 StructureAssessment¶∋sts

Structureassessmenttestsaskwhetherthemodelisconsistentwithknowledgeof therealsystemrelevanttothepurpose.Structureassessmentfocusesonthelevel ofaggregation,theconformanceofthemodeltobasicphysicalrealitiessuchas conservationlaws,andtherealismofthedecisionrulesfortheagents.

Inbothboundaryadequacyandstructureassessmenttestlng,youShouldlook forfreelunches,inconsistencies,andinapproprlateaSSumPtlOnSabouttheavail- ability,flexibility,andcostoftheresourcesneededforactivltytOoccur.Identify externalitiesandsideeffectsthatshouldbecapturedendogenously.Makesurethe fullcostsandbenefitsofactionsarecaptured.Ifnecessary,createnewmodelstruc- turetoaccountforthesecosts,eveniftheaccountlngSystemsintherealsystemdo not(see,e.g"thediscussionofthecostsofinstabilityinchapter19).

ⅥOlationsofphysicallawssuchasconservationofmatterorenergyusually arisebecausethemodeldoesnotapproprlatelycapturethestockandflowstructure ofthesystem.Othercommonviolationsofphysicallawinvolvestocksthatcan becomenegative.Realquantitiessuchasinventories,populations,andcashbal- ancescannotbenegative.ThereforetheoutflowsfromallsuchstocksmustapI proachzeroasthestockapproacheszero.Thismeanstheremustbeafirst10rder negativefeedbackloopthatrestrictsalltheoutflowsfromrealstockssothatthe flowiszerowhenthestockiszero(section13.3).Theseloopsmustbefirst-order becauseanytlmedelayintheloopcouldcausetheratetocontinueevenafterthe stockreacheszero,aphysicalimpossibility･Youcancheckforthepresenceof first10rdercontrolbydirectinspectionoftheequations.

Freelunchesarisewhenactivitiesthatrequlreimportantresourcesinthereal systemareassumedtooccurwithoutthoseresourcesinthemodel.Forexample, thefirstsupplychainmodelinchapter18assumedproductionstartsequaledthe desiredproductionstartrate,implyingthefirmcouldadjuststartstothedesired rateinstantlyandwithoutcost.RelaxlngthisassumptionSignificantlyaltersthe dynamicsofasupplychain.

StructureassessmenttestsarecarriedoutuslngmanyOfthesametoolsuseful inboundaryassessment.Subsystemdiagramsandstockandflowmapshelpreveal thelevelofaggregation.Policystructureandcausaldiagramsrevealtheinforma- tioncuesusedineachdecision.Directinspectionoftheequationsrevealsthe

864 PartVIModelTesting

heuristicsassumedateachdecisionpoint.Partialmodeltests(chapter15)Can

demonstratetheintendedrationalityoftheindividualdecisionrules.Inaddition,

laboratoryexperimentscanrevealhowpeopleactuallymakedecisionsinsitua-

tionsanalogoustothoserepresentedinthemodel(e.g.,Sterman1989a,b).Another

techniquetotesttheapproprlateneSSOfaggregationassumptionsistodevelopa

moredetailedsubmodel,thencompareitsbehaviortothatofthemoreaggregate

formulation.As inboundaryadequacytests,disaggregationofasuspectstructure

mayshowthattheextradetailisimportant.Whendisaggregationdoesnotsignifi-

cantlyaffectmodelresultsandpolicyimplications(relativetothepurpose,asal-

ways)thentheoriginal,simplermodelcanberetained.

Example:WaterFlowlngUphill

ThePecosriverorlglnateSinNewMexicoandalsoflowsthroughTexas.Begin-

nlnginthe1940sbothstatesclaimeditswater.Thedisputeledtoaseriesoflaw-

suitsoverwaterrights.EngineerlngandhydrologlCStudiesofthewatersheddating

asfarbackas1949Wereusedbybothstatestopleadtheircasewithvariouscourts.

AsdescribedbyAllisonetal.(1994,p.21),areviewinthe1980srevealedthat

themodelusedbyNewMexico"violatedbasicphysicalflowrelations...For

somereachesoftheriver" waterwouldhavehadtoflOwupstreamtosatisfythe

hydrologlCalmassbalancerequlrementS."Themodeldevelopersfailedtoconduct

basictestsforconformancetophysicallaws.Evenmoreremarkably,theerrorwent

undetectedforyearsdespitethescrutlnyappliedtoexperttestimonylnanadver-

sarialproceeding.Oncetheerrorwasdiscovereditformedakeypartofthecase

forTexas.TheUSSupremeCourtultimatelyruledinfavoroftheLoneStarstate.

Example:FPeverslnglnleVerSibleDecl'sions

Alinearprogrammlngmodeloftheleathermarketconsistentlyoutperformedthe

actualmarket.ExaminlngWhythemodeldidsomuchbetterthanrealpeople,the

developersdiscoveredthatthemodelmadeexceptionallygooduseofitsequations

describingthesupplyofleather.Duringperiodsofeconomicdownturn,themodel

simplyconvertedtheleatherbackintocows･8

Example:NegatlrVeStocks

AndersenandSturis(1988)proposedamodelofamanufacturingfirmtoexplore

chaoticdynamicsinamanagementsetting.Themodelincludedthefollowing

structurefortheshipmentrate:

Inventory-INTEGRAL(ProductionRate-ShipmentRate,Inventoryto) (21-1)

ShipmentRate-Customers*AverageSalesperCustomer (21-2)

whereAverageSalesperCustomerwasconstant･Thestockofcustomerswasin-

creasedbyrecruitmentresultingfromsaleseffortanddecreasedascustomersdel

fectedtoothersuppliers.

Customers-INTEGRAL(CustomerRecruitment-CustomerDefection,Customerst｡) (21-3)

8source･･prof･MarshallvanAIstyne,UniversityOfMichigan,personalcommunication･

Chapter21TruthandBeauty:ValidationandModelTesting 865

Thecustomerlossrateincreaseddramaticallywheneverinventoryfellbelowthe

desiredlevel,ascustomersrespondedtolowproductavailability:

Customer / Customers

Defection ＼N ormalCustomer *EffectofAvailability

onDefection EffectofAvailability_JDesiredlnventory

onDefection J＼ DesiredInventory

(21-4)

>0 (21-5)

Inspectionoftheequationsshowsthemodellacksfirst10rdernegativefeedback

controlovertheshipmentrate(Settinginventorytozerodoesnotimmediately

forceshipmentstozero).Thoughzeroinventorydoescausethestockofcustomers

tofallrapidly,thedropISnotinstantaneous,allowlngInventorytOfallbelowzero.

Imaginethecasewhereafiredestroysallinventoryonenight.Thenextmornlng, therehasnotyetbeenanychangeinthestockofcustomers,soshipmentscontinue

thoughthereisnoproducttoship.Reformulatingthemodeltocorrectthisand

otherflawsslgnificantlychangesitsdynamicsandstability.

Example:RecoveryoftheUSEconomyfromNuc/earWar

DuringtheColdWartheUSgovernmentcommissionedstudiestoassesstheec0-

momicimpactofnuclearwar.Onesuchmodel,dubbedtheHEconomicRecovery Model"(DreschandBaum1973)wasusedtoevaluatetheeffectsofdifferentSo-

vietattacksontheUS,includinga500megatonattack･Tbputthatinperspective,

thebombthatdestroyedHiroshimayielded14kilotons,36,000timesless.The

modelsuggestedthatthegrossnationalproduct(GNP)oftheUSwouldrecoverto

80%ofpreattackproductionafterjust9years-andthat'stotalGNP,notGNPper

capitalTheyalsoexaminedtheeffectsofanattackdirectedatthepetroleumsec-

tor･Officialsfearedthatafewmissiles,bydestroylngthepetroleumsectorand

causlngmassivefuelshortages,mightcrlppletheentireeconomy･9Themodelsug一

gestedtherewasnothingtoworryabout.Immediatelyaftera250-megatonattack

directedatthepetroleumsector,totalGNPfellto22%ofthepreattackrate.But

after1year,GNPjumpedto61%ofprioroutput,andafter5yearsitreached94%

ofpreattackoutput.

Theamazlngrecoverypotentialsuggestedbytheseresultsmeansboth血eUS

andUSSRneededverylargearsenalsofnuclearweaponstoensurethattheycould "win"anuclearwarandthusserveasadeterrent.Resultssuchasthesewerecited

bycoldwarriorsasevidencethattheUSneededstillmorenuclearweapons.

Sastry,RommandTsipis(1987)conductedboundaryandstructureassessment

testsonthemodelandfoundanumberofunreasonableassumptions.Thoughos-

tensiblydynamic,itwasactuallyageneralequilibrium Input/outputmodelin

whichtheentireeconomywasassumedtobeinequilibrium atalltimes.The

modeldidnotrepresentstocksofmaterials,energy,andotherresourcesasdy-

namicquantitiesthatcouldaffecttheabilityofindustriestofunction.Inequilib-

rium,stocksareconstant,sotheyareusuallyomittedfromgeneralequilibriumand

I/0models,whichtreatonlythesteadystateflOwsofgoodsandservicesthrough

9Destroyingthepetroleumindustryrequirestargetingoilfields,ports,andrefineries(nearlythe entireeast,west,andGulfcoastsoftheUS,plusTexas,Oklahoma,Alaska,Ohio,andotherstates whereoilfieldsandrefineriesarelocated),causingaregrettablenumberofciviliancasualties･

866 PartVIModelTesting

theeconomy.Whetherequilibriumisareasonableassumptionfortheeconomy undernormalcircumstancescanbedebated.Butthenotionthattheeconomylm一 mediatelyreturnstoequilibriumafteranuclearwar,withoutanyshortagesofma- terials,energy,labor,andotherresourcesuponwhichproductiondepends,beggars belief.

DreschandBaum(1973),notingtheflawsintheirownmodel,commented thattheneartreblingofGNPinaslngleyear"islargelyaconsequenceofthetwo- yearlagassumedtoberequiredforcapitalreplacement."Intheirmodelcapital stocksalwaysreachedoptlmallevelsin2yearsindependentofthecapacltyOfthe capitaトproducingindustries,theirabilitytoacqulrethenecessaryrawmaterials andenergy,theavailabilityofliquidfuelstooperateconstructionequlpmentand shipproducttocustomers,theavailabilityofskilledworkers,andtheabilityofthe governmenttomaintainorder-inshort,withoutregardtotheeffectsofthevery attacktheirmodelwasdesignedtoevaluate.

Sastryetal.(1987)modifiedasystemdynamicsmodeldevelopedfortheFed- eralEmergencyManagementAgencytoeliminatethese丘.eelunchesandequilib- rium assumptions.Intherevisedmodel,smallattacksfocusedonpetroleum refineriescouldcrlppletheeconomythroughacascadingchainoffuelshortages thatshutdownproductionofkeyindustriessuchastransportation,construction, andmanufacturing,thwartingeffortstorebuildtheenergysectorandcausingfood shortagesthatledtostarvationandanarchy.Theresultsimpliedthataverysmall strategicarsenalprovidedsufficientdeterrentcapabilityandthatthestrateglCmis-

siledefensesystem(so-calledstarwars)thenadvocatedbytheReaganadminis- trationwouldhavetobenearlyperfecttoprotecttheUS.

21｡乱3 Dimemsiom盈Eeonsisをe閃ey DimensionalconsistencylSOneOfthemostbasictestsandshouldbeamongthe veryfirstyoudo.Youshouldalwaysspecifytheunitsofmeasureforeachvariable asyoubuildyourmodels.Donotwaituntilafterwardtofillintheunitsandcheck forconsistency.Dimensionalinconsistencymayrevealnothingmorethanatypo- graphicalerror,aninvertedratio,oramisslngtimeconstant.Moreoften,units errorsrevealimportantflawsinyourunderstandingofthestructureordecision processyouaretrylngtOmodel.

Somesimulationsoftwarepackagesforsystemdynamicsnowincludeauto- mateddimensionalanalysissoyoucantestfordimensionalerrorswithaslngle command.However,amodelthatgeneratesnoerrormessageswhenyourunthe dimensionalconsistencycheckdoesnotnecessarilypassthetest.Everyequation mustbedifrlerlSional1ycorlSistentwithouttheinclusionofarbitraYlySCalingfactors thathavenorealworldmeamng.Theonlywayyoucanidentifysuchfudgefac- torsisbydirectinspectionoftheequations.Parameterswithmeaninglessnames, strangecombinationsofunits(widgets2/S/month3),ornondimensionlessparame- terswithvaluesofunityaresuspect.

21.4.4 ParameterAssessment

Beforedecidinghowaparametershouldbeestimatedorwhetheritsvalueisrea- sonablemakesureeveryconstant(andvariable)hasaclear,real-lifemeaning.

Chapter21 TruthandBeauty:ValidationandModelTesting 867

Nextyoumustdecidehowtoestimatethevaluesofeachparameter.Thebasic

choiceisformalstatisticalestimationfromnumericaldata,orjudgmentalestimation.

Theestimationofparametervaluesfromnumericaldatareceivesagreatdeal

ofattentioninmodeling,particularlytheeconometrictradition.Systemdynamics

modelersarewelladvisedtostudyeconometricsandotherapproachestoformal

parameterestimation.Itisessentialtoknowhowtheimportantregressiontech-

nlqueSWOrk,whattheirmaintainedhypothesesandlimitationsare,andwheneach

toolisappropriate.ThemaintainedhypothesesaretheassumptlOnSaboutthedata

andmodelthatmustholdfortheestimationtechniquetoglVereliableandaccurate

results,Themostcommonmethod,multipleregressionbyordinaryleastsquares

(OLS),isoftennotappropriateindynamicmodels･OLSestimatesarenotaccurate

inthepresenceofcollinearity(wherethevariablesontherighトhandsidearemu-

tuallycorrelated),autocorrelation(wherethedependentvariabledependsonits

ownpastvalues,thatis,wherethereisfeedback),andheteroscedasticity(where

thevarianceofthevariablesisnotconstantthroughoutthesample).Other,more

robustestimationmethodsareavailable,ranglngfromrelativelysimplemaximum

likelihoodandGLS(generalizedleastsquares)methodstosophisticatedmethods

suchasKalmanfiltering.Eachhasitsstrengthsandweaknesses;youshouldknow

howtoselectthesimplestmethodthatisapproprlatetOthefeedbackstructureof

yourmodelandthestatisticalpropertiesofthedata･10

Atthesametime,limitationsonnumericaldataavailabilitymeanitisoften

impossibletoestimateallparametersinamodel･Youmustalsodeveloptheabil-

1tytOestimateparametersjudgmentallyuslngexpertOPlniongleanedfrominter-

views,workshops,archivalmaterials,directexperience,andothermethods(See

chapter14).Parameterscanalsobeestimatedbydevelopingadisaggregatedsub-

model(seetheexamplebelow).ll

Inpractice,statisticalandjudgmentalmethodsareusedtogether,Knowledge

oftherealsystemconstrainstheplausiblerangeformanyparameters;statistical

estimationprovidesacheckonjudgmentalestimates･

Inalargemodelitisusuallyimpracticaltoestimateallthecriticalparameters

simultaneously.Evenwhenpossible,simultaneousestimationcanleadtoproblems

sincelargemodelsareoftenunderidentified(i.e･,morethanonesetofparameter

valuesfitthedataequallywell).Inthesecasesjudgmentalestimatesgroundedin

knowledgeofthesystemareessentialinselectlngreasonableparameters.

Partialmodelestimation(Homer1983b)isalsousefulforparameterselection.

Asinpartialmodeltestingforintendedrationality(chapter15),themodeleriso-

latesakeystructureordecisionrule,cuttlngthefeedbackloopsinthefullmodel.

The inputstoeachdecisionruleorformulationarethendrivenbytheactualhis-

toricaldataandtheparametersarechosen(judgmentallyorformally)sotheoutput

10TextssuchasBerndt(1991)andGreene(1993)providesolidcoverageofeconometric techniquesandapplications.

llResponsesurfacemethods(e.g.,BoxandDraper1987)allowyoutocapturetheresponseof acomplexdisaggregatemodelwithafewequations･Inessence,thebehav10rOfthefullmodelis capturedbyapolynomialapproximationcorrespondingtothefirstfewtermsoftheTaylorseries expansionoftheunderlyingsystemintherelevantparametersandpolicylnStrumentS･Theapproxi一 matioIICanthenbeembeddedinalargermodel.

868 PartVI ModelTesting

ofthesubsystembestfitsthedata(forexamplesseeHomer1983b;Fiddaman 1997;01iva1996;andTaylor1999).

Acaution:ThestatisticalsignificanceofparametersrelatingVariablesinan equationisnotanindicatorofthecorrectnessoftherelationship.Statisticalsignif-

icanceindicateshowwellanequationfitstheobserveddata;itdoesnotindicate whetherarelationshipco汀eCtlycharacterizescausalrelationshipsintherealworld. Astatisticallyslgnificantrelationshipbetweenvariablesshowsonlythattheyare

highlycorrelatedandthattheapparentcorrelationisnotlikelytohavebeenthere- sultofmerechance.Assertlngarelationshipiscausalisavaluejudgmenttobe madebyconsideringalltheevidence,numericalandqualitative.

Usingstatisticalsignificanceasthetestofmodelvaliditycanalsoleadmodel-

erstorejectequationsdescribingImportantrelationships.Arelationshipmaybe statisticallyInsignificantsimplybecausetherearetoofewdatapolntSOrbecause thedatadon'tvaryenough.Whendirectknowledgeofthesystemsuggestsarela- tionshipisrealandimportant,youmustincludeit,usingyourbestjudgmenttoes- timateitsvaluesevenifthenumericaldatadonotallowyoutoestimateits strength.

Example:StatisticalEstlJmatl'onofSoftVan'ables

Oliva(1996)developedamodeltoexplorethedeterminantsofservicequalityin high-contactsettlngSandappliedittoretailbanking･Asdiscussedinsection14.3, 01ivawasabletoestimatestatisticallytheresponseoftheworkweekandtimeal-

locatedtoeachcustomertoworkload.Resultsshowedthatloanofficerswere

nearlytwiceaswillingtocutcornersbyspendinglesstimewitheachcustomer thantoworkovertimewhentheworkloadwashigh.01ivafurtherhypothesized thatloanofficers'standardsforthetimetheyshouldspendoneachcustomerin- qulryWereVariable,adjustlngovertimetotheactualtimespent.Thetimespent witheachcustomerco汀elatedhighlywiththecustomers'judgmentaboutservice quality.

Inmanymodelswithdynamicgoals,normadjustmentissymmetric-norms riseasfastastheyfall.Otherssuggestnormerosionisasymmetric,Withquality normsfallingmorereadilythantheyrise.01ivatestedforasymmetricnormad- justmentbyestimatingthetimeconstantsinthenonlinearsmoothingstructurede-

scribedinsectionll.4.1.SurprlSlngly,theestimatesshowedthatwhilequality

normsfellquicklywhentheworkloadwashigh,theyneverrose,evenwhenthe workloadwaslight:Theestimatedvalueofthetimeconstantforrevisingthetime

percustomernormupwardwasessentiallyinfinite.Furtherdiscussionsandreview ofthedatashowedthattheorganizationdidnothaveanylnStrumentSinplaceto monitorcustomersatisfactionandfeeditbacktothemanagers.Wheneverworkl

loadswerehigh,workersreducedthetimetheyspentwitheachcustomertoclear thebacklogandsoonbecamehabituatedtothenewlevels･Withoutanywayto measuretheresultingdroplnCustomerSatisfaction,managementinterpretedthe

droplnqualityasanimprovementinproductivlty･Whenworkwasslow,thework- ersfeltcontinulngPressuretOmeettheorganization'snew,lowernormsforthe timespentpercustomer(appendixBprovidesfurtherdiscussion)｡

Theformalestimationprocessrevealedanimportantfeatureofthedynam- icsthatpriorworkhadnotandmotivatedadditionalresearchthatconfirmed

Chapter21 TruthandBeauty:ValidationandModelTesting 869

theresultsofthestatisticalestimationprocess.Thecombinationofformaland judgmentalparameterestimationmethods,fieldwork,andarchivaldataanalysis yieldedamoreaccurateandreliableunderstandingoftheorganization'sdynamics thananymethodalone.

Example:DeveloplngaDetailedSubmodel

Parameterscanoftenbeestimatedbystatisticalormodelingworkbelowthelevel ofaggregationofthemodelitself.Homer(1999)developedamodeldesignedto improvetheperformanceofasemiconductorequipmentmanufacturer'sfieldser- viceorganization.Animportantstructureinthemodelrelatesfieldservicedeliv- erytotheavailabilityoftechniciansandtheextenttowhichtechniciansare cross-trainedonthecompany'smultipleproducttypes.Intherealsystem,thereare differenttechniciansindifferentlocations,eachwithhisorherownskills,backlog ofworkorders,andavailability.Thefullmodelaggregatedthesedifferentre-

sourcesanddemandsintoasimplestructureconsistlngOfanaggregatebacklogof servicerequestsandanaggregatecapacltytOProvideservice,bothtreatedascon- tinuousvariables.Servicelevelsweremodeledasasimplefunctionoftheratio ofthebacklogandaggregatecapacity,modifiedbyanonlineareffectofcross- trainlng.Tbtestwhethertheaggregatestructurewasapproprlate,Homerde- velopedanindependentsubmodeltreatlngthearrivalofworkanddispatchof techniciansuslngaStOChastic,queulngtheoryframeworkcombinedwithalinear programmlngalgorithmforperiod-to-periodoptimizationofservicethroughput･ Individualjobsandtechniciansweremodeledasdiscreteentitieswithemplrically estimatedprobabilitiesforarrivalandcompletionofworkforeachtypeofproduct andjob(e･g･,repair,preventivemaintenance,orengineeringchange)･Thedetailed submodelshowedthattheaggregatestructurewasacceptableforthepurposeof thefull,strategicmodelandallowedHomertoderivetheshapeandvaluesofthe nonlinearfunctiongovemlngtheeffectofcross-trainlng･

21.4.5 ExtremeCondition¶∋Sts Modelsshouldberobustinextremeconditions.Robustnessunderextremecondi- tionsmeansthemodelshouldbehaveinarealisticfashionnomatterhowextreme

theinputsorpoliciesimposedonitmaybe.inventoriescanneverdropbelowzero nomatterhowlargethedemandmaybe.Thedemandforproductsmustfalltozero whentheprlCeriseshighenough.Productioncannotoccurwithoutmaterials, labor,equlPment,andotherresources.Extremeconditiontestsaskwhethermod- elsbehaveapproprlatelywhentheinputstakeonextremevaluessuchaszeroor infinity.

Extremeconditiontestscanbecarriedoutintwomainways:bydirectinspec-

tionofthemodelequationsandbysimulation.Youshouldexamineeachdecision rule(rateequation)inthemodelandaskwhethertheoutputoftheruleisfeasible andreasonableevenwheneachinputtotheequationtakesonitsmaximumand minimumvalues.Besuretoconsidertheresponseoftheequationwhenallinputs simultaneouslytakeontheirextremevalues.

Youshouldalsoimposeextremeconditionsaspoliciesinsimulationsofthe model･ByuslngSWitchesthatzerooutvariablesandtestInputsSuchasthestep

870 PartVI ModelTesting

andpulseyoucansimulateconditionssuchasthecompleteremovalofallworkers

fromthefirmorafactorofonebillionincreaseinthepriceOfthefirm'sproduct･ Intheformercase,productionmustimmediatelygotozero.Inthelattercase,the demandforthefirm'Sproductsmustimmediatelydroptozero.Suchtests,termed

"realitychecks"byPetersonandEberlein(1994),quicklyuncoverflaws,agreat advantageinalargemodeHnaddition,wholemodelextremeconditiontestsmay revealsubtleflawsthatdirectinspectionmaymiss.Whenanextremecondition

simulationgeneratesimplausiblebehavioryoushouldexaminetheequationsofthe affectedformulationstoidentifytheprecisesourceoftheflaw.

Example:ExtremeConditionsintheEnergySystem

ln1979iworkedfわrtheUSDepartmentofEnergy.Thedepartmentusedavariety ofmodels,includingsystemdynamicsmodels,toanalyzeenergydemand,supply, prlCeS,andsoon･Acriticalissuewasthefeedbackbetweentheenergysector andtherestoftheeconomy.Wouldenergypricehikesreducethegrossna- tionalproduct,boostunemployment,andaccelerateinflation?Whatwouldbethe economicconsequencesofanotheroilembargo?Lackinganin-housemodelof

energy-economyInteractions,thedepartmentsolicitedaproposal丘.omahighlyre- spectedmacroeconomicforecastingfirm,whichclaimeditsmodelcoulddothe job.IwasglVenthetaskofevaluatlngthesuitabilityofthemodel.Thefirsttest lconductedwasanextremeconditiontest.iaskedwhatwouldhappentotheGNP oftheUnitedStatesifallenergysources(oil,gas,coal,nuclear,hydro,etc.)in- stantlyandunexpectedlydisappeared.Suddenlydeprivedofallformsofenergy,

theGNPmustrapidlydropclosetozero(assoonasinventoriesaredepleted). Accesslngthemodelviaatime-sharinglink,Iimplementedthetest｡Theresult: TheGNPwentup.

Examinlngthemodelequationsshowedthat,consistentwithitsorlglnSaSa traditionaldemand-sideKeynesianmodel,GNPwasformulatedasdependingon aggregatedemand･AggregatedemandconsistsofconsumptlOn,investment,gov- emmentexpenditure,andnetexports(thefamousidentityGNp-C+Ⅰ十G+Ⅹ familiar血.omintroductorymacroeconomics)｡C,I,andGwereformulatedasde- pendingonfactorssuchasconsumers'incomes,businessprofitability,Interest rates,andsoon.OutputofgoodsandservicesdidnotrequlreInputsOfenergy,and

alOO%embargodidlittle･WhythendidtheGNPgoup?Oilimportsfelltozero, sonetexportsincreased.

Youmayobject,asthemodel'sdevelopersdid,thatthetestwasirrelevant sincesuchextremeconditionscouldneverariseinreality･Themodelreplicatedthe historicalbehavioroftheeconomyandtheenergysectorquiteWell,so,theyar- gued,itwasareliableguidetotheirlikelybehaviorinthefuture｡Thesearguments aremistaken.

Tbetestuncoveredlimitationsofthemodelthatrendereditunusableforour

purpose･Weneededtoknowhowaphysicalshortageofoil(causedbypossible embargoes)wouldaffecttheeconomy.Amodelinwhichproductionrequiresno

energycannotanswersuchquestions.Theenergysectorhadbeentackedonasa setofadhocadditionstotheorlglnalmodeLProductiondroveenergyconsump- tioninthemodelbutenergyavailabilityhadnoimpactonproduction･Lacking suchbasicphysicalrealities,theonlywaythemodelerscouldanswerthequestions

Chapter21 TruthandBeauty:ValidationandModelTesting 871

Weposedwasthroughstillmoreadhocadjustmentstomodelstructure,oradd-

factoringbasedontheirmentalmodels.

Thefactthatamodelreplicateshistoricaldatawellisirrelevantifitfailsim-

portantextremeconditiontests･ModelsareusuallyIntendedtodesignpoliciesto

solveproblems,improveperfわrmance,oranalyzecontlngenCiesfわrwhichexperi-

enceprovidesnoguide.Thegoalofpolicydesignistomovethesystemoutside

血elimitedrangeofhistoricalexperience.Extremeconditiontestsprovideacriti-

caltestoftheextenttowhichmodelscaptureunderlyingphysicalrealitiesandcon-

straintsthataffectbehavioroutsidetheconditionsobservedinthepast.

ExtremeConditionTests

Foreachofthefollowing,useextremeCOnditionteststoevaluatetheproposed

formulations.Ifyouidentifyanyproblems,proposeasolutionandshowthatyour

solutionpassestheextremeconditiontest.

1. Afirmoperatesamake-t0-Ordersystem.Ordersaccumulateinabacklog

untiltheyareshipped.AnanalystproposesthefollowlngStructuretOmodelthe

firm'sorders,shipments,andrevenues･

Backlog-INTEGRAL(Orders-Shipments,Backlogb) (21-6)

TheorderraterespondstoprlCe;theanalystassumesaconstantelasticlty

demandcurvewithelastlCltyedく0:

Orders-ReferenceOrders*(Price/ReferencePrice)ed

ThefirmrecognizesrevenueWhentheproductisshipped:

Revenue-Price*ShipmentRate

Shipmentsaredeterminedbycapacltyandcapacltyutilization:

ShipmentRate-Capaclty*CapacityUtilization

CapacityUtilization-i(DesiredProduction/Capacity)

DesiredProduction-BacklogrrargetDeliveryDelay

(21-7)

(21-8)

(21-9)

(2ト10)

(21-ll)

Assumethecapacityutilizationfunctioniswellformulated,withf(0)-0,

I(1)-1,andf(∞)-f-ax=竺aximumutilization･ 2･ InForrester'S(1968)OrlginalmarketgrowthmodelproductioncapacityPC

wasmodeledastheaccumulationofnetproductioncapacltyreceiptsPCR:

PC-INTEGRAL(PCR,PCh) (21-12)

NetcapacltyreCelptSWeredeteminedbyproductioncapacityOrdersPCOwitha

delayglVenbytheproductioncapacltyreCeivlngdelayPCRD.Forresterassumed

athird-ordermaterialdelay:

PCR-DELAYS(PCO,PCRD) (21-13)

ThestockofcapacityonorderaccumulatedcapacityOrderslessrecelptS:

PCOO-INTEGRAL(PCO-PCR,PCOOt｡) (21-14)

872 PartVIModelTesting

Thefirmexpandscapacitybyanetcapacltyexpansionfraction,CEF,peryear:

PCO -PC*CEF (21-15)

Thecapacltyexpansionfractiondependsontheperceiveddeliverydelayrelative

tothecompany'sgoal,asinchapter15.

3. Modelsofcompetitivedynamicsamongfirmsmustmodelthedemandfor

eachfirm'sproductsasitdependsonfactorssuchasprlCe,availability,marketl

lng,quality,andsoon.Considerthefollowingformulation:

Demand-ao+alPrice+a2DeliveryDelay+a3Advertising+a4(〕uality (21-16)

ThecoefficientsalCapturetheresponseofattractivenesstoeachproductat-

tribute.Thelinearformoftheequationfacilitatesestimationbyregression.

Estimationresultsshow,asexpected,thatalanda2arenegativewhilea3anda4

arepositive.

Consideralsotheloglinearvariantofequation(21-16):

Demand-ao*Priceal*DeliveryDelaya2*Advertisinga3*Qualitya4 (21-17)

where,agaln,al,a2くOanda3,a4>0.

4. Inamodelofacomplexproductdevelopmentproject,ananalystproposesthe

followingformulationforstockofworkremainlngandtherateatwhichworkis

completed:

TasksRemalnlng

-INTEGRAL(NewTasksAssigned-CompletionRate,Tasksh) (21-18)

CompletionRate -MIN(TasksRemaining/DT,Labor*Productivity*Workweek) (2ト19)

whereDTisthetimestepusedinthesimulation.Thebacklogoftasksremainlng

aggregatesactivitiesincludingdesign,prototypefabrication,andtestlng.The

modelernotesthattheMINfunctionin(21-19)preventsthestockoftasks

remainingfromdroppingbelowzeronomatterhowlargethelaborforce･

21｡乳6 Emをegraを盲omEworVes官s Systemdynamicsmodelsareusuallyfomulatedincontinuoustimeandsolvedby

numericalintegration.Youmustselectanumericalintegrationmethodandtime

stepthatyieldanapproximationoftheunderlyingcontinuousdynamicsaccurate

enoughforyourpurpose.Theresultsofyourmodelsshouldnotbesensitivetothe

choiceoftimesteporintegrationmethod;thewrongtimesteporintegration

methodcanintroducespuriousdynamicsintoyourmodel･Alwaystestforsuch"DT

errorHbycuttlngthetimestepinhalfandrunnlngthemodelagalnJftheresults

changeinwaysthatmatter,thetimestepwastoolarge.Continueuntiltheresults

arenolongersensitivetothechoiceoftimestep.Likewiserunthemodelwithal-

ternateintegrationmethods.Theintegrationerrortestshouldbethe丘rstsimulation

testyoucarryout,sincefailurehererendersallmodelresultsmeanlngless･Appen-

dixAdescribesthenumericalintegrationprocessandvariousintegrationmethods.

Chapter21 TruthandBeauty:ValidationandModelTesting 873

Example:DI'ScovenngandCorrectingIntegrationError ShantzisandBehrens(1973)developedasystemdynamicsmodeloftheTsembaga

tribeinPapuaNewGuinea･TheTsembaga,likemanyindigenouspeoplesinthe region,practicedslashandburnagrlCultureandalsokeptpigs,amajorSOurCeOf wealthandstatus.Every12to15yearstheyheldanelaboratefestivalduring

whichmostofthepigswereslaughtered,followedbytheliftingofatabooagalnSt warwithneighboringclans.Duringthesewarsabout10%ofthepopulationwas killed.Afterhighlyrltualizedfunerals,atrucewasconcludedandconflictwaspro- hibiteduntilthenextpigfestival,atwhichtimeunavengeddeathsfromthelastwar

providedtheimpetusforthenextcycleofconflict･Earlywesternobserversfわund theseritualsbizarreandtookthemasevidenceforthesavageryofindigenouspeo-

ples･Inapathbreakingstudy,anthropologistRoyRappaport(1968/1984)Showed howpigfestivalsandwarsweretrlggeredbypopulationgrowth,thuspreventing

thedegradationoflandfertility･Insteadofacruelandirrationalritual,thepig-war cyclewasactuallyafinelyhonedfeedbacksystemthatkeptthehumanandpig populationswithinthecarryingCapacityOftheenvironment,enablingtheTsem- bagatolivesustainablylntheirfragileforestecosystem.

ShantzisandBehrenscreatedasystemdynamicsmodeltotestRappaport's theory.Oneoftheearliestformalmodelsintegratlngbiological,agrlCultural,de-

mographic,andculturalvariables,itendogenouslyrepresentedthehumanandpig populations,foodproduction,andthequantltyandfertilityoftheland.Thepigfes-

tivalsalldwarsweretrlggeredendogenouslyasthepigandhumanpopulationsbe一 gantooutstripfoodproduction.Themodelreproducedtheobservedbehaviorof periodicfTestivalsandwars.ShantzisandBehrensshowedthatthepigfestival/war

cyclekeptTsembagasocietystable.Theirpolicyanalysisfurthershowedthatthe introductionofwestemcultureandtechnology,suchasabanonwarandimproved healthcare,CouldcausepopulationtooutstripthecarrylngCapaCltyOftheland. Declininglandfertilityandfoodproductionwouldthenleadtostarvation,forced mlgrationfromtheirlands,andthedestructionoftheirculture.

Kampmann(1991)analyzedtherobustnessoftheseresults.Theoriginal

modelwascompletelydocumentedandfullyreplicable･However,themodelfailed theintegrationerrortest.Theorlglnalmodelusedatimestepoflyear.Shortening thetimestepcausedthebehaviortochangedramatically.Withasmalltime

stepthemodelgeneratedacontinuoussmallskirmishratherthananintensewar followedbyalongtruce.Insteadofagreatpigfestivaleverydecade,thedaily lunchwasahamsandwich.

Thetimesteplnmodelsisnotafeatureofrealitybutanartifactofthenumer- icalmethodusedtosolvethemodel.Hencethedecisionrulesinmodelscannotde-

pendonthetimestep.ShantzisandBehrenswereinadvertentlyuslngthelongtlme stepasabehavioralparametertocontrolthedurationofthewarandthenumberof

casualties.ThesensitivltyOftheresultstothetimestepthrewalltheirresultsinto question.

Kampmannreformulatedthemodelsothatthedurationandlethalltyof thefestivalandwarwerespecifiedasexplicitparameters.Healsocorrecteda numberofotherformulationerrors.Theperiodicplg-Warfestivalsreemergedin

874 PartVI ModelTesting

thecorrectedmodel.Kampmann'sanalysisidentifiedamajorerror,butintheend

thereformulatedmodelstrengthenedtheconclusionsoftheorlglnalstudy･12

21.4JT 萱ehalF'k'5°芦宅や相加･T･甑 F'･T鮮モさ

Manytoolsareavailabletoassessamodel'sabilitytoreproducethebehaviorofa

system.MostcommonaredescrlptlVeStatisticstoassessthepolnt-by-polnt臥

Point-by-polntmetricscomputesomemeasureoftheerrorbetweenadataseries

XdandthemodeloutputXm ateverypointforwhichdataexistandthenreport

somesortofaverageovertherelevanttimehorizon.nlble21-5listssomeofthe

mostcommonmeasuresofpoint-by-polntfit.

ThemostwidelyreportedmeasureoffitisR2,thecoefficientofdetermination･

R2measuresthefractionofthevarianceinthedatauexplained"bythemodel･

Ifthemodelexactlyreplicatestheactualseries,R2-1;ifthemodeloutputis

constant,R2-0･R2isthesquareofthecorrelationcoefficient,r,whichmeasures

thedegreetowhichtwoseriescovary･13

Themeanabsoluteerror,MA巴;meanabsolutepercenterror,MAPE;meanab-

soluteerrorasapercentofthemean,MA巴/Mean;and(root)meansquareen･or,

(氏)MSEallprovidemeasuresoftheaverageerrorbetweenthesimulatedandac-

tualseries.MA巴weightsallerrorslinearly;RMSEweightslargeerrorsmuch

moreheavilythansmallones.Bothmeasuretheerrorinthesameunitsasthevari-

ableitself.MAPEshouldnotbeused,ofcourse,ifthedataseriesincludesany

pointsClosetozero.Insuchacase,theMAEdividedbythemeanofthedatapro- videsamorerobustdimensionlessmeasure.

Whichmeasuresarebest?MSE(andRMSE)penalizelargeerrorsfarmore

thansmallones;usuallythereisnostrongbasisforpreferringRMSEoverMAE.

TheMAPEandMAE/Meanprovidedimensionlessmetricsfortheerror,whichare

easiertointerpret･R2,thoughitiswidelyreportedandyouraudiencemayexpect

it,isactuallynotveryuseful.Twoserieswiththesameabsoluteerrorcangenerate

verydifferentvaluesforR2dependingontheircommontrend･Considerthesitua-

tionXm -Ⅹoexp(gt);Ⅹ d-Ⅹ m +e.Thedataandmodelgrowexponentiallyatthe

samerategandthemodelisperfectexceptforarandomerror,e.Thehigherthe

growthrate,thegreaterthecorrelationrbetweenthemodelanddataand,there-

fore,thehigherthevalueofR2,thoughtheerrorbetweenthemodelanddataisthe sameinallcases.

Itisimportanttoknowthesourcesoferroraswellasthetotalsizeoftheerror,

Largeerrorsmaybeduetoapoormodeloralargeamountofrandomnoiseinthe

data.Thetotalerrormaybelargeifamodeofbehaviorintherealsystemisdelib-

eratelyexcludedasirrelevanttothemodelpurpose.Whilethereisultimatelyno

12Kampmann'scritlqueOftheTsembagamodelprovidesanexemplaryapplicationofthetests describedinthischapterandlswellworthconsulting,whetheryourmainconcernisanthropology, biology,orbusiness(seealsochapter14).

13ThetraditionalformulaforR2usedinregressionanalysis,R2-1-∑e2/∑(xm一文d)2, wheretheerrore-Xm -Xd,aSStlmeSthatthemeansofthesimulatedandactualseriesareequal (bias-0).TheequivalentfbmulationR2-r2worksevenwhenthereisabias.

Chapter21 TruthandBeauty:ValidationandModelTesting

TABLE21-5

Commonsummarystatisticsforassesslngmodelfittodata

875

Metric Definition Formula

MA臣

MAPE

MA臣/Mean

(R)MSE

Theil's

Inequality Statistics

Coefficientofdetermination;the fractionofthevarianceinthe

data"expJajned"bythemodel (dimensionless)lr-correlation coefficientbetweenmodeland dataseries

MeanAbsoluteError(units)

MeanAbsolutePercentError

(dimensionless)

MeanAbsoluteErrorasafraction

ofthemean(dimensionless)

(Root)MeanSquareError (RMSE:units;MSE:units2)

DecomposesMSEintothree components:bias(UM),unequal variation(US),andunequal covariation(UC)(dimensionJess); UM+uS+uC-1

R2- r 2;r-三∑ (xd盲dXd)(Xm ~Xm)Sm

戻-三∑x;S-

･AE-三∑ixm -xd 】

NAPE-三∑転語 ;(mu.tip･ybylOOfor%'

MAE/Mean-MAE/Xd;(multiplybyloofor%)

･sE -三∑ (xm-xd)2;RM SE -∨両面

UM- ー 2 - 2

Xm - Xd

MSE

u s= 更正二転 MSE

2(1-r)smsd

Allsummatl0nSareCarriedoutoverthesetofdatapoints.

substituteforplottlngthesimulatedandactualdatatogether,Severalstatistical

methodshelpdecomposetheerrorintosystematicandunsystematiccomponents･

TheTheilinequalitystatistics(Theil1966)provideanelegantdecomposition

oftheerrorbydividingtheMSEinto血reecomponents:bias,unequalvariation,

andunequalcovariation.Biasariseswhenthemodeloutputanddatahavedifferent

means.Unequalvariationindicatesthatthevariancesofthetwoseriesdiffer･

Unequalcovariationmeansthemodelanddataareimperfectlycorrelated,thatis,

theydifferpointbypoint･DividingeachcomponentbytheMSEgivesthefraction

oftheMSEduetobias(UM),thefractionoftheMSEduetounequalvaria-

tion(US),andthefractionoftheMSEduetounequalcovariation(UC).since

UM 十 US+uC-1,theinequalitystatisticsprovideaneasilyinterpretedbreak-

downofthesourcesoferror.Table21-6illustratestheinterpretationoftheTheil statisticsfordifferentsituations.

Alargebias,indicatedbybothalargeMSEandalargeUM,revealsasystem-

aticerror,asseenincase(a).Errorsduetobiasarepotentiallyseriousandareusu-

allyduetoe汀OrSinparameterestimates.Errorsduetounequalvariancemayalso

besystematic.WhenunequalvariationdominatestheMSE,themodelanddata

876 PartVI ModelRsting

TABLE21-6 1nterpretationoftheTheilinequalitystatistics

Example UM uS UC characterization Interpretation

1 0 0 Xm-Xd+BIAS

Simulatedvariable

equalsactualdata

transratedbyabias

0 1 0 Xm-Xd+k(Xd-Xd)

Simulatedvariableis astretchedversionof theactualdataabout theircommonmean

o 1 0 Sameasabove

0 1 0 Xm-Xd;Xd-Xd+f(t)

SimuFatedvariable

equalsmeanofdata; actualhasnoiseor

cycles.Modeland dataareuncorrelated becausemodel

variance-0

0 0 1 Xd-Xd+Asin(wt)

Xm-Xd+Asin(wt- Moderfluctuateswith

thesamemean,

amplitude(A),and frequency(W),as databutwitha

phaseshift(p).

Systematicerror: biasinmodelshou一d becorrected

byparameter adjustment

Systematicerror: modelanddata havedifferenttrends

Systematicerror: mode一anddata havethesame

phasingbut differentamplitude f一uctuations

Systematicerror

ifmodelpurpose involvesstudyofthe cyclesinthedata.

Unsystematicif cyclesandnoise arenotrelevantto

thepurpose

Systematicif

p)phasingimportant topurposeandif

modeldrivenby historicaldata;

unsystematicif

modeldrivenby randomnoise

0 a 1-a Xm-f(I);Xd-∫(t)+e(I) Modeltracksactual

dataexceptforan errorterme(I)with ZerOmean.

Mode‖1aSSame

meanandtrendsas databutdinersfrom

datapoint-by-point, Unsystematicerror

unlesspurposeis tostudythecyc一es inthedata

"Data"shownbyso=d一ine;"slmulatl0∩"shownbydashedl】ne.

Chapter21 TruthandBeauty:ValidationandModelTesting 877

matchonaverageandarehighlycorrelatedbutthevariationinthetwoaround theircommonmeandiffers.Onevariableisastretchedoutversionoftheother.In

case(b),USislargebecausethetrendinthetwovariablesisdifferent.Suchacase

revealssystematicerroranddirectsattentiontotheassumptlOnSOfthemodel.Sys-

tematicerrorisalsotheverdictincase(C),inwhichthemodeldoesnotcapturethe

magnitudeofacyclicalmodeinthedata,thoughthephasinglScorrect.Sucha

casewoulddirectattentiontothefactorscontrollingtheamplitudeanddampingOf thecycle.

Ifbothserieshavethesamemean(UM-o)andeitherthemodelordataseries

isnearlyconstant,thenUCwillbesmallbecausethestandarddeviationsmorsd

willbesmall.Asshownincase(d),theerrorwouldreflectrandomnoiseora

cyclicmodeinoneoftheseriesnotpresentintheother･Theinterpretationdepends

onthepurposeofthemodeLIfthemodelisdesignedtoinvestlgatethecycleinthe

data,failuretogeneratethecyclewouldclearlybeasystematicerror･Ifthepur- poseofthemodelisanalysisOflong-runbehaviorthatabstractsfromshorHerm

movements,failuretocapturethecycleisunimportant.Thecyclebecomesunsys-

tematicnoiserelativetothemodelpurpose.

IfthemajorityOftheerrorisconcentratedinunequalcovariation,UC,the

modelcapturesthemeanandtrendsinthedatawell,differingfromthedataonly

pointbypoint(Caseseandf)･Thesecasesmightindicateafairlyconstantphase

shiftofacyclicalmodeotherwisereproducedwell･Morelikely,alargeUCindi-

catesthepresenceofnoiseorcyclicalmodesinthedataseriesnotcapturedbythe model･WhenUCislargethemaJOrltyOftheerrorisunsystematic;amodelshould

notbefaultedforfailingtomatchtherandomcomponentofthedata.

TheTheilstatisticshelpyoucharacterizethesourcesoferror,ideally,theerror

(indicatedbyMAPE,RMSE,etc.)shouldbesmallandunsystematic(concentrated

inUC)｡Largeerrorsandlargebiasorunequalvariationfractionsindicatesystem-

aticerrorandshouldleadtoquestionsabouttheassumptlOnSOfthemodel.Thecri-

teriafordecidingwhetheranerrorislargeorsystematicdependonthepurposeof

themodelJftheerrorsarise丘･ommodesofbehaviorexcluded丘･omthepurpose,

thentheerrorsdonotcompromisetheutilityofthemodelforthatpurpose.

E汀OrmeasuresSuchasMAPEandR2measurethepolnt-by-polntcorrespon-

denceofthemodelanddata.Thereareseveralcircumstancesinwhichyoushould

notexpectyourmodeltocorrespondtothedataonapoint-by-polntbasis.Many

systems,includingthesupplychainsandcommoditymarketsexaminedinchap-

ters17-20,Selectivelyamplifycertainfrequenciesintherandom shocksthat

constantlyperturbthem.Sincenomodelcancapturealltherandomvariationsin

theenvironment,modeldynamicscandivergefromthedataevenlfthemodelis

perfectlyspeclfied･14Further,inpath-dependentsystemssmalldifferences.inran- domeventscandramaticallyalterthetrajectoryOfthesystem,includingItsulti-

mateequilibrium(see,e･g･,FigurelO125).Thedatamightshowacertainproduct

14Inchaoticsystemsitisevenworse･BecausechaoticsystemshavethepropertyknOwnas sensitivedependenceoninitialconditions,themodeldivergesfromthetruesystemexponentially evenwhentherearenorandomshocks,glVenOnlyasmalle汀Orininitialconditions.

878

FIGURE21-1

Noisedestroys point-prediction ability

Twosimulations

oftheinventory- workforcemodelin section19.2with randomnoisein

laborproductivity, Thenoisese-

quenceinproduc- tivitychangesin week200.

PartVI ModelTesting

トl■

(∈ n F Lq!l!n b O o1

0! l e

)

uO !) O nPOJI

･Reality" "Modelll

180 190 200 210 220 230 240 250 260 270

Week

growlngtOdominateitsmarket.Runnlngthemodelwithdifferentrandompertur- bationsmightcausethatproducttowinsometimesandlosetothecompetition sometimes･Therealworldthatgeneratedthedatacanbethoughtofasjustonere- alizationoftheprocess;smalldifferencesinunobservableperturbationsmight haveledtoacompletelydifferentoutcome.

Ingeneral,thegreatertheextenttowhichthemodel'sdynamicsaredrivenby exogenouslnputS,thegreaterthepoint-by-polntcorrespondenceofthemodeland datashouldbe.TheexogenousInputs,includingtheirblipsanddips,forcethe modeltodancetoaparticularbeat.Inamodelthatisnotforcedbyanyhistorical dataseriesitiso洗ennecessarytoexcitethemodel'Slatentmodesofbehaviorwith randomnoise.Evenwhentherandomnoiseisdrawnfromthecorrectdistribution,

thepoint-by-pointValueswilldifferfromhistoricalexperience,andsowillmodel Output･

Figure21-1illustratesthisdynamicwithtwosimulationsoftheinventory- workforcemodeldevelopedinchapter19.Thesystemisdisturbedfromequilib- riumbyarandomvariationinlaborproductivltyWithastandarddeviationof5% andacorrelationtimeof4weeks(seeappendix良).Theserandomshockscause thesystemtooscillateirregularly.Onesimulationcanbeinterpretedasthereal

dataandtheother,astheoutputofthemodel.Themodelisaperfectreplicaofthe realsystem-identicalstructure,initialconditions,andparameters.ThetrajeCtOries ofthetwosimulationsareidenticalaslongasthe"modelHisdrivenbyexactlythe samerandomshocksasthe"realsystem.HBeginninglnWeek200,therandom shocksperturbingthemodelbegintodiffer.Therandomvariationsaredrawnfrom

thesamedistribution,Withthesamevarianceandcorrelationtime,butdifferpoint bypoint.Thebehaviorofthemodelquicklydivergesfromthedata.Theinertiaof thesystemcausesthetrajectoriestoremaincloseforonlyafewweeks;afterthat

thereisnopolnt-by-polntCOrreSpOndencebetweenthemodelandtherealsystem thoughthemodelisperfect.Obviously,point-by-polntmeasuresOferrorsuchas R2,MAPE,OrRMSEwouldbegrosslymisleadingasindicatorsoftherealismand utilityofthemodel.

Point-by-polnterrormeasuresarenotmeaningfulwhenamodelishighlysen- sitivetonoiseJnstead,agoodmodelshouldexhibitthesamemodesofbehavior

Chapter21 TruthandBeauty:ValidationandModelTesting 879

observedinthedata.Fluctuationsshouldhavethesamefrequenciesandam -

plitudes･Thephaserelationships(leadsandlags)amongthevariablesshouldbe

thesameasobservedinthedata.Thevariabilityoffeaturessuchasamplitude,

frequency,andphaselagsshouldalsocorrespondtothedata.Theabilityofa

modeltogeneratetheapproprlatepattemSOfbehaviorcanbeassessedqualita-

tively,byjudgment,orstatistically.Tわolssuchasspectralanalysismeasurethe

strengthoffluctuationsateachfrequency.Theautocorrelationfunctionquantifies

theinertiaorpersistenceinavariable;cross-correlationfunctionsshowhowone

variabledependsoncurrentandpastvaluesofanother.Barlas(1989,1990)

describeshowtheseandrelatedtoolscanbeusedtoquantifythecorrespondence

ofthemodelanddataintermsofrelativeamplitudes,frequencies,phaselags,and

otherrelationships.

Evenwhenyouusestatisticalmeasurestoassessthecorrespondenceofthe

modeltothedatayoushouldalwaysplotthesimulatedandactualdatatogether.

Examinethemodeltoseeifitcapturesasymmetriesandothersubtlefeaturesof thebehaviorobservedinthedata.

Bewareamodelerwhoassertsthatthemodel'sabilitytofitthedataindicates

thatthemodelisvalidorconfirmsthemodel.Anysuchassertionislogicallyfal-

lacious.Behaviorreproductiontestscannotproveamodeliscorrectorreliable.¶)

arguethatfittingthedataimpliesthatthemodelmustbecorrectorsuperiorto

othermodelscommitsthefallacyofaffirmlngtheconsequence:Theremaybe

manymodelsthatreplicatethedatawell;Observlngthatonedoescannevershow

thatthebehavioroftherealsystemwasgeneratedbyanyparticularstructure,

Asshowninsection9.3.2,differentmodelscanfitadatasetequallywellyet

glVeradicallydifferentforecastsorpolicyresultsoutsidethehistoricalrange.In-

deed,glVenanySetOfdata,therealwaysexistsaninfinitenumberofmodelsthat

fitthosedatatoanyarbitrarydegreeofaccuracyyoucaretospecify,allyielding

differentbehavioroutsidetherangeofexperience･u

Theproperuseofthebehaviorreproductiontestistouncoverflawsinthe

structureorparametersofthemodelandassesswhethertheymatterrelativetothe

purpose.Insteadofshowinghowwellyourmodelfits,youshouldpointOuttO

yourclientsalltheplacesitdoesn't.Thesediscrepanciesmarkthetrailsthatcan

guideyoutoerroneousparameterestimatesandinapproprlateassumptionsyou

shouldrevisebeforeuslngthemodelforpolicyanalysis.Everydiscrepancyshould

bediscussed.Thosediscrepanciesyoubelievearesignificantmustleadtomodel

revision,untilyouandyourclientagreethattheremainingdifferencesbetweenthe

behaviorofthemodelandthedatadonotmattertothepurposeandneednotbe

corrected.Therevisionsyouundertaketoresolveimportantdiscrepanciesbetwe e n modelbehavioranddatamustalsobeconsistentwithallthe otherformulati o n

prlnCiplesdiscussedabove.Itisnotacceptabletointroduce fudgefactorsore x -

ogenousvariableswhosesolefunctionistoimprovethehistoricalfitofthemod e l .

15Thisisbecauseanydatasetcanbeapproximatedarbitrarilywellbydifferentfamiliesoffunc-

tions,suchastheTaylorseriesorFourierseries,ifenoughtermsareincluded.Addingadditional higher-ordertermstothesefunctionschangestheirbehavioroutsidetherangeofhistoricaldata.

880 PartVIModelTesting

Doingsoservesonlytolulltheclientintoacceptlngthemodelwhilecoverlngup itsunderlyingflaws.

Example:Cap/'talPunlJshment

Whatistheeffectofcapitalpunishmentonthemurderrate?Thisemotionally chargedissuehasbeenthesubjectofmanyempiricalstudies.Often,regression techniquesareusedtoestimatehowthemurderratediffersbetweenstateswithand

withoutthedeathpenalty,Leaner(1983)conductedaboundaryadequacytestby exploringtherobustnessofsuchregressionstodifferentsetsofexplanatoryvari- ables･Thedependentvariableisthemurderrateper100,000people,andtheex-

planatoryvariablesincludemeasuresofdeterrencesuchastheprobabilityof executionglVenCOnVictionfb∫murder,themediantimeservedgivenconviction,

andtheprobabilityofconvictiongivenarrest.Ofcourse,sincethedifferentstates varylnmoreWaysthanwhethertheyexecuteconvictedmurderers,theregressions mustincludeadditionalexplanatoryvariablesinanattempttocontrolforthese othersourcesofvariation.Thechoiceofthese"nuisancevariables"isamatterof

judgment,anddifferentinvestigatorsSelectdifferentexplanatoryvariablesbased ontheirideologlCalperspective.Leanerselectedasetofcontrolvariablescom- monlyusedinsuchstudies,includingeconomicindicators(e･g"medianfamilyor personalincome,thefractionofhouseholdsbelowthepoverty1ine,theunemploy- mentrate,laborforceparticipation)andsocialvariables(e,蛋.,racialcomposition,

thefractionofthepopulationyoungerthan25,thefractionofthepopulationliving inlargecities,thefractionoftwoIParentfamilies).

SelectlngdifferentsetsofexplanatoryvariablesgivesWildlydifferentresults, allstatisticallysignificant:Asingleexecutioncoulddeterasmanyas29murders oractuallyleadtoanincreaseofmorethan12murders･TheextremesensitivltyOf theresultstochoiceofmodelvariablesleftLeamer(1983,p･42)"withthefeeling thatanyinferencefromthesedataaboutthedeterrenteffectofcapitalpunishment istoofragiletobebelieved."

21t4.8 5eぎ1謂ViorAnoEV癖yT芯苗モs

Datalimitationsoftenmeanitisnotpossibletoestablishthesignificanceor strengthofimportantrelationshipsorfわrmulationsbystatisticalmeans.Behavior anomalytestsexaminetheimportanceofthesestnlCtureSbyaskingwhetheranom-

alousbehaviorariseswhentherelationshipisdeletedormodified.Anomalousbe- haviorgeneratedbydeletionofarelationshipprovidesyouwithsomeevidencefわr itsimportance.

Loopknockoutanalysisisacommonmethodtosearchforbehavioranomalies.

InloopknOckouttestsyouzerooutatargetrelationship.Forexample,indecision rulesoftheformCorrectiveAction-(DesiredState-State)/AdjustmentTime, youknockouttheloopspasslngthroughthecorrectiveactionbysettlngthe adjustmenttimetoanessentiallyinfinitevalue.Youcanalsoeliminateloopsby settingthedelaytimesininformationdelaystoinfinityandbysettlngnOnlinear functionsy-i(x)tounityforallvaluesofx.Anomalousbehaviorresultingfrom aknockouttestsuggeststheimportanceoftheloopandmayhelpestablishaplau- siblerangefortheparametersandrelationships.

Chapter21 TruthandBeauty:ValidationandModelTesting 881

Loopknockoutanalysiscanberevealingwhenthemodelisoperatlngunder historicalconditionsbutisparticularlyeffectiveinconjunctionwithextremecon-

ditiontests･OftenaloopISnotactiveundernormaloperatlngCOnditionsbutbe- comesdominantinunusualcircumstances.Ifaloopknockouttestgenerates bizarreorphysicallyimpossiblebehaviorunderextremeconditionsyouhaveevi- dencethattherelationshiplSimportantandmustbeincluded,evenifitisnotnor一

mallyactiveandcannotbeestimatedstatisticallyfromthedata.

Anotherformofbehavioranomalytestreplacesadisequilibriumstructure withasimplifiedstructurethatassumesasubsystemisinequilibrium.Forexam- ple,perceptlOnandmaterialdelayscanbeeliminated,ineffectassumlngdecision

makerscaninstantlyrecognlZeChangesinthestatesofthesystemandinstantlyal- terthosestates･Senge(1978,1980)usedbehavioranomalytestsasacomplement toeconometricestimationtoshowthatcertaindisequilibriumformulationswere importantincapitalinvestment(sectionll.5).Forexample,assumingmanu-

facturingfirmsbasedcapitalinvestmentonlyontheirforecastoforders,implicitly assumlngInventoriesandbacklogswerealwaysinequilibrium,generatedimplau- siblebehaviorunderbothhistoricalandextremeconditions.

21･乱9 Fam毒tyMembellNresもs

Thefamilymembertestaskswhetherthemodelcangeneratethebehaviorofother instancesinthesameclassasthesystemthemodelwasbuilttomimic.Amodelof

corporategrowthshouldnotonlyexplainwhyoneparticularcompanygrewbut

alsowhysomeothercompanies,Withdifferentpoliciesandparameters,experience growthpunctuatedbyperiodiccrises,whysomestagnate,andwhysomefailalt0- gether(Figure3-6).AmodelofurbangrowthsuchasForrester'sUrbanDynamics model,HwithappropriateChoiceofparameters‥.shouldbehavelikecitiesas differentasNewYork,Dallas,...BerlinandCalcutta"(ForresterandSenge1980,

p･221)･Chapter20ShowedthatthegenericcoIIlmOditymodelgeneratedthecyclic behaviorobservedinthepulpandpaperindustry･Itshouldalsogeneratetheap- proprlatefrequencies,amplitudes,phaserelationships,andothercharacteristicsob- servedincommoditiessuchascopper,cocoa,andcoffeewhentheparameters

characterlZlngthesecommoditiesareused･Withsuitablestructuralchangestorep- resentlivestock,thesamemodelshouldgeneratethehogcyclewhencalibrated

withhoggestationtimes,littersizes,andsoforth,andthecattlecyclewhencali- bratedwithcattleparameters.

Themorediversetheinstancesofasystemamodelcanrepresentthemore

generalthetheoryltembodies･Thefamilymembertestisparticularlyhelpful whentheclassofsystemsthemodeladdressesincludesawiderangeofdifferent

pattemsofbehavior.YoushouldbesusplCIOuSOfanymodelthatcanexhibitonly asinglemodeofbehavior.Considerinnovationdi軌ISion.ModelssuchastheBass

dimlSionmodel(chapter9)canonlygenerateonemodeofbehavior:S-Shaped growth.Inreality,manynewproductsandnewinnovationsfail.Othersfluctuate

astheymoveinandoutoffashion.Ageneralinnovationdiffusionmodelshouldbe

capableofcapturlngallthesepatterns.Incontrasttothesimplegrowthmodels, Homer(1983a,1987)developedarichbehavioralmodelforthediffusionofnew

medicaltechnologies.Besidesthebasicwordofmouthandmarketingfeedbacks

882 PartVI ModelTesting

intheBassmodel,itincludedendogenoustechnologicalprogress,experiencedi- lutionandlearnlngCurvesamongClinicians,changesintheindicationsgovermng

theuseofthetechnology,changesinpatientoutcomes,andfollow-upstudiesas-

Sesslngtheeffectivenessofthenewtechnology.Themodelsuccessfullyreplicated

verydifferentemergencepatternsforseveralmedicalinnovationsranglngfrom highlysuccessfuldevicessuchasthecardiacpacemaker,tofailures,toanantibi- oticwhosesalesfluctuatedassideeffectswerediscoveredandnewapplications

werefound.Themodelhassincebeenusedtoexaminenewmedicaltechnologies rangingfromdrugstoartificialskin.

21.乳巧O Surpr日SeBehav岳⑳『Tes竜s Discrepanciesbetweenmodelbehaviorandexpectationindicatethatthereare flawsintheformalmodel,thementalmodel,orboth.Often,ofcourse,discrepan- ciesbetweenmodeloutputandyourunderstandingofthesystem'sdynamicsindi- catedefectsintheformalmodel.Occasionally,however,itisyourmentalmodel andyourunderstandingofthedatathatrequirereVision･Thesurprisebehaviortest ispassedwhenamodelgeneratesacertainbehavior,previouslyunrecognized,and itdoesindeedoccurintherealsystem.Einstein'stheoryofgeneralrelativltypro- videsafamousexample.Einsteinsuggestedthatgravltybendsthefabricofspace- time,causlnglighttofollowwhatappeartobecurvedpaths･In1919theBritish astronomerSirArthurEddingtontestedthetheorybyphotographingstarswhose lightpassednearthesunduringatotaleclipse.Generalrelativltypredictedthatthe ligbt丘.omthesestarswouldcurvebyacertainamountasitpassedclosebythe sun.Eddingtonshowedthattheapparentpositionsofthesestars,brieflyvisible duringtheeclipse,wereindeedshiftedbyanamountconsistentwiththepredic-

tionsofEinstein'stheory･Findingtheunexpectedbehaviorgavegeneralrelativlty apowerfulboost.

Totakeanexamplefrombusiness,Forresteroncedevelopedamodelfora largeautomotivecomponentsmanufacturer･Thecompanyhadbeenloslngmarket shareforsomeyearsdespitethetechnicalsuperiorltyOftheirproducts｡Manyln thecompanyblamedincreaslngCOmpetition･Mostassumedmarketsharewas erodingfasterduringexpansionsthanrecessions,reasoningthatcustomerswould turntothecompetitiononlywhenthefirm'sproductswereinshortsupply.How- ever,inthesimulationsmarketsharefellfasterduringrecessionsthanbooms.

Initially,Forrestersuspectedtherewasaprobleminthewayhehadcaptured thefirm'sinventorymanagementpolicies.Furthertesting,however,revealedno errors.Thecounterintuitiveresultarosefrom thefirm'Sextremeaversionto

holdingInventories.Wheneverordersturneddown,theyslashedpartordersand

productionsoaggressivelythattheproductwasactuallylessavailableduringmar- ketdownturnsthanduringexpansions.Aclosereviewofthedatashowedthat marketsharewasinfactfallingfastestduringrecessions.ThissurprlSlngresult eventuallypromptedachangeinthefirm'sproductionpolicies(Forrester,personal communication).

Notethatthesurprisebehaviortestdoesnotrequirethemodeltopredictfuture eventssuchaswhowillwintheKentuckyDerbynextyear.Thesunhadbeen warplngSpace-timeallalong,butuntilEinsteinsuggestedthesurprlSlngresultthat

Chapter21 TruthandBeauty:ValidationandModelTesting 883

gravltyCOuldbendlight,noonethoughttolook.Soitiswithmodelsoflesscos-

micsignificance:UntilForrester'smodelsuggestedthecounterintuitiveresultthat

productcouldactuallybelessavailableduringrecessionsthanbooms,theideathat

recessionsledtoproductglutswentunchallenged･Weneverhaveallthedata,nor

thetimetosearchforalltheimportantpatterns｡AmainbenefitofmodelinglSSug-

gestingWhattolookfor.

Forthesurprisebehaviortesttobeeffectiveyoumustanalyzemodelbehavior closely.Lookatthebehaviorofallvariables,notonlythemajorindicators,Track

downthesourcesofallunexpectedoranomalousbehavior(Mass1991).Likeany

goodscientistyoushouldkeepalaboratorynotebookthatdocumentsyourwork.

Youmustalsoovercometheproblemsofhindsightbiasandreconstructivemem-

ory･A洗eryoupresentyouranalys上sitiscommonfortheclientoraudienceto

claimthattheresultsareobvious,saying"Youdon'tneedamodeltofigurethat

out"or"Iknewitallalong."BecausemodelinglSiterative,leamlnglSOftengrad-

ual,andpeoplefindithardtorememberhowtheyperceivedthesituationbefore

theprq】ectbegan.Tbovercomehindsightbiasyoushouldcarefullydocumentthe

mentalmodelsoftheclientteampriortothemodelingeffort(animportantpartof

theprocessofestablishingthepurposeoftheeffortinanycase).

21.4.7i Sensitiv軸糸11alysis

Sinceallmodelsarewrongyoumusttesttherobustnessofyourconclusionstoun-

certaintylnyourassumptions.Sensitivltyanalysisaskswhetheryourconclusions

changeinwaysimportanttoyourpurposewhenassumptlOnSareVariedoverthe

plausiblerangeofuncertainty.

Therearethreetypesofsensitivlty:numeriea且,behaviormode,andpolicy

sensitュvlty.

NumericalsensitivityexistswhenachangeinassumptlOnSChangesthenu-

mericalvaluesoftheresults.Forexample,Changlngthestrengthofthewordof

mouthfeedbackinaninnovationdiffusionmodelwillchangethegrowthratefor

thenewproduct.Allmodelsexhibitnumericalsensitivlty.

BehaviormodesensitivityexistswhenachangeinassumptlOnSChangesthe pattemsofbehaviorgeneratedbythemodel.Forexample,ifplausiblealternative

assumptionsChangedthebehaviorofamodelfromsmoothadjustmenttooscilla-

tionor丘.oms-Shapedgrowthtoovershootandcollapse,themodelwouldexhibit behaviormodesensitivlty.

PolicysensitivityexistswhenachangeinassumptlOnSreVerSeStheimpactsor

desirabilityofaproposedpolicy.IfcuttlngprlCeSboostedmarketshareandprof- itabilityunderonesetofassumptionsbutledtoruinousprlCeWarsandbankruptcy

underanother,themodelwouldexhibitpolicysensitivlty.

ThetypesofsensitivityOfconcerninanyprojectdependonthepurposeofthe

model.NumericalsensitivltymattersagreatdealinthemodelsNASAusestoplan

thetrajectoryOfthespaceshuttle.Thepurposeofthesemodelsdemandstremen-

dousprecision,andthereislittleuncertaintylnmodelstructureorthelawsof

physicsthatgovemthedynamics.Inmodelsofhumansystems,however,numeri-

calsensitivltymaymatterlittle,ifatall.Thepurposeofmostbusinessmodelsis

nottopredictwhenthenextsalesslumpwillcomebuttoredesignthesupplychain

884 PartVI ModelTesting

sosalesaremorestable;nottopredictwhatprofitswillbenextquarterbuttode- SlgnPOliciestohelpthefirmbecomeprofitable.Formostpurposeswhatcountsis behaviormodesensitivltyandespeciallypolicysensitivlty.

SensitivltyanalysュsrequlreSmuchmorethanvarylngparameters.Youmust

alsoconsiderthesensitivltyOfyourresultstoassumptionsabouttheboundaryof themodel,tochangesinthelevelofaggregation,andtochangesinthewaypeo-

pleareassumedtomakedecisions｡TheuncertaintylnparameterValuesisimpor- tantandmustbetested.ButmodelsaretyplCallymuchmoresensitiveto

assumptionsabouttheboundaryandformulationsthantouncertaintylnnumerical values.

InassesslngSensitivitytOParametricassumptlOnSyouShouldfirstidentifythe plausiblerangeofuncertaintyinthevaluesofeachparameterornonlinearrela- tionship.YoushouldthentestthesensitivltytOthoseparametersoveramuch

widerrange･Asdiscussedinsection8.2.5,peopletendtobeoverconfidentintheir judgments.Judgmentalparameterestimatesarelikelytobemoreuncertainthan

people'sintuitiveconfidenceboundssuggest.Overconfidencealsoariseswhenpa- rametersareestimatedstatistically.Formalestimationproceduressuchasregres-

sionyieldconfidenceboundsaroundthebestestimate･Theestimatedvalueof,say, theprlCeelasticltyOfdemandmightbe10.5,withthe95%confidencebounds

ranglngfrom10･4t0-0.6,indicatingthatthereisonlya5%Chancethatthetrue valueliesoutsidethisrange.Theseconfidenceboundslikelyunderestimatethe

trueuncertaintylntheparameterbecausetheyaccountonlyforonesourceofun- certainty-samplingerror.Theconfidenceboundsestimatedinregressiondonot includetheeffectsofmeasurementerror,faultyspecificationofthemodel,Orviol

lationsofthemaintainedhypothesesoftheregressionmethod.Thesesourcesofer-

rorarelikelytobemuchlargerthantheestimatedstandarderrorsreportedforthe

regressioncoefficients,butbecausetheyaredifficultorimpossibletoquantifythey areoftenlgnOred･Agoodruleofthumbistotestoverarangeatleasttwiceaswide asstatisticalandjudgmentalconsiderationssuggest,thoughconsiderationofthe

sourcesofuncertaintylnparticularcasesmaysuggestamuchwiderrange. Mostsystemdynamicsandsimulationsoftwarepackagesincludeautomated

sensitivltyanalysIStOOIs･First,youspecifywhichparameterstovary,thenprovide arangeofvaluesforeach.ThesoftwarethenrunsthemodelasmanytlmeSaSyou like,usingthespecifiedvaluesforeachparameter,eitheroneatatime(univariate testing)orallatonce(multiv∬iatetesting).

Comprehensivesensitivltyanalysisisgenerallyimpossibleevenwhenre- strictedtoparametricsensitivity.Sincemostmodelsareslgnificantlynonlinearthe

impactofcombinationsofassumptlOnSmaynotbethesumoftheimpactsofthe assumptionsinisolation.ComprehensivesensitivityanalysiswouldrequlreteStlng allcombinationsofassumptlOnSOVertheirplausiblerangeofuncertainty.The numberofcombinationsisoverwhelmingeveninmodelsofmodestsize.Given

thelimitedtimeandresourcesinanyprq】ect,Sensitivltyanalysismustfocuson

thoserelationshipsandparametersyoususpectarebothhighlyuncertainandlikely tobeinnuential.Aparameteraroundwhichnouncertaintyexistsneednotbe

tested･Likewise,ifaparameterhasbutlittleeffectonthedynamicsitneednotbe

Chapter21TruthandBeauty:ValidationandModelTesting 885

FIGURE21･2 Bestandworst

casesensitivity analysJS Simulationsofthe

new-product diffusionmodelin

Figure9-22･ Bestcase:

Advertising Effectiveness-

0.75★BaseCase; ContactRate-

0.75★BaseCase; Consumptionper Adopter-2★ BaseCase.

WorstCase.･

Advertising Effectiveness-2

★BaseCase; ContactRate-

1.5★BaseCase; Consumptionper Adopter-0.5★ BaseCase.

(jt20 ^ JS t ! u n u O !H

∈ )

¢ tt2 ∝

S 心一e S

汀 Worst Base 〆

Best

ら,-守/十千㌦ -〟--〇〇m"NW"MnWX洲洲剛 ∝》○》》〇m○○WVm》○ⅣY∝∝Y》洲ゆり∝+/+++ 0 1 2 3 4 5 6

Year

COnSequenCe･ Anumberoftoolshelpyouexploresensitivityefficiently･Onecommon

methodistodefinebestandworstcasescenarios.Inthebest(worst)Casescenario

yousetthevaluesofallparametersandrelationshipstothevaluesmost(least)fa- vorabletotheoutcomesyoudesireorthepoliciesyouwanttotest･Considerthe new-productdi軌lSionmodeldescribedinFigure9-22｡Themodelrelatessalesto advertlSlng,Wordofmouth,andconsumptlOnperCapita･Supposeyourclientsare uslngthemodeltoplancapacltyacqulSition.Theyworryaboutboomandbust, wheresalesofanewproductinitiallynseveryrapidlyonlytocollapseasthemar- ketsaturates,leavlngthemwithexcesscapacity･Theworstcasescenariotoad- dresstheirconcemmightassumerelativelystrongwordofmouthandadvertlSlng effectsandlowreplacementpurchasespercaplta･Thebestcasescenariomight assumeweakwordofmouthandadvertislngeffects,andhighconsumptlOn.Fig-

ure21-2Comparesthesescenariostothebasecase･Inthebasecase,theeffective- nessofadvertlSlngis0.01/year,thecontactrateis100/year,andconsumptionper adopteris0.2units/year/adopter.Thebest(worst)casesetsadvertisingeffective- nessto0.0075(0.02),thecontactrateto75(150),andpercapitaconsumptionto 0.1(0.4).Inthebasecase,salesfalltoaboutone-thirdofpeaklevelswhenthe marketsaturates.Thepatternofbehaviorinthebestandworstcasesisthesame, buttheimplicationsforcapacltyaCqulSltionareverydifferent･Inthebestcase, Slowerdemandgrowthandhigherreplacementconsumpt10nmeanthedropfrom thepeakisonlyabout40%･HigherconsumptlOnalsomeansthepeaksalesrate isaboutthesameasthebasecase.Intheworstcase,demandpeaksafterJust

1.5years,thenplummetsby90%overthenextyear･Thebestandworstcasespro- videboundsforthebehaviorthefirmislikelytoface.

Theextremesituationsrepresentedbybestandworstcasesarenotthemost likelyoutcomes.MonteCarlosimulationsallowyoutogeneratedynamicconfi- denceintervalsforthetrajectoriesofthevariablesinyourmodelsJnMonteCarlo analysis,youspecifyaprobabilitydistributionthatcharacterizesthelikelyvalues ofeachparameter.Forexample,youmightassumethevaluesofeachparameter

886

FIGURE21-3

Dynamic confidencebounds

frommultjvariate

sensit'NityanaJysrs

Simulationofthe

newproduct diffusionmodelin

Figure9122, showlngthe confidencebounds

forsa一esfroma

samp一eof500 simulations,

Adver【ising Effectiveness,

ContactRate,and

Consumptionper

Aclopterdistributed

normallywith standarddevia-

tionsof25%.

PartVIModelTesting

) 0

7 LL)

()tZaAJSl!unu O≡!uJ)

alt2 t J S a l

0 1 2 3 4 5 6

Year

aredistributednormallyaroundyourbestestimatesandspecifythestandarddevi-

ationforeach.Thesoftwarerandomlydrawsavalueforeachparameterfromthe

distributionsyouchoose,thensimulatesthemodel.Thetrajectoriesgeneratedina

largesampleofsimulationsdefinedynamicconfidenceboundsforeachvariable.

Figure2113showstheresultsofaMonteCarlosimulationoftheproductdif-

fusionmodel.Thefigureshowsthe50%,75%,and95%confidenceboundsfor

salesinasampleof500simulations.Advertislngeffectiveness,thecontactrate,

andpercapltaCOnSumptlOnareallassumedtobedistributednormallyandinde-

pendentlywithstandarddeviationsof25%oftheirbasecasevalues･16Giventhese

assumptlOnS,thereisa50%chancethatsaleswillbebetweenabout35and75mil-

lionunits/yearinyear2anda95%chancethatsaleswillbebetween10and90

millionunits/year.Notehowtheconfidenceintervalswidenduringthegrowth

phase,thennarrowagainaSthemarketstabilizes.TheuncertaintylnSalesismuch

greaterduringthegrowthphasebecausethepositivewordofmouthfeedback

dominates.Smallchangesintheparameterscontrollingthewordofmouthloop

compoundtoyieldlargedifferencesinpeaksales.Afterthemarketsaturates,Word

ofmouthandadvertisingnolongermatter,andtheonlyremaininguncertainty(in

thissimpleanalysis)isinreplacementconsumptionpercapita･Theinteractionsof

thefeedbackloopsandaccumulationsindynamicmodelsmeanthatthedynamic

confidenceboundsgeneratedbymultivariatesensitivityanalysisCanbeverydif-

ferentfromadistributionofagivenVariancearoundthebasecasetrajeCtOry･17

16TheseemlnglynaturalassumptlOnthateachparameterisindependentlydistributedisactually notrealistic.Typically,amodeliscalibratedtodata.Varyingtheparametersindependentlyresults inmanycombinationsthatsignificantlydegradehistoricalfit,indicatlngthatthesecombinations aremuchlesslikelythantheindependenceassumptlOnWOuldsuggest.Supposethebasecase trajectoryforsalesfitthehistoricaldatawell.Withindependentsampling,allthreeparametersin thesensitivityrunSwillmanytlmeStakeonhighvalues,leadingthemodeltogrosslyoverestimate historicalsales.Inreality,ifwordofmouthwerestrongerthanassumedinthebasecasetheef- fectivenessofadvertislngandconsumptlOnPerCaPltawouldhavetobesmallerthantheirbase

casevaluesforthemodeltocワrrespondreasonablywelltothedata.Ford(1990)describeshowto accountforsuchcorrelationslnmultivariatesensitivityanalysis.

17Ininterpretingdynamicconfidenceboundsrememberthattheyrepresenttheenvelopeof valuesinasampleofsimtllationsandnotaparticulartrajectory.Forexample,salesdonotfollow thepathoftheupper95%confide一一ceintervalinanyofthesimulations･

Chapter21 TruthandBeauty:ValidationandModelT∋sting 887

Sensitivltyresultssuchasthesecanhelpthefirmdecidehowmuchdedicated

capacltytObuildandhowmuchcapacltytOleaseoroutsourcesoitcanmeetpeak

demandwhileavoidingexcesscapacltyWhenthemarketsaturates･18

Anothersensitivityanalysistool,dubbedthe"AutomatedNonlinearTest"or

ANTbyMiller(1998),askswhe血erparametervaluescanbefoundthatgenerate

anomalousresults･ANTanalysislssimilartopolicyoptlmization･Inpolicyoptト

mizationthemodelerspecifiesanobjectivefunctionsuchasmaximizlngthepres-

entvalueoffirm profits.ThemodelerthenselectsasetofpolicyInstruments,Such

astheparametersinthedecisionrulesforprlClng,marketingexpenditure,andca-

pacltyplannlng.Thesoftwarethen丘ndsthesetofparametersthatmaximizesthe

objectivefunction.Manysystemdynamicsandsimulationpackageshavebuiltin

policyoptlmizationcapability.InANTanalysis,themodelerspecifiesanobjective

functiondesignedtobreakthemodelbyfindingunrealisticbehavior.

Miller(1998)demonstrated血eANTusing也eWORLDSmodel(Meadowset

al.1974).Thebasecaseofthemodelgeneratedanovershootanddeclineofworld

populationsometimebeforetheyear2100(Seesection12.1.5).Bysettingtheob-

jectivefunctiontomaximizetheworldpopulationintheyear2100,theANTauto-

maticallyidentifiedcombinationsofparametersthatkeptpopulation血.om

declining(withinthetimehorizon).Ifanyoftheseparametercombinationswere

plausible,theANTwouldcalltheresultsofthestudyintoquestion.TheANTisa

veryflexibletool.Addingatermtotheobjectivefunctionthatreducesthepayoff

asthesquareofthenumberofperturbedparametersincreasescausestheANTto

findthemostinfluentialparameters(withrespecttothespecifiedobjectivefunc-

tion),automatingthesearchforhighleveragepoints.ANTscanalsobeusedtodo

traditionalpolicyoptlmization･AnygeneraLpurposeoptimizationmethodsuitable

forruggedlandscapeswithmultipleoptlmaCanbeusedinANTs･Millercompared

hill-climbingandgeneticalgorithmsasoptlmizationmethods,findingbothworked

wellandsignificantlyoutperformedtraditionalmultivariateMonteCarloanalysts.

Miller'sanalysisoftheWORLDSmodelshowedthattherangeofpopulations

generatedintheyear2100iswide･TheANTsalsofoundseveralofthehigh 1ever-

ageparameters.Thefundamentalmodeofbehavior,however,remainedovershoot

andcollapse,Showingthatthemodelexhibitsslgnificantnumericalsensitivitybut

lowbehaviormodesensitivity.Millerdidnottestforpolicysensitivity,thoughthe

ANTtechniquecouldbeusedforthispurpose.

21.4-12 SysiemlmprovementTests

TheultimategoalofmodelinglStOSolveaproblem.SystemilnprOVementtestsask

whetherthemodelingprocesshelpedchangethesystemforthebetter･Topassthe

test,themodelingprocessmustidentifypoliciesthatleadtoimprovement,those

policiesmustbeimplemented,andtheperformanceofthesystemmustactually

improve･Inpractice,assesslngtheimpactofamodelisextremelydifficult.Itis

hardtoassesstheextenttowhichthemodelingprocesschangedpeople'smental

181nverylargemodelsthenumberofsimulationsrequiredtoexploreparameterspaceuslnga simpleMonteCarloapproachcanbeprohibitive･VariousefficientsamplingschemessuchasLatin hypercubedesignscanreducethenumberofsimulationsrequired.Ford(1990)describesthese toolsforsensitivityanalysisOflargemodels,withexamplesfromtheelectricutilityindustry.

888 PartVI ModelTesting

modelsandbeliefs.Itisrarethatclientsadopttherecommendationsofanymodel

promptlyorwithoutmodification.Whennewpoliciesareimplemented,ittakesa longtlmefortheireffectstomanifest.Manyothervariablesandconditionschange

atthesametimenewpoliciesareimplemented,confoundingattemptstoattribute anyresultstothepolicies.PerformanceimprovementfollowlngaStudydoesnot

meanthemodeトbasedpolicieswereresponsible;thesystemmayhaveimproved forreasonsunrelatedtothemodelingprocess.Likewise,deterioratingPerformance afterpolicylmPlementationdoesnotmeanthemodelfailedsincetheoutcome couldhavebeenevenworsewithoutthenewpolicies.

Thekeystosuccessfulassessmentofamodelinginterventionare(1)prospec- tiveevaluation,(2)useofmultipledatasources,and(3),totheextentpossible,ad-

herencetoproperexperimentalprotocols.Rigorousfollow-upresearchisessential tobuildastrongfoundationfortherefinementandwiseuseofthetoolsofsystem dynamicsandsystemsthinking-agoalofacademicsandpractitionersalike.

First,modelingprojectsShouldbedesignedwithevaluationinmindfromthe beginnlng.Prospectiveevaluationsaremoreeffectivethanretrospectivestudies. Afterthefactyoumaydiscoverthatthedatayouneedwerenotcollected,memo-

riesaredistortedbyhindsight,andkeyactorshaveleftthescene.Discusswith yourclientshowyouwillknowiftheprojectissuccessfulaspartoftheinitial

problemdefinitionphase.Resourcesforassessmentshouldbeallocatedwhenbud- gets,staff,andtimelinesfortheprojectareSet.

Second,modelinglnterVentionscanchangepeople'sbeliefsandattitudes,their

behavior,formalorganizationalpolicies,and,ofcourse,theactualperformanceof thesystem.Youshouldmeasurechangeinallthesedimensionstoassesstheextent towhichanychangesinperformancecanbeattributedtotheinterventionOften youwillhavetocreateinstrumentssuchasinterviewprotocolsandsurveystodoc-

umentpeople'smentalmodels,behavior,andchangesinpolicies(seeDoyle1997). Third,totheextentpossible,designyourinterventionasanexperiment.While

mostorganizationalinterventionscannotbecarriedoutuslngthedouble-blindran- domizedtrialsrequiredintheassessmentofnewmedicaltreatments,youshould usethesetechniqueswhereverpossible.Createcontrolandtreatmentgroups.Look

foropportunitiestoconductnaturalexperiments,forexample,comparingtheper- formanceoftheinterventiontothatofbusinessunitsorcompaniesthatdidnotun- dertakethemodelingprocess.Considerpartnershipswithacademicsandothers

whocanserveasneutralobserverstodocumenttheimpactofyourwork. Inpractice,follow-upstudiesforanytypeofmanagementinnovationareall

toorare.Itisunderstandablethatproperdesignandresourcesforevaluationand assessmentsufferwhenanewprojectbegins.Identifyingpotentialpartnerorgani- zations,negotiatlngentry,buildingtrust,andworkingwiththeclientteamtoun- derstandthebusinessisdifficultanddemanding.Often,clientsdonotappreciate

thatfollow-upresearchisnotonlyforacademicpurposesbutalsobenefitsthem directly.Theyarereluctanttoprovidetheresourcestosupportitortopermitbasic

protocolssuchastreatmentandcontrolgroupsandrandomizedasslgnment. Nevertheless,asamodeleritisinyourbestinterestandthebestinterestsofthe

clientstoovercometheseproblemsanddesignassessmentintoyourprojectsfrom thestart.WithoutrlgOrOuSfollow-upresearchtheefficacyofallmanagementin-

terventionsremainstheprovinceofanecdote.Anecdotesareunreliablebecause

Chapter21 TruthandBeauty:ValidationandModelTesting 889

theyarenotsubjecttoindependentconfirmation,becausepeopletendtohighlight

theirsuccessesandhidetheirfailures,becausepeopleoftenhaveafinancialorrep- utationalstakeinthesuccessoftheirwork,andbecauseevenapparentlysuccess- fulinterventionsmayhavesucceededduetoplaceboeffectsorotherfactors unrelatedtotheintervention.Withoutrigorousfollow-upresearchitisdifficultfor

modelersandclientstolearnwhichtoolsandprocessesworkorhowtoimprove them.Atbest,theresultisinefficiency;atworstithurtstheorganizationandthe

peopleinit.

Example:Avo/'dI'ngProofbyAnecdote

CavaleriandSterman(1997)evaluatedtheimpactofasystemdynamicsintervenl tiondesignedtoimprovequalityandperformanceintheclaimsprocesslngunitof aUSinsurancefin.Theintervention,beguninthelate1980S,usedtoolsinclud-

inggroupmodeling,managementflightsimulators,andlearnlnglaboratories.The interventionwaswidelycitedasasuccessfulapplicationdemonstratlngtheeffi-

cacyofthesesystemsthinkingtools(seeSenge1990)･Throughaquestionnaire, interviews,andextensivereviewofcompanyrecordsweestablishedthattheinter- ventiondidsucceedinchanglngthementalmodelsandbehaviorofkeymanagers.

Wefoundcompellingevidencethatthemanagersredesignedpoliciesforhiring andworkloadmanagementinaccordancewiththerecommendationsarisingfrom

themodelingprocess.However,becausetheorlginalstudywasnotdesignedwith

evaluationinmind,itwasimpossibletofindclearevidencethattheintervention improvedbusinessperformance.Thereweretoomanyconfoundingchangesinthe environment.Dataneededtotesttheseplausiblerivalhypotheseswerenotcoレ

Iectedduringtheorlglnalproject,Weakeningclaimsforprojectsuccess.Failureto documenttheimpactoftheprq】ectmayalsohavehurtthecompany,whichisno

longeruslnganyOfthesetools. Itisencouraglngthatanincreaslngnumberofsystemdynamicsinterventions

havebeendesignedtofacilitateevaluationfromthestart(see,e.g.,Vennix1996 andthepapersinVennix,Richardson,andAndersen1997).Despiteitsdifficulties

rlgOrOuSfollow-upstudyisvitalifthepotentialtoleanabouttheefficacyofsys- temsthinkinglnOrganizationsistobefullyrealized.

Mode一Tesモing

Applythetestsdescribedabovetothefollowlngmodels.Thegoalofyourtesting

istoidentifyproblemsinthemodelsthatrenderthemunsuitablefortheirpurposes. Ifthepurposeofthemodelisnotmadeexplicitbythedocumentation,thensuggest plausiblepurposesforwhichthemodelmightbeusedandevaluateitrelativeto eachofthese.Notalltestscanberunonallmodels.Forexample,quantitativebe- haviorreproductiontestscannotbecarriedoutonanillustrativemodelthatisnot

calibratedtoaparticularcase.

1.Theepidemicandinnovationdl軌lSionmodelsdescribedinchapter9.

2.Themodelofpathdependenceandmarketdominancedescribedin chapter10.

890 PartVIModelTesting

3.Themarketgrowthmodeldescribedinchapter15.

4.Thesupplychainmodelsdescribedinchapters17-19.

5.Thecommoditymodeldescribedinchapter20.

6.Modelsintheliterature(manyarecitedinthereferences).

21.5 SuMMARY

Thewordvalidationshouldbestruckfromthevocabularyofmodelers.Allmod- elsarewrong,Sonomodelsarevalidorverifiableinthesenseofestablishingtheir truth.Thequestionfacingclientsandmodelersisneverwhetheramodelistruebut whetheritisuseful.Thechoiceisneverwhethertouseamodel.Theonlychoice iswhichmodeltouse.Selectingthemostapproprlatemodelisalwaysavalue judgmenttobemadebyreferencetothepurpose.Withoutaclearunderstandingof thepurposeforwhichthemodelistobeused,itisimpossibletodetermine whetheryoushoulduseitasabasisforaction.

Modelsrarelyfailbecausethemodelersusedthewrongregressiontechnique orbecausethemodeldidn'tfitthehistoricaldatawellenough.Modelsfailbecause morebasicquestionsaboutthesuitabilityofthemodeltothepurposearen'tasked, becausethemodelviolatesbasicphysicallawssuchasconservationofmatter,be- causeanarrowboundarycutcriticalfeedbacks,becausethemodelerskepttheasI sumptlOnShiddenfrom theclients,Orbecausethemodelersfailedtoinclude importantstakeholdersinthemodelingprocess.

Tbavoidsuchproblems,whetherasamodelerormodelconsumer,youmust insistonthehigheststandardsofdocumentation.Yourmodelsmustbefullyrep- 1icableandavailableforcriticalreview.Usethedocumentationtoassessthe

adequacyofthemodelboundaryandtheapproprlateneSSOfitsunderlying assumptlOnSaboutthephysicalstructureofthesystemandthedecision一making behaviorofthepeopleactlngWithinit.Considerextremeconditiontestsandsen- sitivltytOalternativeassumptlOnS,includingassumptlOnSaboutmodelboundary andstructure,notonlysensitivltytOVariationsinparametervalues.

ModeltestlnglSiterativeandmultidimensionalandbeginsatthestartofthe projeCt.Buildintothebudgetandtimelinesufficientresourcestoassesstheim-

pactoftheworkandtodocumentitfullysootherscanhelpyouimproveit｡ Noonetestisadequate.Awiderangeoftestshelpsyouunderstandthero-

bustnessandlimitationsofyourmodels.Thesetestsinvolvedirectinspectionof equationsandsimulationsofthewholemodel,theassessmentofhistorical恥 and behaviorunderextremeconditions.

Usealltypesofdata,bothnumericalandqualitative･Multipledatasources provideopportunitiesfortriangulationandcross-checking.

Testtherobustnessofyourconclusionstouncertaintylnyourassumptions.

WhileparametricsensitivltyteStlnglSimportant,modelresultsareusuallyfar moresensitivetoassumptlOnSaboutthemodelboundary,levelofaggregation,and representationofdecisionmaking.

Chapter21 TruthandBeauty:ValidationandModelTesting 891

TestasyougotTestinglSanintegralpartoftheiterativeprocessofmodeling. BycontinuouslytestingyouraSSumptlOnSandthesensitivltyOfresultsasyoude-

velopthemodelyouuncoverimportanterrorsearly,avoidcostlyrework,andgen- erateinsightsthroughouttheproject,thusinvolvingyourclientsmoredeeplyand

buildingtheir-andyour-understandingoftheproblemandthenatureofhigh leveragepolicies.

Openthemodelingprocesstothewidestrangeofpeopleyoucan.Implemen- tationsuccessrequlreSChanglngtheclients'mentalmodels.Todosotheclients

mustbecomepartnerswithyouinthemodelingprocess･Ultimately,yourchances ofsuccessaregreatestwhenyouworkwithyourclientstofindthelimitationsof

yourmodels,mentalandformal,thenworktogethertocorrectthem.Inthisfash-

ionyouandyourclientsgraduallydevelopadeepunderstandingofthesystemand theconfidencetousethatunderstandingtotakeaction.

Designassessmentintoyourworkfromthestartsoyoucandetermineboth

theextenttowhichyoumeetyourgoalsandhowyoucanimprovetheprocess inthefuture･Workwithyourclientstocollectdatathatcanrevealhowyourwork

affectedthebeliefs,attitudes,andbehaviorofthepeopleinthesystem,alongwith changesinsystemperformance･Tracktheimpactofyourworkwithlong-term follow-upstudies.Acarefultestingandassessmentprocesshelpsyouandyour clientsimproveyourabilitytothinksystemicallyineveryaspectofyourlives,not Justinoneproject.

豊豊

e短軸喝eSflSjぎ油eぎ彊!Jiぎe

Itisnotknowledge,buttheactoflearning,notpossessionbuttheactofgetting

there,whichgrantsthegreatestenjoyment.

-Kar一FriedricbGauss(1777-1855)

ThischapterbrieflydescribesthemajorChallengesfacingthefurtherdevelopment

ofsystemdynamics･Idiscussfiveimportantareasoffuturedevelopment:theory, technology,education,implementation,andapplications.Thecategoriesarenei-

thermutuallyexclusivenorexhaustive,andanysuchlistisnecessarilysubjective,

incomplete,andbiased･llinviteyoutodevelopyourownprlOritiesandtowork towardtheirrealization｡

22.1 THEORY

Systemdynamicsmodelsrestonthetheoryofnonlineardynamics,anareain

whichtremendousprogresshasbeenmadeoverthepasttwodecades.Wherenon-

1ineardynamicsystemswereoncelargelyterr礼incognlta,nowthereisalargebody

oftheorydescribingthelocalandglobaldynamicsofawiderangeofcomplex nonlinearsystems.However,importantchallengesforthefutureremain,andthe mathematicalfoundationsarebutoneareainwhichbasicresearchisneeded.

･Theoryofnonlineardynamicsandcomplexsystems.Whenandhowdo

systemsself-organizetoproducecoherentpatternsinbothtimeandspace?

Towhatextentaredynamicsandcomplexsystemsself-similaracross

differenttemporalandspatialscales?Whatdeterminesthesescaling

1Richardson(1996)providesaparticularlythought丘11approachtotheseissues.

895

896 PartVIICommencement

relationships?Whatforcescreateentrainmentofindividualsubsystems

intocoherentmacrodynamics(e.g.,theentrainmentofindividualfirmsinto coherentaggregatebusinesscycles)?Whataretheunderlyinggeneric structuresthatcreatesimilardynamicsindifferentdomains?

｡Agent･basedmodeling.Stimulatedbyimprovementsincomputerpower, applicationsofagent-basedmodelingaregrowlngrapidly,Inanagent- basedmodel,theindividualmembersofapopulationsuchasfirmsinan economyorpeopleinasocialgrouparerepresentedexplicitlyratherthan

asaslngleaggregateentity.Importantheterogeneitiesinagentattributes anddecisionrulescanthenberepresented.Therearedifferentsimulation methodsforagenトbasedmodeling,rangingfromsimplecellularautomata todetailed,disagreggatesystemdynamicsmodels･Thoughmuchprogress hasbeenmadelately,muchremainstobelearnedaboutthedynamicsof agent-basedmodelsaswellastechniquesforanalyzingtheirbehavior,for testlngtheirdecisionrules,andsoon.WhatprlnCiplesshouldguidethe choiceofmodelingmethodandlevelofaggregation?Howshouldmodelers tradeoffthenumberofdifferentagentstheycanrepresentinthemodel agalnStthecomplexltyOftheindividualagents?Whatrulesofinteraction,

levelofrationality,andlearnlngCapabilitiesshouldbeascribedto theagents?

｡Mentalmodels,dynamicdecisionmaking,andlearnlng｡Laboratory researchandfieldworkhaverevealedmuchaboutthewaypeoplemake decisionsincomplexdynamicsenvironments,butourunderstandinglS stillpoor,Whatarethementalmodelspeopleuseinsituationsofdynamic complexity?Howsensitivetothecharacteristicsoftheenvironmentarethe decisionrulespeopleuse?Arethemisperceptionsoffeedback(chapter1) documentedinsomanycasesinnateorlearned?Whattypesofexperience andeducationmightmltlgatethemanddevelopoursystemsthinking capabilities?Whatincentives,informationsystems,andorganizational structureswouldcatalyzesuchleamlng?Howcantheselearnlngprocesses

becapturedinmodels?

･Organizationalandsocialevolution.Evenifindividualslearnslowly,

socialstructuressuchasorganizationsmightimprovethroughevolution, asthehigher-performingagentsProsperandareimitatedwhilethelow

performersareselectedoutofthepopulation.Formalmodelingofsocial evolutionisgrowlngrapidly,butmanyquestionsremain,Whatare theunitsofselection?Whatarethe"genesHinanorganization?What

determinesthelengthofageneration?Whatrulesdeterminetheselection ofwinnersandlosers,andwhatdoesreproductivesuccessmeaninan

organization?Whencanselectivepressuresrewarddysfunctionalbehavior

andperpetuatelowperformance?

22.2 TECHNOLOGY

Untilrecentlylearnlngaboutthedynamicsofamodelproceededessentiallyby trlalanderror,guidedbyintuitionandexperience,onesimulationatatime.Since complexnonlinearsystemscangenerateawiderangeofbehaviors,manyofwhich

Chapter22 Challengesfor仙 eFuture 897

arecountertointuition,developingInsightintothedynamicsofacomplexsystem hasoftenbeendi任icult.

Ascomputersbecomeeverfasterandmorecapable,simulationswillnot

merelyrunfaster,butthenatureofthemodels,simulationsoftware,andwaysof interactlngWithmodelswillbetransformed.Amongthetoolsfuturesimulation softwarewillincludeare:

･AutomatedmappingOfparameterspace.Hittingtherunbuttonwill

generateahigh-resolutionmapofmodelbehavioroverauser-specified rangeofparametersandinitialconditions.

･Automatedsensitivityanalysis.Thesoftwarewillautomaticallyidentify thehighlleveragepoliciesandmostinfluentialparametersinthemodel (relativetouser-specifiedcriteria).

･Automatedextremeconditiontesting･Themodelerorclientwillspecify extremeconditionsthemodelmustsatisfy(e.g.,nolabor,noproduction;no inventory,noshipments).Thesimulationsoftwarewillautomatically implementthese"realitychecksHandreporttheresults(seePetersonand Eberlein1994).

｡Automatic,interactiveparameterestimation,Calibration,andpolicy

optimization.Modelerscannowspecify(possiblynonlinear)criteriaand weightsfordifferentvariablesandconstraintsontheplausiblevaluesof

parameters;thesoftwarethenfindsthebestparametervaluesand confidenceboundsaroundtheestimatedvalues(usingmethodsfrom

ordinaryleastsquarestoKalmanfiltering).However,theprocessisoften tediousanditisdifficulttocombinequantitativeandqualitative information.Futuresimulationsoftwarewillautomatemodelcalibration,

allowlngtheusertoexploretheconsequencesofalternatecriteria

interactivelylnrealtime,Similarly,optlmizationofsystemdynamicmodels hasalonghistory(see,e.g.,Coyle1985,1998).Cu汀entlyavailable

softwareallowstheusertospecifya(possiblynonlinear)multiattribute objectivefunctionandasetofpolicyinstruments(parameters),then

searchesthepolicyspacefortheoptlmalsolution･Inthefuture,thisprocess willbesofastthatitcantakeplaceinteractivelyandinrealtime,Withthe usergettlngImmediatefeedbackontheconsequencesofalternative objectivefunctionsandpolicyinstruments.

･Automatedidentificationofdominantloopsandfeedbackstructure.

Severalmethodsnowexisttoidentifythedominantloopsatanypolntina simulation,quantifythecontributionofanyparameterorlooptoaglVen mode,andshowhownonlinearitieschangethedominantfeedbackstructure

(see,e.蛋.,Eberlein1989;Kampmann1996;Mqjtahedzadeh1997;and N.Forrester1982).Futuresimulationsoftwarewillautomateandspeed

thesecomputationssothatuserscangetimmediatefeedbackshowing thedominantloopsinthesystemandhowtheinfluenceofparameters andfeedbackstructureswaxesandwanesasthedynamicsunfold.

･Automatedhelp.Throughexpertsystems,patternrecognltlOnsoftware,

andotherartificialintelligencetoolsitshouldsoonbepossiblefor simulatiOnsoftwaretoserveasanautomatedmodel-buildingtutorand

898 PartVIICommencement

guide.Themodelingtutorcould,forexample,examineeachequation asitisenteredfordimensionalconsistency,robustnessunderextreme

conditions,andotherbasicprinciplesofgoodformulations.Thetutor wouldthensuggestimprovedformulationsfromalibraryofstandard structures,linkstorelatedmodelsandliterature,andreasonableparameters,

Imaginebuilding,say,amarketingmodel.Thesoftwaremighttellyouthat

yourformulationforcustomerdefectiontocompetitorslacksfeedbackfrom thestockofcurrentcustomers(allowingthecustomerstocktobecome

negative),suggestanimprovedformulation,andguideyouthroughaseries

ofquestionstohelpyouspecifytheparametersandnonlinearrelationships. Similarly,thesoftwaremaysuggesttestsyoucanconductandhintstohelp youbetterunderstandthebehaviorofyourmodel.

AmajorChallengefacingsoftwaredesignersisorganizlngandpresentlngthe hugemassesofdatageneratedbythetoolsdescribedabove.Datapresentationand

visualizationwillbeacriticalarenaforfuturesoftwaredevelopment,including

･Visualizationofmodelbehavior.Improvementsingraphicsandanimation

areneededtodisplaytheglobaldynamicsofcomplexmodelswithhigh- dimenslonalstateandparameterspaces.

｡Linkingbehaviortogenerativestructure.Computationsofdominant

structureandparametersensitivltyShouldautomaticallybedisplayedon thestructuraldiagram.Imaglnethesize,color,andotherattributesofthe

stocks,flows,variables,andloopsdisplayedonthescreenchangingtO indicateshiftsinloopdominanceorparametersensitivltyaSaSimulation unfolds,OrasyouvaryinputCOnditionsandpolicies.

｡Datainput.InputdevicessuchasJOySticksanddataglovescanprovide

rapid,continuouslnputOfparametervaluesandcontrolgraphicaldisplays. ImaglneusingaJOyStickto"fly"Overathree-dimensionalprojectionof modelbehaviorasafunctionofanymodelparametersyouwishtoexplore.

Linkingmodelswithoneanotherandwithawiderangeofdatabasesisanother

importantareaoftechnologicaldevelopment.Atpresent,finding,checking,and updatingdataisdifficult,expensive,andtime-consumlng.Incompatibilities

abound.FuturesimulationsoftwarewillseamlesslyIntegratedatafromavarietyof sources,automaticallyidentifyinconsistencies,andautomaticallyupdatethe

modelbyquerylngthedataserversoverpublicorprlVatenetWOrks.integratingdy- namicmodelswithenterprlSemanagementSOftwarewillenablemanagerstogo beyondspreadsheets.

Thekeychallengeisuslngtechnologytolearnmoreeffectivelyaboutthedy- namicsofourmodels,todeveloptoolstoaidunderstandingofcomplexsystems. Therearedangers,however.Modelersmustresistthetemptationtousegreater

computerpowertobuildbiggerandbiggermodelsinthevainbeliefthatthemore detailedandcomprehensivethemodel,thebetteritmustbe.Whilecomputer powergrowsexponentially,Ourabilitytoabsorbinformationremainsthesame.

Largerandlargermodelsmayonlyresultinlessandlessunderstanding,fewerin- Sightsandlessimplementationsuccess.

Chapter22 ChallengesfortheFuture 899

22.3 lMPLEMENTAT10N

Improvementsintheoryandbettertechnologyalonewillnotimprovethechances

ofsuccessfulimplementation･Ultimatelytheclientteammuststillcometoadeep understandingoftheproblemissueanddevelopenoughconfidenceinmode1- generatedpolicylnSightstoact.DespltegreatStrides,successfulimplementation remainsanart.Issuesforfurtherresearchinclude

･Communicatingmodelingmsights･Howcanmodelsbemadetransparent andaccessibletoclientsastechnologyImprovesandmodelsgrowmore

complex?Howdoyoureachtheclientwhentheclientistheentiresociety andyourmessageisfilteredbythemedia(see,e.g.,Meadows1989)?

･Improvinggroupmodeling.Muchprogresshasbeenmade(e.g.,Vennix 1996;Vennix,Richardson,andAndersen1997;andMorecroftandSterman

1994)andmodelshavelongbeenusedindisputeresoludon(see,e.g., section2.3).Howcanmodelingbeusedwellinthelargergroupsoften

requiredtoachieveconsensusforimplementation?Howcanmodelingbe usedwiselylnadversarialcontexts,forexample,topromoteintegrative disputeresolution(see,e.g"DiStefano1992･,NyhartandSmarasan1990; ReicheltandSterman1990;WeilandEtherton1990)?

･Speedingtheprocess.Fastercommunication,shorterproductlifecycles, andlongerworkhoursareincreaslngthepressureonmanagersfわrfast answerstotoughquestions.Canthecycletimeforthedevelopmentofa

modelbereduced?Shoulditbe?Perhapsthemodelingprocessshould encouragemeditativereflectionandpreventkneeJerkreactions.

｡Integratingmodelingmethodologies.Systemdynamicsdoesnotstand

alone･WhatsynergleSCanbeachievedbyintegratingdynamicmodeling withothermodelingapproaches,includingmultiattributeutilityassessment, decisionanalysis,marketresearchmethods,andothertools(see,e.g., Reagan-Cirincioneetal.1991)?

｡Creatingmanagerialpracticefields･Rehearsalandpracticehavelong beencentraltosuccessfulteamperformanceinsportsandthearts,and simulationhasfor50yearsbeenabasicelementofmilitaryplannlngand trainlng.Developmentsintechnologyandgroupprocessnowenable

managerstodevelopandusemodelstocreaterich,interactivepractice fieldstodesignnewpolicies,testnewideas,andexplorealternative

theoriesfornewphenomena.Thesemanagementflightsimulatorswillplay avitalroleinemergingdecentralized,networkedorganizations(Sengeetal. 1994).Atthesametimetheresearchclearlyshowshowdi仇cultitcanbe forpeopletolearneffectivelyfromsimulationsandgames(seechapter1; alsoIsaacsandSenge1992;PaichandSterman1993).Creatingeffective

practicefieldsrequiresmuchmorethanexcitingandrealisticflight simulators.

･AssesslngOutcomes.Someorganizationshaverecentlyrealizedthatitis

intheirlong-runbestinteresttosharealltheirexperienceswithmodeling, notonlytheirsuccesses,Tわomany,however,continuetowithholdtheir

900 PartVIICommencement

experiences,evenfromtheirownemployees,forfearofrevealing

proprletaryinformation,theperceivedshort-runcostsofdocumentationand

follow-up,orembarrassment.Howcantheincentivestocarryoutrigorous

follow-upstudiesbestrengthened?

22.4 EDUCAT10N

Systemsthinkingandsystemdynamicsmodelingarenolongerrestrictedtoad-

vancedstudyingraduateschoolsoruniversltyCOurSeS･Overthepastdecademany

dedicatedteachers,administrators,andparentshaveworkedtointroducethese

conceptsandtoolsinprlmaryandsecondaryschools｡AlthoughexcitlngeX-

perimentsincurriculumandpedagogyareunderwayaroundtheworld(see,e.g.,

Brown1992;DraperandSwanson1990;FisherandZaraza1997;Could1993;

MandinachandCline1994;RobertsandFeurzeig1999)wearestillveryearlyin

thisprocess･2Muchworkremainstodevelopsystemdynamicscurriculaapproprト

atetotheK112grades,todeveloppedagogyforchildren(andadults)thatworks,

andtodevelopInstrumentsandmethodstoassessthelong-runimpactofthese

approaches.

Likewise,Organizationsshoulddevotesignificantresourcestocontinuinged-

ucationforall･Fewhaveyettakenthechallengeseriously.Morecommonly,orga-

nizationslookforthequickfix,faddishlyembracingthelatesthotmanagement

tool,onlytoabandonitforthenext"flavorofthemonth"program.Theresultis

cynicism andresentmentamongemployeesandseniormanagementalike(see,

e･g･,StermanandWittenberg1999andKeatlngetal.1999formodelsofthis

process).Afterworkingintensivelywithsystemsthinkingandsystemdynamics

forseveralyears,amanagerataUSautomakerreflectedontheprospectsforcom-

mitmenttosustainedlearnlnglntOday'sorganizations:

Ithastakenmealongtimetobegintogetwhatthisnewworldview[systemdy- namics]isallabout.I'mbeginningtofeellikeIfeltinmyfreshmancalculusclass. A氏ermonthsofconfusion,Ibegantogetit.Withinayear,ihadbeguntodevelop somecompetence.Withinfouryears,thebasictoolsandwayofthinkingwerean integratedpartofmyprofessionalskills...Theproblemis,ifcalculuswereinvented today,Ourorganizationscouldneverlearnit.Wewouldsendeveryoneofftothe three-daycrashcourseandthentellthemtogooffandapplyit.Afterthreemonths we'dcheckifitwasworking.Sincelittlewouldhavebeenachieved,we'dcon- cludethattherereallywasn'tmuchthere,andweヮdmoveontothenextprogram (KinandSenge1994,p.278)I

Forrester,inhisprescientpaper"ANewCorporateDesign"(Forrester1965/1975a,

p.107-108),prescribes

Some25percentofthetotalworkingtlmeOfallpersonsinthecorporationshould bedevotedtopreparingfortheirfutureroles.Thismeanstimedevotedtocompe- tencesomefiveyearsinthefutureanddoesnotincludethelearningthatmaybea necessarypartoftheimmediatetask.Overaperiodofyearsthisstudywouldcover

awiderange-individualandgrouppsychology,writing,SPeaking,law,dynamics

2TheCreativeLearningExchangeservesasaclearinghouseandresourcecenterforpeople teachingsystemdynamicsintheK-12setting.See<http:〟sysdyn.mit･edu/cle/home.html>.

Chapter22 ChallengesfortheFuture 901

ofindustrialbehavior,corporatepolicydesign,advancesinscienceandenglneer- 1ng,andhistoricaldevelopmentofpoliticalandcorporateorganizations…Theedu- cationalprogrammustbecomeanintegralpartofcorporatelife,notafewweeksor monthsonceinalifetimeatanotherinstitution.Theover-allpoliciesoftheorgani- zationmustcreateincentivesthatprotectthetimeforeducationfromencroachment byshort-termpressures.

Forcenturiesthereductionistprogramofever-finerspecializationhasbeenvery

successful,oftenleadingtodeepandusefulknowledge.Today,mostoftheprob- 1emswefacearefundamentallyinterdisciplinary.Asamanager,youwon'tface

marketingproblems,financialproblems,andhumanresourceproblems.Asanin-

dividual,youdon'tfaceeconomicproblems,socialproblems,andpersonalprob-

1ems･Youjusthaveproblems･Weimposethesecategoriesontheworldtosimplify

itsoverwhelmingcomplexity･Someboundariesarenecessaryandinevitable.But

alltoooften,1gnOrlngWhatliesoutsidethefam iliarwallsofourunderstandingcuts

criticalfeedbacksandbreedsarroganceaboutourabilitytocontrolnatureand

otherpeople･Thereductionistprogramisverypowe血 1,andshouldnotbere- placedbyvaguegeneralizationsaboutsystemsandinterconnectedness.Thechal-

1engeistodesignaneducationforourselvesandourchildrenthatpreservesthe

powerofspecializedstudywhilesimultaneouslyteachingpracticalandrigorous

approachestocomplexltyandcross-disciplinarycommunication-thenusingthese

systemsthinkingcapabilitiestoaddressthepresslngproblemswefaceinourpro- fessionalandpersonallives.

22.5 AppLICAT10NS

System dynamicshasbeenappliedtoissuesfrom physicstophysiologyand

psychology,fromarmsracestothewarondrugs,fromglobalclimatechangeto

organizationalchange.Yettherearecountlessproblemsandissueswhereunder-

standingislackingandthedominanttheoriesareevent-oriented,exogenous,and

staticratherthanstructural,endogenous,anddynamic･Theresultispolicyresis-

tance,thelossofhopeforthefuture,andthefeelingofhelplessnessafflictingso manypeopletoday.

PEjtt岳ngSystemDyr;,-3mics⊆n紬Actiorl

Whataretheissuesyoucaremostdeeplyabout?Whatapproacheshavebeentried,

withwhatrecordofsuccess?Learnwhat'sbeendonebefore･Talktothepeople

livinginthesystem.Whatfeedbackstructuresanddynamicsdoyousee?

Becomeanexpertontheissues.Getinvolved.Startapplyingyourknowledge

andmodelingskillstohelpimprovethesituation･Buildanetworkofcolleagues

anddecisionmakers.Behumbleaboutwhatyouknowandlistentoyourcritics. Strivealwaystomakeadifference.Andhavefun.

鞘~韻Fi-_Y!_e海員呈葺i_7S音更等開音主串･i3.

Systemdynamicsmodelsaresystemsofnonlinearordinarydifferentialequations. Almostallthetime,andcertainlyforanymodelofmoderaterealism,analyticso- 1utionscannotbefoundandthebehaviorofthemodelsmustbecomputednu- merically,aprocessknownasnumericalintegration･Thetheoryofnumerical integrationfordifferentialequationsissubtleandsophisticatedandtheliteratureis large.Thisappendixfocusesonthemostcommonmethodsandthepragmaticsof theprocess.Whichmethodshouldyouuseandinwhatcircumstances?How shouldthetimestepbeselected?Howcanyoumakesuretheresultsofyoursiml

ulationsarenotcorruptedbyerrors?Readersinterestedinthemathematicalunder- plnnlngSShouldconsultintroductorynumericalmethodstextssllChasAtkinson (1985),BurdenandFaires(1989),orMaron(1987).

Asdescribedinchapters6and7,thestocksinamodelSaccumulate(inte- grate)theirinflowsIlesstheiroutflows0.Theflows,inturn,dependonthe stocks,anyexogenousvariablesU,andparameters(constants,C):

St-INTEGRAL(It-0｡Sto) (A-1)

It-f(St,Ut,C);Ot-g(St,Ut,C) (A-2)

TheinitialconditionSbglVeSthequantltylnanyStocktoday･Whatwillitsvalue betomorrow?Thequantltyinthestocktomo汀OWWillbetheamountinthestock now,plusthequantitythatflowsinbetweentodayandtomorrow,lesstheamount thatflowsout.However,thevaluesoftheflowsareonlyknownatthecurrentin-

stant,andtheyusuallywon'tremainconstantbetweentodayandtomorrow･The challengeisestimatingtheaverageflowoverthenextday(orwhatevertimeinter- valyouuse),recognizingthattheaverageovertheintervalusuallywon'tequalthe flowrightnow.

ThesimplestassumptlOnisthattherateswillremainconstantbetweentoday andtomorrow.Denotingthetimeintervalbetweenperiodsasdt(for"deltatime"), theassumptlOntheratesremainconstantduringthenextintervalimplies

St+dt-St+dt*(It-Ot)

904 AppendixA

Equation(A13)isthemostbasictechnique,knownasEulerintegrationafterthe greatmathematicianLeonhardEuler(1707-1783).Theassumptionthattherates

remainconstantthroughoutthetimeintervaldtisreasonableifthedynamicsofthe systemareslowenoughanddtissmallenough.Thedefinitionsof"reasonable"

andHsmallenough"dependontheaccuracyyourequlre,Whichintumdependson

thepurposeofthemodel;SeebelowforguidelinesfortestingthesensitivltyOf yourmodeltothechoiceofdt,

Asthetimestepshrinks,theaccuracyofEuler'sapproximationimproves.In thelimit,whendtbecomesaninfinitesimalmomentoftime,equation(A-3)re- ducestotheexactcontinuous-timedifferentialequationgoverningthedynamicsof thesystem:

dltij- .萱篭蓬 -慧 -(It-Ot) (A-4)

SoftwarepackagesforsystemdynamicssuchasDYNAMO,ithink,Powersim,and VensimuseEulerintegrationastheirdefaultsimulationmethod･Theonlydiffer- encebetweenthenumericalandanalyticSOlutionoftheunderlyingdifferential equationsystemisthesizeofdt.Thedifferentialequationusesaninfinitesimal, atrueinstant,Digitalcomputersmustproceedbydiscretestepsanduseafinite timestep,

SampleSimu/ationSequence

Theinitialconditionsforthestocks,theinitialvaluesofanyexogenousvariables,

andthevaluesoftheconstantsallowyoutocalculatetheinitialvaluesoftheflows. Assumlngtheflowsremainconstantthroughoutthenexttimestepdtallowsyouto calculatethestockinthenextperiod.Fromthenewvalueofthestock,thenew valuesoftheratesarethencalculatedandthenextvalueofthestockisdetermined.

Eachperiodthevaluesofthestocksareusedtocalculatetherateswhicharethen usedtoupdatethevaluesofthestocks.

Considerasimplemodelofapopulation.ThepopulationPisincreasedbythe BirthRateBanddecreasedbytheDeathRateD.BirthsanddeathsareproI portionaltopopulation.ForsimplicityaSSumetheFractionalBirthRateFBRand AverageLifetimeALareconstant,at4%/yearand80years,respectively.The

initialpopulationisonemillion.Theequationsforthesystemare

p -INTEGRAL(B-D,Pto)

Pt｡-leら

B-FBR*P

D-P/AL

FB良 -0.04

AL-80

L.I.

･-

1一

0ノ

一

【

･l1- (A-10)

Themodelisalinearfirst-ordersystemandcanbesolvedanalytically･Theexact solutionis

Pt-P一o*expl(FBR-1/AL)*t] (A-ll)

Numericallntegration 905

Thatis,populationgrowsexponentiallyatthenetfractionalbirthrateFBR-1/AL

(Seechapter8)･Withtheseparametersthenetfractionalbirthrateis2.75%/year. TableAllShowshowthedynamicsarecalculated･ThetimestepISSettOO125

yearS･

Time0.Thevalueofpopulationattimet-0isonemillionpeople.Thebirth rateequalsFractionalBirthRate*Population,orO･04*leら-40,000people/year. TheDeathRate-Population/AverageLifetime-le6/80-12,500people/year. Thenetbirthrateistherefore27,500people/year.Thesevaluesaretheinstanta- neousratesofflowatt-0.

1nEulerintegration,theseratesareassumedtoremainconstantthroughoutthe

timeintervaldefinedbydt.Thetimestepdtinthisexampleis0.25years,sothe

totalchangeinthepopulationisdt*NetBirthRate-0.25years*27,500peo- ple/year-6875people.EqulValently,0.25years*40,000people/year-10,000

peoplearebomduringthefirstquarteryear,andO125years*12,500-3125peo- pledie･Thesimulatedpopulationatt-0.25istherefore1,006,875.

Time0+dt. Giventhecalculatedvalueofpopulationfort-0+dt,thebirth ratenow equals0.04*1,006,875- 40,275people/year.Thedeathrateis

l,006,875/80-12,586people/year･Thenetbirthrateatthatinstantis27,689peo- ple/year･Againassumlngtheratesremainconstantoverthenextquarteryear,the

quantltyaddedtothepopulationbytimet-0･5isO･25years*27,689people/year -6922people･Equivalently,0.25years*40,275people/year-10,069peopleare born,and0.25years*12,586peopleyear-3147peopledie｡Thepopulationatt -0･5thusequals1,013,797.

Time0+2dt･ Attimet-0.5,thebirthrateis40,552people/yearandthe deathrateis12,672people/year,yieldinganinstantaneousnetbirthrateof27,880 people/year.Overthenextquarteryear,assumlngthatrateremainsconstant,6970

peopleareadded,sothepopulationatt-0･75yearsis1,020,767people.Thesim- ulationcontinuesinthisfashionaslongasyoudesire.

lntegralionError

Theuseofafinitetimestepandresultingapproximationtotheaverageratesover

theintervalintroduceerror,knownasintegrationerrof;Ordterror:Themagnitude

TABLEA-1 SimulatingamodelwithEulerintegration

Poputation BirthRate DeathRate NetBirthRate PeopleAdded Time (peop一e) (peop一e/year) (people/year) (people/year) (peop一e)

0.00 1,000,000 40,000 12,500 27,500

0.25 1,006,875 40,275 12,586 27,689

0.50 1,013,797 40,552 12,672 27,880

0.75 1,020,767 40,831 12,760 28,071

1.00 1,027,785 41,111 12,847 28,264

906

TABLEA-2

Integrationerror dependsonthe timestep.

AppendixA

SimuJated %Error

TimeStep(dt) PopulationatI=100 (exactsolution- (years) (miHionpeople) 15.643miHion)

｣

. 1

ofintegrationerrordependsonhowquicklytherateschangerelativetothetime

step.Thefasterthedynamicsofthesystem,orthelongerthedt,thegreaterthe

integrationerrorwillbe.TableA-2Comparesthesimulatedvaluesofpopulation

afterlooyearstotheexact,continuoustimesolutioninequation(A-ll)fordiffer- eIltValuesofdt.

Theexactvalueofpopulationafter100yearsinthecontinuoustimemodelis

le6*exp(0.0275*100)- 15.643millionpeople.Thetimestepisequivalentto

thecompoundingIntervalforthecomputationofinterestonabankaccount･The

moreofteninterestiscompounded(thesmallerthetimestep),thefasterthebal-

ancegrows,uptothecontinuouscompoundinglimit.Inthisexample,wherethe

behaviorispureexponentialgrowth,populationgrowsexactlylikeabankbalance,

andthesimulatedvaluesarealwayslessthanthecontinuouscompoundingcase.

Forsmalltimesteps,theerrorsaresmall.WithatimestepofO.25years,thesim-

ulationislessthanl%toolowafter100years.IncreaslngthetimestepIncreases

themagnitudeoftheerror･

Themagnitudeofintegrationerroralsodependsonthestabilityofthesystem.

Thesamplemodelhere,apurepositivefeedback,isunstable･Smallerrorsgrow

overtimeatexponentialrates,justasabankbalanceof$1001willeventuallyex-

ceedabalanceof$1000earningthesameinterestratebyanarbitrarilylarge

amount,becausetheextra$lgrowsexponentiallyattheinterestrate.Inmodels

tendingtowardastableequilibriumtheintegrationerrorwouldprobablybemuch

smallerthanshowninTableA-2andwoulddiminishasthesystemapproached

equilibrium･1

1Technically,thepopulationmodelgovernedbypositivefeedbackistermed‖ill-conditionedH

because.smallerrorsaccumulatewitheachtimestep(aprocessknownaserrorpropagation)AInthe populatlOnexampletheerrorgrowsexponentiallyovertlme.InHwell-conditionedHmodelserrors dieawayovertime･Roughlyspeaking,astablesystem,dominatedbynegativefeedback,tends tobewell-conditioned･Sincethestabilityofasystemcanchangewithinaslnglesimulationas thenonlinearitiesalterthedominantloops,aparticulartimestepmayworkwellinonepartof asimulationandfailinanotherpart.Whethertheresultingerrorsmatterdependsontherateat whicherrorspropagateordieawayandofcourseonthepurposeofthemodel.

Numericallntegration 907

SelectinganAppropriateTimeStep Howshouldyousetthetimestep?Whenyouneedtocomparesimulationoutput agalnStdata,youshouldobviouslychooseatimestepthatisevenlydivisibleinto

thedata-reportlnglnterValJtdoesn'tdotocalculateamodelwithquarterlydata uslngatimestepofO.20years.

TheprlmaryCOnSiderationinselectingthetimestep,however,istheaccuracy ofthenumericalintegrationprocess.Thesmallerthevalueofdt,themoreaccurate

theassumptionthattheratesofchangeremainconstantbetweentimestepsandthe closertothetruecontinuoustimesolutionyourmodeloutputwillbe.However,the

smallerthevalueofdt,thelongeritwilltakeyoursimulationtorun｡Moresubtly, thesmallerthetimestepthegreatertheround10ffandtruncationerror.Roundl0ff

andtruncationerrorsarisebecausecomputersoperatewithfiniteprecisionarith- metic･Thetotalnumericalerrorinasimulationconsistsoftheintegrationerrorand theround-offerror.Round-Offerrormeansyoucannotincreasesimulationaccu-

racyarbitrarilybyshrinkingthetimestep.AssomepolntSmallertimestepsactu-

allycausethetotalerrortoincreaseasthecumulativeeffectsofroundoffoutweigh thereductioninintegrationerror.

Selectlngthetimestepforyoursimulationsisthereforeamatteroftradingoff integrationerroragalnStSimulationcostandround10fferror.Ascomputersbecome

faster,thetimestepyoucanselectandstillsimulatequicklyisdropping;likewise youcanelecttousehigherprecisionwithoutmuchcostincomputationtime.The accuracy/simulationtimetrade-offiseaslngaStechnologyImproves.

Awidelyusedruleofthumbistosetthetimestepbetweenone-fourthand

one-tenththesizeofthesmallesttimeconstantinyourmodel.However,inalarge

modelitisdifficulttoestimateallthetimeconstantsandselectanapproprlatetime step,soyoumustalwaystestthesensitivltyOfyourresultstothechoiceoftime step(andintegrationmethod;seebelow).

Testforintegrationerrorbyrunnlngyourmodelwithyourbestestimateofan

approprlateValuefordt.Thencutthevalueofdtinhalfandrunthemodelagaln. Ifthereisnosignificantchangeinthebehavior-thatis,ifthebehaviordoesnot

changeinwaysthatmattertothepurposeofthemodel-thenyourorlglnalchoice wasfine.Ifthebehaviorchangesinasignificantway,repeatthetestwithdtcutin

halfagain.Continueuntiltheresultsnolongerdiffer. InthepopulationexampleEulerintegrationwithdt-0,25yearsyieldsaner-

roroflessthanl%after100years.TheelTOrisfarsmallerthanlikelyuncertainty intheparametersorinitialconditionsandfar,farsmallerthantheerrorcausedby

theassumptlOnthat血.actionalbirthanddeathratesremainconstantoverthisspan. Round-offerroralsoaffectsthecomputationoftimeinyourmodels.Timeis

calculatedasastockthatincreasesonetimesteppertimestep:

Timel+dt-Timet+dt (A-12)

Inprinciple,thevalueofTimenperiodsoflengthdtfrom now shouldbe

Timeto十 n*dt･However,ifdtcannotberepresentedexactlywiththeprecision usedinthecomputations,theamountaddedtoTimeeachperiodwillnotbecor-

rect･Supposeyouselecteddt-y6year,Or0.1666....Ifyouusedonlythefirsttwo digits,truncatlngtherest,thevalueoftimea氏erthreeiterationswouldbeonly

908 AppendlxA

0.96,not1year.Thoughcomputersusemorethantwodigits,theystilltruncateor round,sotheproblemremains.

Sincecomputersusethebinarysystem youcanminimizetruncationand round-ofFerrorinthecalculationoftimebychooslngatimestepthatcanberep- resentedexactlyinbase2giventheprecisionofyourcomputer.Powersof2are mostcommon(e.g.,dt-4,2,1,0.5,0･25,0.125,0･0625,andsoon)ASetting dt-0.3isnotagoodchoice;itsbase2representationisO･01001001001001‥. andwillberoundeddowntoasmallernumbersothatafterntimestepsthecom-

putedvalueofTimewillincreaseless血ann*dt. Occasionallyyouwillneedtoselectavalueofdtthatdoesnotmeetthiscrite-

rion.Theproblemarisesmostoftenwhentimeismeasuredinyearsandhistorical dataareavailablemonthly.Inthiscasedtmustbesettoシi2-0.0833.‥yearsto

matchthedatareportlnglnterVal･Insuchcases,enterasmanydigitsforthetime stepasyoucan(e.g.,0.08333333333,notO･083)･Still,thecomputedvalueoftime willeventuallyfallshortastheround10fferroraccumulates･Ifthetimehorizonof themodelisnottoolong,theproblemmaynotarise･Anothersolutionistomea- suretimelnmonthsinsteadofyears,setdt-1month,anddividealltimecon- Stantsandotherparametersinwhichtimeappearsbyafactorof12.

BeyondEuler

Eulerintegrationissimpleandadequateformanyapplications･Inmodelsofsocial andhumansystemsthee汀OrSininitialconditions,parameters,andespecially modelspecificationarelargeandthedataagainstWhichyoumightcomparemodel outputareoftencorruptedbysignificantmeasurementerror･Insuchsituations, Euler'serrorsareinconsequential.Spendyourtimeimprovlngthemodelrather thanfine-tuningthenumericalintegrationmethod.However,therearesomesys- temsandsomemodelpurposes,particularlyinenglneerlngandphysics,where Rulerisnotappropriate,eitherbecausetheerrorsltgeneratesaretoolargeorthe timesteprequiredtogaintheneededaccuracyslowmodelexecutiontoomuch.

Therearemanymoreadvancedtechniquesfornumericalintegrationofdiffer- entialequations.Themostpopularare血eRunge-Kuttamethods,Euler'smethod assumestheratesattimetremainconstantovertheentireintervaltotimet+dt,

也atis,that也eaveragerateovertheintervalequals也erateatthestartofthein- terval.TheRunge-Kuttamethodfindsabetterapproximationoftheaveragerate betweentandt+dt.First,provisionalestimatesofthestocksatt+dtarecalcu- latedbyEuler'smethod.Nexttheratesattimet+dtarecalculatedfromtheEuler estimateofthestocksattimet+dt.Theestimatedratesattimetandt+dtareav-

eragedandusedtocalculatethevalueofthestocksatt+dt.Thismethod,known assecond-orderRunge-Kutta,glVeSamoreaccurateapproximationoftheactual averageratesovertheinterval[t,t+dt]･

Higher-orderRunge-Kuttamethodsworkinessentiallythesamewaybutesti- matetheaveragerateoversubintervalswithinlt,t+dt]toyieldastillbetterap- proximation.Mostsimulationpackagesofferfourth-OrderRunge-Kutta･

WhileRunge-KuttarequiresmoreCOmputationpertimestep,theaccuracyof theapproximationismuchgreaterthanEuler'smethod･Integrationerrorsfora comparablechoiceofdtaremuchsmallerandpropagateatmuchsmallerrates,a1- lowlngthemodelertousealargertimesteporgainadditionalaccuracy･

NumericalIntegration 909

ErrorControlandVariableTl'meStepMethods

Innonlinearsystemsthedominantfeedbackloopsdrivingthedynamicscan

changeasthesystemevolves.AsystemcanbechanglngSlowlythensuddenlyshift

toanewreglmeWherechangeisveryfastJnsuchasystemtheoptlmaltimestep

mayvarydependingonthespeedofthedynamics･Duringcalm periodswhere

changeisslowalargetimestepwouldbesttradeofFintegrationerror,round-offer-

ror,andcomputationtime.Butthatlargetimestepwouldyieldlargeintegrationer-

rorsduringperiodsofturbulence.Settingthetimesteptoasmallvalueapproprlate

totheturbulentregime,however,mightcauseyourmodeltorunfartooslowlyor

togeneratetoomuchround-ofFerror.

Variabletimestepmethodsautomatetheheuristictestforintegrationerrorin

whichyoucutdtinhalfandaskwhetherthebehaviorchangesinasignificantway.

Theuserspecifiesanerrortoleranceandaninitialtimestep.Thesimulationpr0-

ccdurecalculatesthenextvaluesofthestocksuslngtheinitialtimestepandalso

calculatesthemusinghalftheinitialstepsize.Ifthedifferencebetweenthetwore-

sultsistoolargethetimesteplSCutinhalfagalnandtheprocessisrepeateduntil

theerrorfallswithinthespecifiedtolerance.Iftheerrorisverysmallthetimestep

canbeincreased(butusuallyonlyuptotheinitialstepsize)･Thesimulationcon-

tinues,testlngforandcontrollingtheerrorateachpoint･2variablestepsizemeth-

odsminimizesimulationtimesubjecttotheconstraintonthemagnitudeofthe

errors,evenasthedynamicsspeedorslow･3Manysimulationpackagesoffervari-

ablestepsizefourth-orderRunge-Kutta,anexcellentmethodforsituationswhere

highaccuracylSrequired,suchassimulationsofphysicalsystemswherethelaws

governingtherates,initialconditions,andparametersareknownpreciselyand

wheresmallerrorsmattertothepurpose.

Choos/ngyourIntegrationMethod

YoucantestwhetherEulerintegrationisacceptablebyrunnlngthemodelwitha

higher-orderintegrationmethod(usingthesametimesteporusingavariabletime

stepmethod).Ifthereisnosignificantchangeintheresults,thenEulerintegration isfine.

Acaveat:Becausehigher-ordermethodssuchasRunge-Kuttaperformcalcu-

1ationsbetweenthespecifiedtimesteps,Caremustbeexercisedwhenyourmodels

includediscontinuousevents.Systemdynamicsmodelsaregenerallyformulated

2Thesemethodsonlycontrolthelocalerror,thatis,theerrorintroducedinthecurrenttimestep･

Modelers,howPver,∬ econcernedwiththeglobal(cumulativetotal)eITOrbetweenthesimulated andexactsolutlOnS.Thoughstrictlyspeakingtheglobalerrorisunknown,itcanbeestimated. Reducingitbelowsometolerance,however,requlreSgOlngbackandresimulatlngfromsome earlierpointintime.Controllingthelocalerrorensuresthattheglobale汀Oralsoremainswithin certaintolerancesfわrmanybutnotallsystems.

3somesystemscontainmixturesofveryfastandveryslowdynamics･Forexample,prlCeSina stockmarketadjustveryrapidlytochangesinbuyandsellorders,whiletheunderlyingeconomic variablesthatdrivechangesincorporateearningsChangemuchmoreslowly.Ifthedifferencesin timeconstantsgovernlngthefastandslowdynamicsareverylarge,thesystemissaidtobe"stiff." Ordinarynumericalmethodscanfailinstiffsystemsbecausethetimesteprequiredtocapturethe

fastdynamicsmustbesosmallthattheevolutionoftheslowvariablesiscorruptedbyround10ff error.Thenumericalmethodstextsreferencedabovediscussstiffsystemproblemsandmethods specificallydesignedtosolvethem.

910 AppendixA

incontinuoustimebutoftenincludediscontinuouselementssuchastestfunctions

(e･g･,asteporpulse),randomnoise,Orqueuing-typeelements.Theimplementa- tionofpoliciescanalsointroducesuddenshocks.Thesediscontinuitiescreateno

problemsforEulerintegration,wheretheratesnowdependofllyonthecurrent

stateofthesystem.Caremustbetaken,however,thatthehigher-orderintegration methodyouareusingdoesnotaverageoutthesediscontinuouschanges.Consult thedocumentationforyoursimulationso氏waretoseehowdiscontinuousevents andrandomnoisearehandledinthehigher-ordermethods.

ChoosingaT岳nleStep

Considerthefirstl0rderlinearnegativefeedbacksysteminwhichthestateofthe systemSadjuststothedesiredstateS*withanadjustmenttimeAT:

S-INTEGRAL(NCS,STD) (A113)

NCS-(Sx-S)/AT (A-14)

whereNCSisthenetchangeinthestateofthesystem･

AssumeS*-100andSt0-0･Theanalyticsolutionofthesystem,presented insection8.3,is

St-Sx-(S* -Sb)*exp(-t/AT) (A-15)

Assumetheadjustmenttimeisltimeunit.SimulatethesystemwithEulerinte- gration.Whathappenswhenthetimestepis1?Whathappenswhenitis2?How smalldoesthetimestephavetobetoglVeagoodapproximationtotheanalyticso- lution?implementtheanalyticsolutionasanauxiliaryvariableinthemodeland createavariabletocalculatethefractionalerrorbetweenthesimulatedandana-

lyticsolutions･WhenthetimesteplSSmallrelativetoAT,dotheerrorsgrowlarger orsmallerovertime?RepeattheanalystsWiththefourth-orderRunge-Kutta method.HowdoesRunge-KuttaaffectthesensitivityOfthesimulationtothetime

step?DoesitimproveontheaccuracyofEulerslgnificantlywhenthetimestep issmall?

SuMMARY

GLJicJe･L戸≦糊S紬rNum部室ca=11teq柑tion

･Selectatimestepforyourmodelthatisapowerof2,suchas2,i,0.5, 0.25,etc.

｡MakesureyourtimesteplSevenlydivisibleintotheintervalbetweendata

polntSOrOtherperiodicexogenousevents.

･Selectatimestepone-fourthtoone-tenthaslargeasthesmallesttime constantinyourmodel.

･Testforintegrationerrorbycuttlngthetimestepinhalfandrunnlngthe

modelagain･IfthereareでO.significantdifferencesOudgedrelativeto yourpurpose),thentheorlglnalvalueisfine.Ifthebehaviorchanges

Numericallntegration 911

slgnificantly,continuetocutthetimestepinhalfuntilthedifferencesin behaviornolongermatter,

NotethatEulerintegrationisalmostalwaysfineinmodelsofsocialand

humansystemswheretherearelargee汀OrSinparameters,initialconditions,

historicaldata,andespeciallymodelstructure.Testtherobustnessofyour

resultstoEulerbynlnnlngthemodelwithahigher-ordermethodsuch

asfourth-orderRunge-Kutta.Iftherearenosignificantdifferences, Eulerisfine.

Consultanumericalmethodstext,yoursoftwaremanual,oranexpert whenindoubt.

Noise

Mostvariables,suchasindustrialproduction(Figure17-1),oftenappeartobe somewhatHnoISy･HWeseepartofthebehaviorassystematic-forexample,the growthtrendandcyclicalmovementsinindustrialproduction-andpartasnoise. Whatwejudgetobeasystematicpatternofbehaviorandwhatwejudgetobe meanlnglessrandomvariationdependsonourperspectiveandpurpose.Ifthepur- poseofyourmodelweretounderstandthedeterminantsoflong-runeconomic growth,movementsinoutputotherthanthegrowthtrend,includingthebusiness cycle,mightbeconsiderednoiseandexcludedfromyouranalysis.Ifyourconcern werethebusinesscycle,yourmodelwouldexplainthesecyclicalmovements,but youmighttreatthemonth-tO-monthmovementsaroundthebusinesscycleas noise･Anevenmoredetailedmodel,however,mightexplaintheserapidvariations inoutputaspartofthefeedbackstructure.Oneperson'snoiseisanother'ssignal, dependingonthequestionsinwhicheachpersonisinterested.

Therateequationsinsystemdynamicsmodelscapturethedecision一making processesoftheagentsorthephysicalandbiologicallaws血atcausechangein systemstates.Becauseallmodelsareapproximations,themodeldecisionmlesdo notcaptureallthesourcesofchangeintheactualflows.Asexplainedinsection 4･3･2,mOiseisthelabelweapplytothatpartoftheactualdecisionstreamour modelcannotexplain･NoisemeasuresourlgnOranCe.

Forexample,productionstartsinthesupplychainmodeldevelopedinchap- ter19dependonthefirm'slaborforce,theworkweek,andlaborproductivlty:

ProductionStartRate-Labor*Workweek*LaborProductivlty (B-1)

Theworkweekandproductivltymightthemselvesbeendogenousvariables,de- pendentonfactorssuchasschedulepressure,workerexperience,andequlpment quality･Theworkweekandproductivltyrepresentaverages:Someworkersare moreproductivethanothers;someputinmorehoursthanothers.

Theactualstartratewillrarelyequaltheaveragevalue.Oneworker'sbaby kepthimupallnight,soheislessproductivetoday.Anotherdiscoversawayto speedupherwork,boostlngproductivity.Anunexpectedmachineproblemslashes

913

914 Appendixち

theproductivltyOfathird.Forsomepurposes,includingthesevariationsaddslittle

tothedynamicsandonlymakesitmoredifficulttounderstandmodelbehavior.

Inthesecases,thedeterministicdynamicsaresufficient.Often,however,un-

predictablevariationsaroundtheaveragevaluesplayacriticalroleinthedynam-

icsandmustbemodeled.Asageneralmodelingstrategyyoushouldfirst

understandthedynamicsofyourmodelwithoutnoise-evenwhennoiseisim-

portant.Theresponseofthemodeltoshockscanbeassessedthroughidealizedtest

inputsSuchasthestepfunction,pulse,ramp,andsinewave･Onceyouunderstand

howandwhythesystemrespondsasitdoesyoucanconsiderhowmorerealistic

InputsSuchasnoiseaffectthedynamics.

Variationsaroundtheaveragevalueofavariableareusuallymodeledassome

typeofrandomprocess.Noiserepresentsthosevariablesandstatesofthesystem

weeithercannotcaptureinthemodelorchoosetoomit.Therearereasonsforthe

v∬iationsinproductivltynotCapturedbythemodel,butwedon'thavetheinfor一

mationneededtocapturethemendogenously.Wedon'thaveawaytomodelwhen

aworkerwilllosesleepbecausethebabycriedallnight.

IftheunmodeledvariationsinproductivltyWereimportanttothemodelpur-

posetheformulationforproductivitycouldbemodifiedtoincluderandomvaria-

tionsaroundtheaverage,whichitselfcouldbeanendogenousorexogenous variable:

Productivlty-AverageProductivity*RandomEffectsonProductivlty (B12)

Howshouldtherandomeffectsbeformulated?Yougraphtheproductivitydata

suppliedbyyourclient(FigureB-I)andfindproductivityvariesrandomlyaround

aconstantlevel.Next,youplotthedistributionofproductivity･Thevaluesclosely

approximateanomaldistributionwithameanofaboutO･25widgets/person-hour

andastandarddeviationof0.0123widgets/person-hour,about5%ofthemean.

GiventhedatainFigureB-1youthenspecifytherandom variationsin

productivltyaS

RandomEffectsonProductivity -NORMAL(1,StandardDeviationinProductivity)

(B-3)

TheNORMAL(Mean,StandardDeviation)functiongenerates,everytimestep,a

valuedrawnrandomlyfrom anormaldistributionwiththespecifiedmeanand standarddeviation.1Yousetthemeanofthedistributionto1andthestandardde-

viationto0.05.SincetherandomInputhasamultiplicativeeffect,productivityWill

benormallydistributedwithameanof0.25andstandarddeviationofO｡0125,as observedinthedata.2

lAllsimulationsoftwarepackagesincludebuilt-infunctionstogeneraterandomvariablesin- cludingthenormalandunifわrmdistributions･Becausethepseudorandomnumbersgeneratedby anysoftwarepackagearenottrulyrandom,however,Cautionmustbe exercisedtoensurethatthey confわrmtotherequiredstatisticalproperties.SeeHellekalek(1998)･

2Thenor禦aldistributiongeneratesvaluesover卜∞,∞]sooc9asionallyproductivityasspeci- fiedinequatlOn(B13)wouldbecomenegative.ArobustformulationrequiresRandomEffectson Productivity≧0.ThiscanbeaccomplishedbytruncatlngthedistributionwithaMAXfunction･ Alternatively,therandomeffectscouldbespecifiedasalognormaldistribution･

Noise

FIGUREB-1

Hypothetical dataforlabo｢

productivity

Top:Timeseriesl Bottom:Histogram showlngthe distributionof

productivity.

520

( L n O LT u O S Ja d Jsl¢ 6

p!Jut)

^ ) !̂ !) 3 n

PO Jd

0.20

.20

.15

>t◆■

ie .10.Q 0 i_ EL.

.05

.00

0 100 200 Week 300 400 500

915

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29

Productivity

Tbyoursurprisesimulatedproductivity(Figureち-2)lookslittleliketheactual productivitydatainFigureB-1.Simulatedproductivitydoesconfわrmtothenor一 maldistributionwiththepropermeanandstandarddeviationbutitchangestoo fast,jumpingfartooquicklyfromvaluetovalue.

Theproblemissubtle.RandomnumbergeneratorssuchastheNORMAL functionyieldanewvalueeverytlmeStepandsuccessivevaluesareindependent. Historydoesn'tmatter-thevaluesthathavecomebeforehavenoeffectonthe nextvaluedrawnfromthedistribution,JustaSthelastresultonaroulettewheel hasnobearingonthenext.ThevaluesgeneratedbytheNORMAL()functionare saidtobeIID-independentlyandidenticallydistributed.Independencemeansthe nextvalueoftherandomeffectcandifferbyanyam ountfromthelastvalue.Pro- ductivltymightbeveryhighrightnow,butindependencemeansoneinstantlater itcouldbeverylow.Thetimestepforthesimulationis0.125weeks.Anewvalue forproductivlty,completelyindependentofthelast,ischoseneighttimesaweek Itisthisfrequentsamplingfromanindependentprocessthatexplainswhysimu-

latedproductivityinFigureB-2jumpsaroundfartoofast･ Engineerscalltherandom variationsgeneratedbyIIDprocessesHwhite

noise.HImaglneyouhaveJustarrivedatalivelyparty.Eachguestisspeakingina perfectlyintelligiblemanner(atleastearlyintheevening),butwhenallthese soundsreachyourearatonce,theresultisanindecipherablecacophony.Anal0- gously,youcanthinkofnoiseasthesumoftonesofallfrequencies,fromthe

916

FlGUREB12 Simulatedlabor

productivity

Top:TimeseriesI Bottom:Histogram showlngthe probabHity distributionof simulated

productivity, generatedby equation(B-3).

AppendixB

520

で

no LT u O S Ja d JSt

a 6p !N t)

^ )!̂ !p

np oA

0.20

.20

.15

>ヽ ≡ .a B .10 0ゝ ■■■

亡L

.05

.00

0 100 200 Week 300 400 500

0.20 0.21 0.22 0.23 0,24 0.25 0.26 0.27 0E28 0.29

Productivity

deepestbassnotetothehighesthighC.Becausewhitenoisecontainsallfrequen- ciesinequalmeasureitscurrentvaluecontainsnoinfomationaboutfuturevalues, eveninthenextinstant.

Whileconvenientstatistically,thewhitenoiseassumptlOnOfindependence doesnotholdintherealworld.Realsystemshaveinertia.Productivlty,Customer demand,theweather,andallotherrealquantitiescannotchangeinfinitelyfast. Supposeamachinebreaksdown,lowerlngprOductivlty･Productivltyremainsde- pressedatleastuntilthemachinecanberepaired.Theeffectsoftherandomshock persistforsomeperiodoftime.Similarpersistenceapplies,tovarylngdegrees,to allcausesofvariationsinproductivltyandtoallvariationsinanyquantlty･The temperaturein1hourobviouslycan'tbetoodifferentfromthetemperaturenow. Similarly,thetemperaturetomorrow,thenextday,andaweekfromnowallde- pend,partially,onthetemperaturetoday.Temperaturechangesonlyslowlybe- causeitdependsonthequantltyOfheatintheair,astockthat,thatlikeallstocks, Changesonlygraduallyasitaccumulatesitsinflowsandoutflows･Similarly,the stockandflOwstructureofallrealprocessesgivesthemacertainamountofin- ertia.Consequently,realnoiseprocessesdon'tcontainallfrequenciesinequal measure.Thestrengthofthehighfrequenciesdiminishesabovesomepolnt,Just asaloudspeakercannotgeneratesoundatfrequencieshigherthan,say,20,000 cycles/second(Hertz)becausetheinertiaofthemechanicalelementsinthespeaker limitshowfastitcanvibrate.

Noise

FIGUREB- 3

Pinknoise: structure

917

Mean NoiseSeed

Itisthereforenecessarytomodelnoiseasaprocesswithinertia,ormemory-

asaprocessinwhichthenextvalueisnotindependentofthelastbutdependsin

somefashiononhistory･Realisticnc･iseprocesseswithpersistencearetermed

"pinknoise."Comparedtowhitenoise,whichcontainsallfrequenciesinequal

measure,pinknoisefiltersoutthehighfrequenciesattheblueendofthespectrum,

leavlngmoreOfthereddishfrequencies.Thechallengeistofわrmulateasimple

modelofrandomnessthatallowsthemodelertospecifythedegreeofpersistence,

orequivalently,thepowerspectrum ofthenoise(roughly,theamplitudeor

strengthofeachfrequency).3Thestatisticalpropertiesoftheresultingnoiseshould alsobeinsensitivetothechoiceofthetimestep(withinbroadlimits).

Theinertiainrealvarlablesimpliestheexistenceofatleastonestockinany

noisegeneratingProcess.Asimpleformulationforpinknoisebeginswithwhite

noise,thensmoothsituslngsometypeOfinformationdelay.Theinformationde-

layrepresentsthesourcesofinertiainthenoisegeneratlngprocess.Thesimplest

formulationisfirst10rderexponentialsmoothing.Asdescribedinchapter11,first-

orderexponentialsmoothingmeansthecurrentvalueistheexponentiallyweighted sumofallpastvaluesoftheinput.FigureBl3showsthestructureforfirst-order

pinknoise,alsoknownasfirst-orderautocorrelatednoise.

3ThepowerofanyslgnalistheenergyltCOntainspertimeintervalandistheintegralofthe squaredsignal･Thepowerspectrumisthedistributionofthetotalpowerbyfrequency.Purewhite noisecontainsconstantpowerinallfrequencyrangesIThepowercontainedintherangefrom1Hz to2Hzisthesameasthatintherangefrom1001to1002Hz･Sincewhitenoisespansallfrequen- ciesfrom0to∞,itcontainsinfinitepower,animpossibility･Allrealprocesseshavefimitepower,

meanlngthepowerperfrequencylnterValmusteventuallyfalltozeroasthefrequencyrises. AfrequencydomainanalysisdecomposesatimeSeriesintosinewavesofdifferentfrequencies andphasesIFrequencydomaintoolssuchasFourleranalystsmeasurethepowerineachfrequency inanytlmeSeries;othermethodssuchasautoco汀elationandcross-correlationfunctions,ARIMA models,andvectorautoregressivemodelshelpmodelersunderstandthewaycurrentvaluesofa timeseriesdependonitsownpastvaluesandpossiblythepastvaluesofothervariables.Warmer (1998)providesanelementarytreatmentofspectralanalysis;GrangerandNewbold(1977) provideamoremathematicalapproachcoverlngfrequencyandtimedomainmethods.See alsoFranses(1998).

918 AppendixB

Pinknoiseisformedbyfirst-orderexponentialsmoothingofawhitenoisein-

put.Thedelaytimeisthecorrelationtimeconstant:

PinkNoise-INTEGRAL(ChangeinPinkNoise,Mean) (B14)

ChangeinPinkNoise-(WhiteNoise-PinkNoise)/CorrelationTime (B-5)

ThewhitenoiseInputisconstructedfromauniformdistributionontheinterval

卜0.5,0.5],sampledeverytimestepoflengthdt.4Theuserspecifiesthemeanand

standarddeviationofthepinknoiseprocess,whichdeterminesthemeanandstan-

darddeviationofthewhitenoiseinput:

whiteNoise-Mean+StandardDeviation*[(24*CoⅠTelationTime/dt)05] *UNIFORM(-0.5,0.5,NoiseSeed)

(B-6)

wheretheUNIFORM(Min,Max,Seed)functiongeneratesasequenceofvalues

drawnfromauniformdistributionontheintervallMin,Max].Theuseralsospec-

ifiesthenoiseseed.Byfixingthenoiseseed,everysimulationwillgenerateex-

actlythesamesequenceofrandomvalues,facilitatlngCOmParisonofsimulations

withdifferentpoliciesandparameters.Changingthenoiseseedchangestherea1-

izationsoftherandomprocessbutnotitsstatisticalproperties･Thescalingfactor

(24*CorrelationTime/dt)05adjuststheamplitudeofthewhitenoisesothatthe

standarddeviationofthepinknoiseoutputequalsthespecifiedvalue･5 Incontinuoustime,noisecanincludeallfrequencies.Sincesimulationspro-

ceedbydiscretetimesteps,thehighestfrequencylnanymodelvariableistwice

thetimestepdt(tocompleteonecycleofup-down-uprequiresaminimumoftwo

timesteps).Exponentialsmoothingattenuateshighfrequencies･Itisknownasa

lowpassfilterbecauseitletslowfrequenciespassessentiallyfullstrengthbutpro-

gressivelyattenuatescycleperiodsnearorshorterthanthetimeconstant･The

longerthecorrelationtime,thegreatertheattenuationatany丘.equency･Thus,the

longerthecorrelationtimeconstant,thelargertheamplitudeofthewhitenoise

mustbe.Thelessfrequentlyrandomvaluesaresampled(thelargerdt),thesmaller

4ThisformulationforpinknoiseassllmeSthemodelissolvedbyEulerintegration(appendixA)･ Higher-orderintegrationmethodssuchasRunge-Kuttachangethepowerspectrumandotherprop- ertiesofnoiseandshouldgenerallybeavoidedinmodelswithrandomdisturbances･

5Thepinknoiseformulationgivenheresmoothsa.umformlydistributedwhitenoisestream･ Nevertheless,thedistributionoftheresultingpinknoiseisasymptotical1ynormal･Analternate formulationsmoothsanormallydistributedwhitenoiseslgnaltoyieldpinknoisethatisalways Gaussian:

WhiteNoise-M+ ls2*g# ]05

*NORMAL(0,1,NoiseSeed) (B-6′)

whereMisthemean,Sisthestandarddeviation,T｡isthecorrelationtimeconsta叫and NORMAL(0,1,NoiseSeed)generatesaGaussiandistributionwithmean0andvariance L

Thestructureofthisalternatepinknoiseformulationisthesameastheoneabove;theonly differenceisthedistributionofthewhitenoiseandtheresultingscalingfactortoensurethepink noisehasthespecifiedstandarddeviation.(Youcaneasilyderivethescalingfactorsforeachfor- mulationbyexpandingtheEulerintegrationforthepinknoisevariableastheweightedsumofthe whitenoiseattimet,t-dt,t-2dt,etc.).Ifyouhadstrongdatashowingtheunconditionaldistri-

butionofno.isFinaprocesstobeGaussian,theformulatiopiヮequation(B-6')wouldbepreferable･ Ⅰnpractice,1tlSunlikelythedatawouldallowyoutodiscrlmlnatebetweenthetwoforms･

Noise 919

theamplitudeofthewhitenoisemustbe,becauselessfrequentsamplingmeans

thepowerinthewhitenoiseisconcentratedinlowerfrequenciesthatarenotat-

tenuatedbythesmoothingprocess.

Thecorrelationtimeconstantcapturesthedegreeofinertiainthenoise

process.Infirstl0rderpinknoisethecorrelationbetweencurrentandpastvalues

decaysexponentiallywithatimeconstantequaltothecorrelationtime･6

ThedatashowninFigureB-1weregeneratedbythepinknoisestructurewith

astandarddeviationof5%,correlationtimeconstantof4weeks,andtimestepof 0.125weeks.

ComparingFiguresB-1andB- 2 itisclearthatthe(unconditional)distribu-

tionsofthetwonoiseInputsareaboutthesame.Thepinknoisestructuregenerates

adistributionthatisessentiallynormal,withthespecifiedmeanandstandardde-

viation(thereportedmeanandstandarddeviationdifferslightlyfromthespecified

valuesbecausethesampleofdataisfinite).However,successivevaluesofpink

noisearecorrelatedwithpastvalues,sothepinknoiseprocessdoesnotchangeas

rapidlyastheindependent,uncorrelatedvaluesgeneratedbythenormaldistribu-

tioninequation(ち-3).

Doesitmatter?Yes.Noiseconsistsofsignalsofvarious丘.equenciesandam-

plitudes.Dynamicsystemsactasfilters,Selectivelyattenuatingsomefrequencies

whileamplifyingothers.Manysystemsresonatestronglyatcertainfrequencies･If thenoisecontainssignificantpowerneartheresonantfrequency,thesystemwill

nuctuate,sometimesviolently.TheTacomaNarrowsbridge,inthestateofWashl

1ngtOn,Vividlydemonstratedthepowerofasystemtoamplifyrandomnoise.Built

in1940,peopleimmediatelynoticeditstendencytoswlnglnevenlightwinds.On

November7,thebridge,drivenbymodestwindsofabout40milesperhour,began

tooscillatethroughhugeswings.Afewhourslateritcollapsed･Unknowntothe

designers,thesuspensionspanhadastrongresonancenearthefrequenciesinthe

vorticescreatedasthewindpassedaroundit･Anewspanwasbuiltonthesame

towers,butthistimestiffenedsoitsresonancepeakwassmallerandfarfromthe

frequenciescreatedbythewind.Itstillstandstoday.Similarresonancephenom-

enaariseinsocialandeconomicsystems,asillustratedbythesupplychainmod-

elslnchapters17-20:Smallrandomvariationsincustomerordersinducelarge

fluctuationsinproductionnearthenaturalfrequencyofeachsystem･

Tbillustrate,FigureB-4andTableB-1comparesimulationsoftheinventory-

workforcemodeldevelopedinchapter19WiththetwonoiseInputsinFigures B-1andB-2.7Inbothsimulations,customerordersareconstantandtherandom

60ccasionallydataanalysisWillshowthattheautocorrelationfunctionisnotwellapproximated byexponentialdecay.Inthesecases,higher-orderpinknoiseformulationsmaybeused,formedby

cascadingseveralfirst10rderpinknoisedelaysinseries(seechapter1l).Thestandarddeviation?of eachstagemustbescaledapproprlatelysotheoutputhastheproperstandarddeviation･Inpractice,

itisrarelynecessarytousehigher-ordernoiseprocesses.ComplexautocoITelationsandcross- correlationsamongtheexogenousrandomeffectsinyourmodelsuggestthereisslgnificantfeed- backandstockandnowstructureyoushouldprobablybemodelingexplicitlyandendogenously･

7Themodelusedinthisappendixisidenticaltotheinventory-workforcemodeldevelopedin chapter19exceptthatexpectedproductivlty,usedin仙 edete-inationofdesiredlabor,ismodeled asafirst-orderinfわrmationdelayofactualproductivltyWithatimeconstantof13weeks･

920

FIGUREB-4

Responseof inventory- workforcemode一 towhiteand

pinknoise

Thesystemres-

onatesnearits

natura=requency whendrivenby noise.Thenoise

lnPutinbothcases hasastandard deviationof5%,

MostoHhepower inwhitenoiseis containedinthe

highfrequencies, whichareattenu-

atedbythesys- tem,Pinknoise containsmore

powernearthe system'snatu｢al frequency,causlng largecycles.

■l

AppendixB

t2a∈ 0 1 0!lt 2))

)̂oiua ûI

〝㌔ ′～＼＼. PinkNoiseJnputヘ A---/ト㌔㌔

＼ WhiteNoise

0 100 200 Week300 400 500

variationsinproductivltyaretheonlyperturbationsdisturbingthesystem.

Bothnoisestreamshavethesamestandarddeviationanddistribution･Theonly differenceisthedegreeofautocorrelation.Thepinknoisesignalhasacorrel a-

tiontimeconstantof4weeks,whilethewhitenoisesignalisindependent(no autocorrelation).

Theresponseoftheproductionsystemtothetwonoisestreamsisverydiffer-

ent｡Verylittlehappenswhenthesystemisperturbedbywhitenoise.Thereare

smallvariationsininventories,theworkforce,andothervariables,butthesystem attenuatesnearlyallofthenoisebecausemostofthepowerisconcentratedinthe

highfrequencies･TheindependentvariationsinproductivltyCauselargechanges inproductionstartsfromdttodt･Sincedtis1/8week,thismeansproductionstarts varywidelyfromdaytoday.LowoutputtodaylSmOrethanlikelytobeoffsetby higherthannormalvalueswithinafewdays.Inventoryabsorbsmostoftheshort- termvariationsandthereislittleneedforthefirmtoalteritsworkforce.

Pinknoise,however,meansthatwhenoutputislowtodayitislikelytoremain

lowforafewweeks･Duringthistime,inventoriescanfallsignificantly,forcingthe firmtohireworkerstoexpandoutputandtriggerlngthesystem'Slatentoscillatory responsetoshocks･ThevariationsinproductivltyaretooSlowtobeabsorbedby

inventoryorfilteredoutbythehiringdelays.Thenoisecontainssignificantpower nearthesystem'snaturalfrequencyofabout1year.Consequently,thesystemres- onatesstrongly-thestandarddeviationofproductionstartsis7.6%ofthemean, eventhoughthestandarddeviationofthenoiseInputisonly5%.

TableBllShowsthestandarddeviationasafractionofthemeanvalueforkey variablesinboththewhitenoisecaseandthepinknoisecase.Underwhitenoise, thesystemstronglyattenuatestherandomshocks.Thestandarddeviationofin-

ventorylSlessthan2%,Showinghowinventorybuffersthesystemfromthehigh frequencyvariationsinproductionstartscausedbythewhitenoise.Thestandard

deviationsofproduction,inventory,andlaborareallmuchlessthanthatofpro- ductivity･OnlythehiringrateamplifiesthewhitenoiseInput.

Undercorrelatednoise,however,inventory,workforce,andotherkeyvari- ablesallfluctuatebymorethanthevariationinproductivity.Thestandarddevia- tionofhiringlSSixtimesgreaterthanwhenthesystemisdrivenbywhitenoiseand

13timesgreaterthanthestandarddeviationinproductivlty.

921

TABLEら-1 Autocorrelated noisealtersthe

amplification generatedby asystem.

Standard Standard

Deviation/Mean Deviation/Mean

PinkNoise WhiteNoise 0EGaR

ProductionStar.ts Ol0760 0.051l

Production 0.0547 0.0087

1nventory 0.1055 0･0160 Labor 0.0591 0.0085

HiringRate 0.6539 0,1097

Variousstatisticaltoolscanhelpyouestimatetheautocorrelationtimecon-

stant,ifsufficientdataareavailable.Mostregressionandtimesseriessoftware

packagesreadilycomputetheautocorrelationfunction,showingthecorrelationbe-

tweenthecurrentvalueofthevariableanditsvaluesateachintervalinthepast.

Fromtheautocorrelationfunctionyoucanestimatethetimeconstantforthepink

noisefunction.Ifnumericaldataareunavailable,useyourbestjudgmentandcon-

ductextensivesensitivltytests.

Tbillustrate,01iva(1996)developedamodelofabank'sretailloanoperation

toexplorethedeterminantsofservicequality(chapters14and21).Customerde一

mandandworkerabsenteeism,twoimportantlnputStOthemodel,bothexhibited

smallvariationsaroundtheiraverages(thestandarddeviationswerelessthan4%

ofthemeans).TbmodeltheserandomvariationsOlivaestimatedtheautocorrela-

tionfunctionsforeach,foldingacorrelationtimeconstantofabout2Weeksforab- senteeismandabout1weekfわrorders.Thatis,customerordersthisweekwere

weaklydependentonorderslastweek,butabsenteeismtendedtopersistforlonger

periods.01ivaalsofoundthattherandom variationsinordersandabsenteeism

wereindependentofeachother,Soeachcouldbemodeledasaseparatepinknoise

process･801ivawasthenabletosimulatetheeffectsofvariouspoliciesaffecting

seⅣicequalitywhilethemodelsystemwasperturbedwithrealisticpatternsofor- dersandabsenteeism.

Withoutrandomnoisetheloancenterremainedinequilibriumwithdemand

andcapacltyinbalanceandconstantservicequality･However,whenrealisticran-

dom variationsindemandandtheworkforcewereaddedtothemodel,quality

standardstendedtoerodeovertime,evenwhencapacltyWasSufficienttomeetde-

mandonaverageandeventhoughtherandom shocksweresmall.Therandom

8Sometimesdifferentnoiseprocessesarenotindependentbutarecross-correlated･Forexample, unpredictableshort-runvariationsininterestratesmightbecorrelatedwit壬lrandomshocksincom-

plOditypricesIItisasimplemattertoincorp.oratesuchcrossICOrrelations(e.g.,theshocksperturb-

ingaVariablecanbemodeledasanapproprlatelyweightedsumofvariable-Specificnoiseandthe noisewithwhichitiscorrelated).Multivariatetimeseriestoolssuchasvectorautoregressivemod- elsandcrossISPeCtralanalysISCanhelpyouidentifythecorrelationalstructureamongthevariables andtheirhistories(seethereferencesinnote3).However,acomplicatedsetofcrossICO rrelations suggeststhereisimportantfeedbackstructureyoushouldprobablybemodelingexplicitly.Agood modelgeneratesthevariances,autocorrelations,andcross-correlationsobservedintherealsystem withoutbeingforcedbytoomanyexogenousInputs.

922 AppendixB

variationsindemandandcapacltymeantthebankoccasionallyfounditselfshort ofcapacity.Loancenterpersonnelrespondedbyspendinglesstimewitheachcus- tomersotheycouldclearthebacklogofworkeachday･Thesereductionsintime percustomergraduallybecameembeddedinworkernorms.Managementinter pretedthereductionintimepercustomerasimprovementsinproductivltyCatlSed bytheirget-toughmanagementpolicies,unawarethatspendinglesstimewithcus- tomersreducedservicequality,eventuallyfeedingbackthrough customerdefec- tionstootherbanks.01ivafoundthatreducingthetimespentpercustomercaused asignificantreductioninthevalueofloansissued,directlyreducingbankrevenue. Lowerrevenuesthenfedbacktofinancialpressureleadingtostaffreductionsand stillmorepressuretospendlesstimeoneachcustomer･Theresultingpositive feedback,ifunchecked,couldactasadeathspiralfortheorganization.Small,ran- domvariationsincapacltyandorderselicitedthelatentself-reinforclngquality erosioncreatedbythepoliciesofthebankandthebehaviorofitsworkersand managerS･

ExpFormgNoise

Usetheinventory-workforcemodelandpinknoisestructuretoexplorethesensi- tivityOfmodelbehaviortothenoisecorrelationtimeandsimulationtimestep.

1.Figureち-4andTableB-1showthatincreaslngthenoisecorrelationtime from0(thewhitenoisecase)to4Weeksincreasestheoscillatoryresponseofthe inventory-workforcemodel.Explorehowthesystemrespondstoevenlonger correlationtimes.Doestheamplitudeoftheproductioncyclecontinueto increase?Whathappensifthecorrelationtimeisverylong?Why?

2.Inallthesimulationsabovethetimestepwas0.125weeks.Explorehowthe behaviorofpinknoiseandoftheinventory-workforcemodeldependonthetime step.Canyoucorrecttheproblemscausedbyrapidchangesinwhitenoiseby uslngalongertimestep?Why/whynot?

3.Sofaronlyonesourceofnoisehasbeenconsidered.Doesthebehaviorof themodelchangeifyoualsoassumecustomerordersv∬yrandomly?Assume customerordersvaryrandomlywithasmallstandarddeviationaroundaconstant average｡Alsoassumeproductivltyandordersareindependentofoneanother. Assumetostartthatthecorrelationtimeforordersis13weeks(one-quarteryear) butconductsensitivityteStS･Howdoestheinclusionofmultiplesourcesofnoise alterthebehaviorofthemodel?Doesitalteranyofthepolicyconclusionsyou reachedinchapter19regardingwaystoimprovethestabilityofthesystem? Explain.

Noise

SuMMARY

923

Guide一inesfortheUseotNoise

｡Itisusuallybesttoomitnoiseuntilyouunderstandthedynamicsgenerated bythefeedbackstructureofyourmodel.UseidealizedtestInputsSuchas thestep,pulse,ramp,andsinewavetodevelopyourunderstandingofthe

system'sresponsetoshocks,thenaddmorerealisticlnputSSuchasnoise orhistoricaldataasnecessary.

｡Afteryouunderstandthedynamicsofyourmodel,askyourselfwhether randomvariationsintheenvironmentarelikelytobeimportant.Ifso, youmustaddrandomvariationsatkeypolntS.Youshouldtesttheeffects

ofrandomvariationsonyourconclusionsandpolicyrecommendations evenifyouthinktheyprobablywon'tmatter.Iftheydon'tmatter,you canomitthem.

･InprlnCiple,effectsoutsidetheboundaryofyourmodelcanperturbevery variable.Allparametersarecandidatesfortheinclusionofsometype ofnoise,andthereportedvaluesofallstatevariablesincludesome measurementerror.Youdonotneedtoincludenoiseineveryvariable

andparameter.Decidewhicharethemostimportantsourcesofrandom variationtoinclude.Importantsourceswillbethoseparametersthat arebothvariableintherealsystemandwhosevariationmatterstothe

dynamics.Thereisnopolntinincludingnoiseinaparameterthathas littleimpactonthebehaviorofthemodel.

｡Allrealnoisesourceshaveinertiaandattenuatehighfrequencies.Neveruse

whitenoiseinyourmodels.Usethepinknoisestructuretomodelrandom shocks.Estimatethedistribution,standarddeviation,andco汀elationtime

constantfromthedata.Useyourbestjudgmentwhennumericaldataare notavailable.

｡Ifyouhavemultiplesourcesofnoiseinyourmodel,considerwhether theyareindependentorcorrelated.Independenceisconvenientbutnot alwaysaccurate.Usetheavailabledatatoestimatethecross-correlations

ofmultiplenoiseInputs.

｡Besureyourresultsarenotsensitivetothechoiceoftimestep.Aswithany

structure,thetimestepshouldbesmallrelativetothesmallesttimeconstant inthemodel,includingthecorrelationtimeforanypinknoiseprocesses (seeappendixA).

･Youcancomparedifferentsensitivityandpolicytestsinmodelswith randomeffectsbyusingthesamenoiseseedineachsimulation.Sincethe

924 AppendixB

sequenceofrandomshockswillbeexactlythesameineachsimulationwith thesamenoiseseeds,anydifferencesamongthemmustbeduetoyour

policyorparameterchanges.

｡WhenuslngrandomInputsbesuretorunyourmodellongenough,or

enoughtimes,toensureyourresultsarenotcontlngentOntheparticular realizationsoftherandomprocesses･Calculatethedistributionsofthe variablesoverlongtlmePeriodsoroveralargesampleofsimulations. Don'tassumeanyonesimulationisrepresentativeofall.

｡Aswithanymodel,conductextensivesensitivltyteststObesureyou assesstherobustnessofyourresultstoplausiblevariationsinassumptlOnS,

includingassumptlOnSaboutthestatisticalpropertiesofanynoiselnputS.

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Imdex

Aarts,E.,615n

Abdel-Hamid,T.,65n,490n

Abelson,良.,16

AcceleratingChange,3-4 Accumulation

creatingdelays,237

creatlnglnertia,235 notationfor,195

Achi,Z.,382

AcqulSitionlag,675-676

AcqulSltlOnrate,671-673

Activeadopters,340

Activities,aggregatlng,213-217

Actual/perceivedconditions,156-157

Acuteinfections;seeSIRmodelofepidemics

Adams,Henry,3-4

Adaptation,22

AdaptlVeexpectations,657

inforecasting,632

ininformationdelay,428-432

Add-factorlng,654,857

Additiveeffects,5291530

Adjustment

inforecastlng,649-653

toagoal,523-524

Adjustmentrateformulation,524

Adjustmenttime,276-277,279-280

Adverseselection,174-177

Advertisingbudgets,365 Aftalion,Albert,697,787n

Agent-basedmodeling,896

Agestructures inChina,480-481

oforganizations,485-490

Aggregatedemand,718-719

Aggregation

example,218-221

guidelinesfor,2161217

parallelactivities,217

instockandflowmapplng,213-216

Agingchains

agestructureoforganizations,485-490

examples

populationandinfrastructure,472-474

populationpyramid,474-480

generalstructure,470-472

integratedwithcoflows,5091511

formodelingstockandflowstructure,470

andpopulationinertia,480-481 instockandflOwnetworks,469-470

worldpopulationandeconomicdevelopment, 481-485

Aircra氏orders,796

Airpollution,delaysinresponseto,446 AirPollutionControlAct,446

947

948 Index

Akerlof,G.,174-175

Aldrich,∫.,395

Alfeld,L.,122n,474

Allison,∫.,864

AmalgamatedCopper,376

Amazon.com,366

Ambiguity,25-26 AMD,374

Amdahl,373

AmericanSmeltingandRefining,376

Amplification

inmanufacturingSupplychain,734

insupplychains,664-666

Amplificationratio,673

AnalytlCalfunctionsversustablefunctions, 562-563

Analyticalintegrationoffluctuation,238

Anchoring

andadjustment,534

inforecastlng,6491653

AnchorpolntS,586 Andersen,D.,864,889,899

Anderson,Ed,359n

Anderson,R.,321n,855-856

Ando,A｡,632n

Angell,∫.,243

AnnalsofAddiction,260

Apollo15moonwalk,848

Argote,L.,338

Argyris,Chris,16,18,32-33,86n,157

Armstrong,∫.,432

Arrow,Kenneth,370n

Arthur,Brian,356,363,387

Asch,S.,654

AsphaltNation(Kay),178n

AtariCorporation,125 Atkinson,良.,442,903 Attention

managlng,601

selectiveperceptlOn,599-600

Attenuation,inforecastlng,646 Attractor,351

Attritionrateoflabor,758-759

AuctionprlClng,813

Autocorrelation,867

Autocorrelationfunction,919n

Autocorrelationtimeconstant,921

AutoleaslngStrategy,42-55

dynamichypothesis,44-48

elaboratlngmodel,48-50

impactandfollow-up,54-55

policyanalysis,51-54

Automatedextremeconditionstesting,897

Automatedhelp,897-898

AutomatedmapplngOfparameterspace,897 AutomatedNonlinearTest,887

Automatedsensitivltyanalysistools,884,897

Automobileindustry market,45

recyclingprogram,225-229

instockandflowmap,2221223

AutomotiveNews,54

AutoNation,42

Auxiliaryhypothesis,848-849

Auxiliaryvariables,202-204

Averagecost,834-835

Averageresidencetime,413 Axelrod,良.,16,28

Axtell,良.,520

Ayer,A.J.,846

AZTdrug,319

Backus,G.,93n

Bahn,P.,125,126,127n

Bakalar,J"261

Baker,Howard,516

BakerCriterion,5161518,584n,620,807,814

Bakken,B.,706

Balancedequilibrium,716-718

Balancingfeedback,13

Balanclngloops,1421143 Barabba,Vince,43,48

Barlas,Y.,858,879

Basinofattraction,351

Bass,Frank,324n,330,332n

Index

Bassdiffusionmodel,332-339,88ト882

behaviorof,334

extending,335-339

phaseplot,3331334

Bassekh,F.,436n

Baum,S.,866

Becker,Gary,516

Beck血ard,R.,86m

BeerDistributionGame,21,34,74,130,131,

132-133,454

0rlglnOfoscillationsand,684-694

Behavior;SeealsoModelinghumanbehavior

arislngfromsystemstructure,28129

modelsof,38

modesindynamicsystems,107

Behavioraldecisiontheory,600

Behavioranomalytests,860,880-881

Behaviormodesensitivity,562

Behaviorreproductiontests,860,874-880

Behaviorsensitivity,883

Behrens,W,574,873

Beliefupdating,428-430,431-132

Belitz,K.,847,849

Bell,∫.,847

Benchmarkingstudy,66

Bemdt,E.,867n

Bessler,D.,447,643-644

Bestcasesensitivltyanalysis,885-886

Betamax,359-364,384,387,392-396,399,403

Beyer,Damon,743n

Bias,Len,260

Biases,30-32

Biasinforecastlng,646

Bigbangtheory,849

BiologicalWeaponsConventionof1972,310

Birthrates,111,286

causalloopnotation,138-140

anddemographictransition,481A85

andpopulationpyramid,479-480

Romanianpolicy,6-7

Blackboxmodeling,80

Blinder,Alan,787n

Bloss,∫.,262m

BlueCross/BlueShield,176-177

Boggs,Wade,31

Bomberger,W,646n

BostonGlobe,176,177

Bottlenecks,7531754

Bottom-upforecasts,453

Boulding,Kenneth,38

Boundaryadequacytests,859,861-863

Boundedrationality,26127,597

indecisionmaking,598-599

individual/organizationalresponsesto, 601-603

inTRENDfunction,638

BovineSpongiformEncephalopathy,312, 314-316

Box,G.,867n

Boyer,C.,847n Braess'Law,184

Braitberg,Karl,449n,454,460

Brandloyalty,48

Brandt,∫.,447,643-644

Breakdownrates,68-71

Brehmer,B.,27,28,694

BritishPetroleum,77-79

BritishRoyalNavy,19

Brown,G.,900

Brown,L.,124

Browndwarves,849

Bruckman,G.,32,90,485n

Bruner,∫.,24

Bubonicplague,300,301,312

Buchanan,∫.,386

Buffers,197

Bull,M.,93n

Bunn,D.,93n

Burchill,G.,158n

Burden,良.,903

Burns,Robert,5

Burr,Aaron,409

Businesscycles,132,757

emplricalassessment,782n

failuretoaccountfortimedelays,697

indicators,115-116

949

950 Index

Businesscycles-(Cont.)

inventor y-workforceinteractions,782-788 inrealestatemarket,698-707

simulation,784

theoriesof,785-788

calculus,232-233

Calibration,897

Camerer,C.,599

Capacitateddelay,554,558

Capacity,555

CapacltyaCqulSltlOn,609-615

cancelingordersfor,8321833

anddesiredcapacity,807-810

ingenericcommoditymarketmodel,798-800

pulpandpaperindustry,826

Capacltyutilization,116,608-609

feedbackofinventoryto,835-836

genericcommoditymarketmodel,798-800, 802-805

livestockindustry,836-840

productioncapacity,805-807

pulpandpaperindustry,824-828

Capacltyutilizationformulation,552-562

CapitalCities/ABC,376

Capitalinvestment

inmacroeconomy,438-445

andstockmanagement,680-682

Capitalpunishment,880

Capitalstock,optlmumlevel,807-810 Carbondioxideconcentrations,242-249

Carbone,R.,632

Cardella,Tbny,66n,73 Carlson,∫.,646n

CarMax,42

Carnegie,Andrew,375

Carroll,J"76

CarrylngCaPaClty,118-121

approachofpopulationto,296-297 EasterIsland,125-127

0vershootandcollapse,123-127

Cartwright,Nancy,845,855n

Caskey,∫.,646n,649,654

Categorykillers,369

Causalattributions,28

Causallinks,138-141

delaysin,150-152

supportedbydata,158

Causalloopdiagrams,13,102,107 alternateconventionfor,140-141

developlngthediagrams,163-166

energydemandexample,150-152

0fexponentialgrowth,109

guidelines

actualversusperceivedconditions, 156-157

causationversuscorrelation,14ト142

delaysincausallinks,150-152

determinlnglooppolarity,143-147

explicitnegativeloops,155-156

graphicdesignprlnCiples,153 1ntermediatelinks,154-155

1abelinglooppolarity,142-143

mamlngloops,148-149

rightlevelofaggregation,154 variablenames,152-153

identifyingkeyvariables,160 iⅣtbenstructure,152

interviewdata,157-159

leadingtopolicyresistance,177-190 limitationsof,166-168,191

marketstructure,169-177

notation,137-141

problemdefinition,159-160 referencemodes,1601163

withstocksandflows,210-213

usesof,137

variables,138-141

Causalpathways,146-147

Causation,141-142 Causeandeffect

incomplexsystems,189-190 feedbackview,10112

linearapproachto,10-12 inmentalmodels,28,91

nonlinearity,22

Cavaleri,S.,889

Ⅰndex

Ceausescu,Nicolau, 6,7

CentrallntelligenceAgency,250

Cervantes,Miguelde,409

Challengerexplosion,273 Chaos,114

chaoticoscillation,132-133

dampedoscillations,129-130

expandingoscillations,130-132

limitcycles,130-132

localstability,129-130

Chaoticdynamics,115n Checkland,P.,36

Cheng,P.,16

Chertow,G.,414n

Chicagorealestatecycle,698-699

China,agestructure,480-181

Chlorofluorocarbons,24-25

ChryslerCorporation,54,384

ChryslerCreditCorporation,47 Churchill,Winston,137

Churchman,C.West,850

Cicerone,氏.,24

Circadianrhythms,131 Ciark,K.,390,508

ClarkUSA,78

Clausewitz,KarlYon,89

CleanAirAct,446

Clientneeds,84-85

Cline,H.,900

Clinton,Bill,310

Cobb,∫.,23

Cobb-Douglasproductionfunction,544

Cobwebmodelofcommoditycycles,798n Coca-Cola,261

Cocaineuse/abuse,250-262

Coe任icientofdetemination,874-880 Coflows

attributesofstocks,4971511

genericstructure,503

integratedwithagingchains,509-511 nonconservedflows,504-505

instockandflOwnetworks,469

Cognitivedissonance,168

CognltlVelimitations,599-600

951

Cognltivemaps,28-29 Cohen,J.,119n,320

Collins,H.,855n

Combinatorialcomplexity,21

Commoditycycles,792-798

cattlecycle,794

classicaltheoryof,798n

copper,795

genericmodel,798-824

hogcycle,799 livestockmarket,836-840

policyanalysis,840-841

0fproductionandprice,791

pulpandpaperindustry,824-828

Commoditypricefbrecastlng,643-645

Companies

deathspiral,378 marketvalue,379

modelingembeddedin,84-85

Companytowns,374-375

CompaqComputer,383

Comparativeadvantage,8621863

Compensatingfeedback,181-185

sourceofpolicyresistance,189-190

Compensationplans,377-378

Complementarygoods,3701371

Complexsystems;seealsoDynamicsystems

applicationsofsystemdynamics,4ト79

causalloopdiagram sfor,1371190

causesofpolicyresistance,10-12

delaysassourceofdynamics,403

dysfunctionin,29 ex仕emeconditions,519

1eamlngabout,4-5 andlimitedinformation,23125

modesofbehavior,263-264

multiplefeedbacks,28

pathdependencein,349-353

andpolicyresistance,5-10

rangeoffeedbacks,10112

reasonsfordynamicscomplexity,21123

requlrementSforsuccessfullearnlngin,33139

theoryof,895-896

Compoundinterest,108-109

952 Index

Comprehensivesensitivityanalysis,884-885

Computerindustry,390-391

Concurrentenglneerlngpractices,60n Confidencebounds,884

Confoundingvariables,25126

CongressionalBudgetOffice,862

Conlisk,J.,598

ConsolidatedTobacco,376

Constants,202

Constructiondelays,423-124

ConsumerBankingAssociation,54

ConsumerPriceIndex,7-8,636-637,645-654 Consumers

activeadopters,340

earlyadopters,324

evaluationoftechnology,388-389

formeradopters,340

andlifecycleofdurableproducts,345-346 networkeffects,400-402

ConsumptlOnmultiplier,718

Continulngeducation,900-901 Continuousdivisibleflows,2071208

Continuoustime,206-207

Cooley,R.,320

Cooper,Ken,55n,56,57,58159,62,64,65n

Copemicanastronomy,848-849

Copernicus,N｡,849

CopperprlCeSandproduction,795

Corporategrowth

ambitionsandaspirations,380-382

andcostofcapital,378-379

creatlngSynergylbr,382-385

fromdiffTerentiation,371-373

marketgrowthmodel,607-628

andmarketpower,374-375

bymergersandacqulSltlOnS,374-376 networkeffects,370-371

mewproductdevelopment,372-374

frompositivefeedback,3641385

prlCeandproductioncosts,368-370

fromproductawareness,365-367

mlesofthegame,380

supplychainreenglneenng,743-755

unitdevelopmentcosts,367-368

workforcequalityandloyalty,376-378

Corporategrowthpattems,99-100

Correlation,141-142

Correlationtimeconstant,918-919

Cosmologicalconstant,849

Costofcapital,378-379 Costs

averageversusmarginal,834-835

unitdevelopment,367-368

up-frontdevelopment,3671368

Costsofproduction,368-370

CouncilonWageandPriceStability,7 Counterintuitivebehaviorofsocial

systems,5-10 Co又,∫.,753

Coyle,R"897 Creativedestruction,389-390

CreativeLearningExchange,ヮoon Crenson,M｡,846

Crissey,B.,846

Cronycapitalism,380 Cruezfbldt-JacobDisease,314-316

Cubbin,∫.,382

Culotta,E.,25 Customers

productawareness,365-367

repeatpurchasebehavior,342-344

Cusumano,M.,360,363,385

Cycletime,17-18

Cyclicaldemand,792

Cyert,良.,381,514,515,598,602,632m,670

Cyrix,374

Daly,H.,23

Dampedoscillations,114,129-130

Dangerfield,B.,321n

Data,typesof,853-855 DataGeneral,391

DataInput,898

Dataintegration,898

Datapresentation,898

Index

DataResources,Inc.,654,857

David,H.,6,7

Davidsen,P.,94n,575n

Davis,H.,30

Dawes,R.,599

Deathrates,286

anddemographictransition,481-485

andpopulationpyramid,479-180

Deathspiral,174-177

Decentralizeddecisionmaking,602-603

Decisionmaking

withboundedrationality,26-27,597-598

boundedrationalityversusrational

expectations,598-599

withcognltivelimitations,599-600

incontextoffeedbackloops,15 contextsof,598

decentralized,602-603

Withdouble-loopleamlng,18-19

event-orientedapproach,10

forecastlnginnation,645-654

forecastlngcommodityprices,6431645

forecastlngenergyconsumption,638-643

hill-climbingoptlmization,537-544

implementationfailure,33

intendedrationality,603-605 withlimitedinformation,23-25

marketgrowthmodel,605-628

modelinggrowthexpectations,634-638

modellngprlnCiples,513-522

problemdecompositioll,602-603

process,16 researchon,896

responsestoboundedrationality,601-603 researchon,896

andstocks,195

andtimedelays,21

unintendedconsequences,5-10

unscientificreasomng,30132 Decisionrules

Bakercriterion,516-518

desiredversusactualconditions,518-519

intendedrationality,603-605

953

andmanagerialpractice,518

inmodelingpnnciples,514-516 inmodels,513

notassumlngequilibrium,519-520

partialmodeltests,605

forproductionstarts,714

typesofdatafor,853-855 Decisions,514-516

andexpectations,63ト634

Decomposlng

decisionmaking,602-603

delays,447-148

Defensiveroutines,32-33,36

Delays;seealsoInformationdelay;Material

delay;nmedelay

averagelengthof,413

basicquestionsfor,412-415

decomposlng,447-448

definitionandtypes,411-112 distributionofoutnowfrom,413

distributionofoutputaround,413-415

durationanddynamicsof,409-410

estimatingduration/distribution

ofdirectinspection,449 numericaldataavailable,437-445

numericaldatanotavailable,445-447 mathematicsof

firsトorderdelay,464-465

generalformulation,4621463

high-orderdelays,4651466

nonlinearadjustmenttimes,4361437 relationofmaterialtoinformation,466

sourceofdynamics,403

testInputs,426,427 variable,434-137

Deliverydeadlines,59n

Deltatime.,seeDT Demand

forcommodities,800

cyclical,792

ingenericcommoditymarketmodel,811-813

andincomeexpectation,718

Demandforecastlng,716

954 Index

Demandshock,723

Demographics

agestructureoforganizations,495-490

0feconomicdevelopment,481-485

populationandinfrastructure,472-174

populationinertia,480-481

populationpyramid,474-480

Demographictransition,474-480,48ト485

DepartmentofEnergy,97,98

Depressions,389-390 Derivatives,197

DescrlptlOnphaseofelicitationmethod,586

Designers,importanceof,84

Designfordisassemblyprogram,228

Designwinmodel,455-456

Desiredversusactualconditions,519

Dewald,W.,855-856

Dewey,John,15

Diacu,F.,115m,284

DICEclimatemodel,242

Diehl,E"27,29,209,688,694

Differentiationstrategy,3711373,391

DigitalEqulpmentCorporation,325,390-391

Dimensionalconsistency,859,866 Dines,James,631

Dioxin,425

Diracdeltafunction,413n

Disaggregation,213-216 ofnetflows,547-549

Discourses(Machiavelli),8

Disequilibriumdynamics,196-197

Displacedemissionvehicles,11

Disraeli,Benjamin,853

DiStefano,J"899

Divisionoflabor,369,386

DNA,353

Dodson,∫.,577

Doman,A.,378n

D6rner,D.,28

Dostoevsky,Fyodor,31

Double-dipbehaviorofsupplierdeliveryrate, 732-734

Double-looplearnlng,18-19,25

Doublingtime,108-109,268-269

Downlng,Mark,66n,73

Downs,A.,178n,189,701

Doyle,∫.,16,888

Drake,EdwinL,92

Draper,F.,900

Draper,N.,867n

Dresch,F.,865,866

Dreyfus,H.,37

Dreyfus,S.,37

DrivlngpattemS,352-353

Drugabuse,250-262

DrugEnforcementAgency,250

DrugEnforcementPolicyBoard,250

DT(deltatime),903-904,907-908

DT(deltatime)error,872,905-906

Duesenberry,James,436

DuFontCorporation,66-79

Durableproducts,345-346

Dvorakkeyboard,387

Dyer,W,86n

Dynamiccomplexity,21-23

Dynamicconfidencebounds,886

Dynamicdecisionmaking,896

Dynamicequilibrium,232

Dynamichypothesis

autoleaslngStrategy,44-47

causalloopdiagrams,102

definition,86

endogenousvariables,95-96

frominterviewdata,157-159

maintenancegame,67-73

modelboundarychart,97-99

policystructurediagrams,102

projeCtmanagementCase,58161

purposeinmodeling,94-95

steps,87

stockandflowmaps,102

subsystemdiagram,99-102

supplychainreenglneerlng,746-749

testlngWithsimulationmodel,102-103

forVCRindustry,364

Ⅰndex

Dynamicsystems;seealsoComplexsystems

andboundedrationality,26 commonmodesofbehavior,108

fastversusslow,909n

generatingharmonics,734n modesofbehavior,107

chaos,129-133

exponentialgrowth,108-111

goalseeking,111-113 interactionsof,118-127

0scillation,114-116

0vershootandcollapse,123-127

processpolnt,116-117 randomness,127-128

stasis/equilibrium,127

SIShapedgrowth,118-121

S-shapedgrowthwithovershoot,121 DYNAMOsoftware,904

Dysfunction,29

Earlyadopters,324

Easing-1nStrategy,32-33 Easterlsland,125-127

Eberlein,R.,870,897

Eckstein,Otto,632m,857

Ecology,carrylngCapaClty,118-121 Econometrics/models,26

added-factored,654

estimatlngtlmelag,437-445

forecastlngWith,857

Economicdevelopment,481-485 Economicfluctuations,132

Economicgrowth,385-386

Economiclongwave,115m

Economicmodeling,96

Economics侶conomy

businesscyclesin,757,782-788

changessince19thcentury,787-788

classicaltheoryofcommoditycycles,798n correctivefeedbackforces,79I

forecastlngCOmmOdityprices,6431645

forecastlngenergyconsumption,638-643

forecastlnginflation,645-654

hiringrates,758-760 limitstolockin,389-391

lockintoinferiortechnology,387-389

longwavetheory,115m,132,784m marketforces,791

modelingpathdependencefor,392-406

pathdependence,359-364

positivefeedbacksin,388 ratcheteffects,436

recoveryfromnuclearwar,865-866

theoryofrationalchoice,599 Economiesofscale,368-369

Economiesofscope,369

Eddington,Arthur,882 Eden,C.,36-37 Effects,ll

Efficientcustomerresponse,7401742

Egypt,482 Einhorn,H.,28,30

Einstein,Albert,128,882

ElectricltyCOnSumptlOn,642

Electricutilitycapabilitymargin,796

Electricutilityindustry,423-424

Electronicdatainterchange,740-742 Elicitationmethod

casestudies,587-595

descrlptlOnphase,586

formodelrelationships,587-595

positionlngphase,586 Emmerson,良.,157

Employeemotivation,147-148

Employees

inagestructureoforganizations,485-493

incompanytowns,374-375

1earnlngCurve,490-493

mentorlng,493-497

0m-theJobtraining,493-497

promotionchains,485-493

qualityandloyaltyof,376-378

Employment,durationof,758-759 Enantiomers,353

Endogenousvariables,95-96

955

956 Index

Energyconsumptionfわrecasts,638-643

Energydemand,150-152

Energy-economyInteractions,97-99

Energyneeds,870-871

Energysupply,laggedresponsetoprice,438

Engineerlng,procurement,andconstruction

process,218-221

Englishauction,813 Entrainment,785n

Environment,carrylngCapaClty,118-121

Epidemics

conditionsfor,305-306

contactnumber,308

extendingSIRmodel,316-318

herdimmunity,312-314 HIV/AIDS,319-323

movlngpasttlpplngpOlnt,314-316

reproductionrate,308

SImodel,300-303

simplemodelofinfections,3001303 SIRmodel,202-209

spreadof,312-313

S-shapedgrowthmodeling,300,301

Epple,D.,338

Epstein,∫.,520

Equilibrium,127 balanced,716-718

anddecisionrules,519-520

lockinto,387-389

andpathdependence,351-352

inPolyaprocess,356

stabilityof,400-401

staticordynamic,232

unstable,130-131,267

EquilibriumprlCe,814-821

Erlangdistributions,462-466 Errorcontrol,909

Errorpropagation,906n Errorrate,583-584

Etherton,R.,Jr.,65n,899

Euler,Leonard,904

Eulerintegration,234n,904-908, 909-111,918m

Event-orientedworldview,10-12

Excesscapacity,776

Excessinventory,746-749,772

Exogenousvariables,95-96,202

Expandingoscillations,130-132

Expectations;seealsoAdaptlVeexpectations;

Growthexpectations;Rational

expectations

modelingformationof,631-634 andmodels,631

Expectedlossrate,671-672

Experience,dynamicsof,5081509

Exponentialdecay,112

fromnegativefeedback,2741280 timeconstantsandhalf-lives,279-280

Exponentialgrowth,108-111,426,427

andcarryingCaPaClty,118-121 counterintuitiveandinsidiouscharacterof,

270

overdifferenttimehorizons,271

doublingtlme,268-269

examples,110

mlSperCeptlOnS,268-272

0vercomlngOVerCOnfidence,2721274

frompositivefeedback,2641274 Ruleof70,268-270

structureandbehavior,109

Exponentialsmoothing first-order,612,634-636,716,803,918

inforecasting,632

ininformationdelay,428-432

Externalprecedencerelationships,587-589, 590,591-592,593

Extrapolativeexpectations,657-658 Extremeconditions,555-556

automatedtesting,897 Extremeconditionstest,337

Fadandfashion,339-342

Falres,∫.,903

Falsification,31

Falsificationism,847n

Index

Familymembertests,860,881-882 Faman,∫.,24

Fashion,339-342

Fatigueandproductivity,577-584

FederalBureauoflnvestlgation,250

FederalEmergencyManagementAgency,866 FederalEnergyAdministration,96

Feedback,12-13;seealsoCausalloopdiagram s driverofadoptionanddiffusion,3231324

generatlngmodesofbehavior,107-108

ininformationsystems,23-24

interpretationof,30

1eamlngaSprocessOf,14-19 linkedwithstockandflowstructure,212-213

meanlnglnSystemdynamics,13-14

mlSperCeptlOnSOf,26-27

0peratlnglnCOmplexsystems,10-12 andoverconfidence,272-273

insystemdynamics,137 Feedbackcontrol,5

Feedbackloops,12-13 automarket,45

andbarrierstolearnlng,19-20

causalloopdiagrams,138-141

incognltivemaps,28

decisionmakingincontextof,15

determinlngPOlarity,143-147

fastway,144 mathematicsof,145-146

rightway,144

unambiguouspolarities,146-147

Withdouble-looplearnlng,18-19

inmaintenancegames,67-73 ofmarkets,168-177

inmodelingprocess,86-89

proJeCtmanagementCase,58

slngle-loopleam1ng,16-17

insystemdynamics,21-23 withvirtualworlds,34-35

Feedbackstructure

adaptiveexpectations,428 automated,897

createdbyfloatinggoals,533

HIV/AIDSepidemic,322-323

Festinger,Leon,168

Feurzeig,W,900-901

Fiddaman,Tわm,93n,242-246,388,868

円FOinventory,414 Finan,∫.,449

Financialmarkets,697-698

Fine,C.,158n

Fine,P.,310,312

First-ordercontrol,545-547

First-orderdelay,mathematicsof,464-465

First-orderexponentialsmoothing,612,803

indemandfbrecastlng,716

modelingpemeptlOnS,429-432 inTRENDfunction,634-636

0fwhitenoise,918

Firsトorderinformationdelay,4291432

First10rderlinearnegativefeedbackstructure,

274-275

First10rderlinearpositivefeedback,29

First-ordermaterialdelay,415-417

FirsLordersystems

inabilitytooscillate,290

multiple-loop,282-285 natureof,263-264

negativefeedback,2741280

nonlinear,263,285-290

positivefeedback,2641274

Fischoff,B.,272

FishBanks,Ltd.,35

Fisher,D.,900

Fisher,Irvlng,631,632n Fisher,S"577

Fitzgerald,H.,38

Flavin,C.,124 Flenley,∫.,125,126,127n

Flexibleworkweeks,776-778

Floatlnggoals,532-535 Flows,140;seealsoStocksandflows

andaccumulation,191-197

continuouslydivisible,207-208 definition,192

instantaneous,206-207

quantized,207-208

957

958 Index

Flows-(Cont.)

rates/derivatives,197

stockchangethroughratesof,204-206 Fluctuations

analyticalintegration,238

incommoditymarkets,792

insupplychain,665-666

Fluepidemicof1978,300,301

Flynn,Vince,66n

Foodchain,425

Ford,A.,42n,93m,424,886n

Ford,D.,16,60n,585n,587

Ford,Gerald,7-8

FordCreditCorporation,47,54,55

FordMotorCompany,43,53,384

Forecastlng;SeealsoInformationdelay

bias,phaseshift,andattenllation,646

bottom-up,453

commodityprlCeS,643-645

demand,716

econometric,857

extrapolationandstability,6561658

implicationsformanagers,655-657

judgmental,432 limitationsandflaws,655-656

majOrissuesin,6331634

modelingexpectationsformation,6311634

modelinggrowthexpectations,634-638

modelsofprocess,632 semiconductordemand,449-462

associal/politicalactivity,633 timeseries,431-132

ForgettlngCuⅣeS,508

Fomeradopters,340

Forrester,JayW,5,15,16,21,28,29,32,37,

38,41,79,84,99-100,107,115n,122m,

130,132,189-190,193,263,289,381,

382n,441,461,472-474,481,484,

485n,513,514,515,520n,526,

605-606,608,617n,619,648,684,709,

782n,783,846,854-855,858,861,881,

882-883,900-901

FoITeSter,N.,897

Fossilfuelproduction,93-94

甲ourieranalysis,917n

Fractionalbirthrate,286-287

Fractionaldecreaserate,523

Fractionalgrowthrate,296 Fractionalrateincrease,522

Fractionalrateofchange,111

Frankel,∫.,823

Franklin,Benjamin,3

Franses,P.,917n

Frazer,W,646m

Frequencydomainanalysis,917n

Freud,Sigmund,261

Friedman,Milton,632n,785

Frisch,氏.,786n

Froot,K.,654,823

Fudgefactor;seeAdd-factorlng

Functionalsilos,740-742

Fundamentalmodesofdynamicbehavior

exponentialgrowth,108-111

goalseeking,11ト113 interactions

overshootandcollapse,123-127

S-shapedgrowth,118-121

S-shapedgrowthwithovershoot,121

oscillation,114-116

processpolnt,116-117

FuzzyMAXfunction,5201532

FuzzyMINfunction,529-530

Galbraith,C.,632 Galbraith,JohnKenneth,173n

Galileo,847-848

Gardiner,B.,24

Gardュner,L.,262n

Garnett,G.,321n

Garud,良.,389

GasolineprlCeS,150-152,172-173,212-213 Gates,Bill

companygrowthasplrations,383-384

useofpositivefeedback,385

Index

Gauss,KarlFriedrich,895

Gaussiandistribution,918n

Gearhardt,Kevin,449n,454

GECapital,54-55

GeneralAccountingOffice,857

Generalizedleastsquares,867 GeneralMotors,384

autoleaslngStrategy,42-55

GeneralMotorsAcceptanceCorporation,43,47, 54,55

Generalrelativitytheory,882

Genericcommoditymarketmodel

capacltyutilization,802-805 demandin,811-813

desiredcapacity,807-810

prlC e-SettlngProcess,813-824

productionandinventory,80ト802

productioncapacity,805-807

forpulpandpaperindustry,8241828 stockandflowstructure,7981800

Gentner,D.,16

Geometriclag',seeKoycklag Gerlow,M.,823

Geroski,P.,382

Gibbs,W,178n

Gilbert,W S.,191

Gillette,良.,93n

Glaser,B.,157

Globalstability,130

Globalwarmlng,241-249,273 Glucksma n ,M.,378n

Goaladaptation,532

Goals,floating,5321535

Goalseeking,111-113

Goal-seekingbehavior,264,274,281-282

Goalsetting,60ト602 Goldbach,Rich,55n,56,63,65-66

Goldratt,E.,753

Goldke,U.,262n

Gompertzmodel,299,327,330 Gordon,R.,784

Gould,J"900

Could,S.,389n

Goulden,M.,247

Graham,A.,15,122n,390n,474,778n

Granger,C.,917m Graphicaldifferentiation,2321233

dynamicsandbehavior,231-232 stocksandflows,2391241

Graphicalintegration,232-233

steps,236 stocksandflows,2341239

linearfirst-ordersystems,266-268

phaseplot,266-267

GraphicdesignprlnCiples,153

GreatDepression,390,651 Green,E.,603n

Greenberger,M･,846 Greene,W,867n

Greenhousegases,241-249

Griffith,J.,78n

Crimes,Glenn,643-645

Grinspoon,L･,261

Gross,D.,208

Grossdomesticproduct

andaggregatedemand,718-719

averagegrowthrate,269

andbusinesscycles,782n

growthfluctuations,115-116

andMicrosoftgrowth,384

Grossnationalproduct,870

Grossworldproduct,273

Grouplearnlng

impedimentsto,32-33

pitfallsofvirtualworlds,35-37 virtuesofvirtualworlds,34-35

Groupmodeling,899

Groupthink,33,36

Growth;seealsoExponentialgrowth;

Populationgrowth;S-Shapedgrowth fractionalrateof,296

limitsto,295

Growthaspirations,380-382

Growthexpectations,634-638

Growthtigers,382-383

Gruber,H.,338

Gtivenen,0.,798n

959

960 Index

班

Ha,Y.,30

HAART(highlyactiveantiretroviraltherapy), 319-323

Haberler,Gottfried,697n

Habit,601

Habituation,532

Halfllife,112,279-280

Halfbrd,G.,16

Hall,R.,28

Hamel,Gary,381 Hamill,D.,320

Hamilton,M.,437

Hansen,M.,178m,184

Harddata/variables,853

Harmonics,734n

Harris,C.,208 HaITis,良.,86n

Haselden,Terry,845 Hauser,∫.,347

Haxholdt,C｡,787n

Hayes,D.,840n

Haynes,Michael,449n Healthinsurance,175-177

Heidenberger,K.,321n Hellekalek,P,914

Henderson,良.,390,508

HepatitisA,316

HepatitisC,316

Heraclitus,22

Herdimmunity,312-314

Herding,654

Hermann,K.,174

Hemandez,K.,701

Heteroscedasticity,867

Higher-orderinformationdelay,432-434

Higher-ordermaterialdelay,417-421

examples,423-425

High-leveragepolicies,22

High-orderdelays,mathematicsof,465-466

HighSchoolSeniorSurvey,250,257

High-techgrowthfirms

modeling,605-628

supplychainreenglneerlng,7431755

Hilbert,David,263

Hill-climbingoptlmization,537-544,615

Hiring,758-760

Hirsch,G.,262n

History-dependentsystems,22 HIV/AIDS,316

HIV/AIDSepidemic

feedbackstructure,3221323

modeling,319-323

simulatlng,323 stockandflowstructure,321

Hogarth,氏.,15,28,30,599-600,814n Holder,H.,262n

Holmes,P.,115n,284

Holt,C.,632n

HomeDepot,383 Homer,Jack,37,38,65n,86m,120,218,251,

252,253,255,256,258,259,262m,

347,381,474,580n,802,823,867-868,

869,881

Horizontalexpansion,375-376

Hoyt,HomerJ.,698,699

Huang,H.,840n Hubbard,良.,855,857

Hubbert,M.King,93-94

Hump-shapedfunction,577-584 Hunter,∫.,440

Hydraulicmetaphor,193-195

IBM,371,372-373,377-378,390-391

If/thendiagram,152 If-then-elseformulation,547

Ⅰ11-conditionedmodels,906n

lmmunlty,lossof,311-312

Immunizationprograms

effectiveness,3101312

eradicationofsmallpox,309-310

Just-in-timevaccination,317-318

Implementation,899-900

failure,33

focuson,80

Index

lncomeexpectation,718

Increaslngreturns,385-386

Incubationperiod,316

Individualresponsestoboundedrationality, 601-603

IndustrialDynamics(Forrester),15,84 Ⅰndustrialrevolution,4

Industrycycles,796-798

Inertia,resultingfromdelays,423

Infectiousdisease,300-303

Inflation,7-8,637

forecastlng,645-654

sea-anchormodel,650-653

Ⅰnfomation

ambiguous,25-26

limited,23-25

selectiveprocess,23-25

Infomationdelay

adaptiveexpectations,428-432

definition,412

exponentialsmoothing,428｣132

first-order,429-432

higher10rder,432-434

relatedtomaterialdelays,466

structureandbehavior,426-434

Infomationeconomics,175

Informationfeedback,16,204

delaysin,426

Informationprocesslngability,599-600

Informationsystems,feedbackin,23124

Infrastructure,472-474

ⅠngallsShipbuilding,55-66

Innovationdi軌lSion,323-346

Bassmodel,332-339

fadandfashion,3391342

1eamlngCurve,337-338

loglSticmodel,325-331

replacementpurchases,342-344

withSIepidemicmodel,324-325

Input

devices,898

tononlinearfunctions,573-576

Insights女ills,30

961

Instability

inlaborsupplychain,779-780

insupplychains,735-740

Instantaneousflows,2061207

Integrationerror,905-906

IntelCorporation,12,349,374,383-384

Ⅰntendedrationality,603-604

0finvestment,810-811

testlng,605

Interactiveparameterestimation,897

Internalprecedencerelationships,587-593

IntemetExplorer,384

Interpersonalimpedimentstolearnlng,32-33

InteⅣiewdata,157-159

Inventory,192;seealsoStockmanagement;

Stocksandflows;Supplychains

excess,746-749,772

expectedlossrate,67ト672

feedbacktocapacltyutilization,835-836

ingenericcommoditymarketmodel,801-802

0rderbacklogs,723-725

0frawmaterials,725-729

vendor-managed,740-742

Ⅰnventorymanagement,764-782

Inventorypolicystructure,710-713

Inventory-workforceinteractions,766-771, 782-788

Ⅰnvestment

decisions,598-599

intendedrationalityof,810-811

Investmentfunction,441-445

Invisiblehand,1691177,791ff

lranianrevolution,212

Iraq,310

Irwin,M.,823

Isaacs,W.,36,858n,899

Iteration,86-89

ithinksoftware,904

∫ Jacobs,R.,646n

Jain,D.,332n

Janis,I.,32,33

962 Index

Java,384

Jenner,Edward,309

Joglekar,N･,110 Johnson,N.,356n

Johnson-Laird,P.,16,31

JointEconomicCommitteeofCongress,857

Jones,A.,536

Jones,P"243

Jones,R.,646n

Jones,S.,36-37

Jorgenson,D･,440

JournalofMoney,CreditandBanking,855-856

Judgmentalerrors,30-32

Judgmentalforecastlng,432

Judgmentalparameterestimates,884 Jusトin-timevaccination,317-318

JVC,360

Kahneman,D.,30,171,600,654,670

Kalmanfiltering,867,897

Kaminsky,P.,741n

Kampmann,C.,27,289,575,873-874,897 Kaれe,H.,124

Kanizsa,Gaetano,17

Kanizsatriangle,17 Kantor,P.,507

Karnopp,D.,265n

Katz,S.,356n

Kay,∫.,178n,184

Keating,E.良.,900

Kelvin,Lord,854-855

Kermack,W1303

Kerr,良.,247

Kestenbaum,D.,698

Keyfitz,Nathan,469,478

Keynes,JohnMaynard,436n Khazzoom,∫.,438,439

Kin,D.,140,209,900

Kindleberger,Charles,173n

Kirch,P.,127

Klayman,J.,30 Kleiner,A.,157

Kleinmuntz,D.,27

Klopfenstein,B･,363 Knetsch,J"171

Kofman,F.,2ln,1001101,113,378n,436,780n

Kondratievcycle,115n,784n

Koshland,D.,25

Koycklag,437,462-466 Krishnan,T.,332n

Krugman,Paul,386 Kuenzli,D.,78n

Kuhn,Thomas,24,849

Kurian,G.,110,113,120

Kuznets,Simon,824

Kuznetscycles,824

KyotoConference,248

Labor,andinventorymanagement,764-782

Laborcapacitatedprocess,563-569 Laborforce,758-760

Laborproductivlty

cuttlngcornersVersusovertime,563-569

stressandfatigue,577-584

Laborsupplychain

addingovertime,774-776

addingtrainlngandexperience,780-782

andbusinesscycles,782-788

costsofinstability,779-780

inventorymanagement,764-782

modeltestlng,760-764

0scillations,767-773

policydesigntoenhancestability,7731774

responsetoflexibleworkweek,776-778

structureoflaborandhiring,758-760

Labys,W･,798n

Laggedresponse

capitalinvestment,438-445 ineconometrics,437-138

energysupplytoprice,438

inmonetarypolicy,785-786 Lakatos,Ⅰ.,848n

Landeen,良.,262n

Lane,D.,37

Index

Langley,P.,38 Lant,T"381,532,602

Laplace,PierreSimonde,231

Large-scaleconstructionprq】ects,218-221 Larsen,E.,93n

LawofAcceleration,4

Lawofunintendedconsequences,5-10

Leadtimes,ofsuppliers,738-740 Leaner,E.,26,880

Leanmanufacturing,787-788

Learnlng

ambiguity,25-26 barriersto,19-20

boundedrationality,26-27

aboutcomplexsystems,4-5

confoundingvariables,25-26

fromcontinuousexperimentation,34 defensiveroutines,32133

double-loop,18-19,25

anddynamiccomplexity,21-22

dynamicsof,508-509 event-Oriented,10-12

feedbackmisperceptlOnS,26127

asfeedbackprocess,14-19

flawedcognitivemaps,28-29

1mplementationfailure,33

interpersonalimpediments,32-33 withlimitedinformation,23125

mentalmodelsin,16-18

needforsimulation,37-39

pitfallsofvirtualworlds,35-37

requlrementSincomplexsystems,33-39 researchon,896

slngle-loop,16-17,25

unscientificreasonlng,30-32 virtuesofvirtualworlds,34-35

LearnlngCurve,337-338,369-370

andpromotionchains,490-493

LearnlngCurvemodels,507

Ledet,Winston∫,66

Ledet,WinstonP.,66167,74-78

Lee,E.,478n

Lenstra,∫.,615n

Lesourd,∫-B.,798n

Levin,G.,262n

Levine,良.,38

Lichtenstein,S.,272

Liebowitz,S.,388m

LIFOinventory,414

Lima,Ohio,oilrefinery,77179

Limitcycle,114,130-132,689n Lincoln,Abraham,350

Lin°,James,19

Linearfirst-ordersystems,263

analyticsolution,265-266

graphicalsolution,266-268

multiple-loop,282-285

negativefeedback,2741280

positivefeedback,264-274

Lineargrowth,109

Linearization,285

LinearPolyaprocess,354-357

Linearsystems,264

Linearthinking,10-12 Link,∫.,174

Linkpolarity,138-141 Sor0notation,140-141

Liquidateddamages,59n Little,John,423

Little'sLaw,421-425,678,724

Liu,T.,823

Livestockmarkets,836-840

Livingston,Joseph,inflationforecasts, 646-652,654

Locallystableequilibrium,351

Locallyunstableequilibrium,351

Localstability,129-130 Lockin,352-353

toequilibrium,387-389 limitsto,389-391

LoglSticgrowthmodel

analyticalsolution,297-298

descrlptlOn,296-297

historicalfit/modelvalidity,3281331 forinnovationdiffusion,325-331

testlng,300

963

964 index

Long-runsupplycurve,834

LongTermCapitalManagementcollapse,698

Longwave,115n,132,784n

Loopknockoutanalysis,880-881

Looppolarlty identifier,13

labeling,142-143

Loops,897 Lotka,A.,120,284

Lotka-Ⅵ)terrapredator-preymodel,284

LotusDevelopmentCorp .,371

Lovins,Amory,643

Low,G,,290n,718

Low-leveragepolicies,22 Lucas,良.,516

Lyneis,J･,780m

M MacCoun,良.,250,258

Machiavelli,N.,8

MacintoshoperatingSystem,370,387,388

Macroeconomy,capitalinvestmentin,438-445 Madcowdisease,312,314-316

Madnick,S.,65n,490n

MagneticⅥdeo,363

Mahajan,V･,324n,330 MaintenanceGame,34,66-79

adoptionof,77-79

dynamichypothesis,67-73

implementationchallenge,74-76 results,76-77

Makridakis,S.,414n,632

Managerialpractice,anddecisionrules,518

Managerialpracticefields,899

Managers

capacltyexpansionbehavior,612-613

forecastlngPractices,632

implicationsofforecastlngfor,655-657

asorganizationdesigners,84

stockmanagementtask,666-667 Mandinach,E.,900

Mann,C.,32

Manrodt,K"632

Manufacturlng

capacltyutilization,116

policystructurediagram,710

ManufacturingGame,74-75

ManufacturingSupplychain,709155

inbalancedequilibrium,716-718

demandforecastlng,716

instabilityandtrustin,735-740

integrationofmanagement,740-742

interactionamongpartners,729-742

modeltestlng,720-723 0rderfulfillment,711-713

policystructureofinventory,710-713

policystructureofproduction,713-714

productionmodelingcase,743-755

productionstarts,714-716

reenglneerlng,74ト742 March,∫.,157,381,514,515,598,602,

632m,670

Marchetti,C,,328

Marcos,Ferdinand,380

Marginalcost,543,834-835

Marginalproductivity,54ト543

Marginalrevenue,543

Margolis,D.,265n

Margolis,S.,388m Marketfailure,1741177

Marketgrowthmodel,607-628

policydesignin,624-628

Marketpower

consolidationof,376

andcorporategrowth,374-375

MarketprlCe,168-171 Markets

feedbackstructure,168-177

high-techgrowthfirms,619-621 Marketshare

determinlng,402-403

pathdependencemodel,3921402

MarkupprlClng,813

Markupratio,803-805 Markus,A.,76

Index

Maron,M.,903

Marshal1,Alfred,386

Mass,Nathaniel∫.,122n,130,378n,441,474,

663,743n,746,785,883

MasstraIISitdeathspiral,185-188

Masuch,M.,378n

Materialdelay

averagelengthof,413

definition,411

distributionofoutputaroundaveragedelay

time,413-415

examples,423-125

first10rder,415-417

higher-order,417-121

Little'slaw,421-425

plpelinedelay,415,416

relatedtoinformationdelays,466

responsetosteps,ramps,andcycles,425-426 stockandflowstructure,411

structureandbehavior,412-426

Mathematicsoflooppolarity,145-146

Matsushita,360,363,371,403

MAXfunction,520-532

Mayer,T.,439

McCloskey,D"847

McKendrick,A.,303

McKinseyandCompany,743n,746

McPhee,John,8n

Meadows,D.Ii"5,24,28,32,90,93n,99,

119m,125n,262n,270,272,481-485,

849m,851,887,899

Meadows,D.L.,24,119n,125n,442,445,447,

485n,798n,838

Meanabsoluteerror,874-880

Meanabsoluteerrorasafractionofthemean, 874-880

Meanabsolutepercenterror,874-880

Meansquareerror,648

Meantimebetweenfailure,76-77

Measurement,asactofselection,23

Medexprogram,175-177

Mediareports,365-366 Medicaid,175

Medicare,175

MedigapInsurance,175-177

Memory,short-ten,600

Mentaldata,853 Mentalmodels

inautoindustry,42-43 causalattributions,28

causeandeffectin,91

dynamicallydeficient,27

improvedbysimulation,37-39

inadequacyof,32

inleamlngprocess,16-18

withlimitedinformation,23-24

researchon,896

shiftin,79

simulationcapability,29

andsimulationmodels,88-89

trafficcongestion,1781180

Mentalsimulation,faulty,29

Mentorlng,493-497,781

MergersandacqulSltlOnS,374-376

Merrill,G.,632,633

Merton,良.,368

Mesarovic,Mihailo,89-90

MetroMachine,65

Michael,D.,86n

MicrosoftCorporation,12,349,371,

383-384,388

MicrosoftDOS,387

MicrosoftWindows,387,388

Mill,JohnStuart,173

Miller,G.,600

Miller,∫.,887

Miller,P.,516

MINfunction,529-530

MisperceptlOn

offeedback,26-27,29

MIT,487-489

Mitchell,B.,122

Modelboundary,81,222-225

Modelboundarychart,97-99

Modelcalibration,897

Modelers,questionsaskedby,851,852

965

966 Index

Modeling

agent-based,896

anchoringandadjustment,534 blackbox,80

withcausalloopdiagrams,159-168 characteristics,83-84

andclientneeds,84-85

continuous,81

designandeffectiveness,8881889

byexperts,81

1ntegratlngmethodologleS,899 asiterativeprocess,80

keystosuccess,888 andmathematics,231-232

andorganizationalpolitics,85

Proactiveversusreflective,858

purposeof,84,330-331

sensitivltyanalysis,562 socialevolution,896

withstocksandflows,2081210

supplychainreenglneerlng,749

Modelingautorecycling,227-229

Modelingbusinesscycles,782-788

Modelingcoflows,4971511

Modelingcommoditycycles,792-798

genericmodel,798-829 livestockmarkets,836-840

pulpandpaperindustry,824-828

Modelingdecisionmaking

commonpitfalls

avoidingif-then-elseformulation,547

disaggregationofnetflows,5471549

outflowsrequiringfirst-ordercontrol, 545-547

formulationflaws,5201522

hill-climbingoptlmization,537-544

prlCeSettlngprocess,539-545

prlnCiples,513-522 Bakercriterion,516-518

decisionsversusdecisionrules,514-516

desiredversusactualconditions,518-519

managerialpractice,518

notassumlngequilibrium,519-520 robustness,519

rateequations,522-545

Modelingdelays

adaptiveexpectations,428-432

exponentialsmoothing,428-132

forecastlngSemiconductordemand,449-162

Modelingdemographictransition,481-185

Modelingexpectationsfomation,631-634

Modelingglobalwarmng,241-249

Modelinggrowthexpectations

energyconsumptionforecasts,6381643

forecastlngcommodityprlCeS,643-645

forecastlnginflation,6451654

withTRENDfunction,634-638

Modelinghigh-techgrowthfirms,6051628

behavioroffullsystem,62ト624

capacltyaCqulSltlOn,609-615 marketsector,619-621

modelstructure,606-607

0rderfulfillment,607-609

salesforceeffectiveness,615-619

Modelinghumanbehavior,517,597-628

boundedrationalityversusrational

expectations,598-599

cognltlVelimitations,599-600

goalsettingandsatisficing,601-602 habit,routines,andrulesofthumb,601

intendedrationality,603-605

managlngattention,601

marketgrowthmodel,605-628

responsestoboundedrationality,601-603

Modelinginformationdelay,4261434

ModelinglnSights,899

ModelingInventorymanagement,7101713;See

alsoModelingproduction

ModelingInventory-WOrkforceinteractions, 764-788

Modelinglaborsupply

interactionswithinventorymanagement, 764-782

laborforceandhiringrates,758-760

modeltesting,760-764

Modelinglargeconstructionprojects,218-221

Modelinglifecycleofdurableproducts, 345-346

Modelingmaterialdelays,412-426

Index

Modelingpathdependence modelbehavior,396-402

modelstructure,392-396

policyImplications,402-103 standardsformation,391-406

Modelingprocess,103 basicactivities,85-86,87

dynamichypothesis

endogenousexplanation,95-96

mapplngSystemStructure,97-102

purpose,94-95

steps,87

iterativecycle,86-89

policydesignandevaluation,103-104

problemarticulation

importanceofpurpose,89-90 referencemodes,90

steps,87

timehorizon,90-94

simulationmodelformulation,87,1021103

testlng,87

Modelingproduction

addingorderbacklogs,723-725

demandforecastlng,716

initializingmodelinequilibrium,716-717

interactionsamongsupplychainpartners, 729-742

modeltestlng,720-723 0rderfulfillment,7111713

policystructureofinventory,710-713

productionratepolicystructure,713-714

productionstarts,714-716

rawmaterialsinventory,725-729

simultaneousinitialconditionequations, 717-720

ModelingS-Shapedgrowth

analyticsolutionofloglSticmodel,297-298

epidemics

extendingSIRmodel,316-318

herdimmunity,312-314 HIV/AIDS,3191323

immunizationprograms,310-312 madcowdisease,314-316

SImodel,300-303

967

SIRmodel,303-309

tlpplngpOlnt,305-309

Gompertzmodel,299 innovationdiffusion,3231346

Bassmodel,332-339

fadandfashion,339-342

logisticsmodel,325-331

replacementpurchases,342-344

logisticgrowthmodel,296-297 Richardsmodel,299

testlnglogisticmodel,300 Weibulldistribution,299

ModelingWaronDrugs,2501262 Models

forcorporategrowth,99-loo decisionrules,513

defenseagalnStadd-factorlng,857 documentation,855,856

DTerror,872

energy-economyInteractions,97-99

andexpectations,631

extremeconditionstest,337

falseandrefutable,847-848

0fforecastingprocess,632 historicalfit,331

ill-conditioned,906n

importanceofpurpose,89-90

initializedinbalancedequilibrium,716-718

1eamlngCurve,507

limitationsof,846

linking,898

manufacturingfirm,710 withnaⅣowboundaries,96

numericalintegration,903-911

partialtests,605

pragmaticsandpoliticsofuse,851-858

productdevelopment,587-595

purposeof,79-80

questionsabout,851,852

relianceonexogenousvariables,95-96

replicability,855-858

simultaneousinitialconditionequations, 717-720

skepticismof,80

968 Index

Models-(Cant.)

specificityof,89190

statisticalsignificance,868 structureof,513-514

andsubmodels,869

Sugarscape,520

systemdynamicsnationalmodel,441-445

typesofdatafor,853-855 visualizationofbehavior,898

well-conditioned,906n

with/withoutnoise,913-914

Modeltesting,87,103

behavioranomalytests,860,880-881

behaviorreproductiontests,860,874-880

boundaryadequacytests,859,8611863

dimensionalconsistency,859,866 errorsin,845-846

extremeconditionstests,860,869-872

familymembertests,860,881-882

impossibilityofvalidation,846-850

integrationerrors,860,872-874 kindsoftests,858-861

inlaborsupplychain,760-764

loopknockoutanalysis,880-881

manufacturlngSupplychain,720-723

parameterassessment,859,866-869

sensitivltyanalysis,861,883-887 structureassessmenttests,859,863-866

supplychainreenglneerlng,749-752

surprisebehaviortests,860,882-883

systemimprovementtests,861,887-889 Modesofbehavior,107

chaos,129-133

exponentialgrowth,108-111,263-264

goaトseeking,1ll-113,263-264 interactionsof,118-127

0scillation,114-116

overshootandcollapse,123-127

processpoint,116-117 randomness,127-128

stasis/equilibrium,127

SIShapedgrowth,118-121

S-shapedgrowthwithovershoot,121

Modigliani,Franco,632n Modis,T.,325,328

Mojtahedzadeh,M･,289,897 Molina,M.,24

Monetarypolicy,785-786

Monopolypower,374 MonteCarlosimulation,885-886,887m

Montgomery,M.,439,441n,680 Monus,Paul,66n,77,78

Moore,G.,784

More,Thomas,5

Morecro托J.,37,42n,79,95m,102,157,602,

605n,606,607,710n,899

Mortality,formulationsfor,479-480 Mosekilde,E.,42m,133m

Motorcycleproduction,536-537

Mowry,G.,376 Moxnes,E.,388n

Mueller,D.,382

Mullen,T.,56,58-59,65n

Muller,E.,324m,330

Mullineaux,D.,646n

Multiple-loopsystems,282-285

Multipleregression,867

Multiplicativeeffects,5281529 Multivariatetimeseriestools,921n

Mundlak,Y.,840n

Murphy'sLaw,5

Murray,J･,131,306n Muth,J"516

Myers,L･,320

Mylonadis,Y.,360,363

Nadiri,M.,440

Naill,Roger,93n,97,217,438,439,575-576

NationalAeronauticsandSpaceAdministration, 24-25,273

NationalBureauofEconomicResearch,782m

NationalHouseholdSurvey,250,252,254, 256-257

NationallnstituteofJustice,250,252

NationallnstituteonDrugAbuse,250

Index

NationalSmallBusinessPrimeContractorofthe

Year,65

NaturalprlCe,168-171 Nautica,383

Neale,M.,434

Negativefeedback

andexponentialdecay,274-280

goal-seekingbehavior,264,274,281-282

governlngSupplychain,665

Negativefeedbackloops,12113

asbalanclngloops,142-143

determinlngpolarity,144

explicltgoals,155-156 in丘･eemarket,168-177

ingoalseeking,111-112

0rlginofoscillations,684 0sclllationbehavior,114-116

inovershootandcollapse,123-127

inPolyaprocess,354-355

S-shapedgrowthwithovershoot,121

stasis/equilibrium,127

withtimedelays,23

Negativelinks,139-140

Negativestocks,547,864-865 Nelson,C.,642

Nelson,F.,395

Nelson,R,,537n,542,598

Nerlove,M.,632n

Nethiringrate,617

Netscape,371 Networkeffects,3701371,401

Newbold,P.,917n

NewEnglandHaddockfisherycollapse,125

NewEnglandJournalofMedicine,260,322

Newideas/products;SeeInnovationdiffusion

Newproductdevelopment,372-374 Newton,Isaac,848

Nike,383

Nisbett,a,16,157

Nixon,RichardM.,7-8,516

Noise,913-924

degreeofinertia,919

frequencies,9181919

969

guidelinesforuslng,9231924

powerspectrum,917 Nonconservedflows,5041505

Nonlinearbirth/deathrates,286

Nonlineardynamics,5

theoryof,895-896 Nonlineareftbcts,525-529

Nonlinear丘rst-ordersystems,263

definitionofloopdominance,288-289

1mabilitytooscillate,290

S-shapedgrowth,285-289 Nonlinearfunctions

building,552-562

commonpitfalls

avoidinghump-shapedfunctions,577-584

impropernormalization,576-577

uslngWrongInput,573-576

domainforindependentvariable,556

elicitingrelationshipsinteractively,585-595

estimatedwithqualitativeandnumericaldata, 569-583

extremeconditions,555-556

formulatlng,5661567 normalization,554-555

plausibleshapes,556

productdevelopmentmodel,587-595

refTerencepolntS,555

referencepolicies,555

sensitivltyanalysis,558-562

specifyingvalues,5561557

testlngformulation,557-558

Nonlinearity,22

NonlinearPolyaprocess,357-359,

397-399,400

Nonlinearrelationships

cuttlngCOrnerSVersusOVertime,case, 563-569

indynamicsystems,551

uslngtablefunctions,552-563

Nonlinearweightedaverage,535-537

Nonrecoursefinanclng,705 Nord,0.,605

Nordhaus,William,217,273

970 Index

NORMALfunction,914-915

Normalization,554-555

improper,576-577

NorthAmericanElectricReliability Counci1,642

NorthAmericanFreeTradeAgreement

modelboundaryassumptlOnS,862-863 Northcraft,G.,434

NorthernSecurities,376

NorthKorea,310

Nuclearwar,865-866

Numericaldata,853

inparameterestimation,867

Numericalintegration

approprlatetimestep,907-908

chooslngamethod,909-910

errorcontrol,909

Eulerintegration,904-908,909-911,918n

guidelinesfor,910-911

integrationerror,905-906

Runge-Kuttamethods,908-911,918n

samplesimulationsequence,904-905

variabletimestepmethods,909

Numericalsensitivity,562,883

Nyhart,∫.,899

0'Connor,Flannery,295

0gata,K.,265n,463n,821m

Oilcrisis,70,172-173,212-213,639

OilproductionandconsumptlOn,91-94,96

Oiltankerindustrycycles,796,797 01iva,R.,490n,569,570,573,580,868,921

"OnCoca"(Freud),261

0n一也eJobtrainlng,493-497,781

Openloopgala,145

Open-loopsteadystategainloop,618n-619n

Openoutcrydoubleauction,813

Optimizationheuristics,615n

Orderbacklogs,608-609 eftbctsof,725

inproductionmodel,723-725

Orderfulfillment,607-609,711-713

Ordinaryleastsquares,867 0reskes,N"847,849

Organizationalevolution,896

OrganizationalLearningCenter,MIT,17

OrganizationofPetroleumExportingCountries, 98,172

0rganizations

agestructure,485-490

mentorlng,493-497

modelingembeddedin,84-85

on-the-jobtrainlng,493-497

Promotionchains,485-190

responsestoboundedrationality,601-603 Oscillations,114-116,426,427

BeerDistributionGame,684-694

chaotic,132-133

incommoditymarkets,840-841

damped,129-130

expanding,130-132

inlaborsupplychain,767-773

lackinginfirst-ordersystems,290

limitcycles,131

inmanufacturingSupplychain,734 realestatemarkets,698-707

instockmanagement,663-664

insupplychains,664-666

0skamp,S.,272 Outcomeassessment,899-900

Outflowsrequiringfirst-ordercontrol,545-547

Output

ofadelay,413-415

indelays,411

ofsupplychains,663 0verconfidence,2721274,884

Overshooting,114

andcollapse,123-127

S-shapedgrowthwith,121 Overtime

versuscuttlngcorners,563-569

andfatigue,5771584

inlaborsupplychain,774-776

Index

responsetoworkweekflexibility,7761778

schedulepressureandworkweek,567-568

Ozonedepletion,24-25

Packer,D.,490n,605,619

Paich,Mark,27,42m,43,66m,67,73,124,

449m,454,899

Papadopolous,H.,208

Papert,S.,34

PapuaNewGuinea,873

Paradigms,849-850 Parallelactivities

aggregatlng,217

disaggregatlng,216,217 Parallelstockandflowstructure,456-157

Parameterassessment,859,866-869

Parameterestimates,884,897

Parameterspace,897

Parker,P.,324n,334,338

Parkinson'sLaw,166,184

Parnell,LeRoy,845 Partee,∫.,38m

Partialmodeltests,605,609

Pascallags,465

Pathdependence,22 characteristics,349-353

definition,349

ineconomy,359-364

andequilibrium,351-352 limitstolockin,389-391

lockintoequilibrium,387-389

modeling,391-406

Polyaprocess,354-359,363

andpositivefeedback,351 standardsformation,391-396

Pathdependentsystems

commonality,353

lockin,352

PCBs,425

PDCAcycle,15

971

Pearce,D.,646n

Peck,S.,642

Pec°sRiver,864

Peek,∫.,646n

PeopleExpressManagementFlight

SimulatoT;35

PerceptlOnSandfeedback,23-25

PersistentPoppy,The(Levinetal),262n

Pesando,∫.,646n

Peterson,David,488,489,870,897

Peterson,Ⅰ.,115n

Peterson,Tわm,43

Petroleumindustry,9ト94,172-173,212-213

Phaselag

inmanufacturingSupplychain,734

insupplychains,664-666

Phaseplot,263,266-267,274-275,288 Bassdiffusionmodel,333-334

linearPolyaprocess,354-357 networkeffects,401

stabilityofequilibrium,400-401

Phaseshift,inforecastlng,646

Phelps-Brown,E･,142

Phillips,A.W,785

Phillips,L.,272 Picardi,A.,94n

Pindyck,R.,599 Pinknoise,917-918,919,920

Pipelinedelay,415,416,432 Planck,Max,128

Plous,Scott,24,28,son,272,649

Pogo,5 Poincare,Henri,284

Poinトof-salesdata,740

Policies,unanticIPatedsideeffects,5110

Policyanalysis

supplychainreenglneerlng,752-753

trafficcongestioncase,1881190

Policydesignandevaluation

endofmodelingprocess,103-104

inmarketgrowthmodel,624-628

steps,87

972 Index

Policyoptlmization,887 automatic,897

Policyresistance,5-10 causesof,10-12

incomplexsystems,22 definition,3

examples,9 Machiavellion,8

Romanianbirthrates,6-7

LewisThomason,8

tramccongestion,177-190

wageandpricecontrols,7-8

Policysensitivity,562,883

Policystructure

ofinventory,710-713 0rderfulfillment,711-713

0fproduction,713-714

Policystructurediagram,102,709

Polya,George,354,356

Polyaprocess,397-399,400

equilibriumdistribution,356 linear,354-359

andlockin,387,389

nonlinear,357-359

andVCRindustry,363

Popper,Karl,847n

Population

agestructureoforganizations,485-490

agestructure,476 Easterlsland,125-127

andeconomicdevelopment,481-485

mortalityformulations,479-480

replacementrates,480-48I

inUrbanDynamics,472-474

Populationgrowth,108-109

carrylngCapacity,1191120

0vershootandcollapse,123-127

S-shaped,285-289

Populationinertia,480-481

Populationpyramid,474-480 Porter,良.,603n

Positionlngphaseofelicitationmethod,586 Positivefeedback

doublingtlme,268-269

ineconomy,388

englneOfcorporategrowth,364-385

generatlngexponentialgrowth,264-274

graphicalsolution,266-268

increaslngreturnsandeconomicgrowth, 385-386

0vercomlngOVerCOnfidence,2721274

pathdependence,349,351

usebyBillGates,385

Positivefeedbackloops,12113

determinlngpOlarlty,144

andexponentialgrowth,109 first10rderlinear,29

inPolyaprocess,354-355

asreinforcingloops,1421143 Positivelinks,139-140

Post,Darren,43

Posted-prlCeSystem,813 Postman,L.,24

Powers,W.,15

Powersimsoftware,904

Powerspectrumofnoise,917 Prabhu,N.,208

Pralahad,C.K.,381

Precedencerelationships,587-595 Predictionhorizon,132

Prerecordedvideotapeindustry,363

Priceexpectations

incommoditymarkets,823

extrapolative,833-834 Prices

ofcommodities,800

andcommoditycycles,792-798

ofcopper,795

anddesiredcapacity,807-810

industrycycles,796-798

laggedresponseofenergysupplyto,438

markupratio,803-805

andproductioncosts,368-370

pulpandpaperindustry,824-828

responsetochangesincosts,818-820

responsetodemand,811-813

responsetoinventorycoverage,820-822

andup-frontdevelopmentcosts,368

Index

Pricesetting/Pricing

ingenericcommoditymarketmodel,813-824

livestockindustry,836-840

process,439-543 Pricewars,603-604

PrimeComputer,391

PrinciplesofPoliticalEconomy(Mill),173

Proactivemodeling,858 Problemarticulation

referencemodes,90

roleinmodeling,89-90

steps,87 timehorizon,90-94

Problemdecomposition,602-603 Problemdefinition

incausalloopdiagrams,159-160

supplychainreenglneerlng,743-745

Problemsolving

evenトorientedapproach,10

bymodeling,83-84 Productattractiveness,392-395

Productawareness,365-367

Productcompatibility,360,387,392-395

Productdevelopment

estimatlngprecedencerelationships,587-595 times,744

Productdifferentiation,3711373,391

Production;SeealsoModelingproduction

commoditycycles,792-798

ofcopper,795

anddesiredcapaclty,807-810 anddistribution,709

ingenericcommoditymarketmodel,801-802

industrycycles,796-798

livestockindustry,836-840

policystructure,713-714

pulpandpaperindustry,824-828

Productioncapaclty

genericcommoditymarketmodel,8051807

livestockindustry,836-838

Productivlty,andnoise,913-916

Productlifecycle

durables,343-346

andproductdevelopmenttimes,744

Products

complementarygoods,370-371 networkeffects,3701371

andup-frontdevelopmentcosts,367-368

Productshortages,366

Profitability

andcapacltyutilization,802

0fnewcapaclty,807-810

ProjectIndependenceEvaluationsystem,96, 97-98

Prqjectmanagement,55-66

dynamichypothesis,58-61

initialmodeldevelopment,57

modelingprocess,61-64 Promotionchains

toexploreworkertrainlng,491

andlearnlngCurve,490-493

inorganizations,485-490

Prusiner,Stanley,314-315

Pryor,Richard,260

Ptolemaicsystem,849 Pudar,Nick,42n,43,47,52-53

Pugh-RobertsAssociates,55n,57,60,64

Pulpandpaperindustry,824-828 Pulsefunction,413n

Putnam,良.,32-33

Putty-claymodel,509-511

Q Quantizedflows,2071208

Quantummechanics,127-128

Quarantine,311

Queuingtheory,208

Quine-Duhemthesis,848,849-850

Qwertykeyboard,387

Railroadgauge,350 RampInput,426,427 Ran°ers,∫.,24,119n,217,485n

Randomevents,363

Randomness,127-128

Randomnumbergenerators,915

Rappa,M.,389

973

974 Index

Rappaport,Roy,873 Ratcheteffects,436-137

Rateequations,264 additiveeffects,5281529

adjustmentrateformulation,524

adjustmenttoagoal,523-524

floatinggoals,532-535 fractionaldecreaserate,523

fractionalincreaserate,522

fuzzyMAXfunction,5301532

fuzzyMINfunction,5291530

hil1-climbingoptlmization,537-544

multiplicativeeffects,5281529 nonlineareffects,525-528

nonlinearweightedaverage,5351537 resourceallocation,544-545

resourceproductivlty,524-525

Rationalchoicetheory,599

Rationalexpectations

indecisionmaking,598-599

theory,515-516

Rawmaterialsinventory,725-729

Rayward-Smith,Ⅴ,615n

RCA,360,363

Reactivemaintenance,72

Reagan-Cirincione,P.,37,95n,899 Realestatemarkets,698-707

Reder,M.,814n

Redman,D.,847

Referencemodes,90,107

incausalloopdiagrams,160-163

supplychainreenglneerlng,746-749

ReferencepolntS,555

Referencepolicies,555

Reflectivemodeling,858 Re乱ltationsim,847n

Reichelt,K.,899

Reinforcingloops,142-143

Repeatpurchasebehavior,342-344

Repellor,352

Repennlng,N.,21n,29m,100-101,113,378n, 436,536,780n

Replacementpurchases,342-343

Replicability,855-858

Reproductionrateforepidemics,308

Researchanddevelopment

increaslngretumSfrom,387

fornewproducts,374 Resonance,919

Resourceallocation,544-545

Resourceproductivity,524-525

Responsesurfacemethods,867n Reuter,P.,250,258

Ricardo,David,862

RichardIll,25 Richards,∫.,299

Richardsmodel,299

Richardson,George,14,42n,141,211,262n,

289,296,575n,889,895n,899

Richardson,J.,32,90,94n,485n

Richmond,Barry,37,222,322 Risch,∫.,378n,824n

RNA,353n

Road-generatedtraffic,184 Roberts,C.,321n

Roberts,EdwardB.,3,38,42n,79,217,262n

Roberts,∫.,347

Roberts,Nancy,533n,900-901 Robinson,∫.,31,99,851

Robustness,519,869

Rockefeller,JohnD.,77

Rogers,Everett,324n,336 Romanianbirthrates,6-7

Romer,Paul,386-387

Romm,J.,865-866

Roosevelt,Theodore,376

Rootmeansquareerror,874-880 Rosa,R.,578

Rosen,S.,840n

Rosenberg,良.,265n Rosenbloom,R.,360,363

Rosenhead,J.,37

Rosner,B.,478n

Ross,L.,28

Rostow,W.W.,791

Roswell,NewMexico,850

Index

Rotemberg,J｡,599 Rot九,G.,157

Roth,M.,321n

Route128,Mass.,184

Routines,601

Rowell,D.,463n

Rowland,F,24

Ruleof70,268-270

Rulesofthegame,380 Rulesofthumb,601

Runge-Kuttaintegration,234n,9091911,918n Russell,Bertrand,845

Russo,∫.,434,Goon,655

Sagaria,S.,29,269

Sahelregion,94

Saint-Exupery,Antoinede,656

Salesbudgets,365 Salesefectiveness,616,619-621

Salesforce,615-619

Smarasan,D.,899

Samuelson,PaulA.,551,718,757

Sanders,N.,632

Sastry,M.,38,378m,390,865-866

Satisficing,601-602 Schank,氏.,16

Scharfstein,D.,654

Schedulecompression,60-61

Schedulepressure

effectontimepertask,568-569,572 effectonworkweek,567-568,571

Scheill,E.,32,86n

Schmitz,A.,840n

Schneiderman,A.,21

Schoemaker,P.,434,600n,655

Scholes,Christopher,387 Sch6n,D.,15,32,34,35,86n

Schrader-Frechette,K,847,849

Schreckengost,良.,262n Schroeder,W,122m,474

Schumpeter,Joseph,389-390

Scientificmethod/reasoning

975

falsification,31

lackoftrainlngin,36 reasonsforfailure,30-32

Scientifictheory

auxiliaryhypothesis,848-849

Quine-Duhemthesis,849-850

subjecttorefutation,847 Scott,David,848

Scrapie,314-316

Scurvy,19

Sea-anchormodelofinflation,6501653

Sealedbidauction,813

Seifert,W.,94n

Selby,R･,385

Selchowand又ighter,340

SelectiveperceptlOn,599-600

Self-correctlngprocesses,13,14

Self-organlZlngSystems,22

Self-reinforcingfeedback,1081109

Self-reinforcingprocesses,13,14

Semiconductordemand,449-462

Semiconductormanufacturer,1001I02

Senge,Peter,36,37,38,74n,140,390m,

440-445,569,680,684n,785,847,858,

861,881,889,899,900

Sensitivedependenceoninitialconditions,132

Sensitivltyanalysis,854 automated,897

automatedtoolsfor,884

bestandworstcase,885-886

comprehensive,884-885

importanceof,830 kindsof,883

formodeltesting,8831887 nonlinearfunction,558-562

forparametricassumptlOnS,884

forstructuralchanges,831-836

Sequentialdebottlenecking,753-754

Serialdisaggregation,215

Servicediscipline,414

Services,andup-frontdevelopmentcosts,368 Servicesector,787

Shanklin,∫.,24

976 Index

Shannon,D.,125n

Shantzis,S.,573,574,873

Shaughnessy,D.,31 ShermanAntitrustAct,376

Shewhart,W,15

Shewhart-DemlngPDCAcycle,15 Shiba,S.,15

Short-termmemory,600 Sideeffects,10-ll

0fcorrectivemeasures,60

Silverprices,124,125 SimchトLevi,D.,741n

Simchi-Levi,E.,741n

SImodelofepidemics,300-303 forinnovationdiffusion,324-325

Simon,HerbertA.,26,29,381,520n,597,598,

599,602,670,849

Sins,D.,36-37

Simulationmodels,35136;seealsoModeling entries;Models

agent-based,896

0fbusinesscycles,784

withEulerintegration,905 formulationof,102-103

maintenanceinitiatives,67

andmentalmodels,88-89

MonteCarlo,885-886,887n

needfor,37139

steps,87

Simultaneousinitialconditionequations, 717-720

Single-looplearning,16,25

SIRmodelofepidemics,303-309

assumptlOnSandextension,316-318

immunizationprograms,309-310

quarantine,311

recoveredpopulation/removals,304n,305n

tlpplngpOlnt,305-309 Sla°e,M.,796

Slovic,P.,30,600,654

Smallpox,309-310 Smith,Adam,168,369,386,788,862

Smith,D.,32-33

Smith,V.,2 7,814n

Snapshottest,199-201 Socialevolution,896

Socialsystems,counterintuitivebehavior,5-10 Softvariables,853

statisticalestimationof,868-869 Software

fornumericalintegration,904

productioncosts,383

Solarsystemregularity,115n

SonyCorporation,346,360-361,363,371,384,

403

SouthSeabubble,173

Speculativebubbles,173

Spicer,Andrew,227

S-shapedgrowth,285-289,295;seealso

ModelingS-shapedgrowth conditionsfor,119-120

withovershoot,121

overshootandcollapse,123-127 stmctureandbehavior,118-121

Stableequilibriumattractor,351 StandardOiltrust,376

Standardsformation,391-406

Stasis,127

State-deteminedsystems,202

Statevariables,197,202

Staticequilibrium,232

Statisticalslgnificance,868 Steadman,D.,125,126,127n

Steadystate,658-660

Steadystateerror,67ト672 Stein,∫.,654

Stepinput,426,427 Sterman,∫.,21,24n,27,29,34,35,37,38,42m,

65n,74n,76,79,94n,95n,97,1001101,

113,115n,124,130,132,157,378n,

388,390n,436,445,454,509,511,569,

575n,585n,587,634,637,640-641,

646,648,652,672,684m,687,688,693,

694,780n,784,785,787n,824n,857,

889,900

Stevens,A.,16

Index

Stevin,Simon,847n

Steward,良.,75n

Stewart,一an,231

Stiffsystem,909n

Stochasticcontrolproblems,599

Stockandflowmapping,102,210-229

aggregationguidelines,216-217

aggregationin,2131216

automobilerecycling,225-229

withcausalloopdiagrams,210-213

largeconstructionprojects,218-221

modelboundary,222-225 Stockandflownetworks

aglngChainsin,469-470 coflowsin,469

conservationofmaterialin,201-202

unitsofmeasure,198-199 StockandflOwstructure

ofcommodityproduction,798-800

HIV/AIDSepidemic,321

integratingCOflowsandagingchains, 509-511

0fmaterialdelays,411

parallel,456-457

andproductawareness,366-367

insupplychains,663-664

Stock-keeplngunits,711-713

Stockmanagement

amplificationratio,673 behavior,672-673

1gnOrlngSupplyline,695-698

steadystateerror,671-672

Stockmanagementproblem,666-675

decisionrulesforacqulSltlOn,668,6711672 stockandnowstructure,668-67l

Stockmanagementstructure,668-671,

6751683;seealsoLaborsupplychain;

ManufacturlngSupplychain behaviorof,680-683

examples,677

toexplainoscillations,663-664 0fhumanresources,757-758

andorlginofoscillations,684-707

977

Stockmanagementtask,666-667 Stocks,140

andaccumulation,191-197

inBassdi軌sionmodel,333

changesthroughratesofflow,2041206

coflowsinmodelingattributesof,4971511 cohortsof,470-474

contributiontodynamics,195-197 definition,192

inequilibrium,232

integrals/statevariables,197

negative,547

asvariablesinfirst-ordersystems,2641265 StocksandflOws

coupledbyinformationfTeedback,204

diagrammlngnotation,192-193

globalwamlng,241-249

identifying,1971210

auxiliaryvariables,202-204

changethroughrates,204-206 conservationofmaterial,201-202

continuoustime/instantaneousflows, 206-207

continuousorquantizedflows,207-208

snapshottest,199-201

stateofdeteminedsystems,202 unitsofmeasure,198-199

linkedwithfeedback,212-213

mathematicalrepresentation,193-195

modelingapproach,208-210

portrayedinpractice,209-210

rateequations,522-545

relationshipsbetween

graphicaldifferentiation,239-241

graphicalintegration,234-239

integrationanddifferentiation,232-234

staticanddynamicequilibrium,232

terminologyfor,1971198

WaronDrugs,250-262 Stolarski,良.,24

Strauss,A.,157

Strogatz,S.,133n,787n

Structureassessmenttests,859,863-866

978 Index

Studentworkloaddiagram,163-168 Sturis,∫.,664,864

Sturm,氏.,508

Submodels,869 SubstanceAbuseandMentalHealthServices

Administration,250

Subsystemdiagram,99-102 Suchanek,G.,27,814n

Sugarscapemodel,520 Suharto,380

Summarystatistics,874-880

Sunkcostfallacy,704,803n

SunMicrosystems,383,384

Superstition,31

Supplierleadtimes,738-740

Suppliermaterialdeliveryrate,732-735

Supply,ofcommodities,800

Supplychaincycletime,17-18

Supplychainmanagement,reenglneerlng, 740-742

Supplychains,130 BeerDistributionGame,684-694

characteristics,664

definition,663

instabilityandtrustin,735-740

livestockindustry,838

manufactunng,709-755

0rlglnOfoscillations,684-707

0scillation,amplification,andphaselag, 664-666

persistentcyclesin,697

stockmanagementproblem,666-675

stockmanagementstructure,675-683

Supplycurve,long-run,834

Supplyline,675

mismanagementof,684-694

reasonsforlgnOrlng,695-698

Supplylineadjustmenttime,680-681

Surprisebehaviortests,860,882-883 Swanson,M.,900

Sweden,482

Sweeney,良.,122n,474

Symbioslnc.,449-462

Synergyforcorporategrowth,382-385

Systemdynamics andbehavior,28-29

andboundedrationality,26

causalloopdiagrams,102

causalloopnotation,137-141 definition,4-5

dynamicsofstocksandflows,231-262 erroneousinferencesabout,29

fastversusslow,909n

feedbackin,12-13,137

feedbackloopsin,21123

first-ordersystems,263-264 futureof

foreducation,900-901

inimplementation,899-900

technology,896-898

theory,895-896

growthexpectationsin,634

guidelinesforcausalloopdiagrams,141-157

maintenancegame,66-79

meanlngOffeedbackin,13114

mentalmodelconcept,16-18

modelboundarychart,97-99

modelingfor,88-89

modelingwithcausalloopdiagrams,159-168

nonlinearrelationships,551

pathdependence,349

policystructurediagrams,102

prlnCiplesforsuccessof,79181

reasonsfordynamiccomplexity,21123

requlrementSfb∫successfulleamlng,33-39

stockandflowmaps,102

stocksandflows,1911197,1911229

subsystemdiagram,99-102

Systemdynamicsapplications

autoleasingStrategy,42-55

automobilerecycling,225-229

commoditycycles,824-828

forecastlngSemiconductordemand,449-462 freemarketstructure,168-177

Ⅰndex

futureof,901

globalwarmlng,24ト249 healthinsurance,175-177

largeconstructionprojects,218-221

overtimeversuscuttlngco∫ners,563-569

populationandeconomicdevelopment, 481-485

proJeCtmanagement,55-66

rangeof,4ト42 studentworkload,163-168

supplychainreenglneerlng,743-755

trafficcongestion,1771190

WaronDrugs,2501262

SystemDynamicsGroup,MIT,74

Systemdynamicsintervention;SeeModeling

Systemdynamicsnationalmodel,441-445

SystemDynamicsSociety,684n

Systems;seealsoComplexsystems;Dynamic

SyStemS

inequilibrium,232 structure,107

Systemsthinking,4-5

Tablefunctions

versusanalyticalfunctions,562-563 definition,552

guidelinesforformulating,553

nonlinearrelationshipsuslng,552-563

refinedwithqualitativedata,5691570

Specifying,552

TacomaNarrowsBridge,919

Targetsalesforce,617

Taylor,H.,229,823,824,868

Technologies

todecreasetrafficcongestion,1881189

infutureofsystemdynamics,896-898 inferior,3871389

andlimitstolockin,389-391

Tenner,Edward,8n

Teplitz,C"338,369

979

Tewskbury,R.,75n Thaler,氏.,171,600n,800,814n

Theil,H.,648,875

Theil'sinequalitystatistics,874-880

Theoryofrationalchoice,599

Thermostat-with-time-delayanalogyofbusiness

cycles,785-786

Themodynamics,119 Thomas,∫.,27

Thomas,Lewis,8

Thornton,L.,701

Thoroughbredhorsemarket,174 3Com,383

Throughput,197

Thursby,J.,855-856

Tightlycoupledsystems,22 Timeconstant,276-277,279-280

Timedelays;seealsoMaterialdelays BeerDistributionGame,6841694

andbusinesscycles,697

indecisionmaking,21

lgnOnngSupplyline,695-698

andinstability,23

andproductawareness,366-367

recognlZlngandaccountingfor,696 stocksassourceof,196

supplylinecorrections,684 variable,434-437

Timehorizon,90-94

exponentialdecay,276-280

andexponentialgrowth,2681272

Time-seriesforecastlng,43ト432

Ⅵmestep

approprlate,907-908

chooslng,910 variable,909

Timmers,H.,29,270

Tippingpolnt,305-309

movlngpast,314-316

Totalqualitymanagement,112 Tわxins,425

Tradetheory,386

980 Index

Trafficcongestion extentof,177-178

masstransitdeathsplra1,185-188 mentalmodelof,178-180

policyanalysュs,189-190

policyresistanceexample,177-190

responsetodecreasein,181-185

sourceofpolicyresistance,189-190

Transportationlag,415,416 TRENDfunction,634-638

behaviorof,638

boundedrationalityof,638

causalstructureof,635

energyconsumptionforecasts,6401641 toforecastinflation,646-653

initializationandsteadystateresponse, 658-660

TrivialPursultgame,340

Troyano-Bemudez,L,378n,824n

Trust,insupplychains,735-740

Tsembagatribe,873

Tsipis,K.,8651866

Tversky,A.,30,600,654,670

Two-stagesupplychain,729-734

Ueda,Yoshisuke,284-285

Unambiguouspolarities,146-147

Undershooting,114

Unemploymentrate,116

Unitdevelopmentcosts,367-368

UnitedAssetManagement,383 UnitedNationsFrameworkConventionon

ClimateChange,242

UnitedNationslntergovemmentalPanelon

ClimateChange,242 UnitedStates

economicrecoverypotential,865-866

electricutilities,796

energyconsumptionforecasts,639-653

incidenceofAIDS,320-321

oilindustry,92-94

pulpandpaperindustry,835

unemploymentrate,116 UnitedStatesCensusBureau,376,481

UnitedStatesDepartmentofEnergy,217, 642-643,870

UnitedStatesDepartmentofJustice,384

UnitedStatesDepartmentoftheinterior,643

UnitedStatesEnergyInformation Administration,249

UnitedStatesHealthcare,383

UnitedStatesNavy,55-66

UnitedStatesNavyAEGISExcellenceAward, 65

UnitedStatesSteel,376

Unitproductioncostsforsoftware,383

Universityfacultypromotionchain,485-490

Unscientificreasoning,30132

Unstableequilibriumrepellor,352

Up-frontdevelopmentcosts,3671368 forsoftware,383

Uranus,848

Urban,G.,347

UrbanDynamics(Forrester),81,122n,4721474,

479,514

USAToday,47

Usedcarsales,48

Usedcarsuperstores,42,47

Vaccination,309-312

Just-in-time,317-318 Validationofmodels,81,846-850

VanAIstyne,Marshall,864n

VanMaanen,∫.,157

VanTilburg,∫.,127n

Variablecapacltylifetime,832 Variablecosts,803 Variablenames

nounsornounphrases,152

positivesenseofdirection,153 Variables

causallinks,138-141

Index

incausalloopdiagrams,160 causationversuscorrelation,14ト142

noisy,913-914

Variabletimedelays,434-437

Variabletimestepmethods,909

Vaupel,∫.,482n

VAX11/750minicomputers,325-328,334

VCRindustry,345-346,359-364,384,387,

392-396,403

VehicleRecyclingPartnership,227

Vehiclesales,service,andmarketing(GM),42, 43

Vendor-managedinventory,740-742

Vennix,∫.,16,95m,889,899

Vensimsoftware,904

Verhulst,FranGOis,284,296

Verhulstgrowth,296 Verificationofmodels,8461850

Verticalintegration,3751376

Ⅵ∋tter,D｡,855,857

VHSfomat,359-364,387,392-396,399,403

Videocassetterecorders',seeVCRindustry Virtualworlds

createdbymodeling,83-84

Pitfallsof,35137 virtuesof,34-35

Ⅵsualizing,586

Wageandpricecontrols,7-8

Wagenaar,W,29,269,270 Walden,D.,15

Wallace,W,85n

Wallis,Lyle,449n,450-454,460,461 WallStreetJournal,43,48,857

WaltDisneyCompany,376

WangLaboratories,391 Wamer,R.,917n

WaronDrugs,250-262

Wason,P.,31

Wasontest,30-31

981

Watson,Thomas,Jr.,372-373

Weaklyinteractlngmassiveparticle,849

1砲althofNations(Smith),168,369,386 Weibulldistribution,299

Weightedaverage,nonlinear,535-537

Weil,班.,65m,899

Wein,L"414n

Well-conditionedmodels,906n

WemerEnterprises,383 WestAntarcticIceSheet,247

Weymar,H.,798m

Wh iteHouseOfficeofNationalDrugControl

Policy,250,258

Whitenoise,915-917

Wigley,T.,243

Wilcox,∫.,646n

Wlllbratte,B.,436n

Williams,A.,27,814n,823

Williams-Sonoma,383

Wilson,T.,157

Winter,S.,537n,542,598

Wisdom,Jack,115n

Wittenberg,∫.,24n,388,900

Wolstenholme,E"37,38

Word-of-mouthreports,365-366

Workforcequalityandloyalty,3761378

Workinprocessinventory,710

inlaborsupplychain,77ト773

modeltestlng,721-723

andproduction,7131718 Ⅵbrkweek

addingovertime,774-776

fatigueandproductivity,577-584

flexible,7761778

WorldDynamics(Forrester),48l

WorldHealthOrganization,310 WORLDSmodel,887

Worldpopulationmodels,48ト485

Wormley,D.,463n

Worstcasesensitivltyanalysis,885-886

Wright,H.,6,7

Wright,P"243

982 Index

Writtendata,853

Wulwick,N.,855n

Yerkes,R.,577

Yerkes-DodsonLaw,577-578,582

Yin,氏.,157

Yoon,Y.,386

Young,Allyn,386

Yourdon,E.,65n

ZamudioIRamirez,Pavel,225,227,229

Zangwill,W,507

Zaraza,氏.,900

Zarella,Ron,42-13,47-48,50,53

Zamowitz,Ⅴ,784

Zcnios,S.,414n

Zerodefectsmanufacturlng,112

Zero-emissionvehicles,11

Ziman,John,850

BusinessDynamics
PartⅠ Perspective and Process
PartⅡ Tools for Systems Thinking
PartⅢ The Dynamics of Growth
PartⅣ Tools for Modeling Dynamics Systems
PartⅤ Instability and Oscillation
PartⅥ Model Testing
PartⅦ Commencement