Fin- ct 9

Interactive Multiple Criteria Optimization forCapital Budgeting in a CanadianTelecommunications CompanyJean-Michel Thizy1, Daniel E. Lane1, Savvas Pissarides2 & Surendra Rawat1;3?1 Faculty of Administration, University of Ottawa, Ottawa ON K1N 6N5, Canada,2 Bell Canada, 160 Elgin St., Ottawa, Ontario, K1G 3J4 Canada,research conducted while at the University of Ottawa,3 Stentor Research Centre Inc., 160 Elgin St., Ottawa, Ontario, K1G 3J4 Canada.Abstract. Decision Support System for Optimal Resource Allocation(DSS ORA) is an interactive mathematical programming system for op-timal resource allocation developed to support decisions of investmentin capital intensive telecommunications projects. The system strives tomaximize corporate goals while respecting �nancial constraints such asthe availability of capital funds, institutional requirements and varied de-pendencies or synergies among projects. The Analytical Hierarchy Pro-cess (AHP) is used for quanti�cation of qualitative managerial judgmentin regard to the relative value of projects through a two stage process. Aninitial resource allocation is found by a linear program, the objective co-e�cients of which are determined by the AHP. Then, a modi�ed simplexalgorithm proposes some rates of funding substitution. Users choose theamount of substitution or can override the substitutions proposed. Thus,users can build gradual con�dence in the constraint checking mechanismof DSS ORA and come to rely on its e�ciency-seeking capabilities. DSSORA has been tested by several groups of managers responsible for themanagement and the implementation of project portfolios with signi�-cantly consistent results. The exibility, user friendliness and quick timeresponse of DSS ORA make it an e�ective negotiation tool in a group set-ting.Keywords. Interactive multiple criteria decision making, optimization,capital budgeting, telecommunications, mathematical programming1 The Capital Budgeting ProcessWhile capital budgeting constitutes a classical resource allocation problem, itsexercise by corporate planners is regulated by institutional procedures to ensureaccountability, respect organizational structures, safeguard minority interests,etc. For example, determining the total amount of capital to be allocated, whatactivities should be considered for funding, which criteria are compatible with the? Research supported by Bell Canada, NSERC Operating Grants OGP 0042197 andOGP 0043693, and AUCC Going Global Program

direction of the �rm are all steps that require careful judgment and deliberationmuch before the decision model leading to a capital allocation is de�ned.The adequate design of an analytical model to meet these requirements ischallenging: capital budgeting models are often hindered by a poor economicmeasure of the costs and bene�ts of each project and their uncertainty. Sys-tematic methods for capital budgeting have been actively investigated by publicutilities such as telecommunications companies (Salo, 1989; Hoadley, 1993). Thedecision support system described here centers around a multiple objective pro-gram (MOP) for the annual capital budgeting exercise of a Canadian telecommu-nications company. It has been used by a functional group of the Company whichis responsible for the management of a portfolio of programs4. These programsare presented to the Company's central capital budgeting committee allocatingresources among all functional groups of the �rm. Each program coordinates acoherent set of projects meeting a common set of objectives. Given the resourcesawarded to a particular program, the method proposed can in turn help allo-cate these resources to individual projects participating in the program. Hence,in agreement with most of the literature on capital budgeting, we will gener-ally use the narrower term project, reserving the term program to the familiarconstruct of mathematical optimization.Limited resources prevent the Committee from funding all the projects ac-cording to the requests of the functional groups. Therefore the projects are pri-oritized, using explicit criteria that re ect the Company's mission. Currently,the evaluation of each project with respect to each criterion involves humanjudgment based upon the knowledge, in uence and experience of each memberin the budgeting Committee. The decision-makers must also consider a numberof organizational and operational constraints, such as project interdependen-cies. The Committee makes decisions that may be contested by some functionalgroups' managers. Legitimate concerns prompt the Committee to reconsider theallocation by modifying the rules used to de�ne the Company's criteria, the con-tributions of the projects to these criteria and the nature of project dependencies.The appeal mechanism provides evidence of the complexity and the uncertaintyexisting in the actual budgeting decision process. Much of the di�culty comesfrom qualitative and subjective views of the Company's mission and the role ofthe projects to accomplish this mission.Our decision support system aims at forming a more explicit, quantitativeevaluation of the mission and goals of the Company and the suitability of alter-native capital projects to achieve them. It can be used either by the Committeeor by di�erent unit managers to prepare their funding request or to respondquickly in the event that resources requested are not fully allocated.4 It is precisely such program planning that lead to the �rst use of linear programming(Dantzig, 1963), originally called Programming in a linear structure.

2 A Multiple Objective Programming System for CapitalBudgetingWe now focus on a mathematical formulation of a multiple objective programfor capital budgeting.2.1 Review of Previous ModelsLinear programming was applied to capital budgeting from its inception; thereexists a vast number of analyses of capital budgeting by linear programming. Webrie y review landmark analyses for MOP; for extensive bibliographies, readersshould consult monographs such as (Bierman, 1988; Bromwich, 1979; Clark,1984; Crum, 1981; Dean, 1951; Wilkes, 1983).Charnes, Cooper and Miller (1959) were the �rst to formulate a linear pro-gram to solve a capital budgeting problem:max nXj=1 cjxjsubject tonXj=1 aijxj � bi for i = 1; . . .; m0 � xj � 1 for j = 1; . . .; nwhere:cj is the net present value of Project j,aij is the amount of Resource i required by Project j,bi is the total amount of Resource i available,xj is the fraction of Project j accepted,n is the number of projects competing in the allocation,m is the number of resources considered in the allocation.Spronk (1981) extended the use of goal programming in capital budgeting byproposing an interactive multiple goal programming method based on a mutualand successive interplay between a decision-maker and an analyst. Spronk viewedhis method, which does not require explicit representation of the decision-maker'spreference function or trade-o�s among competing objectives, as superior toconventional goal programming techniques.Deckro, Spahr, and Herbert (1985) presented a non-linear goal program withthree basic sets of goals: maximization of net present value, cash ow budgetingand control of risk.

2.2 The Multiple Objective Program of DSS ORADecision Support System for Optimal Resource Allocation (DSS ORA) is an in-teractive multiple objective programming system for e�cient resource allocationdesigned to support collective capital budgeting decisions.The allocation of resources to the projects is made subject to a number ofinequalities, the most important of which is the capital funds constraint thatrepresents the total availability of capital that may be allocated to all projects.Other constraints include overall short term �nancial impact of the portfoliosuch as the maximum level of acceptable depreciation expense for each projectfor the planning period. Constraints can also be used to represent dependenciesor synergies among projects: for example, some projects cannot be implementedunless at least a certain portion of another project is implemented. Finally, thefunding of every project is limited by upper and lower bounds. Our preciseformulation is:E�cient fMission satisfaction(x1; . . .; xn)g (1)subject to:Availability of Capital: nXj=1 xj � C (2)Depreciation Limit: nXj=1 djxj � D (3)Employees for implementation: nXj=1 ejxj � E (4)Software and other expenses: nXj=1 sjxj � S (5)Dependencies & Synergies: nXj=1 aijxj � bi for i = 1; . . .; r (6)Bounds: lj � xj � uj for j = 1; . . .; n (7)where xj measures the level of funding of Project j. DSS ORA assesses satisfac-tion of the corporate mission via a multi-valued function F in (1) that can beimproved by increasing corporate criteria such as revenue generation, revenueprotection, savings and strategic importance, themselves implicitly known func-tions of the allocation. Inequality (2) represents the capital constraint, in whichC denotes the total budget to be allocated among the n projects. Inequality (3)represents the depreciation constraint, where the coe�cients dj are the numberof dollars depreciated per dollar allocated and D is the total amount of depre-ciation allowed. In a similar way, ej represents the number of employees needed

per dollar allocated and E is the total number of employees; sj denotes thesoftware and other expenses per dollar allocated to Project j and S is the totalbudget for software and other expenses. Constraints (6) represent dependenciesand synergies between projects. Finally, in (7), uj and lj represent the upperand lower limits of allocation to Project j. For ease of presentation, the modelis summarized as: E� fF(x)g (8)s.t.Ax = b (9)x � 0 (10)where x = (x1; . . .; xp)T, A is a full row rank m� p matrix, b is an m-vector andF is a multi-valued function. The operator E� seeks the e�cient region speci�edby the program, although the interactive procedure described in Paragraph 2.4is designed for more exible exploration.2.3 The Analytic Hierarchy ProcessAn initial allocation will �rst be obtained by calculating linear approximationsof the multi-valued criterion function: F = (Fh(x))h=1;...;H, where Fh is a linearcriterion. The Analytic Hierarchy Process (Saaty, 1980) is used to assess thevalue of each of its coe�cients, called priority.Step 1: Decision makers must choose a number of criteria important to the Com-pany's mission.Step 2: The relative importance of each pair of criteria is measured in order to obtainan overall scale of importance. When individuals in the evaluation group dis-agree, a compromise on a given comparison can be obtained either by discus-sion, vote or by taking the geometric mean of every member's comparison.This measurement resembles the familiar MOP method of point estimateweighted sums that de�nes nonnegative multipliers �h for h = 1; . . .; H suchthat: PHh=1 �h = 1; these can be used to reduce the criterion function to thelinear objective: max HXh=1 �hFh(x1; x2; . . .; xn)(the similarity will be re�ned in Step 4 of the procedure.)Step 3: Assess the value of each of the coe�cients of Fh, i.e. the relative impact ofeach pair of projects on each criterion h, by a series of pairwise comparisonsanalogous to those of Step 2.Step 4: The overall priority of each project is obtained as the inner product of thevectors obtained in Step 2 and Step 3 (for this project).Consider for example the allocation of resources to four projects, P1, P2, P3and P4.

Step 1: Suppose that the capital budgeting decision group chose the criteria: revenuegeneration, revenue protection, savings and strategic importance (labeled A,B, C and D). The corresponding hierarchy is displayed in Fig. 1. Mission

Revenue protection

(B)

Operational savings

(C)

Project P3

Project P1

Project P4

Project P4

Project P2

Strategic Importance

(D)

Revenue generation

(A)

Fig. 1. AHP hierarchy for selection of telecommunications projectsStep 2: For the sake of simplicity, we assume that every comparison was made unan-imously by the decision-making group. The following is the comparison ma-trix for the criteria (for instance, the second coe�cient: 5 signi�es that thecriterion B is valued as more important than A):0BB@ A B C DA 1 5 3 5B 1=5 1 1=3 1C 1=3 3 1 3D 1=5 1 1=3 1 1CCA yielding � = 0BB@A 0:558B 0:096C 0:249D 0:0961CCA

Step 3: Next are the matrices of comparisons of the projects under each criterion:0BB@A : P1 P2 P3 P4P1 1 1 7 5P2 1 1 7 5P3 1=7 1=7 1 1=3P4 1=5 1=5 3 1 1CCA 0BB@B : P1 P2 P3 P4P1 1 1=5 1 3P2 5 1 5 7P3 1 1=5 1 3P4 1=3 1=7 1=3 1 1CCA0BB@C : P1 P2 P3 P4P1 1 3 5 1=5P2 1=3 1 1 1=9P3 1=5 1 1 1=9P4 5 9 9 1 1CCA 0BB@D : P1 P2 P3 P4P1 1 5 7 1P2 1=5 1 3 1=3P3 1=7 1=3 1 1=7P4 1 3 7 1 1CCAFollowing the method of Step 2, for each criterion, comparisons betweenprojects yield one column of the following matrix:0BB@ A B C DP1 0:424 0:153 0:199 0:440P2 0:424 0:632 0:066 0:121P3 0:050 0:153 0:058 0:052P4 0:102 0:062 0:677 0:3871CCAStep 4: By multiplying this matrix by the vector of multipliers � found in Step 2,one gets the overall priorities 0BB@P1 0:34P2 0:33P3 0:06P4 0:271CCA.The priorities are then used as objective coe�cients of a linear program withconstraints (2)-(7) to produce an initial allocation of resources:max 0:34x1 + 0:33x2 + 0:06x3 + 0:27x4The constraints of the example include only Capital Availability (2) with anoverall allocation of $180 million, and a dependency constraint (6):0:5x1 + x3 � 80:Given individual bounds (7) displayed in Table 1, the capital allocation obtainedby linear programming is contained in its last column.

Table 1. Allocation constraints (the rightmost three columns display $ million)Project Priorities Dependency Lower Upper InitialLimit Limit AllocationP1 0.34 0.5 20 50 50P2 0.33 0 25 35 30P3 0.06 1 35 65 55P4 0.27 0 45 55 45Capital available : $ 180 millionDependency right hand side : � 802.4 The Interactive AllocationThe allocation delineated previously may need further re�nement or sensitivityanalysis. To these ends, the decision system o�ers an interactive procedure thatleaves a great leeway to decision-makers while enforcing the budget or otherconstraints.In fact, it was found that not only the values of the priorities, but even theanalytical form of each criterion could be elusive. Thus, the decision system doesnot resort to an interactive optimization in the space of criterion multipliers �as classical MOP methods propose, but allows users to assess their preferencesdirectly in the space of budget allocations. At each step, a modi�ed simplexalgorithm proposes some rates of funding substitution. Then, users decide inter-actively what amount of substitution is preferable, and can override the ratesproposed. Therefore users can propose their own solutions, build gradual con�-dence in the constraint checking mechanism of the simplex method, and come torely of the e�ciency-seeking capabilities patterned after (Geo�rion, 1972; Zionts,1976).Consider the preceding formulation (8){(10). Let the current solution x bepartitioned as x = (xN; xB), where xN is the subvector of nonbasic variables andxB is the subvector of basic variables. Correspondingly, A is partitioned as A =[NjB], where N consists of the nonbasic columns of A and B consists of the basiccolumns. Hence: NxN + BxB = b:Multiplying both sides by B�1 yields:B�1NxN + IxB = B�1b;which is equivalent to: xB = B�1b � B�1NxN :De�ne the matrix Y = B�1N. Each of its components yij describes the amountof decrease in the basic variable xBi caused by a unit increment in the non-basic

variable xNj. Hence, its columns y1; y2; . . .; yp�m can be used to de�ne trade-o�vectors. At the t-th iteration of the following algorithm for interactive resourceallocation, each of the preceding quantities receives a superscript t.Step 0: Set the iteration counter t at 0. Select an initial solution (e.g. from the initiallinear program): xoB = (Bo)�1(bo � NoxoN):Step 1: For every nonbasic variable xtNj, j 2 [1; . . .; p � m], a trade-o� vector ytj iscalculated and presented to users.Step 2: Either select a proper amount of trade-o� �xtNj for some j 2 [1; . . .; p�m],using: mini:ytij > 0�xtBiytij � � �xtNj � max��xtN; maxi:ytij < 0�xtBiytik ��;and let: x'B = xtB � ytj�xtNj;x'Nk = xtNk for k 6= j;x'Nj = xtNj + �xtNj;or terminate with solution xt.Step 3: If, for some index q 2 [1; . . .; m], x'Bq = 0, then letxt+1 = (e1; . . .; ek�1; ep�m+q; ek+1; . . .; ep�m+q�1; ek; ep�m+q+1; . . .; en)x';�k = (�y1k=yqk;�y2k=yqk; . . .; 1=yqk; . . .;�ym�1=yqk;�ym=yqk)and (Bt+1)�1 = (e1; . . .; ek�1; �k; ek+1; . . .; en)(Bt)�1;else let xt+1 = x'.Set t = t + 1 and go to Step 1.For example, at the optimum of the linear program displayed in Table 1, partof the rows of the matrix �Y corresponding to the original variables x1; x2; x3;and x4 is shown below: 0BB@P1 �1: 0:0 0:0 0:0P2 0:5 �1: �1: �1:P3 0:5 1:0 0:0 0:0P4 0:0 0:0 0:0 1:0 1CCA: (11)To illustrate the use of the preceding matrix, suppose users choose a trade-o�characterized by the direction of the �rst column, in an amount �xtN1 = 5. Theallocation to Project P1 decreases by 5, the allocations to Projects P2 and P3

each increase by 2:5. The allocation to Project P4 stays the same. Thereforeafter decreasing the funding of Project P3 by 5, the allocation is given by (12).0B@ 4532:557:545 1CA (12)The third column of the matrix (11). indicates that it is feasible to simplydecrease the allocation to Project 2. Unlikely at �rst brush, such a decisionof purely reducing resources for a project may be useful both from a practicalstandpoint (it enables decision makers to reduce the resources allocated) andfrom a theoretical one: users can avoid the pervasive assumption that their util-ity function must be pseudoconcave, under which larger allocations are alwayspreferred to smaller ones (Zionts, 1976).3 Computer ImplementationDSS ORA provides a decision support environment that comprises modules for �-nancial information management and resource allocation. Each module is imple-mented as a small library of objects written for Microsoft Windows (Pissarides,1992). Financial information modules are designed to monitor capital resourceavailabilities and project requirements, e.g., by storing information about capitalrequirements, allowable depreciation expense, software and other expenses, man-power needs and relationships between projects. Among the modules supportingdirectly the interactive resource allocation:{ a module for project value assessment implements the AHP methodology tocalculate priorities for each project,{ an optimizing module uses them to determine an initial allocation by linearprogramming, and{ a module of budget reallocation allows users to explore alternative fundingby proposing some substitutions, one of which to be selected by decisionmakers.Fig. 2 represents the mutual relationships between the modules of DSS ORAwhich are described in more detail next.3.1 Project Value AssessmentThis module implements the AHP methodology on a hierarchy formed by a toplevel comprising criteria for the corporate mission and a bottom level for theprojects, as described in Sect. 2.3 and Fig. 1.

Interactive resource allocation

Resource availability

Initial resource allocation

Project evaluation

Project requirements

Fig. 2. DSS ORA module diagramComparisons of mission criteriaUsers are �rst asked to input at most �ve names of criteria characterizing thecorporate mission. Although there is no theoretical limit on the number of crite-ria, it has been found that �ve kept the number of comparisons within tolerablelimits. Users must then compare each criterion with each of the other ones,choosing one of the following characterizations:{ Equal{ Moderately More Important

{ Strongly More Important{ Very Strongly More Important{ Absolutely More ImportantThe interface used for the comparisons is shown in Fig. 3. Users are required to�ll in the boxes with appropriate symbols. When all the comparisons are made,the system presents users with a vector of priorities for the criteria depicted inthe rightmost column of Fig. 3. Fig. 3. Project value assessment: mission criteria; projects.Comparisons of projectsFor the second level of the hierarchy, users must compare each pair of projects, asshown in Fig. 4. The projects are compared pairwise according to each criterion,following the same procedure as for criterion comparisons. At the end of thecomparisons for a given criterion, the system presents users with the projectpriorities according to the current criterion together with an inconsistency ratio(Saaty, 1980). If this ratio is too high, users can go back and compare the pairs ofprojects again. When all the projects are compared according to all criteria, thesystem presents users with the overall project and criterion priorities togetherwith the overall inconsistency ratio. Again, if the ratio is too high, users canrevise the comparisons in order to obtain a better ratio.

Fig.4. Project value assessment: projects.3.2 Initial Resource AllocationThe priorities are used as objective function coe�cients of a linear program thatdetermines an initial allocation of resources to projects. Designing a simplexalgorithm was eased by implementing it as an object for an integrated manipu-lation of the simplex tableau, performing the following functions:{ keep track of all the elements in the tableau,{ keep track of the size of the tableau,{ perform pivot operations.3.3 Interactive Resource AllocationThe module for interactive allocation displays the current allocation in an easyformat. It allows users to change some of the inputs from the previous modulesin order to obtain a more desirable allocation, or directly to swap some resourcesbetween projects without violating the constraints. For each project, the interac-tive analysis displays information on objective coe�cients of the original linearprogram, its modi�ed values and corresponding allocations, as shown in Fig. 5and itemized below:{ original objective coe�cient determined by AHP analysis,{ current objective coe�cient,

Fig. 5. User interface for interactive resource allocation by sensitivity analysis{ a scroll bar to change the objective coe�cient,{ original allocation determined by linear programming,{ current allocation,{ a scroll bar to change the allocation.For sensitivity analysis of the resources, the module also displays the followinginformation relative to each constraint:{ original right hand side value{ current right hand side value{ a scroll bar to allow the change of the right hand side value,{ original value of the left hand side determined by linear programming,{ current value of the left hand side.The module o�ers four options to change the allocation of resources:{ change of objective function coe�cients,{ change of amounts of resources (the right hand side of the constraints),{ computer-assisted change of funding allocation, and{ unassisted change of funding allocation.In the �rst two options, the allocation is modi�ed by selecting the menu item\Optimize" on the screen, which accepts the new data as input to the simplexalgorithm contained in the module described previously and displays the new

allocations both numerically and on scroll bars. Therefore users can performsensitivity analysis on both the objective coe�cients and the constraint righthand side values by dragging the scroll bar cursors in either direction. In Fig. 5,for a new objective functionmax 0:31x1 + 0:31x2 + 0:06x3 + 0:32x4;the allocation becomes:x1 = 50; x2 = 25; x3 = 55; x4 = 50:The last two options, illustrated in Fig. 6, allow users to by-pass re-optimizationby linear programming: in particular, they need not express the mission criteriaas algebraic functions. In the last option, i.e. unassisted change, they can simplychange the allocation of resources to the projects by changing the position ofthe cursors on the scroll bars, using the mouse. Each cursor on the scroll barscan move until one of the constraints is violated. For example, users can achievea more desirable solution by decreasing the allocation to Project P2 from 30 to26 and increasing the allocation to Project P4 from 45 to 47. In this unassistedchange, any arbitrary allocation will be possible within the constraints speci�ed.Of course, the new solution may not be optimal with respect to the objectivecoe�cients displayed by the interface. Fig.6. User interface for interactive resource allocation: computer-assisted trade-o�s

In an assisted change, users can select one allocation trade-o� from a listgenerated by the system, shown in Fig. 6, that transposes the matrix of reducedcoe�cients (11).Each trade-o� indicates a rate of funding substitution. Users can decide tochange the allocation by pressing a button on the screen. The changes are re- ected by the position of cursors on the scroll bars and the corresponding displayof values, both of which representing the allocation levels to each project. Forexample, choosing the �rst trade-o� yields the new allocation given by (12).Users are allowed to switch to a di�erent trade-o� at any time. When oneof the right hand side values becomes zero, the system performs a pivot andupdates the list of trade-o�s.The algorithm is designed to help users get a better understanding of theproblem at hand by exploring the region speci�ed by the constraints. It doesnot require any analytic expression of the objective or utility function whichin particular need not be pseudoconcave, a quali�cation that would restrict thesearch to extreme points only.4 Field TrialA �eld trial was conducted to test whether DSS ORA could support group deci-sions as required by the Company's budgeting process. Two groups that workedwith DSS ORA consisted of �ve managers. First, a functional group of sta�managers responsible for the funding of a portfolio of �ve programs labeled P1,P2, P3, P4 and P5 (each consisting of numerous projects) had to develop theirfunding allocation request for the programs. The group held a managerial view ofeach project and its role in the portfolio, rather than a technical understandingof its functions and value in the corporate telecommunications network. Conse-quently, its members di�ered fairly substantially in their initial evaluation of theimportance of each program toward each corporate mission criterion, as shownin Table 2. Yet, consensus was required of this request by the line managersresponsible for implementation of these programs before the request could beforwarded to the control committee responsible for funding allocation.Saaty (1990) noted that the hierarchical representation and the pairwise com-parisons have intuitive appeal, pinpointing internal inconsistencies of judgment.This was con�rmed in our case, as a �rst evaluative session sparked a discus-sion aimed at developing a common understanding of the role of the projectsin satisfying corporate mission criteria, and of critical underlying assumptionsunder which all projects had to compete for funding allocation. Attesting to theadequacy of the method, the outcome of the second session of pairwise evalua-tions was that the priorities of each of the managers for the programs were closeenough to reach a unanimous consensus about the validity of the values basedon the average input of the group, displayed in the last column of Table 2. Therole each session of DSS ORA toward this progressive conciliation is representedin Fig. 7.

Fig.7. Using DSS ORA for consensus building

Table 2. Project importance assessment resultsBased on inputs Based onfrom Manager averageProject 1 2 3 4 5 inputsP1 0.079 0.045 0.037 0.061 0.066 0.063P2 0.322 0.170 0.466 0.351 0.251 0.311P3 0.135 0.067 0.111 0.078 0.158 0.111P4 0.239 0.467 0.169 0.125 0.086 0.206P5 0.226 0.250 0.216 0.386 0.474 0.306The second group using DSS ORA comprised line managers responsible forthe implementation of the projects within the corporate telecommunicationsnetwork. Consensus was reached in one session, and the resulting project evalu-ations were signi�cantly close to the results obtained by the �rst group of sta�managers. Given the consensus, in neither experiment did the managers feel thatan interactive resource allocation was necessary.5 ConclusionDSS ORA has been tested with very consistent results by several groups ofproject managers. Beyond the interactive MOP methodology, the �eld trialproved that the system was an e�ective negotiation tool in a group setting.Applying DSS ORA to resource allocation within a functional unit limits thenumber of projects under consideration, with several ensuing bene�ts:{ familiarity of the managers with the projects,{ relatively few pairwise comparisons,{ increased likelihood of consensus building,{ limited interference of external constraints with the consensual evaluations,{ possible acceptance of results as a base for implementation.Capital budgeting in the Company spans many units and associated programs.To adapt DSS ORA to inter-unit budgeting, current research focuses on e�ectivedecomposition and aggregation techniques (Liang, 1994). A central issue is theformation of subportfolios of programs balancing two requirements:{ ease the comparisons of projects,{ circumscribe projects that share important technological or operational de-pendencies.In this setting, resource allocation could proceed along several tiers: allocation toportfolios of programs, followed by intra-program allocation to the constitutingprojects.

ReferencesBierman, H. Jr.: Implementing Capital Budgeting Techniques. Ballinger PublishingCompany, Cambridge, Massachusetts, 1988Bromwich, M.: The Economics of Capital Budgeting. Pitman Publishing Limited, 1979Charnes, A., Cooper, W., Miller, M. H.: An Application of Linear Programming toFinancial Budgeting and the Cost of Funds. The Journal of Business (1959) 20{46Clark, J. J., Hinderland, T. J., Pritchard, R. E.: Capital Budgeting. Prentice-Hall Inc.,Englewood Cli�s, New Jersey, 1984Crum, L. R., Derkinderen, F. G. J.: Capital Budgeting Under Conditions of Uncer-tainty. Martinus Nijho� Publishing, 1981Dantzig, G. B.: Linear Programming and Extensions. Princeton University Press,Princeton, New York, 1963Dean, J.: Capital Budgeting. Columbia University Press, New York, 1951Deckro, R. F., Spahr, R. W., Herbert, J. E.: Preference Trade-o�s in Capital BudgetingDecisions. IIE Transactions 17 (1965) 332{337Geo�rion, A. M., Dyer, J. S., Feinberg A.: An Interactive Approach for Multiple Op-timization with Applications to the Operation of an Academic Department. Man-agement Science 19 (1972) 357{368Hoadley, B., Katz, P., Sadrian, A.: Improving the Utility of the Bellcore business.Interfaces 23 1 (1993) 27{43Liang, Y.: Capital Budgeting Decision Making: Database, Aggregation and Disaggre-gation Methods for a Large Scale Problem. Master's thesis, University of Ottawa,1994Pissarides, S: Interactive Multiple Criteria Optimization for Capital Budgeting. Mas-ter's thesis, University of Ottawa, 1992Saaty, T. L.: The Analytic Hierarchy Process. McGraw-Hill Inc., 1980.Salo, A., Hamalainen, R. P.: A Modelling and Decisions Aid for Supporting Telecom-munications Investments. Proceedings of the IIEE International Conference on Sys-tems, Man and Cybernetics 1 (1989) 115{118Spronk, J.: Interactive Multiple Goal Programming as an Aid for Capital Budgetingand Financial Planning with Multiple Goals, in: Capital Budgeting Under Condi-tions of Uncertainty. Martinus Nijho� Publishings (1981) 188{212Wilkes, F. M.: Capital Budgeting Techniques. Wiley, 1983Zionts, S., Wallenius, J.: An Interactive Programming Method for Solving the MultipleCriteria Problem. ManagementScience 22 (1976) 652{663 This article was processed using the LTEX macro package with LLNCS style