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Chapter11
ManagingUncertaintyinthe
SupplyChain:SafetyInventorySupplyChainManagement
(3rdEdition)
11-1RoleofInventoryintheSupplyChainCostAvailabilityEfficiencyResponsiveness2OutlineTheroleofsafetyinventoryinasupplychainDeterminingtheappropriatelevelofsafetyinventoryImpactofsupplyuncertaintyonsafetyinventoryImpactofaggregationonsafetyinventoryImpactofreplenishmentpoliciesonsafetyinventoryManagingsafetyinventoryinamulti-echelonsupplychainEstimatingandmanagingsafetyinventoryinpractice3TheRoleofSafetyInventory
inaSupplyChainForecastsarerarelycompletelyaccurateIfaveragedemandis1000unitsperweek,thenhalfthetimeactualdemandwillbegreaterthan1000,andhalfthetimeactualdemandwillbelessthan1000;whathappenswhenactualdemandisgreaterthan1000?Ifyoukeptonlyenoughinventoryinstocktosatisfyaveragedemand,halfthetimeyouwouldrunoutSafetyinventory:Inventorycarriedforthepurposeofsatisfyingdemandthatexceedstheamountforecastedinagivenperiod4RoleofSafetyInventoryAverageinventoryisthereforecycleinventoryplussafetyinventoryThereisafundamentaltradeoff:RaisingthelevelofsafetyinventoryprovideshigherlevelsofproductavailabilityandcustomerserviceRaisingthelevelofsafetyinventoryalsoraisesthelevelofaverageinventoryandthereforeincreasesholdingcostsVeryimportantinhigh-techorotherindustrieswhereobsolescenceisasignificantrisk(wherethevalueofinventory,suchasPCs,candropinvalue)CompaqandDellinPCs5TwoQuestionstoAnswerinPlanningSafetyInventoryWhatistheappropriatelevelofsafetyinventorytocarry?Whatactionscanbetakentoimproveproductavailabilitywhilereducingsafetyinventory?6DeterminingtheAppropriate
LevelofSafetyInventoryMeasuringdemanduncertaintyMeasuringproductavailabilityReplenishmentpoliciesEvaluatingcycleservicelevelandfillrateEvaluatingsafetylevelgivendesiredcycleservicelevelorfillrateImpactofrequiredproductavailabilityanduncertaintyonsafetyinventory7DeterminingtheAppropriate
LevelofDemandUncertaintyAppropriatelevelofsafetyinventorydeterminedby:supplyordemanduncertaintydesiredlevelofproductavailabilityHigherlevelsofuncertaintyrequirehigherlevelsofsafetyinventorygivenaparticulardesiredlevelofproductavailabilityHigherlevelsofdesiredproductavailabilityrequirehigherlevelsofsafetyinventorygivenaparticularlevelofuncertainty8MeasuringDemandUncertaintyDemandhasasystematiccomponentandarandomcomponentTheestimateoftherandomcomponentisthemeasureofdemanduncertaintyRandomcomponentisusuallyestimatedbythestandarddeviationofdemandNotation:D=AveragedemandperperiodsD
=standarddeviationofdemandperperiodL=leadtime=timebetweenwhenanorderisplacedandwhenitisreceivedUncertaintyofdemandduringleadtimeiswhatisimportant9MeasuringDemandUncertaintyP=demandduringkperiods=kDW=stddevofdemandduringkperiods=sRSqrt(k)Coefficientofvariation=cv=m/s=mean/(stddev)=sizeofuncertaintyrelativetodemand10MeasuringProductAvailabilityProductavailability:afirm’sabilitytofillacustomer’sorderoutofavailableinventoryStockout:acustomerorderarriveswhenproductisnotavailableProductfillrate(fr):fractionofdemandthatissatisfiedfromproductininventoryOrderfillrate:fractionofordersthatarefilledfromavailableinventoryCycleservicelevel:fractionofreplenishmentcyclesthatendwithallcustomerdemandmet11ReplenishmentPoliciesReplenishmentpolicy:decisionsregardingwhentoreorderandhowmuchtoreorderContinuousreview:inventoryiscontinuouslymonitoredandanorderofsizeQisplacedwhentheinventorylevelreachesthereorderpointROPPeriodicreview:inventoryischeckedatregular(periodic)intervalsandanorderisplacedtoraisetheinventorytoaspecifiedthreshold(the“order-up-to”level)12ContinuousReviewPolicy:SafetyInventoryandCycleServiceLevelL: LeadtimeforreplenishmentD: Averagedemandperunittime
D:StandarddeviationofdemandperperiodDL:
Meandemandduringleadtime
L:StandarddeviationofdemandduringleadtimeCSL:Cycleservicelevelss: SafetyinventoryROP:ReorderpointAverageInventory=Q/2+ss13Example11.1:EstimatingSafetyInventory(ContinuousReviewPolicy)D=2,500/week;
D=500L=2weeks;Q=10,000;ROP=6,000DL=DL=(2500)(2)=5000ss=ROP-RL=6000-5000=1000Cycleinventory=Q/2=10000/2=5000AverageInventory=cycleinventory+ss=5000+1000=6000AverageFlowTime=Avginventory/throughput=6000/2500=2.4weeks14Example11.2:EstimatingCycleServiceLevel(ContinuousReviewPolicy)D=2,500/week;
D=500L=2weeks;Q=10,000;ROP=6,000
Cycleservicelevel,CSL=F(DL+ss,DL,
L)==NORMDIST(DL+ss,DL,
L)=NORMDIST(6000,5000,707,1)=0.92(ThisvaluecanalsobedeterminedfromaNormalprobabilitydistributiontable)15FillRateProportionofcustomerdemandsatisfiedfromstockStockoutoccurswhenthedemandduringleadtimeexceedsthereorderpointESCistheexpectedshortagepercycle(averagedemandinexcessofreorderpointineachreplenishmentcycle)ssisthesafetyinventoryQistheorderquantity
ESC=-ss{1-NORMDIST(ss/
L,0,1,1)}+L
NORMDIST(ss/
L,0,1,0)16Example11.3:EvaluatingFillRatess=1,000,Q=10,000,sL=707,FillRate(fr)=?ESC=-ss{1-NORMDIST(ss/
L,0,1,1)}+
L
NORMDIST(ss/
L,0,1,0) =-1,000{1-NORMDIST(1,000/707,0,1,1)}+ 707NORMDIST(1,000/707,0,1,0) =25.13fr=(Q-ESC)/Q=(10,000-25.13)/10,000=0.997517FactorsAffectingFillRateSafetyinventory:Fillrateincreasesifsafetyinventoryisincreased.Thisalsoincreasesthecycleservicelevel.Lotsize:Fillrateincreasesonincreasingthelotsizeeventhoughcycleserviceleveldoesnotchange.18Example11.4:Evaluating
SafetyInventoryGivenCSLD=2,500/week;
D=500L=2weeks;Q=10,000;CSL=0.90DL=5000,L=707(fromearlierexample)ss=FS-1(CSL)
L=[NORMSINV(0.90)](707)=906 (thisvaluecanalsobedeterminedfromaNormalprobabilitydistributiontable)ROP=DL+ss=5000+906=590619EvaluatingSafetyInventory
GivenDesiredFillRateD=2500,sD=500,Q=10000Ifdesiredfillrateisfr=0.975,howmuchsafetyinventoryshouldbeheld?ESC=(1-fr)Q=250Solve20EvaluatingSafetyInventoryGivenFillRate(trydifferentvaluesofss)21ImpactofRequiredProductAvailabilityandUncertaintyonSafetyInventoryDesiredproductavailability(cycleservicelevelorfillrate)increases,requiredsafetyinventoryincreasesDemanduncertainty(sL)increases,requiredsafetyinventoryincreasesManagerialleverstoreducesafetyinventorywithoutreducingproductavailabilityreducesupplierleadtime,L(betterrelationshipswithsuppliers)reduceuncertaintyindemand,sL
(betterforecasts,betterinformationcollectionanduse)22ImpactofSupplyUncertaintyD:Averagedemandperperiod
D:StandarddeviationofdemandperperiodL:Averageleadtime
sL:Standarddeviationofleadtime23ImpactofSupplyUncertaintyD=2,500/day;
D=500L=7days;Q=10,000;CSL=0.90;sL=7daysDL=DL=(2500)(7)=17500ss=F-1s(CSL)sL=NORMSINV(0.90)x17550=22,49124ImpactofSupplyUncertaintySafetyinventorywhensL=0is1,695SafetyinventorywhensL=1is3,625SafetyinventorywhensL=2is6,628SafetyinventorywhensL=3is9,760SafetyinventorywhensL=4is12,927SafetyinventorywhensL=5is16,109SafetyinventorywhensL=6is19,29825ImpactofAggregation
onSafetyInventoryModelsofaggregationInformationcentralizationSpecializationProductsubstitutionComponentcommonalityPostponement26ImpactofAggregation27ImpactofAggregation
(Example11.7)CarDealer:4dealershiplocations(disaggregated)D=25cars;sD=5cars;L=2weeks;desiredCSL=0.90Whatwouldtheeffectbeonsafetystockifthe4outletsareconsolidatedinto1largeoutlet(aggregated)?Ateachdisaggregatedoutlet:ForL=2weeks,sL=7.07carsss=Fs-1(CSL)xsL=Fs-1(0.9)x7.07=9.06Eachoutletmustcarry9carsassafetystockinventory,sosafetyinventoryforthe4outletsintotalis(4)(9)=36cars28ImpactofAggregation
(Example11.7)Oneoutlet(aggregatedoption):RC=D1+D2+D3+D4=25+25+25+25=100cars/wksRC=Sqrt(52+52+52+52)=10sLC=sDC
Sqrt(L)=(10)Sqrt(2)=(10)(1.414)=14.14ss=Fs-1(CSL)xsLC=Fs-1(0.9)x14.14=18.12orabout18carsIfrdoesnotequal0(demandisnotcompletelyindependent),theimpactofaggregationisnotasgreat(Table11.3)29ImpactofAggregationIfnumberofindependentstockinglocationsdecreasesbyn,theexpectedlevelofsafetyinventorywillbereducedbysquarerootofn(squarerootlaw)Manye-commerceretailersattempttotakeadvantageofaggregation(Amazon)comparedtobricksandmortarretailers(Borders)Aggregationhastwomajordisadvantages:IncreaseinresponsetimetocustomerorderIncreaseintransportationcosttocustomerSomee-commercefirms(suchasAmazon)havereducedaggregationtomitigatethesedisadvantages30InformationCentralizationVirtualaggregationInformationsystemthatallowsaccesstocurrentinventoryrecordsinallwarehousesfromeachwarehouseMostordersarefilledfromclosestwarehouseIncaseofastockout,anotherwarehousecanfilltheorderBetterresponsiveness,lowertransportationcost,higherproductavailability,butreducedsafetyinventoryExamples:McMaster-Carr,Gap,Wal-Mart31SpecializationStockallitemsineachlocationorstockdifferentitemsatdifferentlocations?Differentproductsmayhavedifferentdemandsindifferentlocations(e.g.,snowshovels)TherecanbebenefitsfromaggregationBenefitsofaggregationcanbeaffectedby:coefficientofvariationofdemand(highercvyieldsgreaterreductioninsafetyinventoryfromcentralization)valueofitem(highvalueitemsprovidemorebenefitsfromcentralization)Table11.432ValueofAggregationatGrainger(Table11.4)33ProductSubstitutionSubstitution:useofoneproducttosatisfythedemandforanotherproductManufacturer-drivenone-waysubstitutionCustomer-driventwo-waysubstitution34ComponentCommonalityUsingcommon
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