Chapter10InentoryModels1INVENTORYMODELS管理科学英文版教学课件

1、Management Science:Operations Research(OR)Chapter 10INVENTORY MODELS4/13/20221Lecture10.1 Basic Concepts in Inventory PlanninglOur inventory models will concern just a single item for which the demand per period (year) is D units. lThe number of items in stock is depleted over time by the demand, bu

2、t also increased from time to time b y instantaneous additions Q called orders, resulting in sudden jumps in the inventory level.4/13/2022Lecture2lThe time between two consecutive replenishments is the inventory cycle length tc. lThe lead time tL is the time between the placement and arrival of an o

3、rder4/13/2022Lecture3lOrder size Q and the lead time tL will usually be the same for all orders. lThe cost for carrying one unit of inventory for one period is called the unit carrying or holding cost ch. lOrdering cost co is the cost of placing an order and having it delivered, considered independe

4、nt of the size of the order.4/13/2022Lecture4lFor some inventory models, backorders are not allowed, otherwise the unit shortage cost cs is the cost charged to be out of stock by one unit for one period of time.4/13/2022Lecture510.2 The Economic Order Quantity (EOQ) ModelAssumptions of the basic EOQ

5、 model are: lInventory is single unperishable good, lthe demand rate is constant over time, lthe same amount is ordered each time, lthere are no quantity discounts, lstockouts are not allowed, lthe planning horizon is infinite.4/13/2022Lecture6The famous sawtooth pattern is shown in the figure below

6、.4/13/2022Lecture7Ordering costslif we place N orders, each of size Q, the total amount ordered is NQ = Dlthe number of orders per period(year) N = D/Qltotal annual ordering costs coN = coD/Q. 4/13/2022Lecture8Holding costlFor holding cost, we compute the total area under the sawtooth curve, which c

7、an be seen to be Q, so that the total annual holding cost is ch(Q).4/13/2022Lecture9Total inventory costlThe total inventory costs TC per period are TC = coD/Q + chQTC : Total CostQ: order quantity Q*:optimal order quantity D: annual demand quantityCo: Unit ordering costCh :Unit Holding cost4/13/202

8、2Lecture104/13/2022Lecture114/13/2022Lecture124/13/2022Lecture13lThe value Q* that minimizes total inventory cost TC, is the optimum order quantity ExampleDemand of D = 800 car battery chargers per year, co = $100 and the holding cost is ch = $4 per charger per year. l(1) What is the optimal order s

9、ize?l(2) What is the optimal number of orders per year?l(3) What is the optimal total ordering cost?4/13/2022Lecture14Solutionl(1) l(2) The optimal number of orders per year N* = D/Q* = 800/200 = 4 orders optimal inventory cycle length is = Q*/D = 200/800 = year = 3 months. (3) TC= TC is $800.The to

10、tal ordering cost is 4(100) = $400, half of the total cost; the other half is total holding cost.4/13/2022Lecture15*ct800640000410080022hocDchocDcQ2* 10.3 The EOQ with Positive Lead TimelAssume a positive lead time tL elapses from the moment an order is placed until it has arrived. lThe optimum orde

11、r quantity Q* still applies.lThe decision on when to order.lWe need to determine the order time in terms of the reorder point R: when IO decreases to the level R, an order is placed, which will arrive after a delay of tL time units, just when the inventory level reaches zero.4/13/2022Lecture16lCase

12、1: . Demand during lead time is tLD, so that if an order of size Q* is placed when the inventory level reaches R* = tLD , the replenishment arrives exactly when inventory on hand has been depleted.4/13/2022Lecture17lCase 2: tL tc* Demand during the lead time is still tLD, but since tL tc* , it follo

13、ws that tLD tc* D =Q*, the arrival of an order will occur during a subsequent inventory cycle & not during the cycle in which it was ordered, 4/13/2022Lecture18Optimal Reorder Point4/13/2022Lecture19*QttDtRcLLlExample: Consider the example above with D = 800, co = $100, and ch = $4, for which we have obtained an optimal order quantity of Q* = 200 at an annual cost o