数据、模型与决策（第12版）课件 第12章排队论

DecisionAnalysisChapter12Copyright©2016PearsonEducation,Inc.

ComponentsofDecisionMakingDecisionMakingWithoutProbabilitiesDecisionMakingWithProbabilitiesDecisionAnalysisWithAdditionalInformationUtilityChapterTopicsCopyright©2016PearsonEducation,Inc.

Previouschaptersusedanassumptionofcertaintywithregardstoproblemparameters.ThischapterrelaxesthecertaintyassumptionTwocategoriesofdecisionsituations:ProbabilitiescanbeassignedtofutureoccurrencesProbabilitiescannotbeassignedtofutureoccurrencesDecisionAnalysisOverviewCopyright©2016PearsonEducation,Inc.

Table12.1PayofftableAstateofnatureisanactualeventthatmayoccurinthefuture.Apayofftableisameansoforganizingadecisionsituation,presentingthepayoffsfromdifferentdecisionsgiventhevariousstatesofnature.DecisionAnalysisComponentsofDecisionMakingCopyright©2016PearsonEducation,Inc.

DecisionAnalysis

DecisionMakingWithoutProbabilitiesFigure12.1DecisionsituationwithrealestateinvestmentalternativesCopyright©2016PearsonEducation,Inc.

Decision-MakingCriteria maximax maximin minimax minimaxregret Hurwicz equallikelihoodDecisionAnalysisDecisionMakingwithoutProbabilitiesTable12.2PayofftablefortherealestateinvestmentsCopyright©2016PearsonEducation,Inc.

Table12.3Payofftableillustratingamaximaxdecision Inthe

maximaxcriterion

thedecisionmakerselectsthedecisionthatwillresultinthemaximumofmaximumpayoffs;anoptimisticcriterion.DecisionMakingwithoutProbabilitiesMaximaxCriterionCopyright©2016PearsonEducation,Inc.

Table12.4Payofftableillustratingamaximindecision Inthemaximincriterionthedecisionmakerselectsthedecisionthatwillreflectthemaximumoftheminimum

payoffs;apessimisticcriterion.DecisionMakingwithoutProbabilitiesMaximinCriterionCopyright©2016PearsonEducation,Inc.

Table12.5RegrettableRegretisthedifferencebetweenthepayofffromthebestdecisionandallotherdecisionpayoffs.Example:undertheGoodEconomicConditionsstateofnature,thebestpayoffis$100,000.Themanager’sregretforchoosingtheWarehousealternativeis$100,000-$30,000=$70,000DecisionMakingwithoutProbabilitiesMinimaxRegretCriterionCopyright©2016PearsonEducation,Inc.

Table12.6RegrettableillustratingtheminimaxregretdecisionThemanagercalculatesregretsforallalternativesundereachstateofnature.Thenthemanageridentifiesthemaximumregretforeachalternative.Finally,themanagerattemptstoavoidregretbyselectingthedecisionalternativethatminimizesthemaximumregret.DecisionMakingwithoutProbabilitiesMinimaxRegretCriterionCopyright©2016PearsonEducation,Inc.

The

Hurwiczcriterionisacompromisebetweenthemaximaxandmaximincriteria.Acoefficientofoptimism,

,isameasureofthedecisionmaker’soptimism.TheHurwiczcriterionmultipliesthebestpayoffbyandtheworstpayoffby1-,foreachdecision,andthebestresultisselected.Here,

=0.4.

DecisionMakingwithoutProbabilitiesHurwiczCriterionDecisionValuesApartmentbuilding$50,000(.4)+30,000(.6)=38,000Officebuilding$100,000(.4)-40,000(.6)=16,000Warehouse$30,000(.4)+10,000(.6)=18,000Copyright©2016PearsonEducation,Inc.

Theequallikelihood

(orLaplace)criterionmultipliesthedecisionpayoffforeachstateofnaturebyanequalweight,thusassumingthatthestatesofnatureareequallylikelytooccur.DecisionMakingwithoutProbabilitiesEqualLikelihoodCriterionDecisionValuesApartmentbuilding$50,000(.5)+30,000(.5)=40,000Officebuilding$100,000(.5)-40,000(.5)=30,000Warehouse$30,000(.5)+10,000(.5)=20,000Copyright©2016PearsonEducation,Inc.

Adominant

decisionisonethathasabetterpayoffthananotherdecisionundereachstateofnature.Theappropriatecriterionisdependentonthe“risk”personalityandphilosophyofthedecisionmaker.

Criterion

Decision(Purchase) Maximax Officebuilding Maximin Apartmentbuilding Minimaxregret Apartmentbuilding Hurwicz Apartmentbuilding Equallikelihood ApartmentbuildingDecisionMakingwithoutProbabilitiesSummaryofCriteriaResultsCopyright©2016PearsonEducation,Inc.

Exhibit12.1DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(1of3)Copyright©2016PearsonEducation,Inc.

Exhibit12.2DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(2of3)EquallikelihoodweightCopyright©2016PearsonEducation,Inc.

Exhibit12.3DecisionMakingwithoutProbabilitiesSolutionwithQMforWindows(3of3)Copyright©2016PearsonEducation,Inc.

DecisionMakingwithoutProbabilitiesSolutionwithExcelExhibit12.4=MIN(C7,D7)=MAX(E7,E9)=MAX(C18,D18)=MAX(F7:F9)=MAX(C7:C9)-C9=C7*C25+D7*C26=C7*0.5+D7*0.5Copyright©2016PearsonEducation,Inc.

Expectedvalue

iscomputedbymultiplyingeachdecisionoutcomeundereachstateofnaturebytheprobabilityofitsoccurrence.

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)=$22,000Table12.7PayofftablewithprobabilitiesforstatesofnatureDecisionMakingwithProbabilitiesExpectedValueCopyright©2016PearsonEducation,Inc.

Theexpectedopportunityloss

istheexpectedvalueoftheregretforeachdecision.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)=50,000Table12.8RegrettablewithprobabilitiesforstatesofnatureDecisionMakingwithProbabilitiesExpectedOpportunityLossCopyright©2016PearsonEducation,Inc.

Exhibit12.5ExpectedValueProblemsSolutionwithQMforWindowsExpectedvaluesCopyright©2016PearsonEducation,Inc.

Exhibit12.6ExpectedValueProblemsSolutionwithExcelandExcelQM(1of2)ExpectedvalueforapartmentbuildingCopyright©2016PearsonEducation,Inc.

ExpectedValueProblemsSolutionwithExcelandExcelQM(2of2)Exhibit12.7Copyright©2016PearsonEducation,Inc.

Theexpectedvalueofperfectinformation(EVPI)isthemaximumamountadecisionmakerwouldpayforadditionalinformation.EVPIequalstheexpectedvaluegivenperfectinformationminustheexpectedvaluewithoutperfectinformation.EVPIequalstheexpectedopportunityloss(EOL)forthebestdecision.DecisionMakingwithProbabilitiesExpectedValueofPerfectInformationCopyright©2016PearsonEducation,Inc.

Table12.9Payofftablewithdecisions,givenperfectinformation

DecisionMakingwithProbabilitiesEVPIExample(1of2)Copyright©2016PearsonEducation,Inc.

Decisionwithperfectinformation: $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)Copyright©2016PearsonEducation,Inc.

Exhibit12.8DecisionMakingwithProbabilitiesEVPIwithQMforWindowsTheexpectedvalue,givenperfectinformation,inCellF12=MAX(E7:E9)=F12-F11Copyright©2016PearsonEducation,Inc.

Adecisiontreeisadiagramconsistingofdecisionnodes(representedassquares),probabilitynodes(circles),anddecisionalternatives(branches). Table12.10PayofftableforrealestateinvestmentexampleDecisionMakingwithProbabilitiesDecisionTrees(1of4)Copyright©2016PearsonEducation,Inc.

Figure12.2DecisiontreeforrealestateinvestmentexampleDecisionMakingwithProbabilitiesDecisionTrees(2of4)Copyright©2016PearsonEducation,Inc.

Theexpectedvalueiscomputedateachprobabilitynode: 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)Copyright©2016PearsonEducation,Inc.

Figure12.3DecisiontreewithexpectedvalueatprobabilitynodesDecisionMakingwithProbabilitiesDecisionTrees(4of4)Copyright©2016PearsonEducation,Inc.

DecisionMakingwithProbabilitiesDecisionTreeswithQMforWindowsExhibit12.9SelectnodetoaddfromNumberofbranchesfromnode1Addbranchesfromnode1to2,3,and4Copyright©2016PearsonEducation,Inc.

DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(1of4)Exhibit12.10Copyright©2016PearsonEducation,Inc.

Exhibit12.11DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(2of4)Tocreateanotherbranch,click“B5,”thenthe“DecisionTree”menu,andselect“AddBranch”InvokeTreePlanfromthe“AddIns”menuCopyright©2016PearsonEducation,Inc.

Exhibit12.12DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(3of4)Clickoncell“F3,”then“DecisionTree”Select“ChangetoEventNode”andaddtwonewbranchesCopyright©2016PearsonEducation,Inc.

DecisionMakingwithProbabilitiesDecisionTreeswithExcelandTreePlan(4of4)Exhibit12.13AddnumericaldollarandprobabilityvaluesinthesecellsincolumnHThesecellscontaindecisiontreeformulas;donottypeinthesecellsincolumnsEandICopyright©2016PearsonEducation,Inc.

Exhibit12.14SequentialDecisionTreeAnalysisSolutionwithQMforWindowsCellA16containstheexpectedvalueof$44,000Copyright©2016PearsonEducation,Inc.

DecisionMakingwithProbabilitiesSequentialDecisionTrees(1of4)Asequentialdecisiontree

isusedtoillustrateasituationrequiringaseriesofdecisions.Usedwhereapayofftable,limitedtoasingledecision,cannotbeused.Thenextslideshowstherealestateinvestmentexamplemodifiedtoencompassaten-yearperiodinwhichseveraldecisionsmustbemade.

Copyright©2016PearsonEducation,Inc.

Figure12.4SequentialdecisiontreeDecisionMakingwithProbabilitiesSequentialDecisionTrees(2of4)Copyright©2016PearsonEducation,Inc.

DecisionMakingwithProbabilitiesSequentialDecisionTrees(3of4)Expectedvalueofapartmentbuildingis:$1,290,000-800,000=$490,000Expectedvalueiflandispurchasedis:$1,360,000-200,000=$1,160,000Thedecisionistopurchaseland;ithasthehighestnetexpectedvalueof$1,160,000. Copyright©2016PearsonEducation,Inc.

Figure12.5SequentialdecisiontreewithnodalexpectedvaluesDecisionMakingwithProbabilitiesSequentialDecisionTrees(4of4)Copyright©2016PearsonEducation,Inc.

SequentialDecisionTreeAnalysisSolutionwithExcelQMExhibit12.15Copyright©2016PearsonEducation,Inc.

Exhibit12.16SequentialDecisionTreeAnalysisSolutionwithTreePlanCopyright©2016PearsonEducation,Inc.

Bayesiananalysisusesadditionalinformationtoalterthemarginalprobabilityoftheoccurrenceofanevent.Intherealestateinvestmentexample,usingtheexpectedvaluecriterion,thebestdecisionwastopurchasetheofficebuildingwithanexpectedvalueof$444,000,andEVPIof$28,000.

Table12.11PayofftableforrealestateinvestmentDecisionAnalysiswithAdditionalInformationBayesianAnalysis(1of3)Copyright©2016PearsonEducation,Inc.

Aconditionalprobability

istheprobabilitythataneventwilloccurgiventhatanothereventhasalreadyoccurred.Aneconomicanalystprovidesadditionalinformationfortherealestateinvestmentdecision,formingconditionalprobabilities: g=goodeconomicconditions p=pooreconomicconditions P=positiveeconomicreport N=negativeeconomicreport P(P

g)=.80 P(N

G)=.20 P(P

p)=.10 P(N

p)=.90

DecisionAnalysiswithAdditionalInformationBayesianAnalysis(2of3)Copyright©2016PearsonEducation,Inc.

Aposteriorprobability

isthealteredmarginalprobabilityofaneventbasedonadditionalinformation.Priorprobabilitiesforgoodorpooreconomicconditionsintherealestatedecision: P(g)=.60;P(p)=.40PosteriorprobabilitiesbyBayes’rule: (g

P)=P(P

G)P(g)/[P(Pg)P(g)+P(P

p)P(p)] =(.80)(.60)/[(.80)(.60)+(.10)(.40)]=.923Posterior(revised)probabilitiesfordecision: P(g

N)=.250 P(p

P)=.077 P(p

N)=.750DecisionAnalysiswithAdditionalInformationBayesianAnalysis(3of3)Copyright©2016PearsonEducation,Inc.

DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(1of4) Decisiontreeswithposteriorprobabilitiesdifferfromearlierversionsinthat:Twonewbranchesatthebeginningofthetreerepresentreportoutcomes.ProbabilitiesofeachstateofnatureareposteriorprobabilitiesfromBayes’rule.Copyright©2016PearsonEducation,Inc.

Figure12.6Decisiontreewithposteriorprobabilities

DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(2of4)Copyright©2016PearsonEducation,Inc.

DecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(3of4)EV(apartmentbuilding)=$50,000(.923)+30,000(.077) =$48,460EV(strategy)=$89,220(.52)+35,000(.48)=$63,194Copyright©2016PearsonEducation,Inc.

Figure12.7DecisiontreeanalysisforrealestateinvestmentDecisionAnalysiswithAdditionalInformationDecisionTreeswithPosteriorProbabilities(4of4)Copyright©2016PearsonEducation,Inc.

Table12.12ComputationofposteriorprobabilitiesDecisionAnalysiswithAdditionalInformationComputingPosteriorProbabilitieswithTablesCopyright©2016PearsonEducation,Inc.

DecisionAnalysiswithAdditionalInformationComputingPosteriorProbabilitieswithExcelExhibit12.17Copyright©2016PearsonEducation,Inc.

Theexpectedvalueofsampleinformation(EVSI)isthedifferencebetweentheexpectedvaluewithandwithoutinformation:Forexampleproblem,EVSI=$63,194-44,000=$19,194Theefficiency

ofsampleinformationistheratiooftheexpectedvalueofsampleinformationtotheexpectedvalueofperfectinformation:efficiency=EVSI/EVPI=$19,194/28,000=.68DecisionAnalysiswithAdditionalInformationExpectedValueofSampleInformationCopyright©2016PearsonEducation,Inc.

Table12.13PayofftableforautoinsuranceexampleDecisionAnalysiswithAdditionalInformationUtility(1of2)Copyright©2016PearsonEducation,Inc.

ExpectedCost(insurance)=.992($500)+.008(500)=$500ExpectedCost(noinsurance)=.992($0)+.008(10,000)=$80 Thedecisionshouldbedonotpurchaseinsurance,butpeoplealmostalwaysdopurchaseinsurance.Utilityisameasureofpersonalsatisfactionderivedfrommoney.Utilesareunitsofsubjectivemeasuresofutility.Riskavertersforgoahighexpectedvaluetoavoidalow-probabilitydisaster.Risktakerstakeachanceforabonanzaonaverylow-probabilityeventinlieuofasurething.DecisionAnalysiswithAdditionalInformationUtility(2of2)Copyright©2016PearsonEducation,Inc.

DecisionAnalysisExampleProblemSolution(1of9)Acorporateraidercontemplatesthefutureofarecentacquisition.Threealternativesarebeingconsideredintwostatesofnature.Thepayofftableisbelow.Copyright©2016PearsonEducation,Inc.

DecisionAnalysisExampleProblemSolution(2of9)Determinethebestdecisionwithoutprobabilitiesusingthe5criteriaofthechapter.Determinebestdecisionwithprobabilitiesassuming.70probabilityofgoodconditions,.30ofpoorconditions.Useexpectedvalueandexpectedopportunitylosscriteria.Computeexpectedvalueofperfectinformation.Developadecisiontreewithexpectedvalueatthenodes.Giventhefollowing,P(P

g)=.70,P(N

g)=.30,P(P

p)=20,P(N

p)=.80,determineposteriorprobabilitiesusingBayes’rule.Performadecisiontreeanalysisusingtheposteriorprobabilityobtainedinparte.Copyright©2016PearsonEducation,Inc.

Step1(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)Copyright©2016PearsonEducation,Inc.

MinimaxRegretDecision: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)Copyright©2016PearsonEducation,Inc.

EqualLikelihoodDecision:Expand Expand $800,000(.5)+500,000(.5)=$650,000 Statusquo$1,300,000(.5)-150,000(.5)=$575,000 Sell