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Slide1，TheNewsvendorModel报童模型Slide2，“Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonefewerunit.Cu=underagecostThecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit.Slide3，BalancingtheriskandbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthechanceofunderage:ExpectedgainontheQthunit=Cux(1-F(Q))0102030405060708008001600240032004000480056006400QthunitorderedExpectedgainorloss.ExpectedgainExpectedlossAsmoreunitsareordered,theexpectedbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.Slide4，NewsvendorexpectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlossontheQthunitequalstheexpectedgainontheQthunit:Rearrangetermsintheaboveequation->TheratioCu/(Co+Cu)iscalledthecriticalratio.（临界比或关键比例）Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratioQFCQFCuo1)(uouCCCQF)(Slide5，TheNewsvendorModel:Performancemeasures绩效指标Slide6，NewsvendormodelperformancemeasuresForanyorderquantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales（期望销售损失）TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales（期望销售）(comparedtoexpecteddemand)Theaveragenumberofunitssold.Expectedleftoverinventory（期望售后剩余库存）Theaveragenumberofunitsleftoverattheendoftheseason.ExpectedprofitExpectedfillrate（期望订单完成率）ThefractionofdemandthatissatisfiedimmediatelyIn-stockprobability（存货满足概率）ProbabilityalldemandissatisfiedStockoutprobability（缺货概率）ProbabilitysomedemandislostSlide7，formulaExpectedsales=-Expectedlostsales:ExpecteddemandL(z):lossfunction(标准正态)损失函数,随机变量超过一个固定值的期望值之和。ExpectedLeftOverInventory=Q-ExpectedSales()ExpectedlostsalesLzzNormsdistzzNormdistzL1*)0,1,0,()(Slide8，formulaExpectedprofitPrice-CostExpectedsalesCost-SalvagevalueExpectedleftoverinventory1ExpectedsalesExpectedsalesExpectedfillrateExpecteddemandExpectedlostsalesIn-stockprobability=F(Q)=Φ(z)Stockoutprobability=1–F(Q)=1–In-stockprobabilitySlide9，TheNewsvendorModel:Thetargetin-stockprobabilityandthetargetfill-rateobjectivesforchoosingQin-stockprobability：缺货情况，对杂货店较重要fill-rate：多少顾客满足的情况，对目录零售商较重要Slide10，ChooseQsubjecttoaminimumin-stockprobabilitySupposewewishtofindtheorderquantityfortheHammer3/2thatminimizesleftoverinventorywhilegeneratingatleasta99%in-stockprobability.Step1:Findthez-statisticthatyieldsthetargetin-stockprobability.IntheStandardNormalDistributionFunctionTablewefind(2.32)=0.9898and(2.33)=0.9901.Choosez=2.33tosatisfyourin-stockprobabilityconstraint.Step2:Convertthez-statisticintoanorderquant...