Topic: Math/Physic/Economic/Statistic Problems

profiletutorthammy
mba_791_unit_4_lectures.xlsx
Home>Mathematics homework help>Topic: Math/Physic/Economic/Statistic Problems

4.3.1

WEEK 4 Continued Analysis with Simulation Models
Business Issue -- a process with variation -- want to understand the impact of that variation.
Business Problem Definition: BusQues: Can we develop a better understanding of …? (maybe) Which is the preferred alternative for the process?
Decision: Perhaps no decisions. Perhaps alternative settings of some aspect of the process or possible changes to process.
Objective Measure(s): One or more measures, e.g., cost, time, profit,... Risk profiles and/or summary measures like mean, 95 percentile, probability of a loss, etc.
Constraints: Structure of the process/system -- current policies, procedures, process design. Historical data of the random events to be used.
Data: Some data items are single values, some data items are specified probability distributions.
Analysis:
SIMULATION MODELING WITH EXCEL covered in week 3 & homework 3
(1) Build a CORE MODEL of the business process (one time through or one hour or eight customers or eight hours or one week, …)
One or more inputs to the model will be random in addition, model has fixed data inputs
Equally likely any value in range 0 - 1: =RAND()
Discrete distribution: values, probs =VLOOKUP(RAND(),cum prob table, col) Model will have formulas for how the process works
Contin- uous Distrib's Normal distribution: mean, stdev =NORMINV(RAND(),mean,stdev) -- shown in output cells:
Exponential distribution: mean value =-mean*LN(RAND())
Uniform distribution: low and high values =lo + (hi-lo)*RAND() Model may or may not have decisions
Disrete Uniform: low and high =ROUND(lo-.5 + (hi+.5-lo-.5)*RAND(),0) (process settings or choices)
Translated exp: constant value and
mean of added variation =const + (- mean*LN(RAND())) Objective: one or more key output measures, calculated with formulas:
NOTE: can make any continuous distribution discrete using =ROUND.
Will demonstrate in week 4
(2) TEST and VALIDATE this core model.
(3) REPLICATE the Core model many times (e.g., 1,000) in order to observe the "behavior" of the output measures -- A LARGE SAMPLE OF THE PROCESS
In Excel: Data --> What If Analysis --> Data Table -- resulting in 1,000 rows of the objective measure values
(4) ORGANIZE & SUMMARIZE the large number of (sample) values of each objective measure
=AVERAGE These describe the "middle" of all the values
=MEDIAN NOTE: Use the mean or average value of the large sample of that measure as the estimate of that measure for the whole population.
=STDEV
=PERCENTILE All these describe the variability or spread
Frequency Table using =FREQUENCY to show frequencies (#s) and proportions for defined classes. of each objective measure
Histogram using Insert Chart --called a RISK PROFILE -- a picture of the whole distribution
(5) PERHAPS, in the core model, change the decision VALUE or process design.
Repeat steps (2) -- (4)
(6) Produce A TABLE OF RESULTS , e.g., one column for each estimated objective measure and one row for each value of the decision variable (design option).
Include perhaps risk profile graphs for each value of the decision variable (design option).
Conclusions/Insights/Recommendations:
"Answers" to the business questions and other insights and/or recommendations.
ANALYSIS PROCESS:
Bus Sit/Ques with Signif Variation Build a Simulation Model Replicate --> Observe a Large Sample Summarize Sample Results - Answer Qs

4.4.1

Issue: Single Barber Shop EXAMPLE OF A COMPLETE ANALYSIS FOR A MGT REQUEST
Problem: Question: Can we understand better the current operations of this barbershop?
Decisions: Understanding may lead to decisions to improve. Exponential InterArrivals BARBER
Objective Measures: Three: wait time of customers -- in shop waiting (avg & 90 percentile), total time in shop, and idle time percent
Constraints: Only one barber; FCFS, estimates of haircut time and time between arrivals Uniform Service Time
Data: Estimated time to cut hair -- Uniform distribution with min = 15 and max = 35. DEMO:
NOTE: Can choose next service time as: =-avg*LN(RAND()) = min + RAND()*(max-min) 26.6 MIN NOTE: This is a fairly common service facility situation: Variable arrivals and variation in service time.
Note that exponential time (minutes) between arrivals is the same as Poisson # of arrivals per minute.
Estimated arrivals -- random with an average of 2 customers arriving every hour ( 1 every 30 minutes).
Interarrival time can be modeled as an Exponential distribution with mean = 30 minutes. NOTE: can't mix hours and minutes -- choose one.
NOTE: Can choose next inter arr time as: =-avg*LN(RAND()) = -30*LN(RAND()) 37.6 MIN
Analysis: Simulation Model (e.g., time to next arrival)
CORE MODEL: Barber shop open for 10 customers.
Haircut Time: Uniform min: 15 max: 35 minutes
Inter Arrival Time: Exponen'l mean: 30 minutes What will rows be used for? Columns?
Core Model here -- 10 customers ALL TIMES IN MINUTES Possible Objective Measures -- One Day
Inter Arrival Time Time Haircut Begins Time Haircut Ends Time in Barber Shop Barber Idle Avg Wait Time Avg Time in Shop
Customer Time of Arriv Haircut Time Time Waiting 8.0 min 33.0 min
NOTE: Core model here could not be one customer because of inter dependence of customers.* StDev Wait Time StDev of Time in Shop
1 48.2 48.2 48.2 17.6 65.8 0.0 17.6 48.2 14.7 min 18.2 min
2 116.3 164.5 164.5 16.4 180.9 0.0 16.4 98.7 90th Percentile Wait Time 90th Percentile of Time in Shop
3 19.0 183.5 183.5 16.5 200.0 0.0 16.5 2.6 22.6 min 50.5 min
4 0.2 183.6 200.0 27.4 227.4 16.4 43.8 0.0
5 59.9 243.5 243.5 27.2 270.7 0.0 27.2 16.1 Max Wait Time Percent of Time Idle These four requested in this case.
6 54.9 298.4 298.4 32.8 331.2 0.0 32.8 27.7 43.7 min 55%
7 12.6 311.0 331.2 27.7 358.9 20.2 47.9 0.0
8 4.1 315.1 358.9 30.7 389.6 43.7 74.4 0.0 Assumptions:
9 137.3 452.4 452.4 24.3 476.7 0.0 24.3 62.8 FCFS
10 77.8 530.2 530.2 28.5 558.8 0.0 28.5 53.5 No "balking" (leaving before service)
Could perhaps build a core model of 8 hours (480 minutes) using =IF statements to determine if 8 hours is exceeded (if so, no further arrivals). No "speed up" if many waiting
. . .
WHY NOT BUILD CORE MODEL OF ONE CUSTOMER ?? *For this system, performance for one customer (wait, idle, etc) is NOT independent of previous customers.
REPLICATE the core model.
Use Data Table to replicate a large number of successive 10 customer days (1,000) recording one or more of the 6 orange cells in the core model.
OR, model one day (=8*60=480 minutes). More complicated model that stops after 480 min. Then, use Data Table to 10 customer days of Barber Shop - 1000
replicate 1,000 days. Freeze the 1000 values -- so that worksheet is manageable. Avg Wait (min) Ave Time in Shop (min) 90 Percentile Wait (min) Percent of Time Idle
Number 8.0 33.0 22.6 55%
Calculate average time waiting and average time in barber shop (perhaps also stdev, percent tiles, etc) 1 4.8788173927 151.3873007684 164.4869887857 0.0010997497
Show risk profile (graph) of time waiting and time in barber shop 2 20.4356574391 69.074573719 109.9969057192 0.277309742
--estimated average wait time for 10-customer period. 3 31.4617263282 97.4187245934 128.0970022182 0.2505891147
--estimated stdev of wait time for a 10-customer period. 4 20.9102136235 25.1412694435 10.2771711722 0.4606629538
5 67.2650311726 23.3678106505 20.3752539227 0.6019494281
6 4.8370607946 91.5026386475 97.0488095934 0.0189462063
7 52.431141311 121.5165678276 164.0062276432 0.0600835521
8 17.654613798 43.1158571625 38.1810215455 0.409414599
9 7.0954742572 21.1777691915 4.6479296302 0.6612900334
10 34.3932097511 66.8186371722 88.1200997091 0.1008948066
11 23.8406666652 80.559879685 135.5273437853 0.0714488163
12 8.0941156329 13.5160872665 1.2029224459 0.6541940949
13 15.8586568561 92.1602997677 90.6249986341 0.1797881411
14 79.0462999224 47.2896775604 39.0859706616 0.4676034747
15 21.7659571907 29.6997634465 48.1807938713 0.5341841792
16 1.7829372342 42.6952251268 56.0923085953 0.4542872755
17 35.3495758656 16.4759906939 1.7092655823 0.5274458356
18 38.4751049235 81.9445718709 103.3513380092 0.3728851845
19 32.8933805212 12.5402299432 5.0969911488 0.6798208363
20 14.7325227487 181.2883518677 236.4555112988 0.1106526777
21 39.1688372149 43.7842135772 60.3349300333 0.2414501476
22 3.3540432992 176.676054093 192.4496437264 0.007877032
23 67.5104571398 28.8679546114 20.9167493451 0.5717200173
24 38.720871645 63.1684228652 57.6907692075 0.020371323
25 58.7789986162 85.6781826547 124.8582849373 0.2135888817
26 9.2822294483 39.5389192289 26.0628268073 0.3240102644
27 52.3372620684 42.8162862603 65.1911804151 0.3232756333
28 40.5196430751 33.4465220368 22.9630247297 0.1619732375
29 21.6324740747 19.0424762936 9.6444873449 0.5327391072
30 33.902774152 26.8786191375 13.8964293023 0.170598875
31 11.3124865699 143.6006447276 174.8689886319 0.3324993916
32 81.5214467292 108.7879245469 134.0889020895 0.2305072115
33 52.0945860304 70.7995922016 70.3439696629 0.1401124939
34 15.7800658904 18.2950805959 0.629481938 0.4866108938
35 1.1246245468 24.7439455974 23.5413162184 0.4910176845
36 35.9909471683 34.9809461644 30.5925745516 0.401350473
37 49.1760488933 14.120580813 3.0345976975 0.7799394242
38 9.7844595694 64.9433550914 61.6503397066 0.1594425822
39 10.806893887 54.1359940393 41.1761982564 0.3317766859
40 6.5332505238 36.8746560215 27.0378388977 0.4978101256
41 61.2281191251 32.0591258846 22.1515608035 0.1713013105
42 64.3831751113 39.6483969252 30.6430410392 0.3114826506
43 14.1108995295 35.7373733485 36.1400029919 0.255193868
44 20.6791502337 31.5664664998 68.3669663737 0.4784678
45 7.7987152228 33.0029612108 39.8212709608 0.3421450108
46 29.8403712272 72.2992241876 72.8630319452 0.2497966778
47 41.2163651125 117.0929479282 105.1422923283 0.0999810821
48 12.4976403289 47.9295632216 56.3776650323 0.0894372826
49 2.5874124093 44.5364357372 98.6982660492 0.5861012904
50 44.418943677 53.4904934149 67.8002272787 0.4383002657
51 24.1086602025 82.0125069515 90.3792855877 0.0451637181
52 8.0177126123 24.6073248135 17.074513992 0.2072215377
53 49.2847510639 15.1293734804 10.8476113384 0.6506625015
54 50.1695939674 32.7510631999 36.7377521353 0.3864544476
55 15.829179278 113.9086506866 127.8801247922 0.1254850491
56 43.2365304487 49.965060569 52.3011936046 0.1891392291
57 43.9832509233 28.3155173916 5.0260370804 0.3974349946
58 53.0628926535 14.2659117654 2.020733848 0.642027755
59 63.3120078239 23.1016801132 27.4933461897 0.5209857778
60 54.0190240292 104.9420530436 108.5252511213 0.0256468672
61 109.0705234392 30.6970300445 19.9161125125 0.3881701701
62 22.2251074162 25.5921613414 12.9815273632 0.407383098
63 37.5394798421 204.1233687401 292.6288093879 0.1416982817
64 4.1107905941 18.2635646832 15.9965370054 0.7273649531
65 42.5412925882 38.8916180687 53.8118778033 0.4799073442
66 29.7928550473 106.2197383133 169.2138105061 0.0839608681
67 5.6506890669 19.3941798053 0.9910852414 0.5847597206
68 52.565280045 40.5327257736 50.6240305769 0.3801468394
69 14.3039155439 123.3213167148 195.026240408 0.0553652535
70 4.6348066168 39.7989821849 34.2766654631 0.2940599774
71 4.598999624 31.4257191023 20.4315063355 0.4163580299
72 11.5035626411 18.6945715458 8.3417346922 0.5002438094
73 6.7667038879 23.5199926005 10.6368845992 0.4135766314
74 16.7469612303 183.8057469031 249.8548968364 0.1501412096
75 57.2372486918 64.4366006918 73.4729157091 0.1258146861
76 3.6502458421 60.9010887143 67.563139884 0.2755842606
77 5.8353587898 93.9658613452 129.0827072864 0.103415188
78 47.9695917111 42.4291655972 61.0619401286 0.1799741991
79 40.5026802642 35.687288585 43.3212988038 0.4434444386
80 62.3603200508 40.195080455 46.951537131 0.2783053319
81 2.0901929623 56.5782682423 55.8231126284 0.1051094867
82 2.0865328916 93.9867234346 105.8368609522 0.291235488
83 4.0362887717 42.0513087524 48.9614240777 0.2544133374
84 31.2151297849 61.6457642165 95.2490201788 0.2347770646
85 31.613846444 27.1906794907 24.5704241029 0.4887892593
86 7.1945763741 37.4782572408 44.736211618 0.3658689028
87 32.8672073574 91.1478983197 138.860941791 0.1738401086
88 31.5086036671 95.3263992657 136.1966024881 0.1082246329
89 26.2412238751 20.004345828 12.687493983 0.6907548946
90 60.2412868298 25.0924283581 18.3346950126 0.5288109808
91 125.4127310854 70.4387791389 104.4395596978 0.336647259
92 18.3338254359 56.0768075858 71.7905798292 0.2331746209
93 32.6177129708 84.0880000042 145.7285445559 0.1720759763
94 26.4020544192 33.0290790225 36.0662258576 0.5654009661
95 4.8286049214 10.5575313074 0 0.7484681988
96 33.8791410314 42.301924295 42.3886438779 0.0850621466
97 19.5022561658 39.7498331228 40.8870679021 0.6912509089
98 2.8455553391 43.7194658417 53.1184959323 0.1739215264
99 27.8725000477 22.1775557516 19.4259621275 0.5810877767
100 18.1793389936 47.3032339518 48.9974767144 0.3668769977
101 57.3887573432 73.0942627355 66.6843023248 0.1585821716
102 39.6595843401 90.65767571 126.5728300715 0.3246869226
103 12.5334343406 87.375561502 101.9320607143 0.1065373346
104 126.7246228487 89.6689103802 100.433086569 0.004875073
105 10.9254191059 40.8908704866 45.388057956 0.4391264577
106 8.2029184416 23.9502635356 25.6544411762 0.453191298
107 70.5892902753 20.2261819816 0.8069661417 0.5149918851
108 44.5984837162 63.5967389702 75.3382906842 0.3676933527
109 54.6264178652 27.8607650498 17.5291036522 0.4762921014
110 12.585873092 28.9524372333 24.72223424 0.5101362771
111 22.1086418514 28.8103466764 46.1653312064 0.400942451
112 3.1705707597 25.1817420311 7.5916704596 0.5545795662
113 7.9624049765 21.4773467804 25.4548514623 0.5485403175
114 2.3796978392 72.7510580322 96.3770182485 0.1303233929
115 12.4177369406 51.2702401987 69.8052098092 0.534952291
116 11.5519136871 32.3114452688 32.3757866096 0.2126428091
117 9.9233303192 30.9722509617 20.300672464 0.4045427934
118 103.9774607213 46.7953632985 42.542458573 0.1594872489
119 5.1918828488 54.5700752191 65.4927238544 0.2158492292
120 14.251517913 168.3543795515 195.9105236299 0.2477035811
121 22.1444498807 57.7444140603 47.481453953 0.3587641567
122 37.3109767298 157.0746780591 185.9962123344 0.1280212086
123 3.7413263389 18.683726079 0.3157912882 0.6375822795
124 21.7614984778 27.1439553611 18.2311015128 0.6735316475
125 40.362812603 15.3735902748 18.5052244027 0.7134700955
126 21.7622168205 47.1456729197 60.3012252638 0.245991052
127 74.5089972237 37.8063775573 31.7249962842 0.4028707015
128 13.4190543059 11.7435024494 0.4500395127 0.6840123725
129 51.9209108088 71.2293424202 100.9655107779 0.3284924517
130 85.482445394 21.8506483209 3.562442333 0.5115519954
131 38.5546318786 60.6149166768 61.7463494215 0.3188480223
132 10.5160338413 26.0268416705 7.3335172166 0.5258140186
133 52.3461804192 141.9280088853 174.610859055 0.0462439141
134 157.7272257884 50.0366549184 88.5087402089 0.4334180818
135 44.7593205172 20.3647332663 22.8569584222 0.5741834035
136 117.9159002841 100.5105335284 121.3551810722 0.1034308489
137 61.0426649039 61.8909158265 70.9068408931 0.2447551196
138 43.4269284679 31.2033106848 32.9786932761 0.4867277072
139 44.5684472801 25.5250211836 14.2790489811 0.3110184384
140 10.5518945995 57.6470884992 85.8308120713 0.3047834535
141 19.4378555579 28.4299406533 15.2525306983 0.4461014021
142 97.1241588331 46.3468008239 34.341759491 0.462198828
143 14.5569929285 37.6479278587 41.3202101144 0.1285708533
144 9.8499907145 90.0233281835 90.873866599 0.1120873258
145 8.9851169795 36.8287683088 56.2082110672 0.2492677346
146 64.9483312775 41.8555847166 56.9473341327 0.1567114482
147 44.7952922294 14.1598662605 12.3898693501 0.6496295097
148 73.935426985 44.4760624013 90.4756602726 0.5145009709
149 14.195975617 40.2912745109 32.8875155433 0.3951272916
150 17.3694883272 23.0522435802 17.8900233584 0.5695385369
151 18.369827187 57.3229810973 63.3599490247 0.2720391491
152 76.6547381333 47.8284060131 63.7397690859 0.3328081665
153 19.8911680583 25.4529673376 15.7276571107 0.3377730015
154 18.9412598567 79.9391877659 118.8747809708 0.0764366916
155 13.3064281064 34.6507654564 59.7831985312 0.5720431484
156 19.5377058021 27.5101167752 34.874706738 0.3300407608
157 21.3137625879 68.1686630821 81.7012850437 0.3439241704
158 57.9311342948 26.1005936579 22.0753061787 0.2657009893
159 121.69237511 61.1025989433 71.6642510345 0.128002688
160 18.3112131443 103.4836594893 146.4061853944 0.0890725727
161 13.6231630549 154.7366057949 167.5043425284 0.0140782732
162 23.2830354976 49.8927358827 77.0663613788 0.4444355335
163 28.7852937592 34.6084475237 35.6828632293 0.4954672249
164 9.2692999766 27.1459523633 10.7446883071 0.3103661756
165 46.564798368 25.3505899948 26.4882892423 0.448760964
166 0.9561480025 62.5751699971 59.2234745892 0.0151440328
167 30.665469966 15.9536008691 9.9694027938 0.6677159908
168 53.4048249256 34.0417058411 35.0388476939 0.1741943373
169 6.5390849093 30.9576000739 34.6973914197 0.5149343353
170 28.2111461278 39.1516927731 59.3949951421 0.4643079485
171 89.03588015 26.3995215266 20.0503928904 0.4698718019
172 21.6731011696 29.2272252903 28.9748003018 0.4474931293
173 24.7067824777 41.9090977551 47.0337008819 0.282638903
174 24.5792643151 14.9161601532 1.6794449009 0.67353666
175 16.6374303604 15.9609965378 12.2535464767 0.6398308677
176 5.8255770897 25.1968150693 10.5806307469 0.4260570182
177 57.093214717 45.1922504658 61.8959403398 0.3206745248
178 18.2369303348 10.6754848567 3.9769814983 0.6286549455
179 20.2822633013 78.400516714 92.961958165 0.1022020824
180 9.0122996939 30.3524820694 26.6145473104 0.5054912338
181 98.5684558269 40.0924550197 29.0564734446 0.36831317
182 46.3103109897 18.9856891773 11.2504864152 0.5082717354
183 11.5105331503 152.1339009341 173.7000797043 0.03641494
184 11.0715810645 40.137914402 48.4361256812 0.324422644
185 16.1958724244 64.5075471903 59.8659776822 0.1296797639
186 70.0561378532 18.4303090487 5.9079040305 0.560136082
187 15.0094317727 97.9732354232 95.2926294832 0.0429232655
188 16.2068054973 25.9126844148 5.3280933897 0.533301006
189 26.0949528213 76.5042712207 108.3536168545 0.1122150137
190 1.007361333 40.2894300631 58.6115976939 0.543841947
191 8.2444817117 40.5835786313 28.563735024 0.3971349445
192 32.9099071337 40.7245422576 19.5714566199 0.3268313805
193 4.1682600332 124.2288074526 145.2887031345 0.0554018641
194 8.5078956871 32.9097721511 36.8006009682 0.3980558422
195 61.3975951765 39.0661441942 38.8011319769 0.4038750009
196 100.2738374226 41.1509181039 31.2342984247 0.3184867026
197 35.5454029221 50.3631198372 64.7298263605 0.3886390887
198 5.8301231914 33.0232512813 51.1079018259 0.3924709162
199 24.2758711135 41.5985419955 37.8874180765 0.2946842315
200 10.5997773583 20.5718746107 8.5792405792 0.548368854
201 4.3982017219 88.813722432 99.0663772997 0.2080811587
202 15.7854347122 15.8266613906 7.0879146516 0.6819443595
203 52.7321147516 94.695155511 143.2805214393 0.0637267168
204 44.89510027 51.4158827553 61.7811763119 0.0905728333
205 40.9765515079 61.2736565432 104.712546457 0.2131836329
206 97.2528515479 41.1765511744 57.1267197238 0.1422523349
207 46.0658733938 30.4764871369 35.674007088 0.2034752529
208 18.560542195 52.2003390823 85.220935513 0.2807717562
209 43.3798830874 76.9593836113 102.0986530786 0.1470041667
210 16.2578897857 54.314038547 98.8743638266 0.0218498834
211 5.8247044804 99.7307701522 114.9697043222 0.0583690598
212 100.2302270009 26.959063354 7.2162185972 0.3662831021
213 18.4144591067 53.6181422551 94.1624738201 0.3371339455
214 31.7277050696 53.3136881835 62.1161182991 0.3260950332
215 8.3703385241 64.4683220392 70.7249313579 0.1489587317
216 2.2740803145 35.1306295064 23.0415070556 0.4729456897
217 89.2146680872 29.0147266661 17.9308902078 0.3394978904
218 1.4063003283 21.7580325971 7.9274349489 0.5494669745
219 10.7565473625 44.8034518471 46.9573235637 0.3198628815
220 31.4264826869 24.8805883802 27.5967221643 0.3364164055
221 19.5472904111 29.1612039635 16.2797980441 0.3638353983
222 25.418752754 65.8410717246 69.3403870572 0.1866528973
223 8.017101057 89.1182514151 98.4073031482 0.1103220845
224 14.4580536122 56.7976622068 69.3419810054 0.2876018218
225 45.3917136054 22.5170654719 21.1182345137 0.6518559998
226 3.0249475345 105.7609661277 115.820023088 0.071267885
227 56.3662383527 79.6758292068 83.6088446607 0.2463125709
228 9.0008207408 14.0711634798 9.2930209503 0.6272158855
229 46.5842933891 41.9835540576 38.6263951248 0.2707521867
230 14.0655824263 78.3017439051 81.6208617488 0.1343843717
231 52.0879231363 35.9697090774 23.5729978064 0.085758041
232 24.5928854609 11.8769256679 12.1345118776 0.6842201918
233 4.2943201323 114.6502233469 135.1359992518 0.1380231007
234 62.016744563 79.8573614613 93.0148350942 0.1574481211
235 34.3762828206 19.7224375514 23.7339733755 0.5937602747
236 6.2020406611 61.7220098496 89.2836169743 0.3443201005
237 14.6981325629 68.7402195325 83.9455641125 0.156851927
238 2.2809535809 14.647804192 12.6619159176 0.6838191925
239 17.5450236115 41.4128623199 37.7662223595 0.3257520307
240 7.4570708696 31.7531285742 26.91226074 0.6045060081
241 8.9941110641 58.6359633551 65.7459941691 0.1872235421
242 68.6650379096 12.3741955201 1.3677172789 0.7848045552
243 4.2739382386 48.6640552809 63.367375012 0.1674685519
244 16.7723839373 15.2224171944 2.9203200309 0.625307462
245 15.3460882508 96.6297114621 136.2310259674 0.2816773389
246 26.4818596955 95.4693414307 102.8944999447 0.0187164621
247 28.5798034934 147.2545753729 214.6061477406 0.1483071868
248 20.7334818789 128.3500371201 202.8574960724 0.2606856963
249 6.9912403165 52.9740327382 82.0681209917 0.1794550525
250 19.2884981348 50.0426034331 93.8779569317 0.4797871442
251 46.3496188723 94.3598508458 153.4424451632 0.1786641543
252 32.0103222573 80.2618559276 126.3820239684 0.1495841801
253 5.7735851797 35.3475748086 23.8273289862 0.4447309991
254 52.1073383904 72.5208985709 67.065582731 0.1394154057
255 7.2612053073 80.1640757331 111.7430108262 0.157502774
256 5.0816570394 25.5581495385 17.0632516391 0.270725488
257 17.139518197 59.7755218884 72.4352100408 0.3734456574
258 4.6273887801 69.4927399256 62.4513734587 0.0405256458
259 9.4325078489 23.1121894842 13.3403867248 0.5800277543
260 2.5418357389 39.6747256787 59.187834538 0.3988081729
261 12.5296936546 22.2063500442 9.9904234196 0.4057773996
262 31.296851876 100.7922968673 118.2472085808 0.0993992042
263 37.0047887508 49.6704759594 55.5790798004 0.2401083991
264 61.7456865605 23.3512949708 13.1603820114 0.5105969748
265 20.5900751154 81.8255238273 122.9391842173 0.3153216048
266 15.554417765 79.2665036793 79.231723548 0.0911715407
267 12.303951956 44.565227565 47.2086264859 0.0928214556
268 3.2738540082 32.294363901 22.4054046358 0.4076948643
269 22.9509606374 30.3918189524 21.4855571181 0.3356013352
270 11.2505762189 40.8173349358 51.5083512325 0.2840462202
271 30.7432464992 42.0482493006 29.5623633191 0.3812822532
272 9.1992635212 93.1268013725 134.2522276677 0.0549620123
273 51.9991327287 48.9859816118 55.5272431205 0.2474161301
274 8.4527370474 37.9673970544 28.0934166629 0.270265696
275 47.9682460966 73.8413969041 132.8752539015 0.0165308154
276 16.509555274 41.7141216595 47.4555913849 0.36782904
277 48.2105084111 20.5783160803 12.4182853574 0.5413339203
278 5.4588857613 85.8097490066 121.4099325688 0.3071269629
279 3.0325190459 39.0283785667 40.9922314513 0.3522828333
280 6.1811768691 66.390263704 80.1728365633 0.0563272621
281 16.9579917637 126.6354790839 158.8350854863 0.0945761084
282 3.8956155316 137.5069285723 146.2065602459 0.0259987241
283 45.9231516683 44.4490650525 30.2267165556 0.2090919786
284 10.0669637331 22.8597507311 5.6621267655 0.2331130396
285 11.0821762517 71.5022907297 64.7234950714 0.2930714387
286 5.6004695812 57.4704268434 67.2509306014 0.369630521
287 25.1625991754 54.4826122239 40.6841354219 0.082374892
288 5.9185787666 69.2639785374 60.97568457 0.2882546598
289 22.4202067532 110.8431383159 169.8480909179 0.2204944474
290 0.3474703866 24.145156529 22.1487661929 0.5203125712
291 27.534267988 32.4711919247 38.4827031412 0.5482220678
292 11.1343914781 95.5071228051 112.8783499186 0.2328739564
293 24.2356941966 85.2715015884 79.3167546501 0.0017501979
294 18.3917591747 201.0120251204 253.4429368148 0.0679580397
295 38.5961012122 49.0075642146 78.7196688488 0.1820564961
296 106.685571423 24.2794159985 16.5749217987 0.4291279165
297 47.2773869972 37.1922047815 54.4851050966 0.2470227491
298 144.3448153912 36.9436393351 40.9688388122 0.3207437072
299 48.6898563471 130.7486132789 149.6176174238 0.101555763
300 19.1626417443 27.8580092458 10.3320825871 0.2626604241
301 15.0023160132 43.2028870409 39.3909281493 0.4834475322
302 16.2068282817 34.3360365138 42.3270933943 0.3216447605
303 118.9232067771 34.0920096184 28.0643583645 0.4909191694
304 72.6489655623 34.1339524252 23.0523950086 0.2921499455
305 76.6160368455 65.2138877282 61.3248070219 0.0538609659
306 13.1734994039 72.29235607 66.3057637744 0.174567019
307 53.8706368163 74.0158234194 110.2364325163 0.3936927648
308 0.4642069551 57.700953896 51.339553138 0.2427065038
309 89.1003004671 64.6700641261 57.3245941265 0.2762585594
310 38.7125824128 20.180407205 9.4127674612 0.5990035254
311 29.6979079501 19.6988282141 15.1243228088 0.6959306474
312 8.8939541264 79.4670507618 89.8043768739 0.4183541882
313 53.1720781164 56.5145915291 59.6416051669 0.1166708215
314 3.5578124279 76.2070558848 93.2354721243 0.2490263584
315 82.7038802287 21.0844553415 23.7938250841 0.6344188415
316 5.4695541753 37.1286419639 45.8245385007 0.5545253786
317 4.8072440666 32.0097353903 26.5888881277 0.1739981962
318 3.2467352679 57.4755538471 84.3114371542 0.6204975565
319 11.4448531746 56.1916299375 82.6921809432 0.5037164075
320 35.0781444631 62.9284987382 89.4188969669 0.1289869606
321 41.0216753766 64.5940227294 89.3809975378 0.2620627126
322 79.6552758473 87.1007761512 82.0725434392 0.1084576754
323 4.8061724391 43.8350287604 41.2388449941 0.4446813038
324 9.7679660205 52.317941625 42.0985059443 0.2116000857
325 8.7522422998 59.1847833932 76.6041448841 0.0615730786
326 94.2239990177 125.1141851862 143.6899692474 0.1473883832
327 18.7671327332 30.4865636121 25.0022456706 0.4232945316
328 8.881295229 38.125398247 25.4691656088 0.2056465264
329 11.3393060516 12.4751376566 3.007323816 0.6527410985
330 51.4682781569 65.6853918325 91.5193412785 0.0788081297
331 27.7378519715 47.9170197833 64.8405668359 0.4301676104
332 7.4782678293 54.393641316 107.810333712 0.4271648711
333 25.4263882694 14.7950668991 1.5667925016 0.5949054226
334 38.7921106358 81.4844588048 135.4003438517 0.1504939876
335 2.2450511578 78.5054193187 92.6627618032 0.0986460716
336 16.9119721413 16.6346622768 9.5234809152 0.3886797041
337 37.1236648574 34.4677237354 37.7097912467 0.0712819765
338 18.3503451634 16.4899283254 1.5187730209 0.6078647036
339 56.1924993828 68.4296427746 103.1528514855 0.1470582961
340 12.8054605312 98.1012037898 130.880594162 0.2290395482
341 35.8016759769 95.9128827728 101.8680478107 0.115815047
342 3.4008599376 36.0021228309 36.5606116694 0.3626812424
343 0.9624647342 48.6564233297 55.1850681626 0.3684696343
344 17.2409464978 51.6261051404 51.4973243258 0.433948887
345 34.3479809824 60.6391793101 68.5488229873 0.4159362532
346 11.576913678 36.6972937401 49.695318379 0.377960833
347 20.7583069043 73.0848173398 94.1609689158 0.3412295485
348 5.9254582069 44.7233986598 62.8602101778 0.3599276888
349 42.4913104199 45.9227430322 43.1069505491 0.0356410347
350 14.4354790972 70.0721987088 72.2608037302 0.0780334861
351 3.0011412604 18.4303957754 16.2322168093 0.3503857664
352 11.215687599 18.0990620539 4.6541437681 0.5151804292
353 24.2480556727 124.9977796231 183.6122863196 0.1700335747
354 15.6856343988 59.9691606285 121.5628572261 0.3484838375
355 19.9913137331 26.3169705456 42.6051361475 0.6020846243
356 27.8494015539 57.2331310424 73.173159294 0.1574364411
357 35.2301342221 135.3278581897 151.8346186155 0.1040892836
358 4.9890164726 69.7290114289 96.2455058156 0.2033545842
359 1.4181851913 33.0398894473 38.9209468724 0.2656281962
360 11.4314951391 58.1985775867 76.4519420037 0.3517671219
361 29.8068683679 26.2065037326 9.840312482 0.5171503956
362 1.1400415395 43.7352590569 32.2157682568 0.3706596009
363 7.7137934278 45.9540700456 53.5974905169 0.0920628699
364 11.3604576573 18.2018374027 9.8539614091 0.5473273605
365 32.7943487398 86.6943178987 151.0460388341 0.3124238464
366 64.6581992952 41.5798692234 72.2199248238 0.3391990949
367 24.4105281113 56.593373753 57.3890792188 0.1884776702
368 4.6065165858 78.8479898942 85.4408111092 0.0424679922
369 39.5046433058 78.0633730305 101.2629735852 0.4030923368
370 2.6296601814 55.9065758984 52.9786037197 0.278768577
371 0.9344297819 32.8446685476 34.0691732553 0.2194103105
372 19.2375494873 18.8768226331 1.4209636968 0.466764405
373 34.6580897125 110.221925222 115.3044807639 0.1058108789
374 8.8018045461 22.4382766253 14.4652750349 0.680038397
375 16.5909755832 34.6919423461 43.0441563756 0.4584423955
376 12.4581523908 80.9300085277 78.5266633608 0.1369315666
377 17.8770769751 39.8418531626 24.7295242993 0.4048385064
378 52.7725563119 38.3695054561 43.2133943978 0.2508106899
379 25.8037468458 67.1448699203 72.2183625432 0.1485275683
380 22.5112240321 19.2520374909 2.3816125663 0.6498049711
381 30.2317343985 41.85646981 39.0731294498 0.0985768798
382 3.7845568199 24.2554003855 10.5866956282 0.5684668
383 62.2569751526 23.3001454837 24.1657374743 0.5050840252
384 99.0180878403 61.0288977614 77.7720131125 0.3464557604
385 34.1413939418 26.1739400972 20.2113372692 0.581979547
386 15.7271362692 29.3763266555 34.7287312569 0.3829393061
387 2.2702538979 24.1287736066 21.2553740129 0.4637105624
388 1.7749520378 70.2646640123 83.884544653 0.1740391243
389 37.4008167999 19.6131700722 0 0.5207600773
390 29.1284534533 47.7769811537 68.0895045596 0.2659298176
391 50.3522255448 19.0254095104 4.1861744236 0.6440467918
392 4.9038330266 40.1768830212 27.0877553482 0.2648326566
393 29.7624113505 32.7093957051 23.0393126743 0.5724501253
394 48.2076949118 22.9099595862 33.3833928134 0.6454470125
395 15.1421406774 85.7025483032 129.1893901596 0.0040952613
396 20.4855446597 80.6229963355 125.2680561443 0.2683314778
397 66.2869793431 26.5647286825 30.9307307155 0.3915328512
398 102.9940007436 83.6584021935 169.5299223423 0.0584872788
399 6.0769476087 40.4455550392 49.449719129 0.2851354033
400 49.4883696717 99.7177626507 97.7482698792 0.0541309238
401 41.913092955 33.3826473805 19.7628465177 0.1337778257
402 89.1007314453 34.835056467 41.8619778657 0.4917869421
403 0 47.2295806786 49.5399303702 0.3946950218
404 8.2585099449 62.9367109267 78.6150518965 0.225491307
405 80.5616329156 58.8668482336 48.2546748586 0.2941950536
406 103.2047239474 37.2700204076 22.9575955128 0.2429196653
407 19.0219702428 30.7497301841 38.8232456191 0.4582282228
408 16.5403420509 45.9809804446 50.9435884295 0.4353213864
409 25.3942836083 150.3012350872 187.1641326028 0.1000979478
410 3.9215392299 134.0307558987 171.698644996 0.0900604313
411 6.9185411839 83.884876713 83.7258778656 0.055255001
412 18.7531689854 116.671973946 207.9537125854 0.2895863392
413 34.279330253 37.9075375407 27.8172512943 0.2319176746
414 31.1497385686 37.8051113332 34.7877072143 0.2098685825
415 17.0651901296 44.5560783323 28.3415353669 0.1997262718
416 4.1262680172 36.2533280658 31.7245843459 0.2923659793
417 15.9080150543 48.6491858641 84.9229687824 0.5328575651
418 25.8069475618 83.4416862929 97.5472381224 0.0747933663
419 8.4825139196 72.8919359872 107.1585363769 0.3566752772
420 77.2670233066 13.6123171623 0.385216967 0.6042876399
421 6.3156206152 35.5127253543 29.1535211553 0.4639979487
422 19.9273135226 123.4720641474 136.807240166 0.0853522264
423 14.6262005895 59.6375910916 57.2280732398 0.2056915363
424 35.8193465151 20.4245294625 13.2097470604 0.546473342
425 17.8484766662 25.1316408346 42.8120675713 0.5472169237
426 12.3054835315 16.961655282 14.7694382559 0.6403137994
427 99.9130320181 57.6023386638 92.420469987 0.1392067603
428 7.6618437655 108.4695968398 99.5965149862 0.1056507569
429 37.7745281942 314.2191796427 421.1198567189 0.0194652097
430 38.8677504847 42.3940371459 39.9822974694 0.3361230304
431 33.0432009384 41.9178096273 44.6721970934 0.2923852847
432 1.678841253 107.607837594 123.0517595381 0.0024838529
433 26.9179207185 29.9904157115 31.7818703921 0.5255760622
434 17.2626241676 25.9560326893 15.9569907727 0.6412360186
435 20.5779764437 37.5500577465 41.4942281452 0.2765761334
436 9.747276314 74.2437187418 120.4466467212 0.2125270952
437 67.1619764547 18.7182852025 0 0.6224582277
438 41.9366527178 35.5064483622 61.1166815657 0.2958672394
439 3.1487553088 129.7137484633 186.1838241922 0.0081843356
440 58.4195329594 109.7670482805 148.8073258535 0.2646004808
441 98.0799731637 85.17035448 124.1396392978 0.288873692
442 117.6850186669 20.1007284581 19.8504060041 0.5129242044
443 77.7057816729 38.2841299864 32.3923006847 0.4452471117
444 11.7437734758 101.6779381633 108.3517529341 0.1450566309
445 23.2486326726 22.9414568653 7.395325135 0.5536584059
446 15.2153516046 21.94322581 6.0265187912 0.4741146219
447 0.2576417227 67.7878018828 111.1120285145 0.1948616502
448 56.5775756832 144.7002109696 167.9203981914 0.0795857042
449 28.8537491364 136.6482140538 146.5147666536 0.0721371761
450 23.4959418688 46.2211388805 43.9870476961 0.0783369148
451 5.4395621314 70.2620835033 73.744404548 0.0043323026
452 9.537541691 108.7658722925 156.7948371377 0.1072070101
453 11.7174426096 84.2781172284 110.2278724166 0.093428155
454 32.9687451706 21.8582984026 13.0224125667 0.5578368775
455 182.7168329509 87.4376711534 72.5106480629 0.1548367298
456 13.5894002431 24.3689654889 14.1560167328 0.4824243009
457 7.4381569163 127.5575379452 139.9970353986 0.0069898103
458 97.3798778231 19.7322085162 1.186468211 0.5649424456
459 23.0177781635 30.1815384759 22.8525876581 0.4843822491
460 7.1569940719 32.6967905294 44.1882970503 0.4325775391
461 11.1533063189 67.0849644819 128.2146085652 0.2679019724
462 7.3700778405 45.3963967111 63.5792729579 0.4655405433
463 19.07600976 8.5708795804 0.472418234 0.736626694
464 9.7508882479 51.3122266215 80.7376822667 0.4434027559
465 53.7553671885 85.0974558203 114.5393809047 0.3082198898
466 7.5505991409 31.2805027197 12.1331840159 0.2934026572
467 17.3670158358 45.5937548646 53.6872530267 0.313758342
468 5.6113243502 48.1709821748 44.3394041037 0.1428568073
469 47.036157861 49.2986698931 57.0368312914 0.1211571084
470 24.4146548664 26.7656802594 2.3828499982 0.56267453
471 111.0313240781 32.7517146516 23.4647931415 0.3511316813
472 25.4657365743 76.812816257 109.478016623 0.1612996977
473 9.4386118328 35.1186707972 30.2558592668 0.3249146609
474 72.7464494336 53.7409261696 63.0989618744 0.1357107135
475 7.5249496333 60.7253926767 80.9537372979 0.2266175264
476 7.1555423994 69.0168103876 84.6569062098 0.0851422231
477 18.3992329844 59.6352512953 72.1716842474 0.2657326987
478 22.2348991249 68.6947311592 63.8181343545 0.0059188238
479 1.7053397649 34.3960388176 36.2323341173 0.5049694678
480 30.8917799789 63.7048809641 56.2519816302 0.1043952819
481 81.4818465375 44.3302375374 61.7132933929 0.2123775638
482 4.5080179605 37.8867924205 57.7661423452 0.4887794321
483 80.520559132 51.2917647413 63.9488944437 0.1955080119
484 8.1337509877 22.2206859826 17.379891777 0.654459045
485 48.4619893339 82.043598811 109.684429483 0.022966642
486 54.8994882309 108.6085105632 131.8775686694 0.0888983524
487 16.8498723645 10.7866131356 1.1744581153 0.717680525
488 40.8368413401 25.3408271509 24.8967762156 0.5941301147
489 13.3919072406 40.9745250312 49.712054144 0.4091202498
490 90.794622295 65.12608175 76.4708811166 0.247232893
491 8.1709334321 91.2001760468 113.8106650824 0.2549323396
492 38.5635663626 52.1931102059 49.4501150754 0.1895008876
493 6.5896605489 31.1215104388 34.2753521012 0.4800094103
494 6.7829101598 43.7223398571 40.7679704781 0.6227245263
495 8.3657145455 97.7404092611 129.4102675166 0.3529009075
496 76.6718235365 42.9915132171 38.8402711383 0.062524716
497 14.8844605509 35.4837811467 37.3606213505 0.5372865034
498 75.7688648094 33.0542355337 27.3613547242 0.4645526561
499 16.8563466709 80.3661968478 104.1290888374 0.2217236026
500 79.650466283 61.9815171644 93.8094332902 0.456148605
501 1.6510974358 69.4382075731 83.4500846377 0.0800638838
502 4.8443206555 25.2595907412 23.5084174999 0.4036962826
503 23.6835009423 95.5430626131 128.7476934956 0.3454066649
504 19.6742124088 46.1274752397 73.15861074 0.3035516799
505 14.3325106586 52.9721254327 71.185121604 0.419341656
506 24.197166121 121.6416227321 128.9346147393 0.0167105455
507 1.250223341 40.8127779986 46.0784024997 0.1145625203
508 0 42.0936132895 37.9111381826 0.463801312
509 46.0317555333 33.0499489101 36.8086362154 0.4943426987
510 71.7206703609 59.5037113781 67.0780509497 0.154707234
511 10.188032687 22.6081469279 17.8359574026 0.4490795594
512 21.0239469155 93.1786867976 122.7451136372 0.2542891867
513 91.6904328912 47.3127322794 65.7584844351 0.3404149359
514 8.073050636 19.4289078732 3.7619103238 0.3317416759
515 11.1038322337 49.1326537676 60.7271021844 0.1824832606
516 76.9377984945 61.937606853 56.8174971103 0.1076627768
517 92.8868544609 106.7162983977 119.9826628111 0.1282378568
518 42.3815380775 73.2225884896 118.8464908401 0.3723589028
519 6.3636612296 36.2590846793 42.5357075813 0.0672150116
520 67.0337912773 63.1289976129 61.7672139821 0.1269491512
521 24.2672088157 32.3949289014 54.6499732867 0.6524563425
522 32.4169678755 41.144617812 35.275546261 0.2617797995
523 9.504603603 22.391192606 11.3608612576 0.4663020842
524 1.3159911507 27.1731199608 17.4312157655 0.4754958251
525 8.1750984297 19.6296796074 10.6824248579 0.435101895
526 17.788244749 88.5806599368 101.1192666975 0.217291892
527 9.7053644146 27.9819116903 31.8568820727 0.4915174825
528 3.0745959658 53.7088435088 45.5745134008 0.2129026184
529 17.7179261109 23.6735047756 15.4929595408 0.7028330192
530 0.3140015101 27.9684544097 18.2350064492 0.3897864128
531 17.1347815502 32.2283411963 42.1396062564 0.5678547211
532 21.6349144899 90.1126621316 85.5174448042 0.1700761436
533 19.0111851236 58.1275304333 54.069874909 0.1665614367
534 84.8128519818 59.2603817999 69.731728163 0.2581225762
535 8.3225069923 65.0928919858 67.752954729 0.3653873682
536 28.0327447833 28.170479413 30.8354259703 0.4116636361
537 13.2281900165 18.8408189044 18.9268297434 0.5596128761
538 4.5731461778 90.1311695549 92.1044571244 0.0659982171
539 38.9623752277 29.5141271678 25.0923413187 0.5176105408
540 1.3895219109 92.0783737634 124.0546240123 0.2330935535
541 10.5318570485 62.1523576241 68.0885182851 0.3700610515
542 80.0965619317 48.7882314292 50.4212321489 0.0540229727
543 24.36557377 41.0010366733 44.4762926629 0.1085349684
544 13.2573969094 46.3931650556 58.5492772418 0.4532190996
545 43.0512863296 94.6913705314 105.279173435 0.0004354493
546 60.3682673754 53.3085740511 59.9898340171 0.2833339174
547 7.7267083631 40.3189620055 39.4397551649 0.3396384345
548 113.0747958479 56.2064234641 60.8258174507 0.0818691407
549 40.6879008423 112.1404487798 125.9487448255 0.1755583264
550 13.9335669916 86.6552399336 115.1100384859 0.0232030105
551 10.7118223204 17.5923316996 7.8809035697 0.3724891472
552 21.8199815856 31.4437037776 33.5619330001 0.349095244
553 9.7520025617 13.8964877389 1.0575706629 0.7209273959
554 24.3225034076 32.8551803999 33.9174066604 0.3813395419
555 39.4817379898 63.4986967141 92.7437004829 0.453192467
556 5.8370089454 68.5608965167 66.6689264563 0.0428003157
557 4.3618769266 138.6759138736 158.396850886 0.0005849831
558 3.6952169383 46.8486307577 36.0677656716 0.251709147
559 11.8931767029 20.4774909781 13.2691460103 0.5682260595
560 19.1354243173 59.6717513023 79.5498191713 0.3746241295
561 35.9132873964 116.6794130966 122.1025413586 0.0822396353
562 8.5406828949 99.0347838743 148.8309798823 0.0578956711
563 44.5674798984 79.4272086602 83.62433402 0.2985219627
564 134.0329232566 58.1190377243 77.7671119164 0.3264478322
565 34.1457819172 35.4897538055 35.9500844665 0.3400678561
566 11.1403221062 66.2321399675 77.9719700605 0.0127522038
567 21.8155681295 35.5188102997 37.7082401884 0.2465316015
568 28.8392070546 26.4563862712 25.4204154306 0.4211116635
569 0.6535612442 32.8186894035 52.6825483363 0.4362908526
570 48.65156359 17.5110393461 4.9714930695 0.6374241584
571 44.1809233369 11.331939973 0 0.7132550119
572 24.83262701 14.0635692613 0.5591969093 0.6648541388
573 8.123029688 30.7514550196 31.651099785 0.5482259801
574 44.0159356661 55.3038232749 99.3159536129 0.3365973635
575 9.2057685103 27.9879292136 8.6800948886 0.5445301564
576 8.0978593017 24.3255451553 20.9015369347 0.619937117
577 37.3347764368 40.9998458447 49.0054646531 0.3271148798
578 21.8889989926 69.9461394103 85.9234642453 0.1406618394
579 5.355236564 22.6657248205 26.726827473 0.4562552387
580 25.1314633418 34.7881186556 36.5960918051 0.6200424529
581 109.0743798416 72.1461387378 76.844439734 0.1191214831
582 18.4041426101 31.6717092014 22.3423066375 0.4628616037
583 94.0360375261 63.4732883203 65.3559131246 0.1130491131
584 12.9285273564 22.6125123137 19.0210696665 0.5923940868
585 11.8171923926 55.9251585533 89.1528717967 0.256982094
586 55.6888181132 43.7008808043 47.5049705201 0.3584503758
587 78.1386836023 39.7436672482 27.2650158005 0.16820844
588 14.1516675243 75.5365855494 105.5520402057 0.3096052041
589 22.9923872626 22.2752701652 19.5127993706 0.3681534501
590 8.1329803586 30.7039864785 18.8049009241 0.2408825061
591 28.7293967556 61.7950561587 59.9114072405 0.2714706744
592 34.9365536307 18.7920326647 7.4101450895 0.6776350364
593 17.1159362851 39.6518085229 58.2814726501 0.3235594453
594 44.5450102452 85.2235611456 138.5374722296 0.482450706
595 3.6636963573 147.800066531 194.2173245549 0.0861281551
596 25.0140778812 93.5223626223 180.9488126754 0.0808344662
597 5.5908113805 97.4603487339 148.7272314119 0.0704248166
598 3.0096296706 25.8970288714 23.494307064 0.6481513135
599 17.5303967337 39.1508987 43.2757407599 0.4323793493
600 48.3253547495 25.5155720536 20.7770675889 0.6413873582
601 53.634457862 47.0526065912 84.0221606477 0.4607200801
602 113.7741806047 54.1192873342 66.8237480487 0.1303166892
603 12.2377772016 48.0100585301 35.3521068792 0.3623529028
604 21.6108060838 119.495856376 124.2962489483 0.0418610607
605 13.0678647073 97.6358892134 87.5353132455 0.0218732281
606 5.9257975964 32.8279890272 46.0612839656 0.2834282196
607 21.2824757156 34.5494501036 27.2641704323 0.6884038657
608 24.8957362855 18.8384588299 11.9003559433 0.6924757403
609 65.7548521647 97.8103230827 136.0202427599 0.1777504817
610 8.6558178419 48.9460171769 47.4273354824 0.3175617668
611 11.2388243477 27.60693316 11.6246127848 0.3155672735
612 87.5217870582 76.2422303267 97.1824783029 0.0928074249
613 7.8480962138 20.0570565251 15.0334479631 0.66707209
614 7.5431101427 40.5274992792 35.9423048341 0.4495738507
615 15.8920013212 24.1420868257 15.6496432791 0.3916446818
616 94.5426030087 76.8804040924 128.4279359863 0.0992755992
617 4.5597841319 19.0466115499 19.4900340095 0.3365268797
618 12.8667284293 81.7138293795 71.4777953172 0.1227217733
619 126.067522984 41.7951485093 28.1714204795 0.2155138738
620 54.6609171268 15.4924683731 14.8974995528 0.5150885363
621 55.5602481354 101.6024343439 103.1925940636 0.2716480041
622 4.8366489983 106.0926395484 144.9629614078 0.1223685026
623 36.7559954613 94.6561465195 113.2490164011 0.0651902991
624 4.5908544861 47.9893393236 44.8583567638 0.3125799413
625 61.9218122137 19.7658657466 11.8988091068 0.6146687304
626 32.2337786274 25.1159448111 22.0548738987 0.4907440128
627 42.0675120451 11.2193909313 1.0961614793 0.7938347447
628 10.8475019915 38.0345119708 47.4623368269 0.2754475275
629 21.74226622 20.6095732223 16.2203399364 0.4062412406
630 15.226738731 46.8021120942 42.0703663068 0.2376540788
631 9.2932865057 45.1698889833 54.84871481 0.1520750994
632 23.2244504523 29.2256422148 1.5447470995 0.5450853584
633 17.7316537722 84.6521502596 116.3185581014 0.1065312514
634 64.9273324604 33.4302218468 43.9390419952 0.3437041396
635 48.9925302736 95.8356481844 92.438148332 0.2385611378
636 8.578696551 52.3530270773 52.9318693876 0.1364583826
637 12.7569191593 61.1019483532 76.9113182995 0.1687007196
638 15.4814760938 139.2325250088 260.8247754302 0.1662533269
639 7.8414011634 31.2566964567 16.5321926339 0.4274751681
640 0.1300390886 51.5249502838 56.0094416968 0.2433955841
641 10.5075379318 54.4885656232 59.4561708991 0.239695752
642 65.0855894383 71.2839401278 86.5975673105 0.0497800069
643 0 172.8594859919 188.2000075509 0.0717343539
644 51.8092377949 34.8661056752 31.7747256397 0.2683321247
645 18.8186963851 37.2844791479 55.9136182415 0.5565502617
646 27.6744538457 30.0837645707 39.0585641516 0.3346332179
647 45.16066688 17.1088587107 6.5301668178 0.6258902386
648 19.0849522717 74.647855415 78.4435760525 0.270848326
649 0.7261216771 44.228248448 56.4511089216 0.3749821317
650 7.1734168393 161.1088795673 202.6127637608 0.0606962626
651 16.1716659442 57.8654067297 62.4714708536 0.2727540543
652 15.4851170425 15.8504520707 11.2524782046 0.6886005532
653 10.7016227057 65.5177720012 78.2322191328 0.0648850524
654 20.9871682429 30.5514886196 16.378606367 0.3320564649
655 91.8365207161 103.5759933873 126.2120572609 0.1501476214
656 28.1164424266 74.1037223621 84.2286047174 0.2806639959
657 8.1379853917 57.2162530978 87.6341979033 0.2964447098
658 16.4099755024 26.9882607383 33.2650771288 0.5588951902
659 1.9069120534 90.3649359925 100.6912590036 0.0302360181
660 53.3739421812 55.844269188 53.4266848159 0.3067942736
661 12.135359519 27.600287157 23.3622444716 0.301059032
662 20.6970844928 76.04554951 140.9997886241 0.2153174865
663 24.434023351 27.6715764085 13.4673256418 0.4058832302
664 3.6216008767 61.4244954889 90.9141000521 0.5111915038
665 47.6942619997 30.7985740293 24.276926333 0.353215778
666 28.4156084513 24.8734902632 19.9856476241 0.1016188566
667 59.2892937997 68.9306520229 112.6130903501 0.2383845716
668 11.845194969 53.6985890906 42.1982596273 0.1531420223
669 21.7676877245 103.6936502158 167.537568823 0.0244054056
670 19.5365756725 20.6794445243 15.5918495725 0.6717469902
671 10.9703378983 16.6541020498 7.4047922688 0.5425235543
672 25.3794696987 101.9583950416 121.6253068565 0.2707883469
673 55.9754971396 75.2762317068 108.3871624702 0.3632544514
674 33.7679370859 38.096899717 46.1819503796 0.4919811563
675 29.8822718008 41.9597646863 37.0869104231 0.1741083713
676 19.72804751 86.9265495353 86.2630144496 0.0131305068
677 70.3078500957 67.1911403223 141.9041642948 0.289182613
678 43.0950285184 34.3209044327 48.9331933431 0.320097863
679 15.8233702552 29.5889391446 23.6589338917 0.6196693407
680 91.3107997441 67.2355481158 136.1032994894 0.1753419347
681 112.4251028529 43.0082800199 50.524443749 0.1858836796
682 12.7334220323 81.5894484735 94.0463208623 0.1852273398
683 31.793234091 26.1144031161 16.598679864 0.5438633098
684 28.0558719799 139.4998366682 176.7676788994 0.0791506265
685 18.6437723397 54.4461198503 77.4190119159 0.4357440295
686 80.5249985818 114.5724683189 175.9994931873 0.1745273212
687 45.6296203418 91.9165333922 121.4324602523 0.1999067886
688 24.6918203969 67.1228870556 62.4212207576 0.0023200155
689 9.5871382656 14.8390322641 2.160504704 0.6165937276
690 104.1202786215 40.5051018728 35.6857803851 0.4998986132
691 43.3019963098 81.9968562565 119.3028101689 0.3655205988
692 16.4057795067 39.4973565269 49.4675845625 0.2345026123
693 26.9979440597 41.709197523 39.1016354362 0.3801614208
694 23.2787019337 32.6197283476 20.2710786152 0.2751070203
695 57.2160693637 131.6979651485 170.8539880276 0.0573095149
696 34.024656016 35.7486536965 28.1619933216 0.2943356804
697 25.0853248931 39.9412714381 31.8868602105 0.0743927221
698 77.8588009896 30.163088717 24.0581988222 0.454091887
699 5.1884916869 124.2569742289 169.3749440715 0.0741511138
700 22.4943194857 23.9739207325 0.8070398969 0.4566510729
701 4.5273073724 87.6249427231 111.920379685 0.1646629707
702 8.6650454167 36.66379458 49.9141226715 0.467234745
703 14.0863259261 51.5919972938 62.2405322789 0.0055202196
704 88.9990210879 113.3261541817 150.0495079611 0.3631271751
705 74.2165155237 77.1463651592 80.8986990205 0.1434327118
706 2.9238749606 31.8900984499 8.5455490841 0.3193853495
707 15.0392116108 23.4234004436 11.3460739018 0.581396344
708 73.6627568097 22.5057901769 35.9972433775 0.457237979
709 21.8465905779 65.5271377236 93.1404869013 0.1682103758
710 84.0526409124 30.2361549578 22.0659117102 0.2774992475
711 18.121123696 86.9259426635 103.8688843026 0.0455333582
712 11.5554310642 48.3630066673 40.3523438455 0.102262825
713 20.0167137418 51.700499517 63.5970037981 0.4694404186
714 3.2261691461 182.5490588673 188.913302109 0.0188215677
715 9.5323758288 37.1130958797 29.5770323489 0.2661135084
716 42.7339355813 38.5191690895 40.8676008151 0.4403415215
717 8.6007517251 29.3567324951 18.8344085309 0.4994073792
718 16.9706709099 50.8324751195 60.2752893022 0.4598302394
719 14.2360567649 33.2749824146 18.9252300601 0.3572308675
720 1.0900321563 45.2378592639 47.7092435138 0.1286989031
721 117.5953017983 69.8037174237 112.8339189593 0.204848791
722 14.4567402279 49.958487126 76.4497091267 0.088069366
723 26.3420881744 63.6717557907 62.6035955903 0.1437795272
724 55.9177675449 78.0567280094 90.8649908037 0.1647064557
725 81.8376350825 55.7980122167 38.4474715951 0.2750082014
726 13.0067774657 39.1259757841 44.3528510946 0.4346769639
727 18.0600237004 21.7253164046 4.2503870638 0.5870838422
728 22.6997689218 23.6831310403 18.3883580905 0.3996927837
729 51.7429437695 13.883641687 2.952035732 0.6436316516
730 25.8531301582 66.748295985 82.3624870764 0.1918033593
731 4.4819832578 23.8731398468 12.8882008604 0.5050948846
732 21.6390803681 46.3468875818 47.3933587758 0.3034691174
733 0.707245839 46.8915414364 47.8854677133 0.3296104606
734 16.9878705166 26.0723226258 7.6578725586 0.5552417182
735 59.9021652359 29.2677744682 30.3124485556 0.5997947035
736 45.9831657719 27.898034922 27.222314401 0.5210120057
737 13.5014934221 62.4148507824 51.3270968524 0.0445745939
738 22.9728000641 35.0159686384 22.0438236809 0.5872360799
739 9.18001555 65.7041994192 58.6892333114 0.243930285
740 12.9311650677 60.5947856991 52.2355585672 0.3428447571
741 44.5034574011 25.7676224745 23.5775232736 0.440606974
742 18.9341385251 32.0850005465 46.7326280639 0.3616046856
743 8.0034571959 50.0209326264 61.3613080243 0.0609124585
744 18.1729280997 51.6309356645 72.3740087746 0.4102425381
745 66.9218159621 70.3148371951 90.2549975275 0.3434412893
746 4.2898932317 52.6942394345 89.0735779747 0.2542459002
747 47.5768354067 159.2596080762 177.3346158481 0.1536560323
748 14.6208442321 20.5725038066 30.6200371831 0.3387248155
749 30.4026261977 46.9693924057 40.5095196041 0.0910542356
750 36.8892733423 155.6888933766 172.686836356 0.0099788283
751 5.6905958586 28.100779788 32.360115525 0.3590407285
752 6.0447228386 52.02374486 48.627232394 0.0796156759
753 60.6157124066 34.0944255495 25.7055448874 0.3184292934
754 12.113446318 80.6395735708 79.8636672325 0.0218696539
755 33.4147934382 57.2737096692 67.1269905543 0.138359165
756 56.5662419237 33.0198327186 28.792477815 0.1592242403
757 31.8109538481 22.8724697836 16.267009337 0.5831127278
758 84.2232759433 39.3107216182 49.0580669835 0.3250194342
759 26.6931160421 54.6951375638 40.8323829163 0.0657206404
760 93.8228813629 40.1124007471 45.6751189557 0.4463969186
761 10.2740821326 34.509098905 36.2933609437 0.3949291202
762 113.6006377864 83.4825168657 119.756413037 0.3552359282
763 2.2182219549 53.2228445843 37.7708218847 0.1333104753
764 5.322256 42.7997790714 61.3759775429 0.3346347303
765 6.4669303968 50.9239508891 83.709304991 0.4053060603
766 6.3252552201 46.899970705 46.3752767666 0.3941318888
767 115.8244385419 122.9067186104 142.5472235708 0.2446796814
768 37.2818137052 17.8724464234 3.3525332696 0.5192621227
769 11.3842069409 15.5419176448 8.1761692089 0.5913241616
770 4.7179601531 50.9661112574 47.7673843187 0.0185980504
771 3.3503563282 110.0478284546 150.5201898408 0.0917129308
772 11.356335527 18.2267766503 4.8460983023 0.6449332416
773 33.3813914835 94.2351012748 183.1964512824 0.2299926017
774 8.044053287 145.6134070391 231.9086811768 0.1597077423
775 23.5063207045 40.6246065889 48.9580513669 0.4555250921
776 30.182187441 39.7513053742 32.9884862893 0.3074245587
777 19.1795954466 52.1209348617 42.7296515624 0.2459822408
778 72.3358751782 21.3063741921 20.1129314758 0.6170964701
779 9.4090569056 52.8923229082 73.6410409996 0.3575085851
780 66.4232380581 67.5956608679 92.2800117557 0.2507533566
781 9.5116561202 60.245213685 87.7633113524 0.4619544519
782 3.4739443919 23.9258173433 7.9569309691 0.4568175221
783 48.9390853249 43.4868315439 42.3983991366 0.4207861797
784 56.0252755552 50.3884224726 44.2952171628 0.0380548221
785 48.4292613089 52.3252861696 64.0112844127 0.2456012108
786 45.7030168287 35.2039050397 38.2962927362 0.1907535079
787 14.4366758318 24.2175481304 13.5194436115 0.3426128688
788 34.2069022608 25.6544117013 32.2215915715 0.3882963222
789 15.7096541992 80.1644149692 93.8001395667 0.2330477521
790 36.950403019 38.7701608847 66.0496504343 0.2491320099
791 68.0416791252 35.4262715689 34.4213958161 0.3299578264
792 16.5081667694 33.4157058636 62.5186540855 0.5325403439
793 6.3217296486 14.985300312 1.1361663343 0.6789198765
794 7.2406222311 24.535158995 22.6659883555 0.5000125875
795 0.2680448029 35.9761423078 37.6323490848 0.5454674781
796 4.0037884017 30.8596309598 34.0774251604 0.1871402268
797 36.0248801181 67.6111039627 65.8369433197 0.0790275269
798 7.1028495335 67.2948029742 69.8270929584 0.242773404
799 56.1209886784 75.6632425763 87.1553722127 0.130148836
800 21.1318908378 19.9068045329 1.9749683386 0.4074339033
801 30.5922037966 45.9354246831 40.5659925073 0.0842417665
802 19.0551559995 35.8783502131 23.1641791199 0.4422246004
803 26.4520402833 29.9292571962 26.8186574752 0.1555879376
804 15.9890340701 140.8396303424 251.8873585255 0.0768938308
805 27.61657187 75.4571057478 80.0321814453 0.0599017581
806 39.335476234 24.4817556015 25.2775818915 0.4015594517
807 90.9024286647 105.0823346504 167.2273120303 0.3662485324
808 37.954417209 60.1514176392 103.455312506 0.2720052235
809 21.6889286506 53.1424452741 70.3844396017 0.1318137768
810 24.0661272158 41.0659210669 38.5578837446 0.0154531786
811 17.8814325059 34.9990140098 34.920028115 0.2854665061
812 18.8135836668 62.3644962596 80.2460378401 0.2968383882
813 7.7336978729 85.3167783326 135.9476083741 0.3932134009
814 97.6943569968 42.8830517566 37.4935029981 0.2545820842
815 6.0054885913 31.0721587917 38.1835129763 0.5119154342
816 9.0143823717 34.5787067148 31.4379600984 0.3050130872
817 23.8003222086 43.9234768157 49.9030011499 0.3905254254
818 39.7894658507 27.3709462789 26.8348351725 0.3920899572
819 1.5090405714 49.3454827218 53.3592416904 0.0728705808
820 78.9045097959 58.7776350829 69.5902308609 0.3965788739
821 32.9965308406 69.8175637415 74.209380728 0.1025861045
822 92.9679458747 47.8407686537 57.0556184799 0.2720993815
823 9.5356286818 10.029428663 5.5059536177 0.6909033388
824 22.8846265163 41.482975189 41.1364106828 0.4221130232
825 2.8452823279 122.7909519931 120.572960946 0.2484774764
826 8.4129597943 164.8983988438 213.8749764241 0.0883370775
827 85.5401774171 26.0504595188 35.165093221 0.6232016996
828 47.8544273249 46.5018385144 67.1037145497 0.3600714346
829 74.0111791099 101.6267243532 121.0645372684 0.1102062392
830 92.2739356531 79.7520455073 73.5786767338 0.1628771692
831 5.3132643821 20.9155118102 15.251047184 0.4799006989
832 6.4817621354 24.5350450732 20.5162807121 0.4954235803
833 29.6784197771 109.9598806298 136.9079794028 0.1169884482
834 60.3283042774 41.5939934674 44.5460856789 0.3194290614
835 10.4054423087 25.948872433 23.6775024894 0.4929563475
836 52.7824668988 15.791351092 12.2090768742 0.6782623273
837 1.8422491817 230.2189430491 355.3905005536 0.0504260216
838 27.3326764149 56.5482235206 54.8250944299 0.2517351871
839 45.6774155272 19.235669486 30.2651770163 0.6886412456
840 16.4490440952 25.3369521453 25.5215294419 0.4830441726
841 94.6192012068 42.1989192763 23.2755961056 0.3591212687
842 48.3591136138 170.5964797603 211.9254087292 0.0360993395
843 47.1689598333 53.0325526119 77.0562168566 0.1999922512
844 0.9758571023 81.8800002307 105.9773595926 0.0414762133
845 11.4294010652 24.8077895983 5.4369742265 0.4886952529
846 30.8878045855 64.7938957119 74.4006518513 0.2664077832
847 20.907727563 75.0555533422 116.353616744 0.2185296177
848 5.8270250508 76.0905083049 85.926249251 0.1926825392
849 11.1440455567 82.2715666047 92.6427301116 0.0154630048
850 76.6744698755 103.0989655385 128.9988832209 0.1908946847
851 49.8847487298 16.9131622452 4.6129605075 0.6281721195
852 74.7137837278 26.6062295783 8.7642097807 0.5927785543
853 6.815078045 49.4029577231 66.545958633 0.3198088161
854 15.1262835393 63.7544057408 75.621938663 0.0955123952
855 58.1339920185 83.2333779581 99.7967083554 0.0624364179
856 45.1593204923 197.1700182163 200.5073236483 0.0709879642
857 7.1232161191 39.2327373355 44.3947469822 0.2374970541
858 7.1135634534 85.9956891985 103.5837896459 0.020158558
859 30.8920411058 98.5085165069 117.4506819927 0.0805711141
860 9.022768909 21.0531066637 21.1996562379 0.55588355
861 14.7213396419 49.3359204263 88.2977717399 0.2938885899
862 6.5298541669 23.0677703867 9.5148421423 0.5619827246
863 38.861473009 21.737687755 3.4741249626 0.5554330246
864 16.3681762997 49.0991551254 37.7007792306 0.1977407881
865 24.9879263527 46.9952344271 71.3443960881 0.1980849573
866 83.6436204562 46.3137535254 39.1550082677 0.1471721977
867 42.3263871688 14.9569406059 1.7117973677 0.6126128962
868 55.9990122398 54.4030594132 71.5519297719 0.2612867154
869 25.5349490729 58.0372037888 72.2655212844 0.00953443
870 27.0816333457 74.4412492337 87.527708409 0.1562411762
871 15.2702578758 28.3159553526 26.2047750356 0.3169568701
872 18.6834322183 16.765241006 18.1403371151 0.6166152411
873 7.2595635861 14.4553544208 6.638134985 0.5580291395
874 2.4502014366 56.8463907261 88.8727524341 0.1571358711
875 44.7125971368 63.6447192341 58.269542571 0.134895588
876 12.0150888999 136.9110991095 143.7691455682 0.0659924214
877 35.7727622097 61.6673713064 81.6688550932 0.1751360745
878 8.7897227957 50.3048729082 38.0612082691 0.0048349747
879 53.5855265627 46.5788430677 42.4340408098 0.2562281732
880 7.3908146092 48.9184977314 45.8063653439 0.1699783378
881 61.2176755367 53.5590465325 85.1848398015 0.3801719847
882 1.7782636737 18.0360137393 5.350861875 0.6224286398
883 86.9770794208 71.5462814615 93.1618861331 0.3057235807
884 50.2610723387 73.538105413 91.0331588713 0.2814277422
885 1.6886942562 27.7120503784 29.2212610402 0.5415466659
886 36.3639410011 36.5725044734 26.6375583928 0.2902832596
887 21.3675901409 30.8701607956 36.5595224977 0.4602937555
888 5.416244671 139.966490831 166.4827925316 0.2237653097
889 16.1820087733 46.9529233307 58.5896083964 0.2529776516
890 36.209524813 84.2803925846 129.9073675517 0.3390780829
891 18.2342555239 51.2175949939 50.6245104835 0.3090670003
892 3.6497657054 26.9247539321 24.433906479 0.4788585664
893 18.3251936797 43.4512821362 44.7705197356 0.2776800865
894 116.0019122872 57.7465287132 64.6431032904 0.0069451994
895 11.3125729032 92.3799054289 134.2412114001 0.0912822801
896 41.5006942257 45.5865391799 30.8365510959 0.1417598504
897 85.0111047132 125.7803826842 174.9680636087 0.0887833611
898 8.94798633 34.1615593151 33.8739945111 0.2109364829
899 6.9137562512 37.7946937286 34.0532388458 0.2732572322
900 115.7296289723 131.1358654826 160.1963136876 0.0316020297
901 42.3186239258 134.7567448873 170.0999002247 0.1713728046
902 36.5106604854 31.7048462202 25.0247069798 0.2963775521
903 3.4033407336 40.0771668168 45.5946599425 0.2052112109
904 23.1430295582 52.5254249919 59.0789031733 0.1677568956
905 5.0167167351 107.8298128531 149.4671379416 0.2075063883
906 74.0823932171 30.846386146 38.6328970296 0.4600193342
907 0.5618492705 78.8277287229 82.3946876666 0.0872858144
908 5.0928718508 119.0179563158 105.3541073133 0.2255208688
909 43.6690751955 47.3783083923 38.2570059674 0.1227864973
910 9.1446758366 33.8211502234 29.59061022 0.4300248453
911 25.6830153545 126.4330458909 241.9646377724 0.2023624278
912 16.306493248 33.3026854378 14.5349205301 0.5211279905
913 44.5865548385 123.4911788597 183.2423196535 0.1706792024
914 57.1473869711 67.0339567475 77.0426533195 0.2780361253
915 50.3722311753 110.9666153192 143.9336355401 0.1827863334
916 40.1070875392 31.1104045593 44.7403789275 0.3738991626
917 28.4553227644 35.3989039083 45.1521056087 0.3749985467
918 7.2637557706 61.4719210561 68.4749718984 0.4068836426
919 11.8571531242 69.4750082967 92.7362282464 0.113401985
920 17.4329032196 162.049499438 190.8558525091 0.0675978619
921 7.6469773211 85.2008878079 70.7142899679 0.1709078484
922 45.622692184 41.5154747907 52.8023230036 0.3928229159
923 22.9149608895 36.58699602 30.9538338067 0.1048610481
924 67.9012985922 52.3706507097 74.012126306 0.255235375
925 8.5188684024 142.3257072192 149.0377978249 0.0330643391
926 5.8136143672 38.5243712049 61.8100495163 0.3729836192
927 10.0725952335 16.9256660455 20.4180079143 0.4391703349
928 24.8689126334 28.5886710704 23.0289928748 0.4478762795
929 9.3390940132 78.223328634 93.7821430834 0.1687473333
930 4.6984493505 118.4387671513 165.675642678 0.085673677
931 7.1379792975 22.6947868006 23.6074505879 0.5710858033
932 12.7490153202 80.8375457276 113.6709909366 0.3885511427
933 4.2543560364 48.5107802812 71.3339318726 0.5893890792
934 45.1062888949 86.5729168628 134.5135248256 0.1833507447
935 53.42270493 11.5454982023 8.3574895827 0.6731431681
936 11.8855780412 26.5510030525 33.9894746516 0.4685108806
937 129.6775678074 33.9792116244 37.7121398199 0.6544808961
938 38.1359427782 35.6585220296 34.9534870342 0.117197621
939 31.2380288161 22.8870348552 18.2421620656 0.5680076758
940 6.4386916261 37.6732596651 58.2415745097 0.4464641732
941 0.6748193899 36.1656458259 20.7799157962 0.3318087593
942 69.735896779 24.5885223597 3.3734835423 0.4353739897
943 25.4258217257 68.3963359015 109.8800603417 0.1511558116
944 27.0747984252 40.4102277691 51.891818852 0.5345886671
945 5.0397271416 66.2059103906 78.4549116645 0.0128333111
946 13.0641941799 43.3345367413 66.8960913622 0.5499877939
947 97.6266206263 22.7845726775 11.7817618251 0.533790353
948 28.2076507449 16.4340485107 6.1303773645 0.588657916
949 64.3843568054 119.3015497149 141.3958643757 0.1332247424
950 18.7812873435 82.1701428735 69.2063610512 0.0233963209
951 24.9998821756 66.5931628565 83.8205885811 0.1052357583
952 6.1579316447 25.1761234873 19.8982372968 0.4546994507
953 3.0847681978 73.8806002935 137.807906641 0.1723744633
954 6.2276976263 96.3031108789 130.2358108419 0.1105683718
955 1.2527507106 56.9941520995 51.3925272376 0.0184018442
956 0.288012533 80.8993631702 102.3789809223 0.243611058
957 2.4677095078 72.8331012335 103.5907860785 0.123689896
958 13.986785467 20.5363969493 17.595303547 0.2515428685
959 54.4844583248 57.4747330916 90.0150804973 0.2988981571
960 140.2835410107 44.7996368597 29.6957030285 0.3606450204
961 2.0153935298 12.8849394344 3.2446218214 0.6617911042
962 12.4444697333 41.1587469841 48.1845124768 0.2067737195
963 31.9854409335 46.5405264577 42.5975694787 0.1172122916
964 13.4524358364 27.1395524219 22.4064784861 0.4212485789
965 26.4783314112 36.8983068402 53.0908278695 0.3568296598
966 9.878575519 53.4747526643 72.0292248854 0.3838101032
967 11.5301339619 27.7009974899 20.1524035169 0.4890836991
968 26.4770370528 26.2335974412 12.2848058866 0.5316755236
969 86.0718631824 42.772934456 50.4530698851 0.1785031467
970 28.0803378401 21.1118296511 22.8517196826 0.5450397507
971 34.244305244 27.1926788948 31.3006217795 0.5646742961
972 17.536350142 61.5616639631 69.5092020006 0.3789098529
973 13.2855573256 44.8432867651 46.7029841076 0.2495616897
974 38.022725203 54.7344875182 94.1076298859 0.3696590565
975 14.878550715 69.4328824052 90.4414430006 0.0584621923
976 52.5538940858 73.1160115787 101.69247865 0.1620337776
977 72.5718299114 65.8641886013 94.1002952779 0.2044534147
978 6.8820220835 25.3950312694 18.0725174548 0.5437926931
979 83.8205837665 116.5840023026 108.7996671435 0.0531657465
980 6.263504446 22.915801589 10.2337467481 0.451777729
981 42.3312949477 32.7745081648 32.246448841 0.5315348352
982 3.5307359126 119.6218545149 150.0336274151 0.1757770926
983 2.6720650904 51.020995632 41.0382788442 0.1217075138
984 12.3061629153 48.2868212688 61.0958530194 0.4617018876
985 35.0566305974 29.1200114978 58.1502164836 0.4966260126
986 36.5145048251 133.7123214875 183.6946502432 0.1516889766
987 33.5101831141 28.1403998984 36.8852571045 0.5954597863
988 59.1247901845 49.0289390962 78.7944072466 0.3342875576
989 20.7945560395 57.2819587158 109.5285916734 0.379606993
990 21.1281316256 29.1790069417 38.5638873204 0.3586795556
991 27.8644848357 74.8752826367 73.1172152616 0.4518999187
992 21.2075662932 21.3653715163 13.9081814329 0.6386686143
993 19.1007381011 43.5985356235 41.8690700437 0.3392099337
994 21.2307097609 126.9311550338 152.1255794728 0.0339219376
Avg Wait (min) -- 10 cust 995 65.6112446461 53.6539260916 69.6711240929 0.0797165479
Freq Table -- Sample of 1000 996 6.8609019719 39.1035244393 30.1437737805 0.4291527583
Class Width Upper Val Classes Freq Proportion 997 8.851303264 85.6014595492 118.9388582638 0.1378331039
5 5 <=5 117 0.12 ORGANIZE/SUMMARIZE 998 2.2052310653 39.2034899974 50.3290183608 0.1304394514
10 15 >5 to <=15 263 0.26 999 6.7946454266 33.0466682269 37.6774642433 0.2853360981
10 25 15 - 25 194 0.19 1000 7.8104363866 70.5906186449 104.806405172 0.3653045705
10 35 25 - 35 106 0.11 Summary Table (10 customers): 10 Customers in Barber Shop Summary Table
10 45 35 - 45 86 0.09 (sample of 1000) Key Measure: Avg Wait (min) Ave Time in Shop (min) 90 Percentile Wait (min) Percent of Time Idle
10 55 45 - 55 72 0.07
10 65 55 - 65 42 0.04 use for best estimate of these objective measures--> Average: 30.3 55.4 64.3 31%
20 85 65 - 85 56 0.06 Est 90 Percentile of Avg Wait for 10 customers --> 90 Percentile: 72.6 101.6 134.6 58% Possible Add'l Measures
20 105 85-105 39 0.04 Est StDev of Avg Wait for 10 customers --> StDev: 28.3 35.3 51.3 19%
135 240 >105 25 0.03 Est Max of Avg Wait for 10 customers --> max: 182.7 314.2 421.1 79%
Totals: 1000 1.00 Est Median of Avg Wait for 10 customers --> Median: 20.7 46.1 51.3 30%
Conclusions and Insights:
For this barbershop, given the estimates of haircut time
and customer arrivals, the average customer wait is
just over 30 minutes. Customers spend about 55 min
in the shop. There is, however, much variation. For
example, About 10 percent of days, the average customer wait
is more than one hour. For a typical day, the barber
is idle (not cutting hair) about 30 percent of the time.
The owner/barber's reaction might be:
Average wait is too long.
90 percentile of wait is too long
"I can speed up some."
What if I make my average haircut 20 minutes?
What if I make my average haircut 15 minutes?
What if I change my pattern -- normal?
Uniform between 20 and 30?
The analyst can easily make modifications to the core model, replicate, organize results, and report on how the performance measures would change.

Risk Profile - Avg Wait for 10 customer day (sample of 1000)

< =5 > 5 to < =15 15 - 25 25 - 35 35 - 45 45 - 55 55 - 65 65 - 85 85-105 > 105 0.11700000000000001 0.26300000000000001 0.194000 00000000001 0.106 8.5999999999999993E-2 7.1999999999999995E-2 4.2000000000000003E-2 5.6000000000000001E-2 3.9E-2 2.5000000000000001E-2

Avg Wait (minutes)

Proportion

4.5.1

Modeling Approach for Repeated Stocking Decision for One Period of Demand
Issue Freddie the News "Boy"
Sells Financial Times Journal each day at a newstand.
Orders, receives copies early, sells some number, if any leftover -- returns next day for small refund
Bus Prob Bus Ques: How many copies should be ordered per day from the distributor ? Can we understand the impacts of different order levels?
Decision: # copies to order
Objective measures: average daily profit (revenues - costs), chance that profit/day is at least $50, average unsatisfied customers
Constraints: system rules, demand random with historical data
Bus Data Costs: Revenues: Daily Demand:
$1.50 per copy delivered $2.50 per copy sold Discrete Uniform between 40 and 70 copies
$0.50 per copy refunded We'll use Uniform Distribution (as before) but will round to integer
value so that only possible values are 40, 41, 42, …,69, and 70.
Analysis:
Simulation Core Model -- One Day or Consecutive Days? Assumptions:
Cost/cy $1.50 Daily DISCRETE UNIFORM Demand distrib same each day
Rev/cy $2.50 Demand: MIN 39.5 No quantity discounts -- cost or rev Q: What will we record for each day?
Refund/cy $0.50 MAX 70.5 No late day discounts A: The details of the decision and its impact
Order Qty 65 No impact of unsatisfied demand focused on the objective measures.
One Day of Operation

4.5.4

One Day of Operation
Day Deliver Demand Sold Unsold Revenues Refund Costs Profit Unsat Cust
1 65 ERROR:#VALUE! ERROR:#VALUE! ERROR:#VALUE! ERROR:#REF! ERROR:#REF! $0.00 ERROR:#REF! ERROR:#VALUE!
Use Data Table to REPLICATE the Core Model: Examine other possible order quantities: Profit Unsat Cust
Order 65 ERROR:#REF! ERROR:#VALUE! NOTE: If you do not "freeze" the Order 50 ERROR:#REF! ERROR:#VALUE! These results have
CORE 1 15 0 Data Table results and repeat 1 50 10 been "frozen"
MODEL 2 39 0 one can "see" the variation 2 50 20
CAN BE 3 63 0 3 38 0
JUST ONE 4 17 0 RESULTS: (Order 65) From your Bus Statistics: 4 50 17 RESULTS: (Order 50) Sampling
DAY 5 31 0 sample 1000 days 95 percent MOE: $1.00 5 50 17 sample 1,000 days 95 percent MOE: $0.35
Why? 6 41 0 Avg Pr $44.77 "possible error in using samp mean 6 38 0 Avg Pr $46.99 "poss error in using samp mean
Answer: Days are 7 43 0 Stdev Pr $15.90 as estimate of true mean" 7 50 4 Stdev Pr $5.50 as estimate of true mean"
independent 8 53 0 95 Percentile Pr $65.00 8 50 11 95 Percentile Pr $50.00
Can't do this with 9 65 3 5 Percentile Pr $19.00 9 50 10 5 Percentile Pr $34.00
a service facilty or 10 51 0 P(Pr>=$50) 0.44 10 50 15 P(Pr>=$50) 0.70
with weather where 11 65 2 Risk Profile Freq Table ----> Histogram (not shown here) 11 50 13 Risk Profile Freq Table ----> Histogram
one day's weather 12 65 3 Avg Unsat Cust 0.39 12 50 3 Avg Unsat Cust 6.85
influences the next 13 23 0 13 48 0
day's weather. 14 25 0 14 50 4
15 49 0 15 46 0
16 15 0 THEN, investigate other possible order quantities. 16 50 14
17 29 0 17 50 7
18 57 0 ORGANIZE/SUMMARIZE 18 34 0
19 65 4 60 19 50 16
20 23 0 65 $44.77 $15.90 $65.00 $19.00 20 50 19
21 65 5 70 21 50 6
22 37 0 22 50 20
23 55 0 23 50 8
24 59 0 24 38 0
25 65 4 25 50 18
26 53 0 26 50 10
27 45 0 27 50 14
28 35 0 28 50 14
29 61 0 29 50 17
30 25 0 30 50 16
31 41 0 31 50 11
32 51 0 32 46 0
33 65 0 33 50 14
34 27 0 34 50 13
35 65 5 35 42 0
36 37 0 36 50 8
37 45 0 37 38 0
38 39 0 38 36 0
39 53 0 39 32 0
40 39 0 40 50 11
41 53 0 41 50 10
42 65 3 42 50 15
43 49 0 43 34 0
44 49 0 44 50 17
45 49 0 45 50 1
46 65 1 46 50 19
47 29 0 47 48 0
48 65 3 48 50 16
49 65 3 49 40 0
50 57 0 50 32 0
51 55 0 51 30 0
52 33 0 52 50 9
53 29 0 53 50 13
54 31 0 54 50 20
55 65 4 55 50 19
56 53 0 56 50 0
57 65 0 57 50 1
58 33 0 58 50 3
59 65 4 59 50 17
60 47 0 60 46 0
61 65 3 61 50 2
62 33 0 62 50 2
63 21 0 63 50 17
64 17 0 64 38 0
65 19 0 65 50 13
66 57 0 66 50 17
67 65 3 67 50 8
68 65 1 68 50 1
69 25 0 69 40 0
70 47 0 70 50 16
71 57 0 71 50 1
72 45 0 72 42 0
73 65 2 73 50 15
74 39 0 74 50 4
75 23 0 75 50 18
76 29 0 76 50 0
77 43 0 77 50 3
78 65 2 78 50 13
79 43 0 79 50 2
80 47 0 80 50 16
81 25 0 81 34 0
82 17 0 82 48 0
83 33 0 83 50 11
84 65 3 84 50 10
85 49 0 85 50 8
86 63 0 86 50 10
87 65 3 87 50 3
88 35 0 88 36 0
89 57 0 89 50 11
90 65 3 90 50 9
91 59 0 91 50 3
92 31 0 92 50 3
93 19 0 93 50 11
94 39 0 94 50 9
95 39 0 95 48 0
96 51 0 96 48 0
97 35 0 97 36 0
98 39 0 98 50 4
99 65 0 99 50 5
100 21 0 100 32 0
101 49 0 101 50 13
102 51 0 102 50 18
103 39 0 103 50 0
104 29 0 104 50 15
105 59 0 105 50 13
106 19 0 106 50 17
107 27 0 107 50 9
108 25 0 108 50 14
109 65 4 109 50 9
110 41 0 110 50 20
111 61 0 111 50 8
112 49 0 112 50 18
113 37 0 113 44 0
114 57 0 114 50 2
115 45 0 115 50 0
116 27 0 116 50 9
117 23 0 117 30 0
118 31 0 118 30 0
119 23 0 119 50 3
120 21 0 120 42 0
121 63 0 121 50 11
122 35 0 122 40 0
123 31 0 123 42 0
124 37 0 124 50 11
125 35 0 125 40 0
126 59 0 126 50 16
127 27 0 127 36 0
128 29 0 128 46 0
129 57 0 129 50 12
130 45 0 130 36 0
131 65 0 131 50 10
132 41 0 132 50 7
133 59 0 133 50 2
134 49 0 134 40 0
135 25 0 135 50 1
136 31 0 136 50 3
137 33 0 137 50 4
138 27 0 138 38 0
139 35 0 139 30 0
140 51 0 140 50 6
141 57 0 141 50 8
142 23 0 142 50 17
143 17 0 143 50 5
144 31 0 144 36 0
145 31 0 145 48 0
146 65 0 146 50 18
147 35 0 147 50 0
148 19 0 148 46 0
149 35 0 149 36 0
150 55 0 150 34 0
151 29 0 151 50 17
152 61 0 152 50 11
153 45 0 153 50 7
154 19 0 154 50 8
155 33 0 155 50 16
156 39 0 156 50 15
157 53 0 157 50 1
158 51 0 158 50 18
159 63 0 159 50 13
160 21 0 160 46 0
161 57 0 161 50 18
162 39 0 162 46 0
163 55 0 163 36 0
164 23 0 164 50 18
165 51 0 165 50 19
166 37 0 166 50 4
167 37 0 167 50 16
168 65 2 168 50 12
169 45 0 169 50 2
170 51 0 170 50 2
171 23 0 171 42 0
172 63 0 172 50 9
173 39 0 173 50 14
174 35 0 174 50 5
175 53 0 175 50 13
176 19 0 176 50 20
177 29 0 177 50 2
178 65 2 178 42 0
179 49 0 179 40 0
180 21 0 180 50 20
181 37 0 181 50 10
182 65 4 182 46 0
183 53 0 183 50 12
184 31 0 184 50 13
185 19 0 185 44 0
186 37 0 186 50 1
187 55 0 187 50 0
188 65 4 188 50 16
189 61 0 189 50 7
190 57 0 190 50 15
191 49 0 191 50 19
192 57 0 192 50 13
193 65 2 193 44 0
194 41 0 194 46 0
195 41 0 195 50 14
196 49 0 196 50 16
197 39 0 197 50 10
198 25 0 198 30 0
199 65 5 199 34 0
200 21 0 200 50 3
201 37 0 201 50 5
202 51 0 202 34 0
203 19 0 203 50 13
204 41 0 204 50 14
205 65 4 205 50 15
206 45 0 206 30 0
207 57 0 207 38 0
208 17 0 208 32 0
209 23 0 209 50 10
210 47 0 210 40 0
211 57 0 211 50 3
212 59 0 212 50 17
213 55 0 213 36 0
214 35 0 214 32 0
215 53 0 215 40 0
216 53 0 216 40 0
217 33 0 217 50 3
218 65 1 218 50 5
219 61 0 219 50 8
220 51 0 220 38 0
221 39 0 221 50 18
222 65 3 222 50 18
223 43 0 223 50 11
224 19 0 224 34 0
225 33 0 225 50 14
226 61 0 226 46 0
227 63 0 227 50 3
228 31 0 228 50 8
229 65 0 229 50 5
230 45 0 230 50 15
231 45 0 231 50 16
232 23 0 232 46 0
233 27 0 233 50 19
234 43 0 234 50 2
235 17 0 235 50 17
236 65 0 236 50 7
237 27 0 237 50 6
238 57 0 238 46 0
239 61 0 239 46 0
240 65 0 240 50 15
241 31 0 241 50 3
242 51 0 242 50 9
243 63 0 243 42 0
244 43 0 244 50 2
245 65 4 245 46 0
246 43 0 246 50 7
247 23 0 247 50 8
248 51 0 248 46 0
249 17 0 249 46 0
250 53 0 250 50 13
251 21 0 251 30 0
252 21 0 252 50 3
253 65 1 253 50 15
254 19 0 254 50 10
255 65 4 255 50 17
256 65 2 256 50 12
257 51 0 257 50 1
258 63 0 258 50 6
259 65 5 259 50 0
260 29 0 260 40 0
261 65 0 261 50 7
262 63 0 262 32 0
263 63 0 263 50 20
264 65 1 264 50 2
265 15 0 265 50 8
266 39 0 266 50 19
267 65 3 267 48 0
268 65 1 268 30 0
269 39 0 269 50 4
270 43 0 270 42 0
271 27 0 271 50 1
272 65 4 272 50 3
273 57 0 273 50 6
274 31 0 274 50 14
275 43 0 275 50 7
276 65 2 276 50 2
277 27 0 277 46 0
278 43 0 278 50 10
279 59 0 279 40 0
280 17 0 280 50 13
281 17 0 281 50 3
282 65 2 282 50 9
283 45 0 283 34 0
284 45 0 284 36 0
285 43 0 285 50 17
286 61 0 286 42 0
287 59 0 287 50 9
288 65 5 288 50 10
289 61 0 289 50 9
290 49 0 290 36 0
291 55 0 291 50 16
292 33 0 292 42 0
293 65 4 293 34 0
294 43 0 294 50 1
295 65 4 295 50 19
296 59 0 296 50 7
297 55 0 297 50 19
298 51 0 298 50 16
299 17 0 299 50 17
300 29 0 300 50 14
301 31 0 301 50 0
302 39 0 302 50 16
303 59 0 303 50 16
304 57 0 304 50 2
305 29 0 305 48 0
306 65 1 306 38 0
307 45 0 307 50 2
308 63 0 308 44 0
309 45 0 309 50 12
310 33 0 310 50 14
311 49 0 311 46 0
312 19 0 312 50 16
313 37 0 313 50 4
314 29 0 314 42 0
315 57 0 315 48 0
316 61 0 316 48 0
317 23 0 317 50 16
318 53 0 318 50 1
319 49 0 319 50 17
320 33 0 320 50 0
321 57 0 321 48 0
322 27 0 322 32 0
323 39 0 323 50 0
324 27 0 324 50 6
325 21 0 325 50 15
326 53 0 326 50 15
327 47 0 327 50 6
328 27 0 328 50 16
329 65 4 329 36 0
330 41 0 330 48 0
331 45 0 331 38 0
332 27 0 332 34 0
333 65 3 333 50 14
334 25 0 334 38 0
335 57 0 335 50 10
336 29 0 336 50 5
337 65 2 337 50 3
338 65 1 338 50 17
339 31 0 339 50 3
340 21 0 340 50 11
341 19 0 341 42 0
342 21 0 342 50 10
343 37 0 343 50 6
344 65 0 344 42 0
345 47 0 345 42 0
346 55 0 346 50 14
347 43 0 347 46 0
348 65 1 348 50 14
349 25 0 349 36 0
350 21 0 350 50 0
351 61 0 351 50 15
352 41 0 352 50 7
353 65 3 353 50 11
354 63 0 354 50 3
355 47 0 355 48 0
356 47 0 356 50 2
357 47 0 357 50 10
358 31 0 358 50 8
359 33 0 359 50 15
360 19 0 360 50 19
361 65 2 361 38 0
362 33 0 362 50 13
363 31 0 363 50 12
364 19 0 364 50 12
365 49 0 365 50 1
366 19 0 366 50 2
367 45 0 367 44 0
368 37 0 368 50 14
369 65 0 369 40 0
370 53 0 370 50 10
371 35 0 371 38 0
372 45 0 372 50 13
373 35 0 373 50 15
374 29 0 374 44 0
375 17 0 375 50 7
376 61 0 376 48 0
377 31 0 377 50 12
378 23 0 378 34 0
379 19 0 379 50 1
380 43 0 380 44 0
381 35 0 381 50 8
382 35 0 382 50 11
383 21 0 383 32 0
384 61 0 384 50 10
385 43 0 385 38 0
386 23 0 386 50 9
387 59 0 387 34 0
388 59 0 388 50 14
389 47 0 389 38 0
390 47 0 390 50 1
391 27 0 391 50 11
392 27 0 392 50 10
393 43 0 393 50 17
394 49 0 394 50 6
395 47 0 395 50 4
396 51 0 396 50 15
397 63 0 397 50 10
398 17 0 398 50 9
399 45 0 399 50 13
400 25 0 400 50 17
401 39 0 401 50 15
402 65 1 402 44 0
403 41 0 403 50 7
404 35 0 404 50 14
405 47 0 405 50 2
406 65 3 406 50 6
407 65 1 407 44 0
408 63 0 408 50 18
409 61 0 409 50 10
410 23 0 410 48 0
411 55 0 411 50 18
412 51 0 412 48 0
413 65 0 413 40 0
414 43 0 414 50 2
415 65 3 415 30 0
416 35 0 416 50 18
417 63 0 417 50 7
418 55 0 418 50 14
419 53 0 419 38 0
420 39 0 420 44 0
421 45 0 421 50 2
422 19 0 422 40 0
423 61 0 423 50 18
424 65 0 424 50 5
425 39 0 425 32 0
426 25 0 426 48 0
427 59 0 427 50 9
428 23 0 428 50 2
429 65 4 429 50 2
430 33 0 430 50 7
431 47 0 431 50 18
432 27 0 432 40 0
433 59 0 433 50 0
434 57 0 434 50 0
435 21 0 435 50 12
436 53 0 436 50 0
437 21 0 437 42 0
438 65 3 438 50 6
439 65 5 439 50 6
440 21 0 440 50 2
441 65 2 441 46 0
442 19 0 442 50 0
443 17 0 443 50 7
444 43 0 444 50 20
445 65 2 445 32 0
446 41 0 446 50 6
447 39 0 447 40 0
448 65 0 448 44 0
449 23 0 449 48 0
450 59 0 450 50 9
451 33 0 451 50 17
452 51 0 452 50 0
453 49 0 453 50 5
454 53 0 454 50 10
455 51 0 455 36 0
456 33 0 456 50 4
457 35 0 457 50 0
458 23 0 458 48 0
459 65 1 459 50 6
460 25 0 460 42 0
461 55 0 461 50 13
462 31 0 462 50 13
463 51 0 463 38 0
464 25 0 464 50 13
465 59 0 465 50 14
466 35 0 466 32 0
467 41 0 467 48 0
468 35 0 468 30 0
469 51 0 469 50 0
470 63 0 470 50 10
471 49 0 471 40 0
472 65 4 472 50 9
473 45 0 473 50 20
474 47 0 474 36 0
475 65 0 475 50 2
476 23 0 476 50 6
477 41 0 477 50 9
478 57 0 478 50 13
479 41 0 479 50 17
480 57 0 480 32 0
481 29 0 481 50 11
482 61 0 482 50 15
483 39 0 483 50 4
484 37 0 484 50 20
485 33 0 485 44 0
486 39 0 486 50 6
487 19 0 487 38 0
488 47 0 488 50 4
489 55 0 489 50 16
490 25 0 490 38 0
491 31 0 491 50 13
492 21 0 492 50 19
493 43 0 493 42 0
494 33 0 494 40 0
495 37 0 495 50 3
496 15 0 496 48 0
497 55 0 497 50 9
498 59 0 498 50 1
499 29 0 499 50 14
500 23 0 500 50 19
501 55 0 501 50 9
502 53 0 502 36 0
503 37 0 503 34 0
504 17 0 504 50 14
505 65 2 505 40 0
506 21 0 506 50 19
507 57 0 507 50 1
508 25 0 508 50 14
509 27 0 509 38 0
510 35 0 510 34 0
511 51 0 511 46 0
512 23 0 512 50 3
513 51 0 513 50 8
514 63 0 514 50 10
515 63 0 515 50 11
516 49 0 516 50 3
517 65 2 517 50 7
518 65 0 518 34 0
519 21 0 519 50 15
520 45 0 520 46 0
521 51 0 521 50 8
522 57 0 522 50 14
523 37 0 523 50 18
524 65 0 524 50 19
525 39 0 525 34 0
526 65 0 526 50 5
527 29 0 527 50 5
528 55 0 528 50 17
529 43 0 529 50 10
530 65 1 530 50 18
531 19 0 531 50 4
532 37 0 532 50 18
533 47 0 533 50 18
534 53 0 534 50 17
535 17 0 535 34 0
536 39 0 536 50 4
537 65 3 537 50 6
538 65 0 538 50 2
539 65 3 539 50 0
540 23 0 540 50 7
541 65 1 541 46 0
542 33 0 542 50 3
543 53 0 543 50 6
544 43 0 544 50 4
545 57 0 545 42 0
546 47 0 546 50 19
547 63 0 547 50 12
548 65 1 548 50 10
549 65 2 549 44 0
550 37 0 550 50 9
551 65 1 551 44 0
552 49 0 552 50 1
553 41 0 553 50 17
554 61 0 554 38 0
555 25 0 555 50 0
556 33 0 556 50 18
557 47 0 557 50 19
558 51 0 558 50 4
559 43 0 559 50 5
560 57 0 560 34 0
561 65 3 561 46 0
562 53 0 562 50 18
563 31 0 563 50 5
564 29 0 564 50 4
565 43 0 565 50 19
566 65 0 566 44 0
567 41 0 567 50 18
568 65 5 568 50 3
569 41 0 569 50 18
570 65 0 570 50 9
571 49 0 571 38 0
572 55 0 572 50 7
573 57 0 573 48 0
574 65 3 574 46 0
575 31 0 575 50 2
576 65 0 576 50 13
577 49 0 577 50 1
578 55 0 578 50 3
579 65 1 579 50 3
580 21 0 580 44 0
581 63 0 581 50 9
582 23 0 582 44 0
583 65 2 583 50 10
584 65 3 584 50 2
585 55 0 585 42 0
586 65 5 586 50 16
587 65 0 587 50 9
588 25 0 588 50 18
589 59 0 589 50 10
590 63 0 590 50 4
591 65 0 591 50 4
592 51 0 592 50 11
593 33 0 593 32 0
594 65 0 594 50 0
595 63 0 595 50 14
596 23 0 596 50 11
597 65 0 597 46 0
598 61 0 598 50 15
599 39 0 599 50 2
600 29 0 600 50 7
601 51 0 601 50 16
602 53 0 602 32 0
603 61 0 603 50 6
604 41 0 604 50 6
605 39 0 605 50 9
606 37 0 606 40 0
607 39 0 607 50 3
608 65 5 608 50 1
609 51 0 609 50 1
610 63 0 610 50 16
611 33 0 611 36 0
612 43 0 612 50 1
613 65 1 613 50 18
614 45 0 614 34 0
615 63 0 615 50 8
616 39 0 616 50 18
617 57 0 617 50 18
618 59 0 618 50 14
619 45 0 619 40 0
620 65 4 620 50 15
621 65 1 621 50 7
622 65 3 622 50 3
623 65 4 623 40 0
624 55 0 624 50 19
625 59 0 625 50 7
626 21 0 626 50 11
627 57 0 627 50 10
628 53 0 628 50 12
629 63 0 629 34 0
630 25 0 630 34 0
631 29 0 631 50 4
632 65 0 632 44 0
633 39 0 633 50 14
634 65 2 634 46 0
635 49 0 635 50 11
636 31 0 636 50 11
637 25 0 637 50 4
638 49 0 638 50 0
639 23 0 639 50 0
640 37 0 640 50 20
641 53 0 641 38 0
642 23 0 642 50 1
643 35 0 643 32 0
644 47 0 644 50 18
645 57 0 645 50 18
646 29 0 646 50 6
647 65 2 647 50 2
648 65 4 648 50 8
649 39 0 649 50 14
650 65 2 650 50 9
651 59 0 651 50 19
652 37 0 652 50 9
653 65 5 653 50 6
654 53 0 654 50 3
655 23 0 655 50 0
656 65 1 656 50 9
657 23 0 657 50 8
658 65 4 658 50 9
659 19 0 659 50 16
660 63 0 660 50 9
661 59 0 661 50 19
662 19 0 662 50 18
663 65 1 663 50 3
664 57 0 664 50 17
665 17 0 665 50 2
666 23 0 666 32 0
667 65 0 667 50 16
668 37 0 668 50 19
669 29 0 669 34 0
670 37 0 670 50 9
671 51 0 671 50 5
672 35 0 672 34 0
673 45 0 673 50 0
674 35 0 674 50 14
675 19 0 675 50 5
676 65 5 676 50 12
677 31 0 677 50 6
678 53 0 678 50 8
679 17 0 679 50 20
680 31 0 680 34 0
681 55 0 681 34 0
682 47 0 682 50 17
683 35 0 683 34 0
684 19 0 684 50 16
685 61 0 685 50 17
686 63 0 686 46 0
687 33 0 687 50 15
688 65 4 688 50 7
689 65 0 689 50 7
690 65 3 690 42 0
691 27 0 691 50 16
692 43 0 692 50 5
693 45 0 693 50 9
694 65 4 694 38 0
695 63 0 695 42 0
696 65 1 696 50 8
697 33 0 697 42 0
698 47 0 698 50 11
699 55 0 699 50 0
700 21 0 700 42 0
701 57 0 701 50 16
702 65 0 702 44 0
703 41 0 703 40 0
704 15 0 704 50 1
705 55 0 705 50 8
706 59 0 706 50 6
707 65 0 707 44 0
708 21 0 708 50 0
709 19 0 709 48 0
710 53 0 710 50 12
711 59 0 711 50 7
712 47 0 712 48 0
713 29 0 713 46 0
714 43 0 714 50 9
715 25 0 715 50 12
716 49 0 716 50 5
717 15 0 717 50 9
718 55 0 718 50 0
719 41 0 719 50 14
720 47 0 720 50 5
721 65 0 721 50 2
722 35 0 722 50 10
723 19 0 723 34 0
724 33 0 724 50 17
725 65 3 725 50 2
726 55 0 726 50 1
727 55 0 727 50 6
728 35 0 728 50 0
729 29 0 729 50 9
730 63 0 730 50 13
731 49 0 731 46 0
732 35 0 732 30 0
733 41 0 733 50 13
734 27 0 734 34 0
735 37 0 735 50 15
736 55 0 736 50 17
737 51 0 737 42 0
738 65 5 738 30 0
739 65 3 739 50 4
740 35 0 740 50 14
741 23 0 741 40 0
742 65 1 742 36 0
743 65 2 743 50 10
744 19 0 744 50 8
745 47 0 745 50 14
746 47 0 746 50 12
747 31 0 747 50 6
748 35 0 748 50 0
749 65 3 749 50 11
750 63 0 750 48 0
751 61 0 751 50 3
752 61 0 752 50 4
753 15 0 753 50 4
754 27 0 754 48 0
755 63 0 755 50 12
756 35 0 756 40 0
757 31 0 757 50 10
758 35 0 758 48 0
759 45 0 759 50 7
760 27 0 760 50 6
761 41 0 761 46 0
762 21 0 762 50 16
763 47 0 763 50 1
764 27 0 764 44 0
765 31 0 765 30 0
766 53 0 766 50 2
767 55 0 767 42 0
768 65 4 768 50 7
769 65 3 769 50 18
770 57 0 770 34 0
771 47 0 771 48 0
772 53 0 772 48 0
773 27 0 773 50 8
774 65 2 774 50 16
775 65 4 775 46 0
776 65 3 776 34 0
777 37 0 777 46 0
778 25 0 778 50 15
779 21 0 779 50 7
780 63 0 780 50 7
781 57 0 781 48 0
782 53 0 782 50 19
783 21 0 783 36 0
784 57 0 784 36 0
785 49 0 785 34 0
786 65 3 786 50 4
787 55 0 787 50 0
788 65 5 788 50 9
789 53 0 789 46 0
790 61 0 790 38 0
791 53 0 791 50 10
792 37 0 792 36 0
793 57 0 793 38 0
794 35 0 794 50 16
795 65 2 795 50 8
796 65 4 796 50 5
797 19 0 797 50 14
798 39 0 798 50 13
799 17 0 799 46 0
800 35 0 800 50 14
801 31 0 801 50 15
802 53 0 802 50 6
803 63 0 803 50 8
804 45 0 804 50 10
805 65 2 805 50 17
806 41 0 806 40 0
807 61 0 807 50 8
808 19 0 808 50 7
809 65 2 809 38 0
810 65 5 810 50 17
811 65 0 811 50 18
812 65 1 812 50 19
813 19 0 813 50 8
814 65 0 814 46 0
815 65 4 815 30 0
816 65 0 816 48 0
817 23 0 817 40 0
818 55 0 818 44 0
819 23 0 819 50 18
820 29 0 820 50 11
821 43 0 821 34 0
822 41 0 822 44 0
823 65 1 823 50 16
824 57 0 824 50 18
825 39 0 825 36 0
826 27 0 826 50 2
827 65 3 827 40 0
828 29 0 828 50 10
829 23 0 829 50 7
830 21 0 830 40 0
831 65 3 831 50 11
832 53 0 832 50 10
833 61 0 833 50 16
834 47 0 834 50 17
835 39 0 835 50 17
836 41 0 836 50 19
837 19 0 837 44 0
838 35 0 838 32 0
839 59 0 839 50 19
840 27 0 840 36 0
841 27 0 841 50 6
842 27 0 842 38 0
843 61 0 843 32 0
844 65 4 844 44 0
845 23 0 845 46 0
846 65 1 846 50 16
847 23 0 847 50 9
848 27 0 848 50 0
849 41 0 849 50 5
850 23 0 850 50 10
851 65 2 851 46 0
852 61 0 852 50 5
853 25 0 853 50 0
854 61 0 854 50 9
855 31 0 855 44 0
856 65 0 856 50 2
857 27 0 857 50 9
858 37 0 858 34 0
859 65 4 859 50 11
860 59 0 860 50 6
861 47 0 861 42 0
862 31 0 862 50 1
863 51 0 863 50 20
864 63 0 864 50 11
865 21 0 865 50 13
866 17 0 866 50 1
867 49 0 867 50 12
868 37 0 868 50 7
869 21 0 869 50 14
870 37 0 870 42 0
871 57 0 871 50 8
872 65 0 872 50 10
873 19 0 873 50 4
874 17 0 874 50 10
875 59 0 875 50 12
876 25 0 876 34 0
877 43 0 877 32 0
878 17 0 878 50 9
879 59 0 879 36 0
880 61 0 880 50 5
881 25 0 881 50 10
882 45 0 882 46 0
883 65 4 883 46 0
884 53 0 884 50 12
885 29 0 885 36 0
886 63 0 886 50 8
887 21 0 887 50 6
888 45 0 888 50 17
889 39 0 889 36 0
890 57 0 890 48 0
891 63 0 891 50 0
892 61 0 892 50 11
893 17 0 893 50 6
894 33 0 894 50 6
895 21 0 895 50 5
896 61 0 896 50 6
897 25 0 897 48 0
898 39 0 898 50 20
899 65 1 899 50 16
900 61 0 900 38 0
901 43 0 901 50 17
902 65 4 902 30 0
903 43 0 903 40 0
904 57 0 904 50 13
905 39 0 905 50 8
906 27 0 906 50 14
907 39 0 907 34 0
908 51 0 908 50 9
909 65 0 909 50 8
910 55 0 910 50 12
911 65 0 911 34 0
912 43 0 912 50 14
913 59 0 913 50 10
914 19 0 914 50 12
915 65 3 915 50 12
916 25 0 916 50 11
917 53 0 917 50 1
918 65 2 918 50 16
919 47 0 919 50 15
920 53 0 920 50 2
921 51 0 921 38 0
922 49 0 922 48 0
923 41 0 923 46 0
924 51 0 924 50 4
925 39 0 925 50 18
926 63 0 926 50 17
927 61 0 927 50 7
928 59 0 928 50 4
929 57 0 929 50 0
930 51 0 930 50 11
931 17 0 931 50 17
932 49 0 932 38 0
933 51 0 933 50 16
934 17 0 934 50 16
935 47 0 935 50 2
936 35 0 936 50 1
937 23 0 937 50 9
938 65 4 938 50 18
939 23 0 939 50 12
940 65 0 940 50 14
941 39 0 941 32 0
942 59 0 942 50 5
943 51 0 943 50 0
944 17 0 944 38 0
945 53 0 945 50 16
946 29 0 946 50 5
947 35 0 947 50 13
948 31 0 948 50 16
949 17 0 949 34 0
950 53 0 950 36 0
951 39 0 951 50 18
952 57 0 952 50 13
953 51 0 953 50 12
954 65 4 954 46 0
955 21 0 955 50 12
956 25 0 956 46 0
957 45 0 957 50 10
958 21 0 958 50 10
959 53 0 959 50 1
960 47 0 960 50 7
961 35 0 961 50 13
962 17 0 962 50 16
963 15 0 963 50 8
964 65 1 964 50 15
965 57 0 965 50 20
966 41 0 966 50 12
967 37 0 967 50 1
968 43 0 968 44 0
969 23 0 969 46 0
970 27 0 970 50 4
971 35 0 971 50 8
972 45 0 972 48 0
973 59 0 973 50 7
974 21 0 974 50 15
975 53 0 975 34 0
976 33 0 976 42 0
977 65 0 977 50 2
978 53 0 978 50 8
979 25 0 979 50 16
980 33 0 980 50 5
981 65 5 981 50 6
982 19 0 982 32 0
983 65 2 983 50 4
984 25 0 984 50 6
985 53 0 985 50 17
986 57 0 986 50 17
987 41 0 987 50 14
988 43 0 988 50 15
989 65 0 989 44 0
990 31 0 ANALYSIS RESULTS: 990 50 5
991 37 0 Possible Order Qty Estimated Profit/day Est Avg Unsat Cust 991 50 7
992 59 0 Average Stdev 95 Percentile P(Pr>=$50) 992 38 0
993 23 0 40 993 44 0
994 15 0 45 994 50 12
995 41 0 50 $46.99 $5.50 $50.00 0.70 6.8 995 50 12
996 15 0 55 996 50 14
997 61 0 60 997 50 19
998 27 0 65 $44.77 $15.90 $65.00 0.44 0.4 998 50 16
999 65 2 70 999 48 0
1000 59 0 1000 50 3

4.6.2

A Financial Investment Analysis:
An investor wants to evaluate her current investment plan. The investor may change the portfolio if the evaluation shows some problems.
Currently (at beginning of this year) there is $10,000 invested in this portfolio. Here is what is predicted for return (return is variable) over the next three years.
(These predictions come based on conversations with investment advisors.)
Year 1 Return 1 Uniform between 5 and 15 percent return
Year 2 Return 2 Normal with mean = 5 percent and stdev = 10 percent
Year 3 Return 3 either -15 percent, 10 percent, or 20 percent -- with equal likelihoods
In this evaluation, the investor would like to know (estimate) the following about portfolio value after three yrs:
average and stdev of all possible portolio values (at end of third year)
10 percentile of value "How bad might it be?"
90 percentile of value "How really good might it be?"
likelihood of value after three years of at least a value of $12,500 "A target she'd like to achieve."
The investor plans to reinvest each year's returns back into the portfolio. Can you help this investor?
BFDA
Issue: Investment portfolio over three years
Problem (to model) Definition:
BusQues:
Decision:
Obj Meas(s):
Constraints:
Data: (we'll put in the model)
Analysis with a Spreadsheet Model: Insert blue input data cells first. Then, what will rows represent? What will columns represent?
Should have blue (fixed input values), green (variable input values), gray (formulas to calculate results), and orange (obj measure formula) cells

4.6.4

Core Model:
to use
in VLOOKUP
Core Model: 3 years of portfolio performance
$ at start $10,000 Return 1 Uniform low: 5% high: 15%
Return 2 Normal mean: 5% stdev: 10% Return Prob CumProb Return
Return 3 Discrete -15% 0.33 0.00 -15%
Portfolio Performance 10% 0.33 0.33 10%
YEAR Start $ RAND Return % Return $ End $ 20% 0.33 0.67 20%
Year 1 $10,000 0.5930 10.9% $1,093 $11,093
Year 2 $11,093 0.2321 -2.3% -$257.4 $10,836 Assumptions:
Year 3 $10,836 0.6798 20.0% $2,167.1 $13,003 Value after 3 years Years' returns are independent
Repl: Three-Yr Value Portfolio Value -- End of three years (1000 simulations)
$13,003
1 $10,628 "Results Table"
2 $14,090 Average $12,097
3 $15,463 Stdev $2,043
4 $16,150 10%tile $9,348
5 $11,146 90%tile $14,776
6 $12,384 Pr(>=12500) 0.45
7 $12,161
8 $10,294 Can you produce a picture -- Risk Profile -- of possible portfolio value? A "Results Figure"?
9 $11,741
10 $12,908
11 $13,197
12 $10,741
13 $13,970
14 $10,449
15 $13,114
16 $12,513
17 $9,789
18 $10,643
19 $13,115
20 $13,651
21 $13,611
22 $15,936
23 $17,433
24 $9,867
25 $15,564
26 $8,962
27 $14,887
28 $10,293
29 $9,898
30 $8,698
31 $10,531
32 $8,741
33 $12,580
34 $11,076
35 $12,904
36 $9,331
37 $13,776
38 $14,372
39 $15,609
40 $15,809
41 $11,429
42 $9,873
43 $9,214
44 $11,840
45 $9,405
46 $13,816
47 $11,119
48 $13,618
49 $14,325
50 $10,297
51 $12,431
52 $12,605
53 $14,960
54 $13,173
55 $13,941
56 $14,924
57 $13,287
58 $13,521
59 $15,905
60 $12,400
61 $10,398
62 $11,224
63 $15,196
64 $8,427
65 $8,536
66 $11,060
67 $15,577
68 $14,717
69 $14,028
70 $11,165
71 $11,973
72 $10,454
73 $12,152
74 $16,488
75 $10,611
76 $12,083
77 $9,926
78 $14,711
79 $11,225
80 $13,630
81 $8,506
82 $12,256
83 $10,452
84 $12,140
85 $13,700
86 $12,413
87 $12,811
88 $10,313
89 $14,561
90 $13,827
91 $7,435
92 $13,104
93 $10,731
94 $12,224
95 $15,583
96 $12,186
97 $9,730
98 $12,319
99 $13,714
100 $10,003
101 $13,680
102 $18,254
103 $12,119
104 $11,107
105 $10,610
106 $12,448
107 $16,465
108 $8,966
109 $15,409
110 $9,616
111 $14,069
112 $11,090
113 $9,505
114 $12,746
115 $11,523
116 $14,138
117 $10,411
118 $13,642
119 $13,436
120 $12,747
121 $15,369
122 $9,815
123 $12,370
124 $13,276
125 $15,572
126 $13,518
127 $12,443
128 $11,109
129 $10,152
130 $9,994
131 $12,860
132 $14,247
133 $10,914
134 $11,764
135 $9,657
136 $10,193
137 $15,218
138 $13,302
139 $13,338
140 $9,867
141 $12,432
142 $11,349
143 $14,486
144 $13,285
145 $14,541
146 $11,842
147 $12,677
148 $13,790
149 $15,976
150 $9,653
151 $12,992
152 $12,152
153 $12,667
154 $10,818
155 $11,579
156 $13,143
157 $12,830
158 $10,814
159 $9,717
160 $13,879
161 $10,010
162 $13,790
163 $11,602
164 $10,809
165 $10,226
166 $12,399
167 $15,810
168 $14,043
169 $11,962
170 $12,912
171 $15,235
172 $10,926
173 $10,634
174 $13,521
175 $11,779
176 $9,262
177 $10,505
178 $10,665
179 $9,681
180 $9,879
181 $15,655
182 $15,182
183 $15,185
184 $9,147
185 $10,067
186 $15,434
187 $12,535
188 $11,852
189 $14,038
190 $12,381
191 $14,456
192 $13,404
193 $8,106
194 $11,427
195 $12,937
196 $13,406
197 $13,935
198 $12,573
199 $11,407
200 $12,912
201 $11,022
202 $16,070
203 $13,688
204 $13,297
205 $11,094
206 $13,267
207 $14,896
208 $9,413
209 $14,174
210 $12,942
211 $13,021
212 $10,661
213 $13,050
214 $11,827
215 $14,132
216 $10,171
217 $12,423
218 $10,406
219 $15,066
220 $13,778
221 $11,786
222 $12,936
223 $13,154
224 $13,686
225 $14,201
226 $13,664
227 $15,104
228 $13,969
229 $13,244
230 $12,911
231 $10,577
232 $10,895
233 $13,099
234 $16,442
235 $11,314
236 $10,383
237 $8,071
238 $8,925
239 $12,826
240 $14,070
241 $9,486
242 $14,856
243 $8,870
244 $9,909
245 $12,938
246 $13,815
247 $12,470
248 $13,648
249 $11,392
250 $13,582
251 $9,118
252 $12,570
253 $11,497
254 $15,461
255 $9,528
256 $8,239
257 $8,994
258 $15,594
259 $13,888
260 $9,095
261 $8,038
262 $13,933
263 $10,420
264 $7,925
265 $8,493
266 $10,787
267 $13,483
268 $16,197
269 $16,879
270 $12,317
271 $11,043
272 $9,491
273 $13,730
274 $12,245
275 $12,998
276 $11,179
277 $13,539
278 $11,215
279 $12,226
280 $11,077
281 $12,547
282 $11,082
283 $16,105
284 $13,013
285 $11,252
286 $13,117
287 $9,540
288 $12,177
289 $13,308
290 $10,479
291 $10,463
292 $13,598
293 $13,625
294 $8,228
295 $12,275
296 $13,276
297 $8,285
298 $13,429
299 $13,554
300 $13,552
301 $10,321
302 $14,816
303 $14,421
304 $14,029
305 $12,979
306 $11,233
307 $14,249
308 $11,423
309 $7,904
310 $13,958
311 $12,163
312 $15,233
313 $13,587
314 $13,618
315 $11,236
316 $11,757
317 $9,478
318 $13,774
319 $9,470
320 $9,376
321 $12,849
322 $12,313
323 $9,583
324 $14,945
325 $9,890
326 $11,726
327 $10,377
328 $9,938
329 $13,294
330 $12,000
331 $13,802
332 $8,903
333 $7,911
334 $11,238
335 $16,741
336 $9,447
337 $14,736
338 $13,818
339 $12,978
340 $9,625
341 $8,802
342 $11,625
343 $14,555
344 $16,268
345 $10,530
346 $10,714
347 $14,600
348 $13,872
349 $12,598
350 $12,635
351 $12,146
352 $8,481
353 $15,250
354 $10,256
355 $11,324
356 $13,934
357 $11,630
358 $12,974
359 $14,765
360 $14,411
361 $10,286
362 $8,192
363 $12,806
364 $11,911
365 $10,595
366 $9,912
367 $13,598
368 $9,691
369 $13,172
370 $11,638
371 $11,112
372 $10,298
373 $15,210
374 $10,478
375 $11,960
376 $15,779
377 $12,702
378 $13,064
379 $11,787
380 $11,068
381 $15,246
382 $12,456
383 $14,231
384 $10,021
385 $11,407
386 $13,071
387 $12,671
388 $12,179
389 $14,140
390 $9,180
391 $11,576
392 $9,355
393 $12,939
394 $14,299
395 $9,410
396 $14,594
397 $15,282
398 $11,262
399 $8,616
400 $14,023
401 $16,236
402 $15,977
403 $11,002
404 $12,984
405 $14,265
406 $14,303
407 $13,142
408 $11,601
409 $9,221
410 $13,857
411 $11,607
412 $13,761
413 $13,162
414 $6,771
415 $14,200
416 $13,309
417 $11,216
418 $13,783
419 $9,774
420 $11,531
421 $14,388
422 $12,927
423 $9,242
424 $12,323
425 $9,831
426 $12,183
427 $11,249
428 $11,772
429 $11,857
430 $12,384
431 $14,835
432 $14,348
433 $13,989
434 $10,179
435 $9,326
436 $14,137
437 $15,594
438 $10,061
439 $10,595
440 $13,704
441 $10,888
442 $11,156
443 $11,507
444 $15,354
445 $8,980
446 $12,007
447 $8,521
448 $12,397
449 $12,019
450 $11,777
451 $12,750
452 $10,297
453 $9,740
454 $13,738
455 $12,260
456 $8,803
457 $13,010
458 $13,239
459 $9,267
460 $10,404
461 $14,828
462 $15,268
463 $11,966
464 $11,793
465 $10,692
466 $12,211
467 $12,218
468 $9,065
469 $15,654
470 $12,019
471 $13,705
472 $11,884
473 $10,938
474 $9,837
475 $14,062
476 $10,304
477 $13,495
478 $9,014
479 $12,538
480 $9,036
481 $11,936
482 $15,108
483 $14,389
484 $13,432
485 $9,409
486 $10,577
487 $15,418
488 $15,089
489 $16,863
490 $14,497
491 $11,722
492 $11,540
493 $12,896
494 $10,417
495 $11,559
496 $9,455
497 $13,136
498 $14,907
499 $11,623
500 $9,993
501 $10,131
502 $9,272
503 $8,981
504 $13,051
505 $10,215
506 $10,420
507 $14,258
508 $12,399
509 $12,103
510 $13,151
511 $12,971
512 $10,790
513 $14,095
514 $14,803
515 $12,945
516 $10,979
517 $10,240
518 $10,204
519 $15,669
520 $10,537
521 $9,667
522 $14,577
523 $11,413
524 $13,214
525 $10,147
526 $12,987
527 $12,974
528 $14,927
529 $11,869
530 $9,078
531 $9,489
532 $9,928
533 $13,333
534 $12,805
535 $13,520
536 $10,714
537 $13,492
538 $14,040
539 $13,470
540 $15,903
541 $10,033
542 $13,507
543 $12,767
544 $10,614
545 $11,896
546 $13,908
547 $11,703
548 $14,701
549 $14,214
550 $12,475
551 $11,697
552 $10,911
553 $9,312
554 $10,384
555 $14,894
556 $11,701
557 $14,074
558 $8,850
559 $11,507
560 $11,350
561 $14,620
562 $12,394
563 $8,469
564 $13,856
565 $10,207
566 $9,649
567 $11,505
568 $14,772
569 $15,553
570 $9,983
571 $11,495
572 $14,561
573 $13,688
574 $12,208
575 $12,840
576 $10,881
577 $7,982
578 $15,850
579 $12,861
580 $13,375
581 $9,789
582 $9,446
583 $10,107
584 $11,852
585 $9,421
586 $15,307
587 $11,552
588 $11,805
589 $12,162
590 $9,103
591 $12,941
592 $13,531
593 $13,863
594 $13,617
595 $12,844
596 $14,970
597 $9,288
598 $12,417
599 $11,337
600 $9,875
601 $9,532
602 $15,126
603 $12,229
604 $15,247
605 $10,545
606 $13,706
607 $10,585
608 $16,301
609 $9,936
610 $14,387
611 $10,405
612 $14,893
613 $9,412
614 $12,660
615 $13,519
616 $12,109
617 $10,823
618 $14,658
619 $8,988
620 $9,833
621 $10,875
622 $10,768
623 $12,656
624 $13,341
625 $11,084
626 $13,574
627 $9,873
628 $9,472
629 $9,966
630 $13,351
631 $13,115
632 $8,317
633 $12,441
634 $12,062
635 $8,388
636 $12,285
637 $16,125
638 $14,144
639 $9,067
640 $8,791
641 $17,427
642 $13,715
643 $10,015
644 $9,847
645 $10,374
646 $10,924
647 $12,883
648 $14,109
649 $11,059
650 $13,229
651 $12,940
652 $11,848
653 $12,876
654 $14,014
655 $10,693
656 $8,347
657 $12,826
658 $13,205
659 $14,279
660 $9,524
661 $14,038
662 $9,597
663 $8,331
664 $8,230
665 $10,135
666 $9,107
667 $11,728
668 $10,403
669 $13,045
670 $14,189
671 $9,773
672 $13,321
673 $9,246
674 $9,433
675 $12,344
676 $12,982
677 $11,209
678 $13,720
679 $13,410
680 $12,202
681 $10,681
682 $10,008
683 $10,476
684 $11,185
685 $11,595
686 $12,293
687 $11,928
688 $8,319
689 $12,097
690 $12,157
691 $10,783
692 $10,260
693 $10,217
694 $12,927
695 $12,869
696 $8,725
697 $12,930
698 $13,648
699 $11,347
700 $9,821
701 $10,534
702 $10,493
703 $9,595
704 $13,223
705 $12,653
706 $14,151
707 $9,326
708 $9,958
709 $12,414
710 $8,827
711 $10,510
712 $8,968
713 $12,231
714 $13,278
715 $10,075
716 $13,028
717 $9,159
718 $13,905
719 $12,957
720 $13,224
721 $9,469
722 $8,710
723 $11,639
724 $11,698
725 $11,808
726 $13,731
727 $13,680
728 $12,411
729 $14,533
730 $10,526
731 $15,008
732 $13,745
733 $10,821
734 $9,295
735 $11,889
736 $10,319
737 $15,637
738 $11,692
739 $12,055
740 $8,534
741 $14,540
742 $9,209
743 $11,769
744 $9,392
745 $14,502
746 $13,297
747 $8,587
748 $14,226
749 $11,963
750 $14,048
751 $12,421
752 $13,344
753 $8,300
754 $10,751
755 $13,083
756 $15,144
757 $13,764
758 $10,156
759 $10,840
760 $8,840
761 $9,588
762 $14,038
763 $9,348
764 $10,372
765 $9,256
766 $9,341
767 $15,277
768 $13,027
769 $12,302
770 $14,800
771 $12,005
772 $9,023
773 $14,077
774 $10,681
775 $13,729
776 $9,938
777 $14,613
778 $12,522
779 $9,691
780 $10,918
781 $11,865
782 $12,509
783 $10,451
784 $11,541
785 $9,265
786 $11,765
787 $13,410
788 $9,226
789 $9,987
790 $12,879
791 $9,299
792 $11,622
793 $10,987
794 $10,480
795 $14,248
796 $9,257
797 $12,842
798 $13,359
799 $8,338
800 $12,316
801 $12,061
802 $10,178
803 $11,232
804 $9,765
805 $9,872
806 $12,798
807 $12,056
808 $12,913
809 $9,951
810 $13,508
811 $10,998
812 $9,880
813 $11,338
814 $15,382
815 $11,763
816 $12,306
817 $9,946
818 $13,733
819 $11,274
820 $15,236
821 $12,722
822 $10,340
823 $13,197
824 $14,726
825 $9,528
826 $8,539
827 $13,616
828 $14,339
829 $13,353
830 $12,690
831 $12,854
832 $10,884
833 $10,128
834 $14,365
835 $12,836
836 $10,555
837 $11,970
838 $14,968
839 $14,950
840 $14,908
841 $11,006
842 $13,149
843 $14,202
844 $14,224
845 $10,452
846 $10,546
847 $11,552
848 $14,383
849 $13,821
850 $9,246
851 $13,937
852 $15,154
853 $12,532
854 $11,391
855 $13,072
856 $14,871
857 $9,262
858 $8,745
859 $15,133
860 $12,017
861 $13,536
862 $14,618
863 $14,728
864 $14,258
865 $14,140
866 $12,796
867 $10,510
868 $10,919
869 $14,030
870 $15,436
871 $13,526
872 $9,897
873 $9,728
874 $12,135
875 $9,602
876 $8,899
877 $11,804
878 $13,004
879 $8,612
880 $12,757
881 $11,037
882 $13,741
883 $11,707
884 $10,007
885 $13,727
886 $14,557
887 $13,901
888 $12,969
889 $14,317
890 $9,459
891 $12,168
892 $9,975
893 $12,973
894 $9,556
895 $13,823
896 $12,000
897 $12,277
898 $10,946
899 $11,999
900 $9,953
901 $10,288
902 $13,956
903 $11,255
904 $12,578
905 $10,221
906 $15,605
907 $11,677
908 $10,207
909 $8,410
910 $15,974
911 $8,256
912 $14,128
913 $10,335
914 $10,091
915 $15,167
916 $15,011
917 $8,859
918 $10,004
919 $10,807
920 $11,812
921 $14,183
922 $12,972
923 $12,594
924 $13,298
925 $12,856
926 $10,418
927 $8,965
928 $13,149
929 $13,172
930 $11,038
931 $10,258
932 $9,430
933 $11,823
934 $12,761
935 $10,647
936 $13,566
937 $13,602
938 $15,774
939 $11,849
940 $10,558
941 $11,284
942 $10,876
943 $11,884
944 $13,732
945 $15,415
946 $9,712
947 $9,465
948 $13,925
949 $14,355
950 $13,056
951 $10,718
952 $10,537
953 $13,163
954 $13,873
955 $13,257
956 $13,502
957 $12,057
958 $13,531
959 $9,342
960 $10,831
961 $9,707
962 $12,802
963 $9,009
964 $13,611
965 $9,191
966 $14,517
967 $12,361
968 $11,426
969 $13,377
970 $13,673
971 $9,941
972 $12,495
973 $11,270
974 $12,007
975 $14,783
976 $13,789
977 $9,308
978 $11,420
979 $12,098
980 $16,624
981 $13,603
982 $13,428
983 $9,100
984 $10,313
985 $14,775
986 $10,670
987 $15,321
988 $9,494
989 $11,914
990 $14,686
991 $12,004
992 $11,871
993 $11,545
994 $10,672
995 $10,697
996 $14,494
997 $13,593
998 $13,655
999 $9,030
1000 $12,603
Business Concl, Insights, Recommendations

4.7.1

REVIEW OF MBA 791: BUSINESS ANALYTICS -- SO FAR
ANALYSIS -- an important function supporting organizational decision making
"Business Analytics" is for some companies part of their business strategy
Get the most out of analysis of all aspects of the business using Big Data Bases
Analytic personnel, technology, methods, continuing development of capabilities
Top management understanding and strategies for competitive advantage.
For any situation:
Business Frame- work for Decision Analysis (BFDA) Issue Name of business area we are concerned about
Problem Definition business question(s) (include all specific business questions to answer)
(to be modeled) decisions (including how many values)
objective measure
constraints (and how many are there)
Data gather/organize
Analysis build model -- LP Models -- one column for ea decision variable; one rows for the constraints (except Transportation models);
one row for decision cells; one row for calculating the objective measure; list of key assumptions. Use color scheme.
Simulation Models -- description of business process with data and formulas using rows and columns
test/validate model
manipulate model -- using Solver & SolverTable (LP models) or replication & change decision cells (Sim models)
what if? or sensitivity analysis with model -- resolving with new data values, sensitivity report (if linear model), SolverTable
summarize analysis results -- into Results Tables and Results Figures
Conclusions, Insights,& Recommendations
Business language "answers" to all the business questions.
TWO MAJOR CATEGORIES OF MODELING & ANALYSIS:
1. DETERMINISTIC OPTIMIZATION MODELS types names
Linear Programming Models 1 Resource Allocation (<=) All can be solved with Solver using Simplex LP
2 Cost-Benefit Tradeoff (>=) 1, 2, & 3 -- one column for ea decision value and one row for ea constr
3 Mixed Constraints (<=, >=, =) 4 -- uses a matrix of decision cells. Integer solns guarranteed.
4 Transportation
What If/ Sensitivity Analysis
Make changes to the model, resolve, record results, repeat
Use Sensitivity Report provided by Solver after solving a model with Simplex LP -- changes to 1 data input value
Top -- changes to per unit objective -- soln doesn't change
Bottom -- change to availability/target -- shadow price doesn't change
Use Solver Table (excel add-in) that resolves the model for a range of values for a data input and provides table of results. <-- most useful.
Special types of Models
Integer Programming models -- restricting values of decisions to be whole numbers. Specify in Solver.
Binary Integer Programming models -- Use of 0-1 variables to represent No (0) or Yes (1) decisions.
All binary integer variable models -- e.g., choosing some combination of possible investments
Mixed binary and non binary variables models
2. PROBABALISTIC SIMULATION MODELS See first worksheet of this file.
ANALYSIS PROCESS:
Bus Sit/Ques with Signif Variation Build a Simulation Model Replicate --> Observe a Large Sample Summarize Sample Results - Answer Qs
REMAINING WORK OF THE COURSE
Problem Set 2
-- to give you more experience in simulation modeling and analysis
-- to prepare you for the exam and for the case
-- MUST BE DONE INDIVIDUALLY -- but can discuss problems and simulation modeling with teammates
-- a solution guide will be provided after turn-in
Project -- Decision Analysis Case Deliverables due at end of week 5.
-- student teams of two
-- take role of professionals working in an organization, boss requests your work to help the organization
-- you receive a written request
-- boss requests a business memo (short report) of the results of your analysis -- company format specified
-- deliverables (each team):
(1) a Word file containing your business memo;
(2) an Excel file containing your BFDA that includes the modeling and analysis work
-- provides backup support your business memo.
The two files constitute the documentation of your work -- so be complete and use plenty of labels.
Final Exam Weekend following week 5
-- three hours in length
-- several cases requiring modeling and analysis (both types) to answer business questions
-- MUST BE DONE INDIVIDUALLY
-- can use any WRITTEN notes you develop or print to bring to the exam -- no other files open
-- NO COMMUNICATING WITH OTHER STUDENTS DURING EXAM
`