【正文】 Inventory Management 61 Analysis1 The reorder point (R) has two ponents: – 1. To account for average demand during lead time: – 2. To account for deviations from average (we call this safety stock) where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is 100%SL. L A V G?z S T D L??Inventory Management 62 Analysis2 reorder point (R): The total orderupto level is (S): The average inventory level is: L A V G Z S T D L? ? ? ?2 K A V GQh?? S Q s??2? ? ?Q Z S TD LInventory Management 63 Example1 The distributor has historically observed weekly demand of: AVG = STD = Replenishment lead time is 2 weeks, and desired service level SL = 97% (z=) Average demand during lead time is: ? 2 = Safety Stock is: ? ? 21/2 = Reorder point is thus 175, or about weeks of supply at warehouse and in the pipeline Month Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sales 200 152 100 221 287 176 151 198 246 309 98 156 Inventory Management 64 Example2 The cost of TV:250 Annual inventory holding cost: of the product cost Fixed ordering cost: 4500 Weekly inventory holding cost: – Therefore, Q=679 Orderupto level thus equals: – Reorder Point + Q = 176+679 = 855 Average inventory level: – (679/2)+=426 Inventory Management 65 變動的前置時間與需求 1 在許多情況下，運(yùn)送至倉庫的運(yùn)輸前置時間被假設(shè)是固定的，而且是預(yù)先知道，實則不然。 期初存貨 為 0。 存貨持有成本 h， 由 每天 所持有的每單位存貨產(chǎn)生。 每次訂購量為固定，以 Q表示 (Q的數(shù)量保持固定 )，亦即每次倉庫訂一次貨為 Q個數(shù)量。Inventory Management 1 Case study ― JAM Electronics: Service Level Crisis JAM USA’s Problem: low service level Reasons and issues – Difficulty forecasting customer demand – Long lead time in the supply chain – The large number of SKUs( stock keeping unit) handled – The low priority given the . subsidiary by headquarters in Seoul Inventory Management 2 全球化趨勢下一般企業(yè)經(jīng)常面對的問題 高度求變動 訂貨前置時間長 不可靠的供應(yīng)程序 大量的儲存單位 (SKUs) Inventory Management 3 Outline Introduction to Inventory Management The Effect of Demand Uncertainty – (s,S) Policy – Periodic Review Policy – Supply Contracts – Risk Pooling Centralized vs. Decentralized Systems Practical Issues in Inventory Management Inventory Management 4 Inventory Where do we hold inventory? –Suppliers and manufacturers –warehouses and distribution centers –retailers Types of Inventory – WIP (work in process) – raw materials – finished goods Inventory Management 5 The reasons of holding inventory Unexpected changes in customer demand – The short life cycle of an increasing number of products. – The presence of many peting products in the marketplace. Uncertainty in the quantity and quality of the supply, supplier costs and delivery times. Delivery Lead Time, Capacity limitations Economies of scale (transportation cost) Inventory Management 6 Goals: Reduce Cost, Improve Service ― Example 1 By effectively managing inventory: – Xerox eliminated $700 million inventory from its supply chain – WalMart became the largest retail pany utilizing efficient inventory management – GM has reduced parts inventory and transportation costs by 26% annually Inventory Management 7 Goals: Reduce Cost, Improve Service ― Example 2 By not managing inventory successfully – In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994) – In 1993, “Liz Claiborne said its unexpected earning decline is the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993) – In 1993, “Dell Computers predicts a loss。 Stock plunges. Dell acknowledged that the pany was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993) Inventory Management 8 Key factors affecting Inventory policy Customer demand Characteristics Replenishment lead Time Number of Products Service level requirements Cost Structure Objectives – Service level – Minimize costs Inventory Management 9 Cost Structure Order costs – Fixed – Variable Holding Costs – Insurance – Maintenance and Handling – Taxes – Opportunity Costs – Obsolescence Inventory Management 10 Example Book Store Mug Sales – Demand is constant, at 20 units a week – Fixed order cost of $, no lead time – Holding cost of 25% of inventory value annually – Mugs cost $, sell for $ Question – How many, when to order? Inventory Management 11 Economic Lot Size Model (EOQ) (Ford W. Harris, 1915) Time Inventory Order Size Note: ? No Stockouts ? Order when no inventory ? Order Size determines policy Avg. Inven Cycle Time =T Inventory Management 12 Assumptions of EOQ model 每天 的需求為 D， 且 保持穩(wěn)定。 固定設(shè)置成本 (setup cost) ， K， 於每次倉庫訂貨時發(fā)生。 前置時間 ，從下訂單到收到貨品間的時間，為 0。 計劃期間為長期的。在許多實際情況下，運(yùn)送至倉庫的前置時間，必須假設(shè)為常態(tài)機(jī)率分配，平均前置時間以 AVGL表示及標(biāo)準(zhǔn)差以 STDL表示 。 2 2 2 ? ? ? ? ? ?R A V G A V G L z A V G L S T D A V G S T D L2 2 2A V G L S T D A V G S T D L? ? ?Inventory Management 66 變動的前置時間與需求 2 因此，應(yīng)維持之安全存貨為： 如前述，訂購量上限為安全存貨加上 Q和前置時間內(nèi)平均需求的最大值，也就是： 2 2 2? ? ? ?z A V G L S T D A V G S T D L2 2 2S Q A V G A V G L z A V G L S T D A V G S T D L? ? ? ? ? ? ?Inventory Management 67 Periodic Review Suppose the distributor places orders every month What policy should the distributor use? What about the fixed cost? Inventory Management 68 BaseStock Policy Inventory Level Time Basestock Level 0 Inventory Position r r L L L Inventory Management 69 Periodic Review Policy1 Each review echelon, inventory position is raised to the basestock level. The basestock level includes three ponents: – Average demand during (r +L) days (the time until the next order arrives – Safety stock during that time – Amount on hand at order