會計學1系統(tǒng)工程學習資料3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第1頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第2頁/共118頁Decisionsoftenmustbemadeinenvironmentthataremuchmorefraughtwithuncertainty.Example:TheGOFERBROKECOMPANYownsatractoflandthatmaycontainoil.Aconsultinggeologisthasreportedtothemanagerthatshebelievesthereis1chancein4ofoil.Becauseofthisprospect,anotheroilcompanyhasofferedtopurchasethelandfor$90,000.However,Goferbrokeisconsideringholdingthelandinordertodrillforoilitself.Thecostofdrillingis$100,000.Ifoilisfound,theresultingexpectedrevenuewillbe$800,000,sothecompany'sexpectedprofit(afterdeductingthecostofdrilling)willbe$700,000.Alossof$100,000(thedrillingcost)willbeincurredifthelandisdry(nooil).第3頁/共118頁Howtoapproachthedecisionofwhethertodrillorsellbasedjustonthesedata.(WewillrefertothisasthefirstGoferbrokeCblem.)However,beforedecidingwhethertodrillorsell,anotheroptionistoconductadetailedseismicsurveyofthelandtoobtainabetterestimateoftheprobabilityoffindingoil.第4頁/共118頁StatusofLandAlternativePayoffOilDryDrillforOil$700,000-$100,000SelltheLand$90,000$90,000ChanceofStatus1in43in4第5頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第6頁/共118頁1.Amanufacturerintroducinganewproductintothemarketplace.Whatwillbethereactionofpotentialcustomers?Howmuchshouldbeproduced?Shouldtheproductbetestmarketedinasmallregionbeforedecidinguponfulldistribution?Howmuchadvertisingisneededtolaunchtheproductsuccessfully?第7頁/共118頁2.Afinancialfirminvestinginsecurities.Whicharethemarketsectorsandindividualsecuritieswiththebestprospects?Whereistheeconomyheaded?Howaboutinterestrates?Howshouldthesefactorsaffecttheinvestmentdecisions?第8頁/共118頁3.Agovernmentcontractorbiddingonanewcontract.Whatwillbetheactualcostsoftheproject?Whichothercompaniesmightbebidding?Whataretheirlikelybids?第9頁/共118頁4.Anagriculturalfirmselectingthemixofcropsandlivestockfortheupcomingseason.Whatwillbetheweatherconditions?Wherearepricesheaded?Whatwillcostsbe?第10頁/共118頁5.Anoilcompanydecidingwhethertodrillforoilinaparticularlocation.Howlikelyisoilthere?Howmuch?Howdeepwilltheyneedtodrill?Shouldgeologistsinvestigatethesitefurtherbeforedrilling?第11頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第12頁/共118頁Thesearethekindsofdecisionmakinginthefaceofgreatuncertaintythatdecisionanalysisisdesignedtoaddress.Decisionanalysisprovidesaframeworkandmethodologyforrationaldecisionmakingwhentheoutcomesareuncertain.第13頁/共118頁Frequently,onequestiontobeaddressedwithdecisionanalysisiswhethertomaketheneededdecisionimmediatelyortofirstdosometesting(atsomeexpense)toreducethelevelofuncertaintyabouttheoutcomeofthedecision.第14頁/共118頁Forexample,thetestingmightbefieldtestingofaproposednewproducttotestconsumerreactionbeforemakingadecisiononwhethertoproceedwithfull-scaleproductionandmarketingoftheproduct.Therefore,decisionanalysisdividesdecisionmakingbetweenthecasesofwithoutexperimentationandwithexperimentation.第15頁/共118頁Inthischapter,thefirstsectionintroducesaprototypeexamplethatwillbecarriedthroughoutthechapterforillustrativepurposes.Sections2and3thenpresentthebasicprinciplesofdecisionmakingwithoutexperimentationanddecisionmakingwithexperimentation.Wenextdescribedecisiontrees,ausefultoolfordepictingandanalyzingthedecisionprocesswhenaseriesofdecisionsneedstobemade.第16頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第17頁/共118頁TheGOFERBROKECOMPANYownsatractoflandthatmaycontainoil.Aconsultinggeologisthasreportedtomanagementthatshebelievesthereis1chancein4ofoil.Becauseofthisprospect,anotheroilcompanyhasofferedtopurchasethelandfor$90,000.However,Goferbrokeisconsideringholdingthelandinordertodrillforoilitself.Thecostofdrillingis$100,000.Ifoilisfound,theresultingexpectedrevenuewillbe$800,000,sothecompany'sexpectedprofit(afterdeductingthecostofdrilling)willbe$700,000.Alossof$100,000(thedrillingcost)willbeincurredifthelandisdry(nooil).第18頁/共118頁Table1summarizesthesedata.Section2discusseshowtoapproachthedecisionofwhethertodrillorsellbasedjustonthesedata.(WewillrefertothisasthefirstGoferbrokeCblem.)However,beforedecidingwhethertodrillorsell,anotheroptionistoconductadetailedseismicsurveyofthelandtoobtainabetterestimateoftheprobabilityoffindingoil.Section3discussesthiscaseofdecisionmakingwithexperimentation,atwhichpointthenecessaryadditionaldatawillbeprovided.第19頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第20頁/共118頁Ingeneralterms,thedecisionmakermustchooseanactionfromasetofpossibleactions.Thesetcontainsallthefeasiblealternativesunderconsiderationforhowtoproceedwiththeproblemofconcern.Thischoiceofanactionmustbemadeinthefaceofuncertainty,becausetheoutcomewillbeaffectedbyrandomfactorsthatareoutsidethecontrolofthedecisionmaker.Theserandomfactorsdeterminewhatsituationwillbefoundatthetimethattheactionisexecuted.Eachofthesepossiblesituationsisreferredtoasapossiblestateofnature.第21頁/共118頁Foreachcombinationofanactionandastateofnature,thedecisionmakerknowswhattheresultingpayoffwouldbe.Thepayoffisaquantitativemeasureofthevaluetothedecisionmakeroftheconsequencesoftheoutcome.Iftheconsequencesoftheoutcomedonotbecomecompletelycertainevenwhenthestateofnatureisgiven,thenthepayoffbecomesanexpectedvalue(inthestatisticalsense)ofthemeasureoftheconsequences.Apayofftablecommonlyisusedtoprovidethepayoffforeachcombinationofanactionandastateofnature.第22頁/共118頁Thedecisionanalysisframeworkcanbesummarizedasfollows:

1.Thedecisionmakerneedstochooseoneofthealternativeactions.2.Naturethenwouldchooseoneofthepossiblestatesofnature.3.Eachcombinationofanactionandstateofnaturewouldresultinapayer;whichisgivenasoneoftheentriesinapayofftable.4.Thispayofftableshouldbeusedtofindanoptimalactionforthedecisionmakeraccordingtoanappropriatecriterion.第23頁/共118頁Oneadditionalelementneedstobeaddedinthedecisionanalysisframework.Thedecisionmakergenerallywillhavesomeinformationthatshouldbetakenintoaccountabouttherelativelikelihoodofthepossiblestatesofnature.Suchinformationcanusuallybetranslatedtoaprobabilitydistribution,actingasthoughthestateofnatureisarandomvariable,inwhichcasethisdistributionisreferredtoasapriordistribution.Priordistributionsareoftensubjectiveinthattheymaydependupontheexperienceorintuitionofanindividual.Theprobabilitiesfortherespectivestatesofnatureprovidedbythepriordistributionarecalledpriorprobabilities.第24頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第25頁/共118頁kindsofDecisionAnalysis1.DeterministicDecisionAnalysis2.IndeterminableDecisionAnalysis3.ProbabilityDecisionAnalysis第26頁/共118頁

1.DeterministicDecisionAnalysis

2.IndeterminableDecisionAnalysis

3.ProbabilityDecisionAnalysis(1)Goal(2)Actions(3)Nature(4)Payoff(1)Goal(2)Actions(3)Nature(4)Payoff(5)Probability(1)Goal(2)Actions(3)Nature(4)Payoff(5)ProbabilityCharacteristicsofDecisionAnalysis第27頁/共118頁3.1IntroductionofDAKnowledgepointsIntroduceexampleApplicationinsomeotherfieldsThefunctionandimportanceofDAExplainaprototypeexampleDecisionmakingwithoutexperimentationKindsofDecisionAnalysisCharacteristicsofDecisionAnalysisFormulationofthePrototypeExampleinThisFramework第28頁/共118頁AsindicatedinTable15.1,theGoferbrokeCo.hastwopossibleactionsunderconsideration:drillforoilorselltheland.Thepossiblestatesofnaturearethatthelandcontainsoilandthatitdoesnot,asdesignatedinthecolumnheadingsofTable15.1byoilanddry.Sincetheconsultinggeologisthasestimatedthatthereis1chancein4ofoil(andso3chancesin4ofnooil),thepriorprobabilitiesofthetwostatesofnatureare0.25and0.75,respectively.Therefore,withthepayoffinunitsofthousandsofdollarsofprofit,thepayofftablecanbeobtaineddirectlyfromTable15.1,asshowninTable15.2.第29頁/共118頁

StateofNatureAlternativeOilDry1.DrillforOil700-1002.SelltheLand9090ChanceofStatus0.250.75第30頁/共118頁

StateofNatureAlternativeOilDry1.DrillforOil700-1002.SelltheLand9090Wewillusethisnexttofindtheoptimalactionaccordingtoeachofthefourcriteriadescribedbelow.(IndeterminableDecisionAnalisys)第31頁/共118頁(1)TheMaxiMaxPayoffCriterionMaximaxpayoffcriterion:Foreachpossibleaction,findthemaximumpayoffoverallpossiblestatesofnature.Next,findthemaximumofthesemaximumpayoffs.Choosetheactionwhosemaximumpayoffgivesthismaximum.第32頁/共118頁

StateofNatureMaximaxpayoffMaximuxSavageAlternativeOilDry1.DrillforOil700-1007002.SelltheLand909090700Action:DrillforOil第33頁/共118頁(2)TheMaximinPayoffCriterionMaximinpayoffcriterion:Foreachpossibleaction,findtheminimumpayoffoverallpossiblestatesofnature.Next,findthemaximumoftheseminimumpayoffs.Choosetheactionwhoseminimumpayoffgivesthismaximum.Thus,sincetheminimumpayoffforselling(90)islargerthanthatfordrilling(-100),theformeralternative(selltheland)willbechosenastheactiontotake.第34頁/共118頁Therationaleforthiscriterionisthatitprovidesthebestguaranteeofthepayoffthatwillbeobtained.Regardlessofwhatthetruestateofnatureturnsouttobe.Forexample,thepayofffromsellingthelandcannotbelessthan90,whichprovidesthebestavailableguarantee.Thus,thiscriteriontakesthepessimisticviewpointthat,regardlessofwhichactionisselected,theworststateofnatureforthatactionislikelytooccur,soweshouldchoosetheactionwhichprovidesthebestpayoffwithitsworststateofnature.第35頁/共118頁Thisrationaleisquitevalidwhenoneiscompetingagainstarationalandmalevolentopponent.However,thiscriterionisnotoftenusedingamesagainstnaturebecauseitisanextremelyconservativecriterioninthiscontext.Ineffect,itassumesthatnatureisaconsciousopponentthatwantstoinflictasmuchdamageaspossibleonthedecisionmaker.第36頁/共118頁Natureisnotamalevolentopponent,andthedecisionmakerdoesnotneedtofocussolelyontheworstpossiblepayofffromeachaction.Thisisespeciallytruewhentheworstpossiblepayofffromanactioncomesfromarelativelyunlikelystateofnature.

Thus,thiscriterionnormallyisofinterestonlytoaverycautiousdecisionmaker.第37頁/共118頁

StateofNatureMaximinpayoffMaximuxSavageAlternativeOilDry1.DrillforOil700-100-1002.SelltheLand90909090Action:SelltheLand第38頁/共118頁(3)TheSavageruleCriterionCriterion:Foreachpossiblenaturestate,findthemaximumpayoffoverallpossiblealternativeactives.Next,findthedifferenceofeachactivepayoffcomparingwiththemaximumpayoff.Choosethemaximumdifferenceofeveryactive,afterthatselecttheactionwhosedifferencegivestheminimum.第39頁/共118頁

StateofNatureSavageRuleAlternativeOilDryMax1.DrillforOil700(0)-100(190)1902.SelltheLand90(610)90(0)610Minimum190Action:DrillforOil第40頁/共118頁

StateofNatureAlternativeOilDry1.DrillforOil700-1002.SelltheLand9090Probability0.50.5(4)TheEquivalentProbabilityCriterion第41頁/共118頁CaseStudy

Anenterprisewantstoproduceanewproduct.Theyestimatethattherewillbefourcasesofthesalesofproduct:high,general,low,andbad.Theycan’tforecasttheprobabilityofeachstate.Theyhavethreealternativeapproaches:buildanewplant;expandtheexistingplant;andusetheexistingplant.Theprofitandlossunderdifferentcasesisshowninthetablebelow.第42頁/共118頁

highgenerallowbadBuildanewoneA1850420-150-400ExpandtheexistingA2600400-100-350ExpandtheexistingA340025090-50第43頁/共118頁PracticeAcompanywantstoproduceakindofwatch.Theexpectedpriceofawatchis$10.Therearethreedesignschemes:thefirstschemeneeds$100,000investment,$5forasinglewatch;thesecondschemeneeds$160,000investment,$4forasinglewatch;thethirdschemeneeds$250,000investment,$3forasinglewatch.Therearethreepossiblemarketingdemandquantity:E1——30000,E2——120000,E3——20000.Question:PleasesetupthepayofftableandrespectivelyselectthebestschemeusingtheMaxiMaxPayoffCriterion,theMaximinPayoffCriterion,andtheSavageruleCriterion.第44頁/共118頁demandquantityschemeE1E2E3schemeI500005000000schemeII20000560000-40000schemeIII-40000590000-110000第45頁/共118頁3.2SolutionofProbabilityanalysisKnowledgepointsTheMaximumLikelihoodCriterionBayes'DecisionRuler第46頁/共118頁3.2SolutionofProbabilityanalysisKnowledgepointsTheMaximumLikelihoodCriterionBayes'DecisionRuler第47頁/共118頁

TheMaximumLikelihoodCriterionIdentifythemostlikelystateofnature(theonewiththelargestpriorprobability).Forthisstateofnature,findtheactionwiththemaximumpayoff.Choosethisaction.第48頁/共118頁Theappealofthiscriterionisthatthemostimportantstateofnatureisthemostlikelyone,sotheactionchosenisthebestoneforthisparticularlyimportantstateofnature.Basingthedecisionontheassumptionthatthisstateofnaturewilloccurtendstogiveabetterchanceofafavorableoutcomethanassuminganyotherstateofnature.Furthermore,thecriteriondoesnotrelyonquestionablesubjectiveestimatesoftheprobabilitiesoftherespectivestatesofnatureotherthanidentifyingthemostlikelystate.第49頁/共118頁Themajordrawbackofthecriterionisthatitcompletelyignoresmuchrelevantinformation.Nostateofnatureisconsideredotherthanthemostlikelyone.Inaproblemwithmanypossiblestatesofnature,theprobabilityofthemostlikelyonemaybequitesmall,sofocusingonjustthisonestateofnatureisquiteunwarranted.Ineffect,thecriteriondoesnotpermitgamblingonalow-probabilitybigpayoff,nomatterhowattractivethegamblemaybe.第50頁/共118頁

StateofNatureMaximinpayoffMaximuxlikelihoodAlternativeOilDry1.DrillforOil700-100-1002.SelltheLand909090900.250.75900.75Action:SelltheLand第51頁/共118頁3.2SolutionofProbabilityanalysisKnowledgepointsTheMaximumLikelihoodCriterionBayes'DecisionRuler第52頁/共118頁Bayes'DecisionRulerUsingthebestavailableestimatesoftheprobabilitiesoftherespectivestatesofnature(currentlythepriorprobabilities),calculatetheexpectedvalueofthepayoffforeachofthepossibleactions.Choosetheactionwiththemaximumexpectedpayoff.第53頁/共118頁Fortheprototypeexample,theseexpectedpayoffsarecalculatedasfollows:

E[Payoff(drill)]=0.25(700)+0.75(-100)=100.E[Payoff(sell)]=0.25(90)+0.75(90)

=90.Since100islargerthan90,thealterativeactionselectedistodrillforoil.第54頁/共118頁ThebigadvantageofBayes'decisionruleisthatitincorporatesalltheavailableinformation,includingallthepayoffsandthebestavailableestimatesoftheprobabilitiesoftherespectivestatesofnature.Itissometimesarguedthattheseestimatesoftheprobabilitiesnecessarilyarelargelysubjectiveandsoaretooshakytobetrusted.Thereisnoaccuratewayofpredictingthefuture,includingafuturestateofnature,eveninprobabilityterms.Thisargumenthassomevalidity.Thereasonablenessoftheestimatesoftheprobabilitiesshouldbeassessedineachindividualsituation.第55頁/共118頁Nevertheless,undermanycircumstances,pastexperienceandcurrentevidenceenableonetodevelopreasonableestimatesoftheprobabilities.Usingthisinformationshouldprovidebettergroundsforasounddecisionthanignoringit.Furthermore,experimentationfrequentlycanbeconductedtoimprovetheseestimates,asdescribedinthenextsection.Therefore,wewillbeusingonlyBayes'decisionrulethroughouttheremainderofthechapter.第56頁/共118頁3.3DecisionmakingwithexperimentationKnowledgepointsContinuingthePrototypeExamplestatesofnatureAnalyzethestates第57頁/共118頁Frequently,additionaltesting(experimentation)canbedonetoimprovethepreliminaryestimatesoftheprobabilitiesoftherespectivestatesofnatureprovidedbythepriorprobabilities.Theseimprovedestimatesarecalledposteriorprobabilities.第58頁/共118頁WefirstupdatetheGoferbrokeCo.exampletoincorporateexperimentation,thendescribehowtoderivetheposteriorprobabilities,andfinallydiscusshowtodecidewhetheritisworthwhiletoconductexperimentation.第59頁/共118頁Asmentionedbefore,anavailableoptionbeforemakingadecisionistoconductadetailedseismicsurveyofthelandtoobtainabetterestimateoftheprobabilityofoil.Thecostis$30,000.第60頁/共118頁Aseismicsurveyobtainsseismicsoundingsthatindicatewhetherthegeologicalstructureisfavorabletothepresenceofoil.Wewilldividethepossiblefindingsofthesurveyintothefollowingtwocategories:USS:Unfavorableseismicsoundings;oilisfairlyunlikely.FSS:Favorableseismicsoundings;oilisfairlylikely.第61頁/共118頁Basedonpastexperience,ifthereisoil,thentheprobabilityofunfavorableseismicsoundingsisP(USS|State=Oil)=0.4,soP(FSS|State=Oil)=1-0.4=0.6.Similarly,ifthereisnooil,thentheprobabilityofunfavorableseismicsoundingsisestimatedtobeP(USS|State=Dry)=0.8,soP(FSS|State=Dry)=1-0.8=0.2.第62頁/共118頁Wesoonwillusethesedatatofindtheposteriorprobabilitiesoftherespectivestatesofnaturegiventheseismicsoundings.PriorProbabilitiesConditionalProbabilitiesJointProbabilitiesPosteriorProbabilities第63頁/共118頁

TheProbabilitytreediagramshowingalltheprobabilitiesleadingtothecalculationofeachposteriorprobabilityofthestateofnaturegiventhefindingoftheseismicsurvey.第64頁/共118頁KnowledgepointsIntroductiontodecisiontreeNodeandbrancesOtherrelatedterms2.4IntroductiontoDecisionTree第65頁/共118頁KnowledgepointsIntroductiontodecisiontreeNodeandbrancesOtherrelatedterms2.4IntroductiontoDecisionTree第66頁/共118頁Decisiontreesprovideausefulwayofvisuallydisplayingtheproblemandthenorganizingthecomputationalworkalreadydescribedintheprecedingtwosections.Thesetreesareespeciallyhelpfulwhenasequenceofdecisionsmustbemade.第67頁/共118頁Decisiontreesmodelsequentialdecisionproblemsunderuncertainty.Adecisiontreedescribesgraphicallythedecisionstobemade,theeventsthatmayoccur,andtheoutcomesassociatedwithcombinationsofdecisionsandevents.Probabilitiesareassignedtotheevents,andvaluesaredeterminedforeachoutcome.Amajorgoaloftheanalysisistodeterminethebestdecisions.Decisiontreeshavethreekindsofnodesandtwokindsofbranches.第68頁/共118頁KnowledgepointsIntroductiontodecisiontreeNodeandbrancesOtherrelatedterms2.4IntroductiontoDecisionTree第69頁/共118頁Adecisionnodeisapointwhereachoicemustbemade;itisshownasasquare.Thebranchesextendingfromadecisionnodearedecisionbranches,eachbranchrepresentingoneofthepossiblealternativesorcoursesofactionavailableatthatpoint.Thesetofalternativesmustbemutuallyexclusive(ifoneischosen,theotherscannotbechosen)andcollectivelyexhaustive(allpossiblealternativesmustbeincludedintheset).第70頁/共118頁Aneventnodeisapointwhereuncertaintyisresolved(apointwherethedecisionmakerlearnsabouttheoccurrenceofanevent).Aneventnode,sometimescalleda"chancenode,"isshownasacircle.Theeventsetconsistsoftheeventbranchesextendingfromaneventnode,eachbranchrepresentingoneofthepossibleeventsthatmayoccuratthatpoint.第71頁/共118頁Thesetofeventsmustbemutuallyexclusive(ifoneoccurs,theotherscannotoccur)andcollectivelyexhaustive(allpossibleeventsmustbeincludedintheset).Eacheventisassignedasubjectiveprobability;thesumofprobabilitiesfortheeventsinasetmustequalone.第72頁/共118頁Thethirdkindofnodeisa

terminalnode,representingthefinalresultofacombinationofdecisionsandevents.Terminalnodesaretheendpointsofadecisiontree,shownastheendofabranchonhand-drawndiagramsandasatriangleorverticallineoncomputer-generateddiagrams.第73頁/共118頁Ingeneral,decisionnodesandbranchesrepresentthecontrollablefactorsinadecisionproblem;eventnodesandbranchesrepresentuncontrollablefactors.Decisionnodesandeventnodesarearrangedinorderofsubjectivechronology.Forexample,thepositionofaneventnodecorrespondstothetimewhenthedecisionmakerlearnstheoutcomeoftheevent(notnecessarilywhentheeventoccurs).第74頁/共118頁KnowledgepointsIntroductiontodecisiontreeNodeandbrancesOtherrelatedterms2.4IntroductiontoDecisionTree第75頁/共118頁Decisiontreemodelsincludesuchconcepts：Nodes:(1)DecisionNode(2)EventNode(3)TerminalNodeBranch:(1)DecisionBranch(2)EventBranch(Probability)Profit(Payoff/Outcome):第76頁/共118頁Typeof

NodeWritten

SymbolComputer

SymbolNode

SuccessorDecisionsquaresquaredecisionbranchesEventcirclecircleeventbranchesTerminalendpointtriangleorverticallineterminalvalue第77頁/共118頁Sometimes,thenodesofthedecisiontreearereferredtoasforks,andthearcsarecalledbranches.Adecisionfork,representedbyasquare,indicatesthatadecisionneedstobemadeatthatpointintheprocess.Achancefork,representedbyacircle,indicatesthatarandomeventoccursatthatpoint.第78頁/共118頁第79頁/共118頁KnowledgepointsConstructingtheDecisionTreePerformingtheAnalysisCaseStudy2.5ConstructingtheDecisionTree

第80頁/共118頁KnowledgepointsConstructingtheDecisionTreePerformingtheAnalysisCaseStudy2.5ConstructingtheDecisionTree

第81頁/共118頁Theprototypeexampleinvolvesasequenceoftwodecisions:1.Shouldaseismicsurveybeconductedbeforeanactionischosen?2.Whichaction(drillforoilorselltheland)shouldbechosen?Thecorrespondingdecisiontree(beforeaddingnumbersandperformingcomputation)isdisplayedinthefollowing.第82頁/共118頁DoSeismicNoSeismicUnfavorableFavorableDrillSellDrillSellSellDrillOilDryOilOilDryDry第83頁/共118頁KnowledgepointsConstructingtheDecisionTreePerformingtheAnalysisCaseStudy2.5ConstructingtheDecisionTree

第84頁/共118頁Havingconstructedthedecisiontree,includingitsnumbers,wenowarereadytoanalyzetheproblembyusingthefollowingprocedure.1,Startattherightsideofthedecisiontreeandmoveleftonecolumnatatime.Foreachcolumn,performeitherstep2orstep3dependinguponwhethertheforksinthatcolumnarechanceforksordecisionforks.第85頁/共118頁2.Foreachchancefork,calculateitsexpectedpayoffbymultiplyingtheexpectedpayoffofeachbranchbytheprobabilityofthatbranchandthensummingtheseproducts.Recordthisexpectedpayoffforeachchanceforkinboldfacenexttothefork,anddesignatethisquantityasalsobeingtheexpectedpayoffforthebranchleadingtothisfork.第86頁/共118頁3.Foreachdecisionfork,comparetheexpectedpayoffsofitsbranchesandchoosethealternativewhosebranchhasthelargestexpectedpayoff.Ineachcase,recordthechoiceonthedecisiontreebyinsertingadoubledashasabarrierthrougheachrejectedbranch.第87頁/共118頁第88頁/共118頁Tobegintheprocedure,considertherightmostcolumnofforks,namely,chanceforksf,g,andh.Applyingstep2,theirexpectedpayoffs(EP)arecalculatedasEP=1/7(670)+6/7(130)=-15.7,forfortf,EP=1/2(670)+1/2(130)=270,forf