G3-不确定决策问题

G3不确定决策问题詹文杰（教授/博导）Office:华中科技大学管理学院611室Tel:[phone]Email:[e-mail]根据环境的不确定性分类确定型决策风险型决策不确定型决策含义指掌握了各可行方案的全部条件，可准确预测各方案后果并从中选择一最有利方案的决策指决策事件的某些条件是已知的，但还不能完全确定决策的后果，只能根据经验和相关资料估计各种结果出现的可能性(概率)指决策事件未来可能出现的几种后果及概率都无法确定，只能依靠决策者的经验、直觉和估计做出决策CertaintyUncertaintyRisk学习目标掌握五种严格不确定决策问题的决策准则：1.乐观准则(Themaximaxcriterion)2.悲观准则(Themaximincriterion)3.Hurwitz准则(TheHurwiczcriterion)4.等概率准则(TheLaplacecriterion)5.后悔值极小化极大(TheminimaxRegretorSavagecriterion)G3不确定决策问题3.1不确定型决策问题的五大准则3.2不确定型决策问题的应用举例3.3不确定型决策问题的研究论文3.1不确定型决策问题的五大准则(1)乐观准则(Themaximaxcriterion)(2)悲观准则(Themaximincriterion)(3)Hurwitz准则(TheHurwiczcriterion)(4)等概率准则(TheLaplacecriterion)(5)最小后悔值准则(TheminimaxRegretcriterionortheSavagecriterion)(1)ThemaximaxcriterionLetusassumeforthemomentthatyouhaveaveryoptimisticviewofthefuture.Ifthiswerethecaseyouwouldtendtochoosethedecisionwhichcouldgeneratethehighestpossiblepay-off.Suchanapproachisknownasthemaximaxcriterion,sincewearesearchingforthemaximumofthemaximumpay-offs.Suchanapproachfollowstwosteps:1.Foreachpossibledecision,identifythemaximumpossiblepay-off.2.Comparingthesepay-offs,selectthedecisionthatwillgivethemaximumpay-off.(1)Themaximaxcriterion:exampleHPLowMBDBAMediumHighLowMediumHighLowMediumHighFig.2-4Themaximaxcriterion-15105510302552040(1)Themaximaxcriterion(cont.)DecisionFuturesaleslevelManufacture(M)Buydomestic(BD)Buyabroad(BA)Low-15105Medium103020High552540maximax553040(1)Themaximaxcriterion(cont.)}{minmin}{min111ijnjmiimikloo}{maxmax}'{max'111ijnjmiimikuooMathematicdefinitionofthemaximaxcriterionwithbenefitMathematicdefinitionoftheminimincriterionwithlose(2)ThemaximincriterionHowever,wearenotalloptimisticaboutthefuture.Thereissomethingtobesaidforexaminingtheworst-casescenario-beingpessimisticaboutfutureoutcomes.Insuchasituationwecanapplythemaximincriterion,sincewesearchforthemaximumoftheminimumpay-offs.Foreachpossibledecisionwedeterminetheminimum(worst)possiblepay-offandthenchoosethelargestofthese.Thesummaryoftheapproachis:1.Foreachpossibledecision,identifytheminimumpossiblepay-off.2.Comparingthesepay-offs,selectthedecisionthatwillgivethemaximumpay-off.(2)Themaximincriterion(cont.)HPLowMBDBAMediumHighLowMediumHighLowMediumHighFig.2-5Themaximincriterion-15105510302552040(2)Themaximincriterion(cont.)DecisionFuturesaleslevelManufacture(M)Buydomestic(BD)Buyabroad(BA)Low-15105Medium103020High552540maximin-15105(2)Themaximincriterion(cont.)}{maxmin}{min111ijnjmiimiklssMathematicdefinitionofthemaximincriterionwithbenefitMathematicdefinitionoftheminimaxcriterionwithloss}{minmax}'{max'111ijnjmiimikuss(3)TheHurwiczcriterionInanattempttoachieveacompromisebetweentheoptimismofmaximaxcriterionandthepessimismofthemaximincriterion,Hurwiczproposedacriterionwhichisaweightedaverageofthetwoextremes.Ok+(1-)Skwhere[0,1],namedtheoptimismparameter;then(1-)isnamedthepessimismparameter.(3)TheHurwiczcriterion(cont.)}minmax1{min}1{min)1(1111jinjjinjmiiimikkllosos}maxmin1{max}''1{max'')1(1111jinjjinjmiiimikkuuososMathematicdefinitionoftheHurwiczcriterionwithbenefitMathematicdefinitionoftheHurwiczcriterionwithlose(3)TheHurwiczcriterion(cont.)DecisionFuturesaleslevelManufacture(M)Buydomestic(BD)Buyabroad(BA)Low-15105Medium103020High552540Maximax(O’k)553040Maximin(S’k)-15105Hurwicz()55-15(1-)30+10(1-)40+5(1-)Sensitivityanalysisof00.10.20.30.40.50.60.70.80.91-20-100102030405060M()=55-15(1-)BD()=30+10(1-)BA()=40+5(1-)f()SensitivityanalysisofSensitivityanalysis(灵敏度分析)isthestudyofhowthevariation(uncertainty)intheoutputofamathematicalmodelcanbeapportioned,qualitativelyorquantitatively,todifferentsourcesofvariationintheinputofthemodel.Itisatechniqueforsystematicallychangingparametersinamodeltodeterminetheeffectsofsuchchanges(4)TheLaplacecriterionTheLaplacecriterionisbasedontheassumptionthatthedecision-makerisinastateofignoranceabouttheprobabilitiesofNature’sstates.EachoftheNature’sstatehasequalprobabilityandisuniformlydistributed.Thedecision-makerwillchoosetheactionthatwillgetthemaximumexpectedmonetaryvalue(EMV).(4)TheLaplacecriterion(cont.)DecisionFuturesaleslevelProbabilityManufacture(M)Buydomestic(BD)Buyabroad(BA)Low1/3-15105Medium1/3103020High1/3552540Laplacecriterion(-15+10+55)/3=50/3(10+30+25)/3=65/3(5+20+40)/3=65/3(5)TheminimaxRegretcriterion(ortheSavagecriterion)Theminimaxregretcriterionispossibleusingtheconceptofopportunitylossorregret.ForeachstateofNatureandeachactionofthedecision-maker,wecancalculatewhatisknowastheregret.Regret:itisthedifferencebetweenthemaximumpay-offNature’sstateandtheparticularpay-offforthedecision-maker’saction.(5)TheminimaxRegretcriterion(cont.)DecisionFuturesaleslevelManufacture(M)Buydomestic(BD)Buyabroad(BA)maximumpay-offNature’sstateLow-1510510Medium10302030High55254055(5)TheminimaxRegretcriterion(cont.)RegretoropportunitylossFuturesaleslevelManufacture(M)Buydomestic(BD)Buyabroad(BA)Low2505Medium20010High03015maximumregret253015DecisionFuturesaleslevelM