1、Ch12 Inventory Management with Known Demand第10章 確定需求下的庫存管理.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 coverageScientific inventory managementThe Basic Economic Order Quantity

2、 (EOQ) Model經(jīng)濟(jì)訂購批量模型The EOQ model with planned shortagesThe EOQ Model with quantity discountsThe EOQ model with gradual replenishment .Focus and difficulty1.The EOQ Model with Quantity Discounts 2.The EOQ model with planned shortages.12.1Scientific inventory management科學(xué)庫存管理.12.1 Inventory Managemen

3、tManufacturers need inventories of the materials required to make their products. They also need inventories of the finished products awaiting shipment.Both wholesalers and retailers need to maintain inventories of goods to be available for purchase by customers. .The costs associated with storing i

4、nventory are very large, perhaps a quarter of the value of the inventory.Just-in-time inventory system (準(zhǔn)時化庫存系統(tǒng)) emphasizes planning and scheduling so that the needed materials arrive just-in-time for their use. JIT的思想可以概括為“在需求的時候，按需求的量消費(fèi)需求的產(chǎn)品 12.1 Inventory Management.12.1 Scientific inventory mana

5、gementManagers use scientific inventory management to improve their inventory policy for when and how much to replenish補(bǔ)充 their inventory. .12.2 A Case StudyThe Atlantic Coast Tire Corp. (ACT) Problem大西洋海岸輪胎公司ACT問題.Background of ACTACT is the distributor分銷商 of Eversafe tires. When the inventory leve

6、l 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 with Eversaf

7、e 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.(因此庫存用完之前的第九天就開場訂貨) Background of ACT.Are you sure?Is 1,000 the optimal amount for the order quantity? IF high inventory level THEN low order frequency IF Low inven

8、tory level THEN high order frequency .12.3 Cost Components of Inventory Models庫存模型中的本錢構(gòu)成. Cost component 1: Acquisition cost (獲得本錢)Retailers and wholesalers (such as ACT) replenish their inventory by purchasing the product. 購買 Manufacturers (such as Eversafe) replenish their inventory of finished pr

9、oducts for subsequent sale to their customers by manufacturing more of the product involved. 本人消費(fèi) .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. Cost c

10、omponent 1: Acquisition cost. Notation: c=unit acquisition cost ACT Example: Purchase price=$20per tirec=$20 per tire Cost component 1: Acquisition cost.The setup cost consists of the various administrative costs (管理本錢) associated with initiating and processing the purchase order, receiving the ship

11、ment, and processing the payment. 準(zhǔn)本本錢由各種管理本錢構(gòu)成，包括預(yù)備和處置購貨單、接納運(yùn)抵的貨物和處置付款手續(xù)等。 Cost component 2: Setup cost預(yù)備本錢.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

12、 is $115. Administration cost for placing an order = $115k=$115 Cost component 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庫存占用資金

13、的本錢，比如利息 as well as the cost of space, insurance, protection etc.Cost component 3: Holding cost 持有本錢 (storage cost).Notation: h=annual holding cost per unit held =unit holding cost (h=每單位貨物的年持有本錢 =單位持有本錢 ) Cost component 3: Holding cost (storage cost). 缺貨本錢是指當(dāng)需求從庫存中取貨而庫存中已無貨時發(fā)生的本錢。 不能立刻滿足客戶訂單的一種能夠的結(jié)

14、果是丟了這筆生意，或者降低客戶稱心度從而喪失未來的訂單等。Notation: p=annual shortage cost per unit short =unit shortage cost p=每單位貨物的年短缺本錢 =單位貨物短缺本錢 Cost component 4: Shortage cost缺貨本錢 .Annual acquisition cost = c*number of units added to inventory per year Annual setup cost = k*number of setups per year Annual holding cost =

15、h*average number of units in inventory throughout a year 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 cost.NO.CostUnitExample (ACT)Annual1獲得成本 c$20c*每年加入庫存的數(shù)量2準(zhǔn)備成本 k

16、$115K*每年準(zhǔn)備的次數(shù)3持有成本 h$4.20h*每年平均庫存數(shù)量4缺貨成本 p$7.50p*每年平均缺貨數(shù)量5庫存成本Total inventory cost.Fixed costFixed 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 costsvariable costs-those c

17、osts 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 variable annual costs .The Basic Economic Order Quantity (EOQ) Model根本經(jīng)濟(jì)訂購批量EOQ模型12.3.The assumptions of the EOQ model A

18、 constant demand rate.固定需求率 D=annual demand rate =number of units being withdrawn from inventory per year為補(bǔ)充庫存而訂購的貨物能在需求時立刻到達(dá). 不允許方案內(nèi)的缺貨. .Lead time提早期Lead time-the amount of time between the placement of the order and its receipt is referred to as the lead time.在下訂單和收到貨物之間的一段時間叫做提早期 如：ACT的提早期是9個任務(wù)日

19、。 .Reorder point再訂購點(diǎn)Reorder point-the inventory level at which the order is placed is called the reorder point.下訂單時的庫存程度 Reorder point=(daily demand)*(lead time) .Safety stock 送貨的延遲將導(dǎo)致庫存短缺，因此庫存經(jīng)理有時會提高一點(diǎn)在訂購點(diǎn)以在送貨延遲時有些盤旋余地。這種額外的防止送貨延遲的庫存叫做平安庫存safety stock .33.EOQ modelNumber of setups per year = ( annu

20、al 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) .ACT Inventory CostDQK($)h ($)k (D/Q) ($)h (Q/2) ($)TVC ($)600010001154.2069021002790600015001154.204603100356060005001154.20138010502430預(yù)備本錢持有本錢年總本錢.Summary With different Q, TVC is different.There exists optimal Q making TVC minimum.How to find the optimal Q?.10.4 the optimal inventory policy for the basic EOQ model根本EOQ模型的最優(yōu)庫存戰(zhàn)略.Optimal order quantity Min TVC=k(D/Q)+h(Q/2) Let Then, Q*=.Result AnalysisOr