确定需求下的库存管理

Ch12

InventoryManagementwithKnownDemand第10章确定需求下的库存管理Teachingaims1.Formulateamathematicalmodeldescribingthebehavioroftheinventorysystem.

2.Seekanoptimalinventorypolicywithrespecttothismodel.

PrimarycoverageScientificinventorymanagementTheBasicEconomicOrderQuantity(EOQ)Model（经济订购批量模型）TheEOQmodelwithplannedshortagesTheEOQModelwithquantitydiscountsTheEOQmodelwithgradualreplenishment

Focusanddifficulty1.TheEOQModelwithQuantityDiscounts

2.TheEOQmodelwithplannedshortages§12.1Scientificinventorymanagement科学库存管理12.1InventoryManagementManufacturersneedinventoriesofthematerialsrequiredtomaketheirproducts.Theyalsoneedinventoriesofthefinishedproductsawaitingshipment.Bothwholesalersandretailersneedtomaintaininventoriesofgoodstobeavailableforpurchasebycustomers.

Thecostsassociatedwithstoringinventoryareverylarge,perhapsaquarterofthevalueoftheinventory.Just-in-timeinventorysystem(准时化库存系统)emphasizesplanningandschedulingsothattheneededmaterialsarrivejust-in-timefortheiruse.

JIT的思想可以概括为“在需要的时候，按需要的量生产需要的产品”

12.1InventoryManagement12.1ScientificinventorymanagementManagersusescientificinventorymanagementtoimprovetheirinventorypolicyforwhenandhowmuchtoreplenish（补充）theirinventory.

§12.2ACaseStudyTheAtlanticCoastTireCorp.(ACT)Problem大西洋海岸轮胎公司（ACT）问题BackgroundofACTACTisthedistributor（分销商）

ofEversafetires.Whentheinventoryleveloftiresgetlow,ACTplacesalargeorderwithEversafetoreplenishtheinventory.Eversafeshipsthetirestoarrivenineworkingdaysaftertheplacementoftheorder.

Thetireshavebeensellingataregularrateofabout500permonth.Manager’spolicyhasbeentoplaceanorderwithEversafefor1,000tiresasneededeverycouplemonths.Theorderisplacedjustintimetohavethedeliveryarriveastheinventoryrunsout.(因此库存存用完之之前的第第九天就就开始订订货)BackgroundofACTAreyousure?Is1,000theoptimalamountfortheorderquantity?IFhighinventorylevelTHENloworderfrequencyIFLowinventorylevelTHENhighorderfrequency§12.3CostComponentsofInventoryModels库存模型中的的成本构成Costcomponent1:Acquisitioncost(获得成本)Retailersandwholesalers(suchasACT)replenishtheirinventorybypurchasingtheproduct.（购买）Manufacturers(suchasEversafe)replenishtheirinventoryoffinishedproductsforsubsequentsaletotheircustomersbymanufacturingmoreoftheproductinvolved.（自己生产）Acquisitioncost---whetheraproductispurchasedormanufactured,thereisadirectcostassociatedwithbringingitintoinventory.Thedirectcostofreplenishinginventoryisacquisitioncost.Costcomponent1:AcquisitioncostNotation:c=unitacquisitioncostACTExample:Purchaseprice=$20pertirec=$20pertireCostcomponent1:AcquisitioncostThesetupcostconsistsofthevariousadministrativecosts(管理成本)associatedwithinitiatingandprocessingthepurchaseorder,receivingtheshipment,andprocessingthepayment.（准本成本本由各种管管理成本构构成，包括括准备和处处理购货单单、接收运运抵的货物物和处理付付款手续等等。）Costcomponent2:Setupcost（准备成本本）Notation:K=setupcostACTExample:Foreachorder,therewillbealaborcostof$90andalsoassociatedoverheadcosts(supervision,officespace,etc.)of$25.Thesumofthesetwofiguresis$115.Administrationcostforplacinganorder=$115k=$115Costcomponent2:SetupcostThesecostsrepresentsthecostsassociatedwithholdingtheitemsininventoryuntiltheyareneededelsewhere.FortheACTexample,thiskindofcostincludesthecostofcapitaltiedupininventory（库存占用用资金的成成本，比如如利息）aswellasthecostofspace,insurance,protectionetc.Costcomponent3:Holdingcost（持有成本本）(storagecost)Notation:h=annualholdingcostperunitheld=unitholdingcost(h=每单位货物物的年持有有成本=单位持有成成本)Costcomponent3:Holdingcost(storagecost)缺货成本是指当需要要从库存中中取货而库库存中已无无货时发生生的成本。。不能立即满满足客户订订单的一种种可能的结结果是丢了了这笔生意意，或者降降低客户满满意度从而而丢失未来来的订单等等。Notation:p=annualshortagecostperunitshort=unitshortagecost（p=每单位货物物的年短缺缺成本=单位货物短短缺成本））Costcomponent4:Shortagecost（缺货成本本）Annualacquisitioncost=c*numberofunitsaddedtoinventoryperyearAnnualsetupcost=k*numberofsetupsperyearAnnualholdingcost=h*averagenumberofunitsininventorythroughoutayearTotalinventorycostAnnualshortagecost=p*averagenumberofunitsshortthroughoutayearTC=totalinventorycostperyear=sumoftheabovefourannualcostsTotalinventorycostNO.CostUnitExample(ACT)Annual1获得成本c$20c*每年加入库存的数量2准备成本k$115K*每年准备的次数3持有成本h$4.20h*每年平均库存数量4缺货成本p$7.50p*每年平均缺货数量5库存成本TotalinventorycostFixedcostFixedcost---acostthatremainsthesameregardlessofthedecisionsmade.Theannualacquisitioncostwillindeedbeafixedcostiftheunitacquisitioncostisfixed.Variablecostsvariablecosts---thosecoststhatareaffectedbythedecisionmade---sincethesearetheonlycoststhatcanbedecreasedbyimprovingthedecisions.TVC=totalvariableinventorycostperyear=sumofthevariableannualcostsTheBasicEconomicOrderQuantity(EOQ)Model基本本经经济济订订购购批批量量（（EOQ）模模型型§12.3TheassumptionsoftheEOQmodelAconstantdemandrate.（固固定定需需求求率率））D=annualdemandrate=numberofunitsbeingwithdrawnfrominventoryperyear为补充库存而而订购的货物物能在需要时时立即到达.不允许计划内内的缺货.Leadtime（提前期）Leadtime---theamountoftimebetweentheplacementoftheorderanditsreceiptisreferredtoastheleadtime.（在下订单和和收到货物之之间的一段时时间叫做提前前期）如：ACT的提前期是9个工作日。Reorderpoint（再订购点））Reorderpoint---theinventorylevelatwhichtheorderisplacediscalledthereorderpoint.（下订单时的的库存水平））Reorderpoint=(dailydemand)*(leadtime)Safetystock送货的延迟将将导致库存短短缺，因此库库存经理有时时会提高一点点在订购点以以在送货延迟迟时有些回旋旋余地。这种种额外的防止止送货延迟的的库存叫做安全库存（safetystock）33EOQmodelNumberofsetupsperyear=(annualdemandrate)/(orderquantity)=D/QAverageinventorylevel=(max.level+Min.level)/2=(Q+0)/2=Q/2TVC=annualsetupcost+annualholdingcost=k(D/Q)+h(Q/2)ACTInventoryCostDQK($)h($)k(D/Q)($)h(Q/2)($)TVC($)600010001154.2069021002790600015001154.204603100356060005001154.20138010502430准备成本持有成本年总成本SummaryWithdifferentQ,TVCisdifferent.ThereexistsoptimalQmakingTVCminimum.HowtofindtheoptimalQ?§10.4theoptimalinventorypolicyforthebasicEOQmodel基本EOQ模型的最优库库存策略OptimalorderquantityMinTVC=k(D/Q)+h(Q/2)LetThen,Q*=ResultAnalysisOriginalQ=1000tires,