《供应链不匹配成本》PPT课件

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1、TheNewsvendorModel报童模型“Toomuch”and“toolittle”costsCo=overagecostThecostoforderingonemoreunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadleftoverinventory(i.e.,youoverordered).Coistheincreaseinprofityouwouldhaveenjoyedhadyou

2、orderedonefewerunit.Cu=underagecostThecostoforderingonefewerunitthanwhatyouwouldhaveorderedhadyouknowndemand.Inotherwords,supposeyouhadlostsales(i.e.,youunderordered).Cuistheincreaseinprofityouwouldhaveenjoyedhadyouorderedonemoreunit.Balancingtherisk

3、andbenefitoforderingaunitOrderingonemoreunitincreasesthechanceofoverage…ExpectedlossontheQthunit=CoxF(Q)F(Q)=Distributionfunctionofdemand=Prob{Demand<=Q)…butthebenefit/gainoforderingonemoreunitisthereductioninthechanceofunderage:ExpectedgainontheQthu

4、nit=Cux(1-F(Q))Asmoreunitsareordered,theexpectedbenefitfromorderingoneunitdecreaseswhiletheexpectedlossoforderingonemoreunitincreases.NewsvendorexpectedprofitmaximizingorderquantityTomaximizeexpectedprofitorderQunitssothattheexpectedlossontheQthunite

5、qualstheexpectedgainontheQthunit:Rearrangetermsintheaboveequation->TheratioCu/(Co+Cu)iscalledthecriticalratio.（临界比或关键比例）Hence,tomaximizeprofit,chooseQsuchthatwedon’thavelostsales(i.e.,demandisQorlower)withaprobabilitythatequalsthecriticalratioTheNews

6、vendorModel:Performancemeasures绩效指标NewsvendormodelperformancemeasuresForanyorderquantitywewouldliketoevaluatethefollowingperformancemeasures:Expectedlostsales（期望销售损失）TheaveragenumberofunitsdemandexceedstheorderquantityExpectedsales（期望销售）(comparedto

7、expecteddemand)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）Probabilit

8、yalldemandissatisfiedStockoutprobability（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(