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ID:20491868
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时间:2018-10-13
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1、TheNewsvendorModel报童模型“Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonefewerunit.Cu=underagecostThecostoforde
2、ringonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit.BalancingtheriskandbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit
3、=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthechanceofunderage:ExpectedgainontheQthunit=Cux(1-F(Q))Asmoreunitsareordered,theexpectedbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.Newsvendor
4、expectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlossontheQthunitequalstheexpectedgainontheQthunit:Rearrangetermsintheaboveequation->TheratioCu/(Co+Cu)iscalledthecriticalratio.(临界比或关键比例)Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandis
5、Qorlower)withaprobabilitythatequalsthecriticalratioTheNewsvendorModel:Performancemeasures绩效指标NewsvendormodelperformancemeasuresForanyorderquantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales(期望销售损失)TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales(期望销售)(
6、comparedtoexpecteddemand)Theaveragenumberofunitssold.Expectedleftoverinventory(期望售后剩余库存)Theaveragenumberofunitsleftoverattheendoftheseason.ExpectedprofitExpectedfillrate(期望订单完成率)ThefractionofdemandthatissatisfiedimmediatelyIn-stockprobability(存货满足概率)ProbabilityalldemandissatisfiedStockoutprobabili
7、ty(缺货概率)ProbabilitysomedemandislostformulaExpectedsales=m-Expectedlostsalesm:ExpecteddemandL(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-ExpectedSalesformulaIn-stockprobability=F(Q)=Φ(
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