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1、Ch12 Inventory Management with Known Demand第10章 确定需求下的库存管理Teaching aims1.Formulate a mathematical model describing the behavior of the inventory system.2.Seek an optimal inventory policy with respect to this model.Primary coverage1.Scientific inventory managementScientific inventory management2.The
2、Basic Economic Order Quantity EOQ Model经济订购批量模型3.The EOQ model with planned shortages4.The EOQ Model with quantity discounts5.The EOQ model with gradual replenishment Focus and difficulty1.The EOQ Model with Quantity Discounts 2.The EOQ model with planned shortages12.1Scientific inventory management
3、科学库存管理12.1 Inventory Managementl Manufacturers need inventories of the materials required to make their products.They also need inventories of the finished products awaiting shipment.l Both wholesalers and retailers need to maintain inventories of goods to be available for purchase by customers.l Th
4、e costs associated with storing inventory are very large,perhaps a quarter of the value of the inventory.l Just-in-time inventory system 准时化库存系统 emphasizes planning and scheduling so that the needed materials arrive just-in-time for their use.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 12.1 Inventory Management
5、12.1 Scientific inventory managementl Managers use scientific inventory management to improve their inventory policy for when and how much to replenish补充 their inventory.12.2 A Case StudyThe Atlantic Coast Tire Corp.ACT Problem大西洋海岸轮胎公司ACT问题Background of ACT ACT is the distributor分销商 of Eversafe tir
6、es.When the inventory level of tires get low,ACT places a large order with Eversafe to replenish the inventory.Eversafe ships the tires to arrive nine working days after the placement of the order.The tires have been selling at a regular rate of about 500 per month.Managers policy has been to place
7、an order with Eversafe for 1,000 tires as needed every couple months.The order is placed just in time to have the delivery arrive as the inventory runs out.因此库存用完之前的第九天就开始订货 Background of ACTAre you sure?Is 1,000 the optimal amount for the order quantity?IF high inventory level THEN low order freque
8、ncy IF Low inventory level THEN high order frequency 12.3Cost ponents of Inventory Models库存模型中的成本构成 Cost ponent 1Cost ponent 1:Acquisition cost 获得成本1.Retailers and wholesalers such as ACT replenish their inventory by purchasing the product.购置 2.Manufacturers such as Eversafe replenish their inventor
9、y of finished products for subsequent sale to their customers by manufacturing more of the product involved.自己生产 Acquisition cost-whether a product is purchased or manufactured,there is a direct cost associated with bringing it into inventory.The direct cost of replenishing inventory is acquisition
10、cost.Cost ponent 1:Acquisition cost Notation:c=unit acquisition cost ACT Example:Purchase price=$20per tire c=$20 per tire Cost ponent 1:Acquisition cost The setup cost consists of the various administrative costs 管理成本 associated with initiating and processing the purchase order,receiving the shipme
11、nt,and processing the payment.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。Cost ponent 2:Setup cost准备成本Notation:K=setup cost ACT Example:For each order,there will be a labor cost of$90 and also associated overhead costs supervision,office space,etc.of$25.The sum of these two figures is$115.Administratio
12、n cost for placing an order=$115 k=$115 Cost ponent 2:Setup cost These costs represents the costs associated with holding the items in inventory until they are needed elsewhere.For the ACT example,this kind of cost includes the cost of capital tied up in inventory库存占用资金的成本，比方利息 as well as the cost o
13、f space,insurance,protection etc.Cost ponent 3:Holding cost 持有成本 storage cost Notation:h=annual holding cost per unit held=unit holding cost h=每单位货物的年持有成本=单位持有成本 Cost ponent 3:Holding cost storage cost 缺货成本是指当需要从库存中取货而库存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丧失未来的订单等。Notation:p=annual short
14、age cost per unit short=unit shortage cost p=每单位货物的年短缺成本=单位货物短缺成本 Cost ponent 4Cost ponent 4:Shortage cost缺货成本 Annual acquisition cost=c*number of units added to inventory per year Annual setup cost=k*number of setups per year Annual holding cost=h*average number of units in inventory throughout a y
15、ear Total inventory cost Annual shortage cost=p*average number of units short throughout a year TC=total inventory cost per year=sum of the above four annual costs Total inventory costTotal inventory costFixed cost Fixed cost-a cost that remains the same regardless of the decisions made.The annual a
16、cquisition cost will indeed be a fixed cost if the unit acquisition cost is fixed.Variable costs variable costs-those costs that are affected by the decision made-since these are the only costs that can be decreased by improving the decisions.TVC=total variable inventory cost per year=sum of the var
17、iable annual costs The Basic Economic Order Quantity EOQ Model基本经济订购批量EOQ模型12.3The assumptions of the EOQ model 1.A constant demand rate.固定需求率 D=annual demand rate=number of units being withdrawn from inventory per year2.为补充库存而订购的货物能在需要时立即到达.3.不允许方案内的缺货.Lead time 提前期l Lead time-the amount of time be
18、tween the placement of the order and its receipt is referred to as the lead time.在下订单和收到货物之间的一段时间叫做提前期 如：ACT的提前期是9个工作日。Reorder point 再订购点l Reorder point-the inventory level at which the order is placed is called the reorder point.下订单时的库存水平 l Reorder point=daily demand*lead time Safety stock l 送货的延迟将
19、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盘旋余地。这种额外的防止送货延迟的库存叫做安全库存safety stock 33EOQ model Number of setups per year=annual demand rate/order quantity=D/Q Average inventory level=max.level+Min.level/2=Q+0/2=Q/2 TVC=annual setup cost+annual holding cost=kD/Q+hQ/2 ACT Inventory CostD Q K$h$k D/Q$h Q/2$TVC$600
20、0 1000 115 4.20 690 2100 27906000 1500 115 4.20 460 3100 35606000 500 115 4.20 1380 1050 2430准备成本持有成本年总成本Summary l With different Q,TVC is different.l There exists optimal Q making TVC minimum.l How to find the optimal Q?10.4the optimal inventory policy for the basic EOQ model基本EOQ 模型的最优库存策略Optimal
21、order quantityl Min TVC=kD/Q+hQ/2 Let l Then,Q*=Result Analysisl Original Q=1000 tires,now Q*=573 l Nearly 43 percent reduction in average inventory levels.l 14 percent reduction in the total variable cost.original$2790,now$2407 准备次数由原来的6次升到了10.47Sensitivity Analysis The accuracy of optimal order qu
22、antity depends on the accuracy of the data that went into the analysis.Each of these data k,h could be off by as much as 10 percent in either direction.Setup cost:$103.50 to$126.50 Unit holding cost:$3.78 to$4.62 Q*=573The EOQ model with planned shortages有方案缺货的EOQ模型12.542The EOQ model with planned shortages TVC=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 shortages演讲完毕，谢谢观看！