运筹学与供应链管理-第4讲

第４讲库存管理（II）Multi-EchelonInventoryinSupplyChainOutsidesupplier(s)CentralwarehouseBranchwarehouseRetailoutletsCustomersBranchwarehouseTwoStageEchelonInventorySequentialstockingpointswithleveldemandTwo-stageprocessQWWarehouseinventorylevelTimeTimeQRRetailerinventorylevelActualphysicalinventorylevelattheparticularlocationEcheloninventoryofthewarehouseitemTwoStageEchelonInventoryTwo-stageprocess:Alittlereflectionshowsthatatleastforthecaseofdeterministicdemanditneverwouldmakesensetohavebeanythingbutanintegermultipleof.Therefore,wecanthinkoftwoalternativedecisionvariablesandwhere(4.1)WQRQnRQ...3,2,1,nnQQRWTwoStageEchelonInventoryTwo-stageprocess:ThefirststagecostThesecondstagecostThetotalcostrvvQQrvQDArvQQDACCQQWRWRWRRWWWWWRRW222,TRCrvQQDACRRRRR2rvQrvQQDACWRWWWWW22TwoStageEchelonInventoryTwo-stageprocess:ThewarehouseecheloninventoryisvaluedatwhiletheretailerecheloninventoryisvaluedatonlyWWvv'WRRvvv'TwoStageEchelonInventoryTwo-stageprocess:Thetotalrelevant(setuppluscarrying)costsperunittimearegivenby=averagevalueofthewarehouseecheloninventory,inunits=averagevalueoftheretailerecheloninventory,inunitsrvIQDArvIQDA,QQRRRRWWWWRW''''TRC'WI'RITwoStageEchelonInventoryTwo-stageprocess:Substitutingfromequation(4.1)andnotingthattheechelonstocksfollowsawtoothpatterns,''''222TRCRWRWRRRRRRWRRWRWvnvrQnAAQDrvQQDArvQnnQDA,QQTwoStageEchelonInventorySelect(aninteger)andinordertominimizePartialderivationofTRCnRQ''2,TRCRWRWRRRvnvrQnAAQDQn02TRC''2RWWRRRvnvrnAAQDQrvnvDnAAnQRWWRR2''*TwoStageEchelonInventorySubstitutetheresultintothecostequationWerecognizethatthenthatminimizesthesimplerexpressionrvnvDnAAnRWWR2TRC''*''RWWRvnvnAAnFTwoStageEchelonInventoryAconvenientwayistofirstsetwhichgivesThissolvesfor0nFn0'2''WWRWRWvnAAnAvnv''*WRRWvAvAnTwoStageEchelonInventoryAscertainandwhereandarethetwointegerssurroundingtheWhichevergivesthelowervalueofFistheappropriatentouse(becausetheFfunctionisconvexinn).1nF2nF1n2n*nTwoStageEchelonInventoryTwo-stageprocess:Step1ComputeStep2Ascertainthetwointegervalues,and,thatsurround.''*WRRWvAvAn1n2n*nTwoStageEchelonInventoryTwo-stageprocess:Step3''111RWWRvvnnAAnF''222RWWRvvnnAAnF121use,IfnnnFnF221use,IfnnnFnFTwoStageEchelonInventoryTwo-stageprocess:Step4Step5rvnvDnAAQRWWRR''2RWnQQTwoStageEchelonInventoryExample1:Letusconsideraparticularliquidproductthatafirmbuysinbulk,thenbreaksdownandrepackages.Sointhiscase,thewarehousecorrespondstotheinventorypriortotherepackagingoperation,andtheretailercorrespondstotheinventoryaftertherepackagingoperation.Thedemandforthisitemcanbeassumedtobeessentiallydeterministicandlevelatarateof1000litersperyear.TwoStageEchelonInventoryExample1:Theunitvalueofthebulkmaterialoris$1/liter,whilethevalueaddedbythetransforming(breakandpackage)operationis$4/liter.Thefixedcomponentofthepurchasecharge()is$10,whilethesetupcostforthebreakandrepackageoperation()is$15.Finally,theestimatedcarryingchargeis0.24$/$/yr.WARAWv'WvWRRvvv'TwoStageEchelonInventoryExample1:Step1:Step2:11n63.1115410*n22nTwoStageEchelonInventoryExample1:Step3:thatis,Thus,usen=2.12541110151F120412210152F21FFTwoStageEchelonInventoryExample:Step4:Step5:liters16724.04121000210152RQliters3341672WQTwoStageEchelonInventoryExample1:Inotherwords,wepurchase334litersatatime;one-halfoftheseor167litersareimmediatelybrokenandrepackaged.Whenthese167(finished)litersaredepleted,asecondbreakandrepackagerunof167litersismade.Whenthesearedepleted,westartanewcyclebyagainpurchasing334litersofrawmaterial.InventoryControlwithUncertainDemandThedemandcanbedecomposedintotwoparts,where=Deterministiccomponentofdemandand=Randomcomponentofdemand.RanDetDDDDetDRanDInventoryControlwithUncertainDemandThereareanumberofcircumstancesunderwhichitwouldbeappropriatetotreatasbeingdeterministiceventhoughisnotzero.Someoftheseare:•Whenthevarianceoftherandomcomponent,issmallrelativetothemagnitudeof.•Whenthepredictablevariationismoreimportantthantherandomvariation.•Whentheproblemstructureistoocomplextoincludeanexplicitrepresentationofrandomnessinthemodel.DRanDRanDDInventoryControlwithUncertainDemandHowever,formanyitems,therandomcomponentofthedemandistoosignificanttoignore.Aslongastheexpecteddemandperunittimeisrelativelyconstantandtheproblemstructurenottoocomplex,explicittreatmentofdemanduncertaintyisdesirable.InventoryControlwithUncertainDemandExample2:AnewsstandpurchasesanumberofcopiesofTheComputerJournal.Theobserveddemandsduringeachofthelast52weekswere:1519912922478111411611918100141289544171814158671215151991091681111181517191414171312InventoryControlwithUncertainDemandExample2:01234560246810121416182022InventoryControlwithUncertainDemandExample2:EstimatetheprobabilitythatthenumberofcopiesoftheJournalsoldinanyweek.Theprobabilitythatdemandis10isestimatedtobe2/52=0.0385,andtheprobabilitythatthedemandis15is5/52=0.0962.Cumul