管理科学决策分析 精选文档.ppt

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1、管理科学决策分析 Chapter 12-Decision Analysis1本讲稿第一页，共五十七页Chapter 12-Decision Analysis 2Components of Decision MakingDecision Making without ProbabilitiesDecision Making with ProbabilitiesDecision Analysis with Additional InformationUtilityChapter Topics本讲稿第二页，共五十七页Chapter 12-Decision Analysis 3Table 12.1Pa

2、yoff TableA state of nature is an actual event that may occur in the future.A payoff table is a means of organizing a decision situation,presenting the payoffs from different decisions given the various states of nature.Decision AnalysisComponents of Decision Making本讲稿第三页，共五十七页Chapter 12-Decision An

3、alysis 4Decision situation:Decision-Making Criteria:maximax,maximin,minimax,minimax regret,Hurwicz,and equal likelihood Table 12.2Payoff Table for the Real Estate InvestmentsDecision AnalysisDecision Making without Probabilities本讲稿第四页，共五十七页Chapter 12-Decision Analysis 5Table 12.3Payoff Table Illustr

4、ating a Maximax DecisionIn the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs;an optimistic criterion.Decision Making without ProbabilitiesMaximax Criterion本讲稿第五页，共五十七页Chapter 12-Decision Analysis 6Table 12.4Payoff Table Illustrating a Ma

5、ximin DecisionIn the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs;a pessimistic criterion.Decision Making without ProbabilitiesMaximin Criterion本讲稿第六页，共五十七页Chapter 12-Decision Analysis 7Table 12.6 Regret Table Illustrating the Minimax

6、 Regret DecisionRegret is the difference between the payoff from the best decision and all other decision payoffs.The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret.Decision Making without ProbabilitiesMinimax Regret Criterion本讲稿第七页，共五

7、十七页Chapter 12-Decision Analysis 8The Hurwicz criterion is a compromise between the maximax and maximin criterion.A coefficient of optimism,is a measure of the decision makers optimism.The Hurwicz criterion multiplies the best payoff by and the worst payoff by 1-.,for each decision,and the best resul

8、t is selected.Decision ValuesApartment building$50,000(.4)+30,000(.6)=38,000Office building$100,000(.4)-40,000(.6)=16,000Warehouse$30,000(.4)+10,000(.6)=18,000Decision Making without ProbabilitiesHurwicz Criterion本讲稿第八页，共五十七页Chapter 12-Decision Analysis 9The equal likelihood(or Laplace)criterion mul

9、tiplies the decision payoff for each state of nature by an equal weight,thus assuming that the states of nature are equally likely to occur.Decision ValuesApartment building$50,000(.5)+30,000(.5)=40,000Office building$100,000(.5)-40,000(.5)=30,000Warehouse$30,000(.5)+10,000(.5)=20,000Decision Making

10、 without ProbabilitiesEqual Likelihood Criterion本讲稿第九页，共五十七页Chapter 12-Decision Analysis 10A dominant decision is one that has a better payoff than another decision under each state of nature.The appropriate criterion is dependent on the“risk”personality and philosophy of the decision maker.Criterio

11、n Decision(Purchase)MaximaxOffice buildingMaximinApartment buildingMinimax regretApartment buildingHurwiczApartment buildingEqual likelihoodApartment buildingDecision Making without ProbabilitiesSummary of Criteria Results本讲稿第十页，共五十七页Chapter 12-Decision Analysis 11Exhibit 12.1Decision Making without

12、 ProbabilitiesSolution with QM for Windows(1 of 3)本讲稿第十一页，共五十七页Chapter 12-Decision Analysis 12Exhibit 12.2Decision Making without ProbabilitiesSolution with QM for Windows(2 of 3)本讲稿第十二页，共五十七页Chapter 12-Decision Analysis 13Exhibit 12.3Decision Making without ProbabilitiesSolution with QM for Windows

13、(3 of 3)本讲稿第十三页，共五十七页Chapter 12-Decision Analysis 14Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence.EV(Apartment)=$50,000(.6)+30,000(.4)=42,000EV(Office)=$100,000(.6)-40,000(.4)=44,000EV(Warehouse)=$30,000(.6)+10,000(.4)

14、=22,000Table 12.7Payoff table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Value本讲稿第十四页，共五十七页Chapter 12-Decision Analysis 15The expected opportunity loss is the expected value of the regret for each decision.The expected value and expected opportunity loss criter

15、ion result in the same decision.EOL(Apartment)=$50,000(.6)+0(.4)=30,000EOL(Office)=$0(.6)+70,000(.4)=28,000EOL(Warehouse)=$70,000(.6)+20,000(.4)=50,000Table 12.8Regret(Opportunity Loss)Table with Probabilities for States of NatureDecision Making with ProbabilitiesExpected Opportunity Loss本讲稿第十五页，共五十

16、七页Chapter 12-Decision Analysis 16Exhibit 12.4Expected Value ProblemsSolution with QM for Windows本讲稿第十六页，共五十七页Chapter 12-Decision Analysis 17Exhibit 12.5Expected Value ProblemsSolution with Excel and Excel QM(1 of 2)本讲稿第十七页，共五十七页Chapter 12-Decision Analysis 18Exhibit 12.6Expected Value ProblemsSoluti

17、on with Excel and Excel QM(2 of 2)本讲稿第十八页，共五十七页Chapter 12-Decision Analysis 19The expected value of perfect information(EVPI)is the maximum amount a decision maker would pay for additional information.EVPI equals the expected value given perfect information minus the expected value without perfect i

18、nformation.EVPI equals the expected opportunity loss(EOL)for the best decision.Decision Making with ProbabilitiesExpected Value of Perfect Information本讲稿第十九页，共五十七页Chapter 12-Decision Analysis 20Table 12.9Payoff Table with Decisions,Given Perfect Information Decision Making with ProbabilitiesEVPI Exa

19、mple(1 of 2)本讲稿第二十页，共五十七页Chapter 12-Decision Analysis 21Decision with perfect information:$100,000(.60)+30,000(.40)=$72,000Decision without perfect information:EV(office)=$100,000(.60)-40,000(.40)=$44,000EVPI=$72,000-44,000=$28,000EOL(office)=$0(.60)+70,000(.4)=$28,000Decision Making with Probabilit

20、iesEVPI Example(2 of 2)本讲稿第二十一页，共五十七页Chapter 12-Decision Analysis 22Exhibit 12.7Decision Making with ProbabilitiesEVPI with QM for Windows本讲稿第二十二页，共五十七页Chapter 12-Decision Analysis 23A decision tree is a diagram consisting of decision nodes(represented as squares),probability nodes(circles),and deci

21、sion alternatives(branches).Table 12.10Payoff Table for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees(1 of 4)本讲稿第二十三页，共五十七页Chapter 12-Decision Analysis 24Figure 12.1Decision Tree for Real Estate Investment ExampleDecision Making with ProbabilitiesDecision Trees(2 of

22、4)本讲稿第二十四页，共五十七页Chapter 12-Decision Analysis 25The expected value is computed at each probability node:EV(node 2)=.60($50,000)+.40(30,000)=$42,000EV(node 3)=.60($100,000)+.40(-40,000)=$44,000EV(node 4)=.60($30,000)+.40(10,000)=$22,000Branches with the greatest expected value are selected.Decision Ma

23、king with ProbabilitiesDecision Trees(3 of 4)本讲稿第二十五页，共五十七页Chapter 12-Decision Analysis 26Figure 12.2Decision Tree with Expected Value at Probability NodesDecision Making with ProbabilitiesDecision Trees(4 of 4)本讲稿第二十六页，共五十七页Chapter 12-Decision Analysis 27Exhibit 12.8Decision Making with Probabiliti

24、esDecision Trees with QM for Windows本讲稿第二十七页，共五十七页Chapter 12-Decision Analysis 28Exhibit 12.9Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(1 of 4)本讲稿第二十八页，共五十七页Chapter 12-Decision Analysis 29Exhibit 12.10Decision Making with ProbabilitiesDecision Trees with Excel and TreeP

25、lan(2 of 4)本讲稿第二十九页，共五十七页Chapter 12-Decision Analysis 30Exhibit 12.11Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(3 of 4)本讲稿第三十页，共五十七页Chapter 12-Decision Analysis 31Exhibit 12.12Decision Making with ProbabilitiesDecision Trees with Excel and TreePlan(4 of 4)本讲稿第三十一页，共五十七页

26、Chapter 12-Decision Analysis 32Decision Making with ProbabilitiesSequential Decision Trees(1 of 4)A sequential decision tree is used to illustrate a situation requiring a series of decisions.Used where a payoff table,limited to a single decision,cannot be used.Real estate investment example modified

27、 to encompass a ten-year period in which several decisions must be made:本讲稿第三十二页，共五十七页Chapter 12-Decision Analysis 33Figure 12.3Sequential Decision TreeDecision Making with ProbabilitiesSequential Decision Trees(2 of 4)本讲稿第三十三页，共五十七页Chapter 12-Decision Analysis 34Decision Making with ProbabilitiesSe

28、quential Decision Trees(3 of 4)Decision is to purchase land;highest net expected value($1,160,000).Payoff of the decision is$1,160,000.本讲稿第三十四页，共五十七页Chapter 12-Decision Analysis 35Figure 12.4Sequential Decision Tree with Nodal Expected ValuesDecision Making with ProbabilitiesSequential Decision Tree

29、s(4 of 4)本讲稿第三十五页，共五十七页Chapter 12-Decision Analysis 36Exhibit 12.13Sequential Decision Tree AnalysisSolution with QM for Windows本讲稿第三十六页，共五十七页Chapter 12-Decision Analysis 37Exhibit 12.14Sequential Decision Tree AnalysisSolution with Excel and TreePlan本讲稿第三十七页，共五十七页Chapter 12-Decision Analysis 38Baye

30、sian analysis uses additional information to alter the marginal probability of the occurrence of an event.In real estate investment example,using expected value criterion,best decision was to purchase office building with expected value of$444,000,and EVPI of$28,000.Table 12.11Payoff Table for the R

31、eal Estate Investment ExampleDecision Analysis with Additional InformationBayesian Analysis(1 of 3)本讲稿第三十八页，共五十七页Chapter 12-Decision Analysis 39A conditional probability is the probability that an event will occur given that another event has already occurred.Economic analyst provides additional inf

32、ormation for real estate investment decision,forming conditional probabilities:g=good economic conditionsp=poor economic conditionsP=positive economic reportN=negative economic reportP(Pg)=.80P(NG)=.20P(Pp)=.10 P(Np)=.90 Decision Analysis with Additional InformationBayesian Analysis(2 of 3)本讲稿第三十九页，

33、共五十七页Chapter 12-Decision Analysis 40A posteria probability is the altered marginal probability of an event based on additional information.Prior probabilities for good or poor economic conditions in real estate decision:P(g)=.60;P(p)=.40Posteria probabilities by Bayes rule:(gP)=P(PG)P(g)/P(Pg)P(g)+P

34、(Pp)P(p)=(.80)(.60)/(.80)(.60)+(.10)(.40)=.923Posteria(revised)probabilities for decision:P(gN)=.250P(pP)=.077P(pN)=.750Decision Analysis with Additional InformationBayesian Analysis(3 of 3)本讲稿第四十页，共五十七页Chapter 12-Decision Analysis 41Decision Analysis with Additional InformationDecision Trees with P

35、osterior Probabilities(1 of 4)Decision tree with posterior probabilities differ from earlier versions in that:Two new branches at beginning of tree represent report outcomes.Probabilities of each state of nature are posterior probabilities from Bayes rule.本讲稿第四十一页，共五十七页Chapter 12-Decision Analysis 4

36、2Figure 12.5Decision Tree with Posterior Probabilities Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities(2 of 4)本讲稿第四十二页，共五十七页Chapter 12-Decision Analysis 43Decision Analysis with Additional InformationDecision Trees with Posterior Probabilities(3 of 4)EV(apart

37、ment building)=$50,000(.923)+30,000(.077)=$48,460EV(strategy)=$89,220(.52)+35,000(.48)=$63,194本讲稿第四十三页，共五十七页Chapter 12-Decision Analysis 44Figure 12.6Decision Tree AnalysisDecision Analysis with Additional InformationDecision Trees with Posterior Probabilities(4 of 4)本讲稿第四十四页，共五十七页Chapter 12-Decisio

38、n Analysis 45Table 12.12Computation of Posterior ProbabilitiesDecision Analysis with Additional InformationComputing Posterior Probabilities with Tables本讲稿第四十五页，共五十七页Chapter 12-Decision Analysis 46The expected value of sample information(EVSI)is the difference between the expected value with and wit

39、hout information:For example problem,EVSI=$63,194-44,000=$19,194The efficiency of sample information is the ratio of the expected value of sample information to the expected value of perfect information:efficiency=EVSI/EVPI=$19,194/28,000=.68Decision Analysis with Additional InformationExpected Valu

40、e of Sample Information本讲稿第四十六页，共五十七页Chapter 12-Decision Analysis 47Table 12.13Payoff Table for Auto Insurance ExampleDecision Analysis with Additional InformationUtility(1 of 2)本讲稿第四十七页，共五十七页Chapter 12-Decision Analysis 48Expected Cost(insurance)=.992($500)+.008(500)=$500Expected Cost(no insurance)

41、=.992($0)+.008(10,000)=$80Decision should be do not purchase insurance,but people almost always do purchase insurance.Utility is a measure of personal satisfaction derived from money.Utiles are units of subjective measures of utility.Risk averters forgo a high expected value to avoid a low-probabili

42、ty disaster.Risk takers take a chance for a bonanza on a very low-probability event in lieu of a sure thing.Decision Analysis with Additional InformationUtility(2 of 2)本讲稿第四十八页，共五十七页Chapter 12-Decision Analysis 49Decision Analysis Example Problem Solution(1 of 9)本讲稿第四十九页，共五十七页Chapter 12-Decision Ana

43、lysis 50Decision Analysis Example Problem Solution(2 of 9)a.Determine the best decision without probabilities using the 5 criteria of the chapter.b.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions.Use expected value and expected opportunity

44、 loss criteria.c.Compute expected value of perfect information.d.Develop a decision tree with expected value at the nodes.e.Given following,P(Pg)=.70,P(Ng)=.30,P(Pp)=20,P(Np)=.80,determine posteria probabilities using Bayes rule.f.Perform a decision tree analysis using the posterior probability obta

45、ined in part e.本讲稿第五十页，共五十七页Chapter 12-Decision Analysis 51Step 1(part a):Determine decisions without probabilities.Maximax Decision:Maintain status quoDecisionsMaximum PayoffsExpand$800,000Status quo 1,300,000(maximum)Sell 320,000Maximin Decision:ExpandDecisionsMinimum PayoffsExpand$500,000(maximum

46、)Status quo -150,000Sell 320,000Decision Analysis Example Problem Solution(3 of 9)本讲稿第五十一页，共五十七页Chapter 12-Decision Analysis 52Minimax Regret Decision:ExpandDecisionsMaximum RegretsExpand$500,000(minimum)Status quo 650,000Sell 980,000Hurwicz(=.3)Decision:ExpandExpand$800,000(.3)+500,000(.7)=$590,000

47、Status quo$1,300,000(.3)-150,000(.7)=$285,000Sell$320,000(.3)+320,000(.7)=$320,000Decision Analysis Example Problem Solution(4 of 9)本讲稿第五十二页，共五十七页Chapter 12-Decision Analysis 53Equal Likelihood Decision:ExpandExpand$800,000(.5)+500,000(.5)=$650,000Status quo$1,300,000(.5)-150,000(.5)=$575,000Sell$32

48、0,000(.5)+320,000(.5)=$320,000Step 2(part b):Determine Decisions with EV and EOL.Expected value decision:Maintain status quoExpand$800,000(.7)+500,000(.3)=$710,000Status quo$1,300,000(.7)-150,000(.3)=$865,000Sell$320,000(.7)+320,000(.3)=$320,000Decision Analysis Example Problem Solution(5 of 9)本讲稿第五

49、十三页，共五十七页Chapter 12-Decision Analysis 54Expected opportunity loss decision:Maintain status quoExpand$500,000(.7)+0(.3)=$350,000Status quo 0(.7)+650,000(.3)=$195,000Sell$980,000(.7)+180,000(.3)=$740,000Step 3(part c):Compute EVPI.EV given perfect information=1,300,000(.7)+500,000(.3)=$1,060,000EV wit

50、hout perfect information=$1,300,000(.7)-150,000(.3)=$865,000EVPI=$1.060,000-865,000=$195,000Decision Analysis Example Problem Solution(6 of 9)本讲稿第五十四页，共五十七页Chapter 12-Decision Analysis 55 Step 4(part d):Develop a decision tree.Decision Analysis Example Problem Solution(7 of 9)本讲稿第五十五页，共五十七页Chapter 1