数据、模型与决策（第12版）课件 第16章 库存管理

InventoryManagementChapter16Copyright©2016PearsonEducation,Inc.

ElementsofInventoryManagementInventoryControlSystemsEconomicOrderQuantityModelsTheBasicEOQModelTheEOQModelwithNon-InstantaneousReceiptTheEOQModelwithShortagesEOQAnalysiswithQMforWindowsEOQAnalysiswithExcelandExcelQMQuantityDiscountsReorderPointDeterminingSafetyStockbyUsingServiceLevelsOrderQuantityforaPeriodicInventorySystemChapterTopicsCopyright©2016PearsonEducation,Inc.

Inventoryisastockofitemskeptonhandusedtomeetcustomerdemand..Alevelofinventoryismaintainedthatwillmeetanticipateddemand.Ifdemandnotknownwithcertainty,safety(buffer)stocksarekeptonhand.Additionalstocksaresometimesbuiltuptomeetseasonalorcyclicaldemand.Largeamountsofinventorysometimespurchasedtotakeadvantageofdiscounts.ElementsofInventoryManagementRoleofInventory(1of2)Copyright©2016PearsonEducation,Inc.

In-processinventoriesmaintainedtoprovideindependencebetweenoperations.Rawmaterialsinventorykepttoavoiddelaysincaseofsupplierproblems.Stockoffinishedpartskepttomeetcustomerdemandineventofworkstoppage.Ingeneralinventoryservestodecoupleconsecutivesteps.ElementsofInventoryManagementRoleofInventory(2of2)Copyright©2016PearsonEducation,Inc.

Inventoryexiststomeetthedemandsofcustomers.Customerscanbeexternal(purchasersofproducts)orinternal(workersusingmaterial).Managementneedsanaccurateforecastofdemand.Itemsthatareusedinternallytoproduceafinalproductarereferredtoasdependentdemanditems.Itemsthatarefinalproductsdemandedbyanexternalcustomerareindependentdemanditems.ElementsofInventoryManagementDemandCopyright©2016PearsonEducation,Inc.

Carryingcosts-Costsofholdingitemsinstorage.Varywiththelevelofinventoryandsometimeswiththelength oftimeheld.Includefacilityoperatingcosts,recordkeeping,interest,etc.Assignedonaperunitbasispertimeperiod,oras percentageofaverageinventoryvalue(usually estimatedas10%to40%).ElementsofInventoryManagementInventoryCosts(1of3)Copyright©2016PearsonEducation,Inc.

Orderingcosts

-costsofreplenishingthestockofinventory.Expressedasthedollaramountperorder,independentof ordersize.Varywiththenumberofordersmade.Includepurchaseorders,shipping,handling,inspection,etc.ElementsofInventoryManagementInventoryCosts(2of3)Copyright©2016PearsonEducation,Inc.

Shortage(stockout)costs-Associatedwithinsufficientinventory,i.e.,whencustomerdemandcannotbemetResultinpermanentlossofsalesandprofitsforitemsnotonhand.Sometimespenaltiesinvolved;ifcustomerisinternal,workdelayscouldresult.ElementsofInventoryManagementInventoryCosts(3of3)Copyright©2016PearsonEducation,Inc.

Aninventorycontrolsystemcontrolsthelevelofinventorybydetermininghowmuch

(replenishmentlevel)andwhentoorder.Twobasictypesofsystems-continuous(fixed-orderquantity)andperiodic(fixed-time).Inacontinuoussystem,anorderisplacedforthesameconstantamountwheninventorydecreasestoaspecifiedlevel.Inaperiodicsystem,anorderisplacedforavariableamountafteraspecifiedperiodoftime.InventoryControlSystemsCopyright©2016PearsonEducation,Inc.

Acontinualrecordofinventorylevelismaintained.Wheneverinventorydecreasestoapredeterminedlevel,i.e.,thereorderpoint,anorderisplacedforafixedamount

toreplenishthestock.Thefixedamountistermedtheeconomicorderquantity,whosemagnitudeissetatalevelthatminimizesthetotalinventorycarrying,ordering,andshortagecosts.Becauseofcontinualmonitoring,managementisalwaysawareofthestatusoftheinventorylevelandcriticalparts,butthissystemisrelativelyexpensivetomaintain.InventoryControlSystemsContinuousInventorySystemsCopyright©2016PearsonEducation,Inc.

Inventoryonhandiscountedatspecifictimeintervalsandanorderisplacedthatbringstheinventoryuptoaspecifiedlevel.Inventoryisnotmonitoredbetweencountsandthesystemisthereforelesscostlytotrackandkeepaccountof.Resultsinlessdirectcontrolbymanagementandthusgenerallyhigherlevelsofinventorytoguardagainststockouts.Systemrequiresaneworderquantityeachtimeanorderisplaced.Usedinsmallerretailstores,drugstores,grocerystoresandoffices.InventoryControlSystemsPeriodicInventorySystemsCopyright©2016PearsonEducation,Inc.

Economicorderquantity,oreconomiclotsize,isthequantityorderedwheninventorydecreasestothereorderpoint.Amountisdeterminedusingtheeconomicorderquantity(EOQ)model.EOQmodel’spurposeistodeterminetheoptimalordersizethatwillminimizetotalinventorycosts.Threemodelversionstobediscussed:BasicEOQmodelEOQmodelwithoutinstantaneousreceiptEOQmodelwithshortagesEconomicOrderQuantityModelsCopyright©2016PearsonEducation,Inc.

Aformulafordeterminingtheoptimalordersizethatminimizesthesumofcarryingcostsandorderingcosts.Simplifyingassumptionsandrestrictions: Demandisknownwithcertaintyandisrelativelyconstantovertime.Noshortagesareallowed.Leadtimeforthereceiptofordersisconstant.Theorderquantityisreceivedallatonceandinstantaneously.EconomicOrderQuantityModelsBasicEOQModel(1of2)Copyright©2016PearsonEducation,Inc.

Figure16.1TheinventoryordercycleEconomicOrderQuantityModelsBasicEOQModel(2of2)Copyright©2016PearsonEducation,Inc.

Carryingcostisusuallyexpressedonaperunitbasisoftime,traditionallyoneyear.Annualcarryingcostequalsthecarryingcostperunitperyeartimestheaverageinventorylevel: Carryingcostperunitperyear=Cc Averageinventory=Q/2 Annualcarryingcost=CcQ/2. BasicEOQModelCarryingCost(1of3)Copyright©2016PearsonEducation,Inc.

Figure16.2InventoryusageEconomicOrderQuantityModelsBasicEOQModel(2of3)Copyright©2016PearsonEducation,Inc.

Figure16.3LevelsofQBasicEOQModelCarryingCost(3of3)Overthetimeperiodt,thesixpointsfrom5,000to0aresummedanddividedby6.Copyright©2016PearsonEducation,Inc.

Figure16.4AverageinventoryBasicEOQModelCarryingCost(2of2)Copyright©2016PearsonEducation,Inc.

Totalannualorderingcostequalsthecostperorder(Co)timesthenumberofordersperyear.Numberofordersperyear,withknownandconstantdemand,D,isD/Q,whereQistheordersize: Annualorderingcost=CoD/Q OnlyvariableisQ,CoandDareconstantparameters.Relativemagnitudeoftheorderingcostisdependentonordersize. BasicEOQModelOrderingCostCopyright©2016PearsonEducation,Inc.

Totalannualinventorycostissumoforderingandcarryingcost:BasicEOQModelTotalInventoryCost(1of2)Copyright©2016PearsonEducation,Inc.

Figure16.5TheEOQcostmodelBasicEOQModelTotalInventoryCost(2of2)Copyright©2016PearsonEducation,Inc.

EOQoccurswherethetotalcostcurveisataminimumvalueandthecarryingcostequalstheorderingcost: TheEOQmodelisrobustbecauseQisasquarerootanderrorsintheestimationofD,CcandCoaredampened.BasicEOQModelEOQandMinimumTotalCostCopyright©2016PearsonEducation,Inc.

I-75CarpetDiscountStore,SuperShagcarpetsales. Giventhefollowingdata,determinethenumberoforderstobemadeannuallyandthetimebetweenordersgiventhestoreisopeneverydayexceptSunday,ThanksgivingDay,andChristmasDay.BasicEOQModelExample(1of2)Copyright©2016PearsonEducation,Inc.

BasicEOQModelExample(2of2)Copyright©2016PearsonEducation,Inc.

Foranytimeperiodunitofanalysis,EOQisthesame.ShagCarpetexampleonmonthlybasis:BasicEOQModelEOQAnalysisOverTime(1of2)Copyright©2016PearsonEducation,Inc.

BasicEOQModelEOQAnalysisOverTime(2of2)Copyright©2016PearsonEducation,Inc.

Inthenon-instantaneousreceiptmodel

theassumptionthatordersarereceivedallatonceisrelaxed.(Alsoknownasgradualusageorproductionlotsizemodel.)Theorderquantityisreceivedgraduallyovertimeandinventoryisdrawnonatthesametimeitisbeingreplenished.EOQModelNon-InstantaneousReceiptDescription(1of2)Copyright©2016PearsonEducation,Inc.

Figure16.6TheEOQmodelwithnon-instantaneousorderreceiptEOQModelNon-InstantaneousReceiptDescription(2of2)Copyright©2016PearsonEducation,Inc.

Non-InstantaneousReceiptModelModelFormulation(1of2)Copyright©2016PearsonEducation,Inc.

Non-InstantaneousReceiptModelModelFormulation(2of2)Copyright©2016PearsonEducation,Inc.

Non-InstantaneousReceiptModelExample(1of2)SuperShagcarpetmanufacturingfacility:Copyright©2016PearsonEducation,Inc.

Non-InstantaneousReceiptModelExample(2of2)Copyright©2016PearsonEducation,Inc.

EOQModelwithShortagesDescription(1of2)IntheEOQmodelwithshortages,theassumptionthatshortagescannotexistisrelaxed.ShortagesarerepresentedbySinthismodelAssumesthatunmetdemandcanbebackorderedwithalldemandeventuallysatisfied.Hence,maximuminventoryleveldoesnotreachQ,butinsteadreaches(Q-S)Copyright©2016PearsonEducation,Inc.

Figure16.7TheEOQmodelwithshortagesEOQModelwithShortagesDescription(2of2)Copyright©2016PearsonEducation,Inc.

EOQModelwithShortagesModelFormulation(1of2)Copyright©2016PearsonEducation,Inc.

Figure16.8Costmodelwithshortages

EOQModelwithShortagesModelFormulation(2of2)Copyright©2016PearsonEducation,Inc.

EOQModelwithShortagesModelFormulation(1of3)SupposeourbelovedI-75CarpetDiscountStoreallowsshortages;theshortagecostCsis$2/yardperyear.Copyright©2016PearsonEducation,Inc.

EOQModelwithShortagesModelFormulation(2of3)Copyright©2016PearsonEducation,Inc.

EOQModelwithShortagesModelFormulation(3of3)Exhibit16.1EOQAnalysiswithQMforWindowsCopyright©2016PearsonEducation,Inc.

Exhibit16.2EOQAnalysiswithExcelandExcelQM(1of2)OptimalQ=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))=D10*(1-D7/D8)Copyright©2016PearsonEducation,Inc.

EOQAnalysiswithExcelandExcelQM(2of2)Exhibit16.3Copyright©2016PearsonEducation,Inc.

Pricediscountsareoftenofferedifapredeterminednumberofunitsisorderedorwhenmaterialsareorderedinahighvolume.BasicEOQmodelusedwithpurchasepriceadded: where:P=perunitpriceoftheitem D=annualdemandQuantitydiscountsareevaluatedundertwodifferentscenarios: Withconstantcarryingcosts WithcarryingcostsasapercentageofpurchasepriceQuantityDiscountsCopyright©2016PearsonEducation,Inc.

QuantityDiscountswithConstantCarryingCostsAnalysisApproachTheoptimalordersizeisthesameregardlessofthediscountprice.Thetotalcostwiththeoptimalordersizemustbecomparedwithanylowertotalcostwithadiscountpricetodeterminewhichisthelesser.Copyright©2016PearsonEducation,Inc.

Universitybookstore:ForthefollowingdiscountscheduleofferedbyComptek,shouldthebookstorebuyatthediscounttermsororderthebasicEOQordersize?Determinetheoptimalordersizeandtotalcost:QuantityDiscountswithConstantCarryingCostsExample(1of2)Copyright©2016PearsonEducation,Inc.

Computetotalcostattheeligiblediscountprice($1,100):Comparewiththetotalcostofanordersizeof90atthebargainpriceof$900:Because$194,105<$233,784,themaximumdiscountpriceshouldbetakenand90unitsordered.QuantityDiscountswithConstantCarryingCostsExample(2of2)Copyright©2016PearsonEducation,Inc.

UniversityBookstoreexample,butadifferentoptimalordersizeforeachpricediscount.OptimalordersizeandtotalcostaredeterminedusingthebasicEOQmodelwithnoquantitydiscount.Thiscostisthencomparedwithvariousdiscountquantityordersizestodeterminetheminimumcostorder.ThismustbecomparedwiththeEOQ-determinedordersizeforaspecificdiscountprice.Data: Co=$2,500 D=200computersperyearQuantityDiscountswithCarryingCostsPercentageofPriceExample(1of3)Copyright©2016PearsonEducation,Inc.

ComputeoptimumordersizeforthepurchasepricewithoutadiscountandCc=$210:Computethenewordersize:

Quantity Price CarryingCost 0-49 $1,400 1,400(.15)=$210 50-89 1,100 1,100(.15)=165 90+ 900 900(.15)=135QuantityDiscountswithCarryingCostsPercentageofPriceExample(2of3)Copyright©2016PearsonEducation,Inc.

Computeminimumtotalcost:Comparewiththetotalcostofadiscountpriceof$900andanorderquantityof90:Optimalordersizecomputedas:Sincethisordersizeislessthan90units,itisnotfeasible,thusoptimalordersizeis90units.QuantityDiscountswithCarryingCostsPercentageofPriceExample(3of3)Copyright©2016PearsonEducation,Inc.

Exhibit16.4QuantityDiscountModelSolutionwithQMforWindowsCopyright©2016PearsonEducation,Inc.

QuantityDiscountModelSolutionwithQMforWindowsExhibit16.5=IF(D10>=B10,D10,B10)=(D4*D5/E10)+(D3*E10/2)+C10*D5Copyright©2016PearsonEducation,Inc.

Thereorderpoint

istheinventorylevelatwhichaneworderisplaced.Anordermustbemadewhilethereisenoughstockinplacetocoverdemandduringleadtime.Formulation:R=dLwhered=demandratepertimeperiodL=leadtimeForCarpetDiscountstoreproblem: R=dL=(10,000/311)(10)=321.54yardsReorderPoint(1of4)Copyright©2016PearsonEducation,Inc.

Figure16.9ReorderpointandleadtimeReorderPoint(2of4)Copyright©2016PearsonEducation,Inc.

Figure16.10Inventorymodelwithuncertaindemand

ReorderPoint(3of4)Theinventorylevelmightbedepletedatslowerorfasterrateduringleadtime.Whendemandisuncertain,safetystockisaddedasahedgeagainststockouts.Copyright©2016PearsonEducation,Inc.

Figure16.11InventorymodelwithsafetystockReorderPoint(4of4)Copyright©2016PearsonEducation,Inc.

DeterminingSafetyStocksUsingServiceLevelsTheservicelevel

istheprobabilitythattheamountofinventoryonhandissufficienttomeetdemandduringleadtime(theprobabilityastockoutwillnotoccur).Thehighertheprobabilityinventorywillbeonhand,themorelikelycustomerdemandwillbemet.Aservicelevelof90%meansthereisa.90probabilitythatdemandwillbemetduringleadtimeand.10probabilityofastockout.Copyright©2016PearsonEducation,Inc.

ReorderPointwithVariableDemand(1of2)Copyright©2016PearsonEducation,Inc.

Figure16.12ReorderpointforaservicelevelReorderPointwithVariableDemand(2of2)Copyright©2016PearsonEducation,Inc.

I-75CarpetDiscountStoreSuperShagcarpet.Forthefollowingdata,determinethereorderpointandsafetystockforaservicelevelof95%.ReorderPointwithVariableDemandExampleCopyright©2016PearsonEducation,Inc.

Exhibit16.6DeterminingReorderPointwithExcelCopyright©2016PearsonEducation,Inc.

ReorderPointwithVariableLeadTimeForconstantdemandandvariableleadtime:Copyright©2016PearsonEducation,Inc.

ReorderPointwithVariableLeadTimeExampleTheI-75CarpetDiscountStorerevisited:Copyright©2016PearsonEducation,Inc.

Whenbothdemandandleadtimearevariable:ReorderPointVariableDemandandLeadTimeCopyright©2016PearsonEducation,Inc.

CarpetDiscountStore:ReorderPointVariableDemandandLeadTimeExampleCopyright©2016PearsonEducation,Inc.

OrderQuantityforaPeriodicInventorySystemAperiodic,orfixed-timeperiodinventorysystem

isoneinwhichtimebetweenordersisconstantandtheordersizevaries.Vendorsmakeperiodicvisits,andthestockofinventoryiscounted.Anorderisplaced,ifnecessary,tobringtheinventorylevelbackuptosomedesiredlevel.Inventoryisnotmonitoredbetweenvisits.Attimes,inventorycanbeexhaustedpriortothevisit,resultinginastockout.Largersafetystocksaregenerallyrequiredfortheperiodicinventorysystem.Copyright©2016PearsonEducation,Inc.

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