管理科學決策分析

管理科學決策分析Chapter12-DecisionAnalysis1第一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

2ComponentsofDecisionMakingDecisionMakingwithoutProbabilitiesDecisionMakingwithProbabilitiesDecisionAnalysiswithAdditionalInformationUtilityChapterTopics第二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

3Table12.1PayoffTableAstateofnatureisanactualeventthatmayoccurinthefuture.Apayofftableisameansoforganizingadecisionsituation,presentingthepayoffsfromdifferentdecisionsgiventhevariousstatesofnature.DecisionAnalysisComponentsofDecisionMaking第三頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

4Decisionsituation:Decision-MakingCriteria:maximax,maximin,minimax,minimaxregret,Hurwicz,andequallikelihood

Table12.2PayoffTablefortheRealEstateInvestmentsDecisionAnalysisDecisionMakingwithoutProbabilities第四頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

5Table12.3PayoffTableIllustratingaMaximaxDecisionInthemaximaxcriterionthedecisionmakerselectsthedecisionthatwillresultinthemaximumofmaximumpayoffs;anoptimisticcriterion.DecisionMakingwithoutProbabilitiesMaximaxCriterion第五頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

6Table12.4PayoffTableIllustratingaMaximinDecisionInthemaximincriterionthedecisionmakerselectsthedecisionthatwillreflectthemaximumoftheminimumpayoffs;apessimisticcriterion.DecisionMakingwithoutProbabilitiesMaximinCriterion第六頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

7Table12.6

RegretTableIllustratingtheMinimaxRegretDecisionRegretisthedifferencebetweenthepayofffromthebestdecisionandallotherdecisionpayoffs.Thedecisionmakerattemptstoavoidregretbyselectingthedecisionalternativethatminimizesthemaximumregret.DecisionMakingwithoutProbabilitiesMinimaxRegretCriterion第七頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

8TheHurwiczcriterionisacompromisebetweenthemaximaxandmaximincriterion.Acoefficientofoptimism,,isameasureofthedecisionmaker’soptimism.TheHurwiczcriterionmultipliesthebestpayoffbyandtheworstpayoffby1-.,foreachdecision,andthebestresultisselected.

Decision

Values

Apartmentbuilding$50,000(.4)+30,000(.6)=38,000 Officebuilding$100,000(.4)-40,000(.6)=16,000 Warehouse$30,000(.4)+10,000(.6)=18,000DecisionMakingwithoutProbabilitiesHurwiczCriterion第八頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

9Theequallikelihood(orLaplace)criterionmultipliesthedecisionpayoffforeachstateofnaturebyanequalweight,thusassumingthatthestatesofnatureareequallylikelytooccur.

Decision

Values

Apartmentbuilding$50,000(.5)+30,000(.5)=40,000 Officebuilding$100,000(.5)-40,000(.5)=30,000 Warehouse$30,000(.5)+10,000(.5)=20,000DecisionMakingwithoutProbabilitiesEqualLikelihoodCriterion第九頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

10Adominantdecisionisonethathasabetterpayoffthananotherdecisionundereachstateofnature.Theappropriatecriterionisdependentonthe“risk”personalityandphilosophyofthedecisionmaker.

Criterion

Decision(Purchase) Maximax Officebuilding Maximin Apartmentbuilding Minimaxregret Apartmentbuilding Hurwicz Apartmentbuilding Equallikelihood ApartmentbuildingDecisionMakingwithoutProbabilitiesSummaryofCriteriaResults第十頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

11Exhibit12.1DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(1of3)第十一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

12Exhibit12.2DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(2of3)第十二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

13Exhibit12.3DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(3of3)第十三頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

14Expectedvalueiscomputedbymultiplyingeachdecisionoutcomeundereachstateofnaturebytheprobabilityofitsoccurrence. EV(Apartment)=$50,000(.6)+30,000(.4)=42,000 EV(Office)=$100,000(.6)-40,000(.4)=44,000 EV(Warehouse)=$30,000(.6)+10,000(.4)=22,000Table12.7PayofftablewithProbabilitiesforStatesofNatureDecisionMakingwithProbabilitiesExpectedValue第十四頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

15Theexpectedopportunitylossistheexpectedvalueoftheregretforeachdecision.Theexpectedvalueandexpectedopportunitylosscriterionresultinthesamedecision.

EOL(Apartment)=$50,000(.6)+0(.4)=30,000 EOL(Office)=$0(.6)+70,000(.4)=28,000 EOL(Warehouse)=$70,000(.6)+20,000(.4)=50,000Table12.8Regret(OpportunityLoss)TablewithProbabilitiesforStatesofNatureDecisionMakingwithProbabilitiesExpectedOpportunityLoss第十五頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

16Exhibit12.4ExpectedValueProblemsSolutionwithQMforWindows第十六頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

17Exhibit12.5ExpectedValueProblemsSolutionwithExcelandExcelQM(1of2)第十七頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

18Exhibit12.6ExpectedValueProblemsSolutionwithExcelandExcelQM(2of2)第十八頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

19Theexpectedvalueofperfectinformation(EVPI)isthemaximumamountadecisionmakerwouldpayforadditionalinformation.EVPIequalstheexpectedvaluegivenperfectinformationminustheexpectedvaluewithoutperfectinformation.EVPIequalstheexpectedopportunityloss(EOL)forthebestdecision.DecisionMakingwithProbabilitiesExpectedValueofPerfectInformation第十九頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

20Table12.9PayoffTablewithDecisions,GivenPerfectInformationDecisionMakingwithProbabilitiesEVPIExample(1of2)第二十頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

21Decisionwithperfectinformation: $100,000(.60)+30,000(.40)=$72,000Decisionwithoutperfectinformation: EV(office)=$100,000(.60)-40,000(.40)=$44,000

EVPI=$72,000-44,000=$28,000 EOL(office)=$0(.60)+70,000(.4)=$28,000DecisionMakingwithProbabilitiesEVPIExample(2of2)第二十一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

22Exhibit12.7DecisionMakingwithProbabilitiesEVPIwithQMforWindows第二十二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

23Adecisiontreeisadiagramconsistingofdecisionnodes(representedassquares),probabilitynodes(circles),anddecisionalternatives(branches). Table12.10PayoffTableforRealEstateInvestmentExampleDecisionMakingwithProbabilitiesDecisionTrees(1of4)第二十三頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

24Figure12.1DecisionTreeforRealEstateInvestmentExampleDecisionMakingwithProbabilitiesDecisionTrees(2of4)第二十四頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

25Theexpectedvalueiscomputedateachprobabilitynode: EV(node2)=.60($50,000)+.40(30,000)=$42,000 EV(node3)=.60($100,000)+.40(-40,000)=$44,000 EV(node4)=.60($30,000)+.40(10,000)=$22,000Brancheswiththegreatestexpectedvalueareselected.DecisionMakingwithProbabilitiesDecisionTrees(3of4)第二十五頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

26Figure12.2DecisionTreewithExpectedValueatProbabilityNodesDecisionMakingwithProbabilitiesDecisionTrees(4of4)第二十六頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

27Exhibit12.8DecisionMakingwithProbabilitiesDecisionTreeswithQMforWindows第二十七頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

28Exhibit12.9DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(1of4)第二十八頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

29Exhibit12.10DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(2of4)第二十九頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

30Exhibit12.11DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(3of4)第三十頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

31Exhibit12.12DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(4of4)第三十一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

32DecisionMakingwithProbabilitiesSequentialDecisionTrees(1of4)Asequentialdecisiontreeisusedtoillustrateasituationrequiringaseriesofdecisions.Usedwhereapayofftable,limitedtoasingledecision,cannotbeused.Realestateinvestmentexamplemodifiedtoencompassaten-yearperiodinwhichseveraldecisionsmustbemade:

第三十二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

33Figure12.3SequentialDecisionTreeDecisionMakingwithProbabilitiesSequentialDecisionTrees(2of4)第三十三頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

34DecisionMakingwithProbabilitiesSequentialDecisionTrees(3of4)Decisionistopurchaseland;highestnetexpectedvalue($1,160,000).Payoffofthedecisionis$1,160,000.

第三十四頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

35Figure12.4SequentialDecisionTreewithNodalExpectedValuesDecisionMakingwithProbabilitiesSequentialDecisionTrees(4of4)第三十五頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

36Exhibit12.13SequentialDecisionTreeAnalysisSolutionwithQMforWindows第三十六頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

37Exhibit12.14SequentialDecisionTreeAnalysisSolutionwithExcelandTreePlan第三十七頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

38Bayesiananalysisusesadditionalinformationtoalterthemarginalprobabilityoftheoccurrenceofanevent.Inrealestateinvestmentexample,usingexpectedvaluecriterion,bestdecisionwastopurchaseofficebuildingwithexpectedvalueof$444,000,andEVPIof$28,000.

Table12.11PayoffTablefortheRealEstateInvestmentExampleDecisionAnalysiswithAdditionalInformationBayesianAnalysis(1of3)第三十八頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

39Aconditionalprobabilityistheprobabilitythataneventwilloccurgiventhatanothereventhasalreadyoccurred.Economicanalystprovidesadditionalinformationforrealestateinvestmentdecision,formingconditionalprobabilities: g=goodeconomicconditions p=pooreconomicconditions P=positiveeconomicreport N=negativeeconomicreport P(Pg)=.80 P(NG)=.20 P(Pp)=.10 P(Np)=.90

DecisionAnalysiswithAdditionalInformationBayesianAnalysis(2of3)第三十九頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

40Aposteriaprobabilityisthealteredmarginalprobabilityofaneventbasedonadditionalinformation.Priorprobabilitiesforgoodorpooreconomicconditionsinrealestatedecision: P(g)=.60;P(p)=.40PosteriaprobabilitiesbyBayes’rule: (gP)=P(PG)P(g)/[P(Pg)P(g)+P(Pp)P(p)] =(.80)(.60)/[(.80)(.60)+(.10)(.40)]=.923Posteria(revised)probabilitiesfordecision: P(gN)=.250 P(pP)=.077 P(pN)=.750DecisionAnalysiswithAdditionalInformationBayesianAnalysis(3of3)第四十頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

41DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(1of4)Decisiontreewithposteriorprobabilitiesdifferfromearlierversionsinthat: Twonewbranchesatbeginningoftreerepresentreport outcomes. Probabilitiesofeachstateofnatureareposterior probabilitiesfromBayes’rule.第四十一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

42Figure12.5DecisionTreewithPosteriorProbabilities

DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(2of4)第四十二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

43DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(3of4)EV(apartmentbuilding)=$50,000(.923)+30,000(.077) =$48,460EV(strategy)=$89,220(.52)+35,000(.48)=$63,194第四十三頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

44Figure12.6DecisionTreeAnalysisDecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(4of4)第四十四頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

45Table12.12ComputationofPosteriorProbabilitiesDecisionAnalysiswithAdditionalInformationComputingPosteriorProbabilitieswithTables第四十五頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

46Theexpectedvalueofsampleinformation(EVSI)isthedifferencebetweentheexpectedvaluewithandwithoutinformation:Forexampleproblem,EVSI=$63,194-44,000=$19,194Theefficiencyofsampleinformationistheratiooftheexpectedvalueofsampleinformationtotheexpectedvalueofperfectinformation:efficiency=EVSI/EVPI=$19,194/28,000=.68DecisionAnalysiswithAdditionalInformationExpectedValueofSampleInformation第四十六頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

47Table12.13PayoffTableforAutoInsuranceExampleDecisionAnalysiswithAdditionalInformationUtility(1of2)第四十七頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

48ExpectedCost(insurance)=.992($500)+.008(500)=$500ExpectedCost(noinsurance)=.992($0)+.008(10,000)=$80Decisionshouldbedonotpurchaseinsurance,butpeoplealmostalwaysdopurchaseinsurance.Utilityisameasureofpersonalsatisfactionderivedfrommoney.Utilesareunitsofsubjectivemeasuresofutility.Riskavertersforgoahighexpectedvaluetoavoidalow-probabilitydisaster.Risktakerstakeachanceforabonanzaonaverylow-probabilityeventinlieuofasurething.DecisionAnalysiswithAdditionalInformationUtility(2of2)第四十八頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

49DecisionAnalysisExampleProblemSolution(1of9)第四十九頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

50DecisionAnalysisExampleProblemSolution(2of9)Determinethebestdecisionwithoutprobabilitiesusingthe5criteriaofthechapter.Determinebestdecisionwithprobabilitiesassuming.70probabilityofgoodconditions,.30ofpoorconditions.Useexpectedvalueandexpectedopportunitylosscriteria.Computeexpectedvalueofperfectinformation.Developadecisiontreewithexpectedvalueatthenodes.Givenfollowing,P(Pg)=.70,P(Ng)=.30,P(Pp)=20,P(Np)=.80,determineposteriaprobabilitiesusingBayes’rule.Performadecisiontreeanalysisusingtheposteriorprobabilityobtainedinparte.第五十頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

51Step1(parta):Determinedecisionswithoutprobabilities.MaximaxDecision:Maintainstatusquo

Decisions

MaximumPayoffs Expand $800,000 Statusquo 1,300,000(maximum) Sell 320,000MaximinDecision:Expand

Decisions

MinimumPayoffs Expand $500,000(maximum) Statusquo -150,000 Sell 320,000DecisionAnalysisExampleProblemSolution(3of9)第五十一頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

52MinimaxRegretDecision:Expand

Decisions

MaximumRegrets Expand $500,000(minimum) Statusquo 650,000 Sell 980,000Hurwicz(=.3)Decision:Expand Expand $800,000(.3)+500,000(.7)=$590,000 Statusquo $1,300,000(.3)-150,000(.7)=$285,000 Sell $320,000(.3)+320,000(.7)=$320,000DecisionAnalysisExampleProblemSolution(4of9)第五十二頁，共五十七頁，編輯于2023年，星期五Chapter12-DecisionAnalysis

53EqualLikelihoodDecision:Expand Ex