【正文】 tion Inventory Management 59 The (Q,R) Policy (Q,R ) Policy: Whenever the inventory position drops below a certain level, R, we order to raise the inventory position to level Q. The reorder point is a function of: – The Lead Time – Average demand – Demand variability – Service level Inventory Management 60 Notation AVG = average daily demand STD = standard deviation of daily demand L = replenishment lead time in days h = holding cost of one unit for one day K = fixed cost (setup cost) SL = service level (for example, 95%). This implies that the probability of stocking out is 100%SL (for example, 5%) Also, the Inventory Position at any time is the actual inventory plus items already ordered, but not yet delivered. 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(shí)則不然。在許多實(shí)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 。在此情況下，再訂購點(diǎn) R的計(jì)算如下： 其中 AVG AVGL表示平均前置時間內(nèi)的平均需求，而 為平均前置時間內(nèi)的平均需求標(biāo)準(zhǔn)差。 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 time (A) Inventory Management 70 Periodic Review Policy2 安全存量為 目標(biāo)訂貨水準(zhǔn) 而進(jìn)貨的前一刻，只剩安全存量 因此平均存貨水準(zhǔn)是此兩值的平均值，即等於： z S T D L?? ? ?()??? ? ? ? ? ? ?L A V G z S T D L Az S T D L?? ? ?2AVG z S T D L? ?? ? ? ? ?(訂購量 =保護(hù)期間的預(yù)期需求 +安全存量 再訂購點(diǎn)時的現(xiàn)有數(shù)量 ) Inventory Management 71 Example (continue) Assume that the distributor places an order for TV set every three weeks. Lead time is two weeks. Average demand during that period is ?5= Safety stock, for 97percent service level, is Average inventory level: 1 . 9 3 2 . 0 8 5 1 3 6 . 3? ? ?3 4 4 . 5 8 1 . 9 3 2 . 0 8 5 2 0 3 . 1 72? ? ? ? ?Inventory Management 72 Risk Pooling ― Question 1 Consider these two systems: Market Two Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One Inventory Management 73 Risk Pooling ― Question 2 For the same service level, which system will require more inventory? Why? For the same total inventory level, which system will have better service? Why? What are the factors that affect these answers? Inventory Management 74 Risk Pooling Example1 Compare the two systems: – two products – maintain 97% service level – $60 order cost – $ weekly holding cost – $ transportation cost per unit in decentralized system, $ in centralized system – 1 week lead time Inventory Management 75 Risk Pooling Example2 Week 1 2 3 4 5 6 7 8P rod A ,M arket 133 45 37 38 55 30 18 58P rod A ,M arket 246 35 41 40 26 48 18 55P rod B,M arket 10 2 3 0 0 1 3 0P rod uct B,M arket 22 4 0 0 3 1 0 0Inventory Management 76 Risk Pooling Example3 Ware hou se Product AVG STD CV Mar ket 1 A 0 .34 Mar ket 2 A 0 .31 Mar ket 1 B Mar ket 2 B Inventory Management 77 Risk Pooling Example4 Warehouse Product AVG STD CV R Q Avg. Inven. % Dec. Market 1 A 0 . . 34 65 132 91 Market 2 A 0 . . 31 62 131 88 Market 1 B 4 25 14 Market 2 B 5 2 4 15 Cent. A 0 .27 118 186 132 2 6% Cent B 0 .81 6 3 3 20 31 % Inventory Management 78 Risk poling Demand variability is reduce if one aggregates demand across locations because, as we aggregate demand across different locations, it bees more likely that high demand form one customer will be offset by low demand from another. The reduction in variability allows a decrease in safety stock and therefore reduces average inventory. Inventor