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1、Ch12 Inventory Management with Known Demand第第10章章 确定需求下的库存管理确定需求下的库存管理Teaching aims1.1.Formulate Formulate a a mathematical mathematical model model describing describing the behavior of the inventory system.the behavior of the inventory system.2.2.Seek Seek an an optimal optimal inventory inventory
2、 policy policy with with respect respect to this model.to this model.Primary coveragePrimary coverage1.1.Scientific inventory managementScientific inventory managementScientific inventory managementScientific inventory management2.2.The Basic Economic Order Quantity(EOQ)The Basic Economic Order Quan
3、tity(EOQ)ModelModel（经济订购批量模型经济订购批量模型）3.3.The EOQ model with planned shortagesThe EOQ model with planned shortages4.4.The EOQ Model with quantity discountsThe EOQ Model with quantity discounts5.5.The EOQ model with gradual replenishmentThe EOQ model with gradual replenishment Focus and difficultyFocu
4、s and difficulty1.The EOQ Model with Quantity Discounts1.The EOQ Model with Quantity Discounts 2.The EOQ model with planned shortages2.The EOQ model with planned shortages12.112.1Scientific inventory management科学库存管理科学库存管理12.1 Inventory Management12.1 Inventory ManagementlManufacturers Manufacturers
5、 need need inventories inventories of of the the materials materials required required to to make make their their products.products.They They also also need need inventories inventories of of the the finished finished products awaiting shipment.products awaiting shipment.lBoth Both wholesalers whol
6、esalers and and retailers retailers need need to to maintain maintain inventories inventories of of goods goods to to be be available for purchase by customers.available for purchase by customers.lThe The costs costs associated associated with with storing storing inventory inventory are are very ve
7、ry large,large,perhaps perhaps a a quarter quarter of of the the value of the inventory.value of the inventory.lJust-in-time Just-in-time inventory inventory system system(准准时时化化库库存存系系统统)emphasizes emphasizes planning planning and and scheduling scheduling so so that that the the needed needed mater
8、ials materials arrive arrive just-in-time just-in-time for their use.for their use.JITJIT的的思思想想可可以以概概括括为为“在在需需要要的的时时候候，按按需需要要的量生产需要的产品的量生产需要的产品”12.1 Inventory Management12.1 Inventory Management12.1 Scientific inventory 12.1 Scientific inventory managementmanagementlManagers Managers use use scienti
9、fic scientific inventory inventory management management to to improve improve their their inventory inventory policy policy for for when when and and how much to replenishhow much to replenish（补充）（补充）their inventory.their inventory.12.2 A Case Study12.2 A Case StudyThe Atlantic Coast Tire Corp.(ACT
10、)Problem大西洋海岸轮胎公司（大西洋海岸轮胎公司（ACT）问题）问题Background of ACTBackground of ACTACT is the ACT is the distributordistributor（分销商）（分销商）of Eversafe of Eversafe tires.When the inventory level of tires get tires.When the inventory level of tires get low,ACT places a large order with Eversafe low,ACT places a lar
11、ge order with Eversafe to replenish the inventory.Eversafe ships to replenish the inventory.Eversafe ships the tires to arrive the tires to arrive nine working daysnine working days after the after the placement of the order.placement of the order.The tires have been selling at a The tires have been
12、 selling at a regular rateregular rate of about 500 per month.Managers policy of about 500 per month.Managers policy has been to place an order with Eversafe for has been to place an order with Eversafe for 1,000 tires as needed every couple months.1,000 tires as needed every couple months.The order
13、 is placed just in time to have the The order is placed just in time to have the delivery arrive as the inventory runs out.(delivery arrive as the inventory runs out.(因此因此库存用完之前的第九天就开始订货库存用完之前的第九天就开始订货)Background of ACTBackground of ACTAre you sure?Are you sure?Is 1,000 the optimal amount for the Is
14、 1,000 the optimal amount for the order order quantityquantity?IF IF high inventory level high inventory level THENTHEN low order low order frequencyfrequency IF IF Low inventory level Low inventory level THENTHEN high order high order frequencyfrequency 12.312.3 Cost Components of Inventory Models库
15、存模型中的成本构成库存模型中的成本构成 Cost component 1Cost component 1Cost component 1Cost component 1:Acquisition cost(:Acquisition cost(获得成本获得成本)1.1.RetailersRetailers and and wholesalerswholesalers(such as ACT)(such as ACT)replenish their inventory by purchasing the replenish their inventory by purchasing the prod
16、uct.product.（购买购买）2.2.ManufacturersManufacturers(such as Eversafe)(such as Eversafe)replenish their inventory of finished replenish their inventory of finished products for subsequent sale to their products for subsequent sale to their customers by manufacturing more of the customers by manufacturin
17、g more of the product involved.product involved.（自己生产自己生产）Acquisition costAcquisition cost-whether a product is-whether a product is purchased or manufactured,there is a direct purchased or manufactured,there is a direct cost associated with cost associated with bringing it into bringing it into inv
18、entory.inventory.The direct cost of replenishing inventory is The direct cost of replenishing inventory is acquisition costacquisition cost.Cost component 1:Acquisition cost:Acquisition cost NotationNotation:c c=unit acquisition cost=unit acquisition cost ACT ExampleACT Example:Purchase price=$20per
19、 tirePurchase price=$20per tirec=$20 per tirec=$20 per tire Cost component 1:Acquisition cost:Acquisition costThe The setup costsetup cost consists of the various consists of the various administrative costsadministrative costs(管理成本管理成本)associated with)associated with initiating and processing the p
20、urchase order,initiating and processing the purchase order,receiving the shipment,and processing the receiving the shipment,and processing the payment.payment.（准本成本由各种管理成本构成，包括准备和处（准本成本由各种管理成本构成，包括准备和处理购货单、接收运抵的货物和处理付款手续等。）理购货单、接收运抵的货物和处理付款手续等。）Cost component 2:Setup cost:Setup cost（准备成（准备成本）本）Notat
21、ionNotation:K K=setup cost=setup cost ACT ExampleACT Example:For each order,there will be a labor cost of$90 For each order,there will be a labor cost of$90 and also associated overhead costs(supervision,and also associated overhead costs(supervision,office space,etc.)of$25.The sum of these two offi
22、ce space,etc.)of$25.The sum of these two figures is$115.figures is$115.Administration cost for placing an order=Administration cost for placing an order=$115k=$115k=$115 Cost component 2:Setup costThese costs represents the costs associated These costs represents the costs associated with holding th
23、e items in inventory until they with holding the items in inventory until they are needed elsewhere.are needed elsewhere.For the ACT example,this kind of cost For the ACT example,this kind of cost includes the includes the cost of capital tied up in cost of capital tied up in inventoryinventory（库存占用
24、资金的成本，比如利息）（库存占用资金的成本，比如利息）as well as the cost of space,insurance,as well as the cost of space,insurance,protection etc.protection etc.Cost component 3:Holding cost:Holding cost（持有成（持有成本）本）(storage cost)(storage cost)NotationNotation:h h=annual holding cost per unit held=annual holding cost per unit
25、 held =unit holding cost =unit holding cost (h=(h=每单位货物的年持有成本每单位货物的年持有成本 =单位持有成本单位持有成本 )Cost component 3:Holding cost:Holding cost (storage cost)(storage cost)缺货成本缺货成本是指当需要从库存中取货而库存是指当需要从库存中取货而库存中已无货时发生的成本。中已无货时发生的成本。不能立即满足客户订单的一种可能的结果是丢了这笔生意，或者降低客户满意度从而丢失未来的订单等。NotationNotation:p p=annual shortage
26、cost per unit short=annual shortage cost per unit short =unit shortage cost =unit shortage cost （p=每单位货物的年短缺成本 =单位货物短缺成本 ）Cost component 4Cost component 4:Shortage cost:Shortage cost（缺货成本）（缺货成本）Annual acquisition costAnnual acquisition cost=c*number of units =c*number of units added to inventory per
27、 yearadded to inventory per year Annual setup costAnnual setup cost=k*number of setups per =k*number of setups per yearyear Annual holding costAnnual holding cost=h*average number of =h*average number of units in inventory throughout a yearunits in inventory throughout a year Total inventory costTot
28、al inventory costAnnual shortage costAnnual shortage cost=p*average number of =p*average number of units short throughout a yearunits short throughout a year TC=total inventory cost per yearTC=total inventory cost per year =sum of the above four annual costs =sum of the above four annual costs Total
29、 inventory costTotal inventory costNO.CostUnitExample(ACT)Annual1获得成本获得成本 c$20c*c*每年加入库存的数量每年加入库存的数量2准备成本准备成本 k$115K*K*每年准备的次数每年准备的次数3持有成本持有成本 h$4.20h*h*每年平均库存数量每年平均库存数量4缺货成本缺货成本 p$7.50p*p*每年平均缺货数量每年平均缺货数量5库存成本库存成本Total inventory costFixed costFixed costFixed cost-a cost that remains the same Fixed
30、cost-a cost that remains the same regardless of the decisions made.regardless of the decisions made.The annual acquisition cost will indeed be a The annual acquisition cost will indeed be a fixed cost fixed cost if the unit acquisition cost is fixedif the unit acquisition cost is fixed.Variable cost
31、sVariable costsvariable costs-those costs that are affected variable costs-those costs that are affected by the decision made-since these are the by the decision made-since these are the only costs that can be decreased by improving only costs that can be decreased by improving the decisions.the dec
32、isions.TVC=total variable inventory cost per yearTVC=total variable inventory cost per year =sum of the variable annual costs =sum of the variable annual costs The Basic Economic Order Quantity(EOQ)Model基本经济订购批量（基本经济订购批量（EOQEOQ）模型）模型12.3The assumptions of the EOQ modelThe assumptions of the EOQ mode
33、l 1.1.A constant demand rate.A constant demand rate.（固定需求率）（固定需求率）D D=annual demand rate=annual demand rate =number of units being withdrawn from =number of units being withdrawn from inventory per yearinventory per year2.2.为补充库存而订购的货物能在需要时立即到达为补充库存而订购的货物能在需要时立即到达.3.3.不允许计划内的缺货不允许计划内的缺货.Lead timeLea
34、d time（提前期）（提前期）lLead time-the amount of time between Lead time-the amount of time between the placement of the order and its receipt the placement of the order and its receipt is referred to as the lead time.is referred to as the lead time.（在下订单和（在下订单和收到货物之间的一段时间叫做提前期）收到货物之间的一段时间叫做提前期）如：如：ACTACT的提前
35、期是的提前期是9 9个工作日。个工作日。Reorder pointReorder point（再（再订购点）点）lReorder point-the inventory level at Reorder point-the inventory level at which the order is placed is called which the order is placed is called the reorder point.the reorder point.（下订单时的库存水（下订单时的库存水平）平）lReorder point=(daily demand)*(lead Reo
36、rder point=(daily demand)*(lead time)time)Safety stockSafety stock l送货的延迟将导致库存短缺，因此库存经理有送货的延迟将导致库存短缺，因此库存经理有时会提高一点在订购点以在送货延迟时有些回时会提高一点在订购点以在送货延迟时有些回旋余地。这种额外的防止送货延迟的库存叫做旋余地。这种额外的防止送货延迟的库存叫做安全库存安全库存（safety stocksafety stock）33EOQ modelEOQ modelNumber of setups per yearNumber of setups per year =(annua
37、l demand rate)/(order quantity)=(annual demand rate)/(order quantity)=D/Q =D/Q Average inventory levelAverage inventory level =(max.level+Min.level)/2 =(max.level+Min.level)/2 =(Q+0)/2=Q/2 =(Q+0)/2=Q/2 TVC=annual setup cost+annual holding costTVC=annual setup cost+annual holding cost =k(D/Q)+h(Q/2)=
38、k(D/Q)+h(Q/2)ACT Inventory CostD DQ QK($)K($)h($)h($)k(D/Q)k(D/Q)($)($)h h(Q/2)(Q/2)($)($)TVC($)TVC($)6000600010001000 1151154.204.2069069021002100279027906000600015001500 1151154.204.204604603100310035603560600060005005001151154.204.20138013801050105024302430准备成本准备成本持有成本持有成本年总成本年总成本Summary lWith di
39、fferent Q,TVC is different.With different Q,TVC is different.lThere exists optimal Q making TVC There exists optimal Q making TVC minimum.minimum.lHow to find the optimal Q?How to find the optimal Q?10.410.4 the optimal inventory the optimal inventory policy for the basic EOQ policy for the basic EO
40、Q modelmodel基本EOQ模型的最优库存策略Optimal order quantityl Min TVC=k(D/Q)+h(Q/2)Min TVC=k(D/Q)+h(Q/2)Let Let lThen,Then,Q*=Q*=Result AnalysislOriginal Q=1000 tires,now Q*=573Original Q=1000 tires,now Q*=573 lNearly Nearly 43 percent43 percent reduction in average reduction in average inventory levels.invento
41、ry levels.l14 percent14 percent reduction in the total variable reduction in the total variable cost.cost.（original$2790,now$2407original$2790,now$2407）准备次数由原来的准备次数由原来的6 6次升到了次升到了10.4710.47Sensitivity AnalysisSensitivity AnalysisThe The accuracyaccuracy of optimal order quantity of optimal order qua
42、ntity depends on the depends on the accuracyaccuracy of the data that of the data that went into the analysis.went into the analysis.Each of these data(k,h)could be off by as Each of these data(k,h)could be off by as much as much as 10 percent10 percent in either direction.in either direction.Setup
43、costSetup cost:$103.50 to$126.50:$103.50 to$126.50 Unit holding costUnit holding cost:$3.78 to$4.62:$3.78 to$4.62 Q*=573Q*=573The EOQ model with planned shortages有计划缺货的有计划缺货的EOQEOQ模型模型12.542The EOQ model with planned shortagesThe EOQ model with planned shortagesTVC=年准备成本+年持有成本+年缺货成本 年准备成本=年持有成本=h(库存水平为正时的平均库存水平)(正库存水平所占时间比例)=年缺货成本=p(当缺货出现时的平均缺货水平)(缺货所占的时间比例)=The EOQ model with planned shortagesThe EOQ model with planned shortages演讲完毕，谢谢观看！