库存管理_企业库存管理详述

第 讲库存管理 II Multi EchelonInventoryinSupplyChain TwoStageEchelonInventory SequentialstockingpointswithleveldemandTwo stageprocess TwoStageEchelonInventory Two stageprocess Alittlereflectionshowsthatatleastforthecaseofdeterministicdemanditneverwouldmakesensetohavebeanythingbutanintegermultipleof Therefore wecanthinkoftwoalternativedecisionvariablesandwhere 4 1 TwoStageEchelonInventory Two stageprocess ThefirststagecostThesecondstagecostThetotalcost TwoStageEchelonInventory Two stageprocess Thewarehouseecheloninventoryisvaluedatwhiletheretailerecheloninventoryisvaluedatonly TwoStageEchelonInventory Two stageprocess Thetotalrelevant setuppluscarrying costsperunittimearegivenby averagevalueofthewarehouseecheloninventory inunits averagevalueoftheretailerecheloninventory inunits TwoStageEchelonInventory Two stageprocess Substitutingfromequation 4 1 andnotingthattheechelonstocksfollowsawtoothpatterns TwoStageEchelonInventory Select aninteger andinordertominimizePartialderivationofTRC TwoStageEchelonInventory SubstitutetheresultintothecostequationWerecognizethatthenthatminimizesthesimplerexpression TwoStageEchelonInventory AconvenientwayistofirstsetwhichgivesThissolvesfor TwoStageEchelonInventory AscertainandwhereandarethetwointegerssurroundingtheWhichevergivesthelowervalueofFistheappropriatentouse becausetheFfunctionisconvexinn TwoStageEchelonInventory Two stageprocess Step1ComputeStep2Ascertainthetwointegervalues and thatsurround TwoStageEchelonInventory Two stageprocess Step3 TwoStageEchelonInventory Two stageprocess Step4Step5 TwoStageEchelonInventory Example1 Letusconsideraparticularliquidproductthatafirmbuysinbulk thenbreaksdownandrepackages Sointhiscase thewarehousecorrespondstotheinventorypriortotherepackagingoperation andtheretailercorrespondstotheinventoryaftertherepackagingoperation Thedemandforthisitemcanbeassumedtobeessentiallydeterministicandlevelatarateof1000litersperyear TwoStageEchelonInventory Example1 Theunitvalueofthebulkmaterialoris 1 liter whilethevalueaddedbythetransforming breakandpackage operationis 4 liter Thefixedcomponentofthepurchasecharge is 10 whilethesetupcostforthebreakandrepackageoperation is 15 Finally theestimatedcarryingchargeis0 24 yr TwoStageEchelonInventory Example1 Step1 Step2 TwoStageEchelonInventory Example1 Step3 thatis Thus usen 2 TwoStageEchelonInventory Example Step4 Step5 TwoStageEchelonInventory Example1 Inotherwords wepurchase334litersatatime one halfoftheseor167litersareimmediatelybrokenandrepackaged Whenthese167 finished litersaredepleted asecondbreakandrepackagerunof167litersismade Whenthesearedepleted westartanewcyclebyagainpurchasing334litersofrawmaterial InventoryControlwithUncertainDemand Thedemandcanbedecomposedintotwoparts where Deterministiccomponentofdemandand Randomcomponentofdemand InventoryControlwithUncertainDemand Thereareanumberofcircumstancesunderwhichitwouldbeappropriatetotreatasbeingdeterministiceventhoughisnotzero Someoftheseare Whenthevarianceoftherandomcomponent issmallrelativetothemagnitudeof Whenthepredictablevariationismoreimportantthantherandomvariation Whentheproblemstructureistoocomplextoincludeanexplicitrepresentationofrandomnessinthemodel InventoryControlwithUncertainDemand However formanyitems therandomcomponentofthedemandistoosignificanttoignore Aslongastheexpecteddemandperunittimeisrelativelyconstantandtheproblemstructurenottoocomplex explicittreatmentofdemanduncertaintyisdesirable InventoryControlwithUncertainDemand Example2 AnewsstandpurchasesanumberofcopiesofTheComputerJournal Theobserveddemandsduringeachofthelast52weekswere InventoryControlwithUncertainDemand Example2 InventoryControlwithUncertainDemand Example2 EstimatetheprobabilitythatthenumberofcopiesoftheJournalsoldinanyweek Theprobabilitythatdemandis10isestimatedtobe2 52 0 0385 andtheprobabilitythatthedemandis15is5 52 0 0962 Cumulativeprobabilitiescanalsobeestimatedinasimilarway TheprobabilitythattherearenineorfewercopiesoftheJournalsoldinanyweekis 1 0 0 0 3 1 2 2 4 6 52 19 52 0 3654 InventoryControlwithUncertainDemand Wegenerallyapproximatethedemandhistoryusingacontinuousdistribution Byfar themostpopulardistributionforinventoryapplicationsisthenormal Anormaldistributionisdeterminedbytwoparameters themeanandthevariance InventoryControlwithUncertainDemand Thesecanbeestimatedfromahistoryofdemandbythesamplemeanandthesamplevariance InventoryControlwithUncertainDemand ThenormaldensityfunctionisgivenbytheformulaWesubstituteastheestimatorforandastheestimatorfor InventoryControlwithUncertainDemand OptimizationCriterion Ingeneral optimizationinproductionproblemsmeansfindingacontrolrulethatachievesminimumcost However whendemandisrandom thecostincurredisitselfrandom anditisnolongerobviouswhattheoptimizationcriterionshouldbe Virtuallyallofthestochasticoptimizationtechniquesappliedtoinventorycontrolassumethatthegoalistominimizeexpectedcosts TheNewsboyModel ContinuousDemands Thedemandisapproximatelynormallydistributedwithmean11 731andstandarddeviation4 74 Eachcopyispurchasedfor25centsandsoldfor75cents andheispaid10centsforeachunsoldcopybyhissupplier Oneobvioussolutionisapproximately12copies SupposeMacpurchasesacopythathedoesn tsell Hisout of pocketexpenseis25cents 10cents 15cents Supposeontheotherhand heisunabletomeetthedemandofacustomer Inthatcase heloses75cents 25cents 50centsprofit TheNewsboyModel ContinuousDemands Notation Costperunitofpositiveinventoryremainingattheendoftheperiod knownastheoveragecost Costperunitofunsatisfieddemand Thiscanbethoughtofasacostperunitofnegativeendinginventory knownastheunderagecost Thedemandisacontinuousnonnegativerandomvariablewithdensityfunctionandcumulativedistributionfunction Thedecisionvariableisthenumberofunitstobepurchasedatthebeginningoftheperiod TheNewsboyModel ContinuousDemands Determiningtheoptimalpolicy ThecostfunctionTheoptimalsolutionequation TheNewsboyModel ContinuousDemands Determiningtheoptimalpolicy TheNewsboyModel ContinuousDemands Example2 continued Normallydistributedwithmean 11 73andstandarddeviation 4 74 SinceMacpurchasesthemagazinesfor25centsandcansalvageunsoldcopiesfor10cents hisoveragecostis 25 10 15cents Hisunderagecostistheprofitoneachsale sothat 75 25 50cents TheNewsboyModel ContinuousDemands Example2 continued Thecriticalratiois 0 50 0 65 0 77 Purchaseenoughcopiestosatisfyalloftheweeklydemandwithprobability0 77 Theoptimalisthe77thpercentileofthedemanddistribution TheNewsboyModel ContinuousDemands Example2 continued TheNewsboyModel ContinuousDemands Example2 continued Usingthedataofthenormaldistributionweobtainastandardizedvalueof 0 74 TheoptimalisHence heshouldpurchase15copieseveryweek TheNewsboyModel DiscreteDemands Optimalpolicyfordiscretedemand Theprocedureforfindingtheoptimalsolutiontothenewsboyproblemwhenthedemandisassumedtobediscreteisanaturalgeneralizationofthecontinuouscase Theoptimalsolutionprocedureistolocatethecriticalratiobetweentwovaluesofandchoosethecorrespondingtothehighervalue Thatis TheNewsboyModel DiscreteDemands Example2 TheNewsboyModel DiscreteDemands Example2 Thecriticalratioforthisproblemwas0 77 whichcorrespondstoavalueofbetween 14and 15 Sinceweroundup theoptimalsolutionis 15 Noticethatthisisexactlythesameorderquantityobtainedusingthenormalapproximation TheNewsboyModel DiscreteDemands ExtensiontoIncludeStartingInventory Theoptimalpolicywhenthereisastartinginventoryofis Orderif Don torderif Notethatshouldbeinterpretedastheorder up topointratherthantheorderquantitywhen Itisalsoknownasatargetorbasestocklevel MultiproductSystems ABCanalysis Thetrade offsbetweenthecostofcontrollingthesystemandthepotentialbenefitsthataccruefromthatcontrol Inmultiproductinventorysystemsnotallproductsareequallyprofitable Alargeportionofthetotaldollarvolumeofsalesisoftenaccountedforbyasmallnumberofinventoryitems MultiproductSystems ABCanalysis MultiproductSystems ABCanalysis SinceAitemsaccountforthelion sshareoftheyearlyrevenue theseitemsshouldbewatchedmostclosely InventorylevelsforAitemsshouldbemonitoredcontinuously Moresophisticatedforecastingproceduresmightbeusedandmorecarewouldbetakenintheestimationofthevariouscostparametersrequiredincalculatingoperatingpolicies MultiproductSystems ABCanalysis ForBitemsinventoriescouldbereviewedperiodically itemscouldbeorderedingroupsratherthanindividually andsomewhatlesssophisticatedforecastingmethodscouldbeused MultiproductSystems ABCanalysis TheminimumdegreeofcontrolwouldbeappliedtoCitems ForveryinexpensiveCitemswithmoderatelevelsofdemand largelotsizesarerecommendedtominimizethefrequencythattheseitemsareordered ForexpensiveCitemswithverylowdemand thebestpolicyisgenerallynottoholdanyinventory Onewouldsimplyordertheseitemsastheyaredemanded LotSize ReorderPointSystems Inwhatfollows weassumethattheoperatingpolicyisoftheform However whengeneralizingtheEOQanalysistoallowforrandomdemand wetreatandasindependentdecisionvariables LotSize ReorderPointSystems AssumptionsThesystemiscontinuous reviewDemandisrandomands