運籌學與供應鏈管理-第4講

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1、第４讲库存管理（II）Multi-EchelonInventoryinSupplyChainTwoStageEchelonInventorySequentialstockingpointswithleveldemandTwo-stageprocessTwoStageEchelonInventoryTwo-stageprocess:Alittlereflectionshowsthatatleastforthecaseofdeterministicdemanditneverwouldmakesensetohavebeanythingbutanintegermultip

2、leof.Therefore,wecanthinkoftwoalternativedecisionvariablesandwhere(4.1)TwoStageEchelonInventoryTwo-stageprocess:ThefirststagecostThesecondstagecostThetotalcostTwoStageEchelonInventoryTwo-stageprocess:ThewarehouseecheloninventoryisvaluedatwhiletheretailerecheloninventoryisvaluedatonlyT

3、woStageEchelonInventoryTwo-stageprocess:Thetotalrelevant(setuppluscarrying)costsperunittimearegivenby=averagevalueofthewarehouseecheloninventory,inunits=averagevalueoftheretailerecheloninventory,inunitsTwoStageEchelonInventoryTwo-stageprocess:Substitutingfromequation(4.1)andnotingthat

4、theechelonstocksfollowsawtoothpatterns,TwoStageEchelonInventorySelect(aninteger)andinordertominimizePartialderivationofTRCTwoStageEchelonInventorySubstitutetheresultintothecostequationWerecognizethatthenthatminimizesthesimplerexpressionTwoStageEchelonInventoryAconvenientwayistofirstse

5、twhichgivesThissolvesforTwoStageEchelonInventoryAscertainandwhereandarethetwointegerssurroundingtheWhichevergivesthelowervalueofFistheappropriatentouse(becausetheFfunctionisconvexinn).TwoStageEchelonInventoryTwo-stageprocess:Step1ComputeStep2Ascertainthetwointegervalues,and,thatsurrou

6、nd.TwoStageEchelonInventoryTwo-stageprocess:Step3TwoStageEchelonInventoryTwo-stageprocess:Step4Step5TwoStageEchelonInventoryExample1:Letusconsideraparticularliquidproductthatafirmbuysinbulk,thenbreaksdownandrepackages.Sointhiscase,thewarehousecorrespondstotheinventorypriortotherepacka

7、gingoperation,andtheretailercorrespondstotheinventoryaftertherepackagingoperation.Thedemandforthisitemcanbeassumedtobeessentiallydeterministicandlevelatarateof1000litersperyear.TwoStageEchelonInventoryExample1:Theunitvalueofthebulkmaterialoris$1/liter,whilethevalueaddedbythetransformi

8、ng(br