确定需求下的库存管理

1、1. Formulate a mathematical model describing the behavior of the inventory system. 2. Seek an optimal inventory policy with respect to this model. 2.The Basic Economic Order Quantity (EOQ) Model（经济订购批量模型经济订购批量模型）3.The EOQ model with planned shortages4.The EOQ Model with quantity discounts5.The EOQ m

2、odel with gradual replenishment 1.The EOQ Model with Quantity Discounts 2.The EOQ model with planned shortages12.1lManufacturers need inventories of the materials required to make their products. They also need inventories of the finished products awaiting shipment.lBoth wholesalers and retailers ne

3、ed to maintain inventories of goods to be available for purchase by customers. lThe costs associated with storing inventory are very large, perhaps a quarter of the value of the inventory.lJust-in-time inventory system (准时化库存系准时化库存系统统) emphasizes planning and scheduling so that the needed materials

4、arrive just-in-time for their use. JIT的思想可以概括为的思想可以概括为“在需要的时候，按需在需要的时候，按需要的量生产需要的产品要的量生产需要的产品” lManagers use scientific inventory management to improve their inventory policy for when and how much to replenish（补充）（补充） their inventory. ACT is the distributor（分销商）（分销商） of Eversafe tires. When the inve

5、ntory 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 an order wit

6、h 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) Is 1,000 the optimal amount for the order quantity? IF high inventory level THEN low order frequency IF Low inventory

7、level THEN high order frequency 12.3 库存模型中的成本构成库存模型中的成本构成 : Acquisition cost (获得成本获得成本)1.Retailers and wholesalers (such as ACT) replenish their inventory by purchasing the product. （购买购买） 2.Manufacturers (such as Eversafe) replenish their inventory of finished products for subsequent sale to their

8、customers by manufacturing more of the product involved. （自己生产自己生产） 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 cost. : Acquisition cost Notation: c=unit a

9、cquisition cost ACT Example: Purchase price=$20per tire c=$20 per tire : Acquisition cost The setup cost consists of the various administrative costs (管理成本管理成本) associated with initiating and processing the purchase order, receiving the shipment, and processing the payment. （准本成本由各种管理成本构成，包括准备和处（准本成

10、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。） : Setup cost（准备成本）（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

11、n cost for placing an order = $115 k=$115 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，比如利息）（库存占用资金的成本，比如利息） as well as the cost of s

12、pace, insurance, protection etc.: Holding cost （持有成本）（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每单位货物的年持有成本 =单位持有成本单位持有成本 ) : Holding 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

13、低客户满意度从而丢失未来的订单等。 Notation: p=annual shortage 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 ） : Shortage cost（缺货成本）（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

14、of units in inventory throughout a year 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 NO.CostUnitExample (ACT)Annual1获得成本获得成本 c$20c*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*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*每年平均

15、库存数量每年平均库存数量4缺货成本缺货成本 p$7.50p*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41iCostTCFixed cost Fixed cost-a cost that remains the same regardless of the decisions made. The annual acquisition cost will indeed be a fixed cost if the unit acquisition cost is fixed . Variable costs variable costs-those costs that are affe

16、cted 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 variable annual costs 12.31.A constant demand rate.（固定需求率）（固定需求率） D=annual demand rate =number of units being withdrawn from inventory per

17、 year2.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.不允许计划内的缺货不允许计划内的缺货. lLead time-the amount of time between the placement of the order and its receipt is referred to as the lead time.（在下订单和收（在下订单和收到货物之间的一段时间叫做提前期）到货物之间的一段时间叫做提前期） 如：如：ACT的提前期是的提前期是9个工作日。个工作日。 lReorder point-the inventory level at wh

18、ich the order is placed is called the reorder point.（下订单时的库存水平）（下订单时的库存水平） lReorder point=(daily demand)*(lead time) 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 stock） 33 Number of setups per year = ( annual

19、 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 = k(D/Q)+h(Q/2) DQK($) h ($)k (D/Q) ($)h (Q/2) ($)TVC ($)600010001154.2069021002790600015001154.204603100356060005001154.20138010502430准备成本准备成本持有成本持有成本年总成本年总成本lWith different Q, TVC is different.lThere exists optimal Q making TVC minimum.lHow to find the optimal Q?10.4 基本EOQ模型的最优库存策略l Min TVC=k(D/Q)+h(Q/2) Let lThen, Q*=hKD2022hQkDdQdTVClOriginal Q=