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1、全球化趨勢下一般企業經常面對的問題,高度需求變動 訂貨前置時間長 不可靠的供應程序 大量的儲存單位(SKUs),案例,三工業的問題(前置時間) 手機的產品壽命週期：200000元 (產品壽週期需求變異) Ipad 對電子書的衝擊 (競爭需求變異) 新機推出後一個月IPhone跌2千；hTC跌5千；三星跌3千 智慧型手機可能帶來衝擊 電子書 遊戲機 隨身聽 衛星導航,Why Is Inventory Important?1,Distribution and inventory (logistics) costs are quite substantial Total U.S. Manufactu
2、ring Inventories ($m): 1992-01-31: $m 808,773 1996-08-31: $m 1,000,774 2006-05-31: $m 1,324,108 Inventory-Sales Ratio (U.S. Manufacturers): 1992-01-01: 1.56 2006-05-01: 1.25,GMs production and distribution network 20,000 supplier plants 133 parts plants 31 assembly plants 11,000 dealers Freight tran
3、sportation costs: $4.1 billion (60% for material shipments) GM inventory valued at $7.4 billion (70%WIP; Rest Finished Vehicles) Decision tool to reduce: combined corporate cost of inventory and transportation. 26% annual cost reduction by adjusting: Shipment sizes (inventory policy) Routes (transpo
4、rtation strategy),Why Is Inventory Important?2,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,The reasons of holding inventory,Unexpected changes in customer demand
5、The short life cycle of an increasing number of products. The presence of many competing 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),問題討論,小米3上市
6、，對智慧型手機市場的衝擊 3DS上市對掌上型遊戲機市場的衝擊,Goals: Reduce Cost, Improve Service Example1,By effectively managing inventory: Wal-Mart became the largest retail company utilizing efficient inventory management GM has reduced parts inventory and transportation costs by 26% annually,Goals: Reduce Cost, Improve Servi
7、ce Example2,By not managing inventory successfully In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994) In 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in invento
8、ry write downs” (WSJ, August 1993),Inventory Management vs. Demand Forecasts,Uncertain demand makes demand forecast critical for inventory related decisions: What to order? When to order? How much is the optimal order quantity? Approach includes a set of techniques INVENTORY POLICY!,Supply Chain Fac
9、tors in Inventory Policy1,Estimation of customer demand Replenishment lead time The number of different products being considered The length of the planning horizon Service level requirements,Supply Chain Factors in Inventory Policy2,Costs Order cost (or setup cost): Product cost Transportation cost
10、 Inventory holding cost (or inventory carrying cost): State taxes, property taxes, and insurance on inventories Maintenance costs Obsolescence cost Opportunity costs,2.2 Single Stage Inventory Control,Single supply chain stage Variety of techniques Economic Lot Size Model Demand Uncertainty Single P
11、eriod Models Initial Inventory Multiple Order Opportunities Continuous Review Policy Variable Lead Times Periodic Review Policy Service Level Optimization,Example,Book Store Mug Sales Demand is constant, at 20 units a week Fixed order cost of $12.00, no lead time Holding cost of 25% of inventory val
12、ue annually Mugs cost $1.00, sell for $5.00 Question How many, when to order?,2.2.1 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,Assumptions,D items per day: Constant de
13、mand rate Q items per order: Order quantities are fixed, i.e., each time the warehouse places an order, it is for Q items. K, fixed setup cost, incurred every time the warehouse places an order. h, inventory carrying cost accrued per unit held in inventory per day that the unit is held (also known a
14、s, holding cost) Lead time = 0 (the time that elapses between the placement of an order and its receipt) Initial inventory = 0 Planning horizon is long (infinite).,Deriving EOQ,Total cost at every cycle: Cycle time T =Q/D Average total cost per unit time:,EOQ:Total Cost,Total Cost,Order Cost,Holding
15、 Cost,EOQ: Optimal Order Quantity,So for our problem (Mug sales), the optimal quantity is 316,EOQ: Important Observations,Trade-off between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit time Total Cost is not particularly sen
16、sitive to the optimal order quantity,Sensitivity Analysis,Total inventory cost relatively insensitive to order quantities Actual order quantity: Q Q is a multiple b of the optimal order quantity Q*. For a given b, the quantity ordered is Q = bQ*,2.2.2 The Effect of Demand Uncertainty,Most companies
17、treat the world as if it were predictable: Production and inventory planning are based on forecasts of demand made far in advance of the selling season Companies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents re
18、ality Recent technological advances have increased the level of demand uncertainty: Short product life cycles Increasing product variety,問題,iPhone 5S 與 iPhone 5C的銷售量(參考iPhone 4？) New hTC one 的銷售量(參考蝴蝶機？),Three principles of all forecasting techniques,The forecast is always wrong It is difficult to m
19、atch supply and demand The longer the forecast horizon, the worse the forecast It is even more difficult if one needs to predict customer demand for a long period of time Aggregate forecasts are more accurate. More difficult to predict customer demand for individual SKUs Much easier to predict deman
20、d across all SKUs within one product family,2.2.3. Single Period Models,Short lifecycle products(例如，ipad) One ordering opportunity only Order quantity to be decided before demand occurs Order Quantity Demand = Dispose excess inventory Order Quantity Lose sales/profits,Single Period Models,Using hist
21、orical data identify a variety of demand scenarios determine probability each of these scenarios will occur Given a specific inventory policy determine the profit associated with a particular scenario given a specific order quantity weight each scenarios profit by the likelihood that it will occur d
22、etermine the average, or expected profit for a particular ordering quantity. Order the quantity that maximizes the average profit.,Swimsuit production,Fashion items have short life cycles, high variety of competitors (智慧型手機？) Swimsuit production New designs are completed One production opportunity B
23、ased on past sales, knowledge of the industry, and economic conditions, the marketing department has a probabilistic forecast The forecast averages about 13,000, but there is a chance that demand will be greater or less than this.,Example Swimsuit production,Demand Scenarios,Example Swimsuit product
24、ion,11%,28%,11%,22%,18%,10%,Costs,Production cost per unit (C): $80 Selling price per unit (S): $125 Salvage value per unit (V): $20 Fixed production cost (F): $100,000 Q is production quantity,Example Swimsuit production,Two Scenarios,Scenario One: Suppose you make 10,000 swimsuits and demand ends
25、up being 12,000 swimsuits. Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000 Scenario Two: Suppose you make 10,000 swimsuits and demand ends up being 8,000 swimsuits. Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = $ 140,000,Example Swimsuit production,Probability of Profitability Scen
26、arios with Production = 10,000 Units,Probability of demand being 8000 units = 11% Probability of profit of $140,000 = 11% Probability of demand being 12000 units = 28% Probability of profit of $350,000 = 28% Total profit = Weighted average of profit scenarios,Expected profit of production quantity Q
27、1,Di=the ith demand Pi=the profit of production quantity Q at demand Di,Expected profit of production quantity Q2,f(Pi)=the probability of profit P at demand Di When production quantity=Q Expect Profit of Q: E(P),Swimsuit production Solution,Find order quantity that maximizes weighted average profit
28、. Question: Will this quantity be less than, equal to, or greater than average demand?,Example Swimsuit production,Order Quantity that Maximizes Expected Profit,FIGURE 2-6: Average profit as a function of production quantity,Relationship Between Optimal Quantity and Average Demand,Compare marginal p
29、rofit of selling an additional unit and marginal cost of not selling an additional unit Marginal profit/unit = Selling Price - Variable Ordering (or, Production) Cost Marginal cost/unit = Variable Ordering (or, Production) Cost - Salvage Value If Marginal Profit Marginal Cost = Optimal Quantity Aver
30、age Demand If Marginal Profit Optimal Quantity Average Demand,For the Swimsuit Example,Average demand = 13,000 units. Optimal production quantity = 12,000 units. Marginal profit =125-80= $45 Marginal cost = 80-20=$60. Thus, Marginal Cost Marginal Profit = optimal production quantity average demand.,
31、Risk-Reward Trade-offs,Optimal production quantity maximizes average profit is about 12,000($371000) Producing 9,000 units or producing 16,000 units will lead to about the same average profit of $294,000. If we had to choose between producing 9,000 units and 16,000 units, which one should we choose?
32、,Swimsuit production Expected Profit,Example Swimsuit production,9000,Risk-Reward Tradeoffs1,FIGURE 2-7: A frequency histogram of profit,Risk-Reward Tradeoffs2,Production Quantity = 9000 units Profit is: either $200,000 with probability of about 11 % or $305,000 with probability of about 89 % Produc
33、tion quantity = 16,000 units. Distribution of profit is not symmetrical. Losses of $220,000 about 11% of the time Profits of at least $410,000 about 50% of the time With the same average profit, increasing the production quantity: Increases the possible risk Increases the possible reward,Key Insight
34、s from this Model,The optimal order quantity is not necessarily equal to average forecast demand The optimal quantity depends on the relationship between marginal profit and marginal cost As order quantity increases, average profit first increases and then decreases As production quantity increases,
35、 risk increases. In other words, the probability of large gains and of large losses increases,Example Swimsuit production,2.2.4. What If the Manufacturer Has an Initial Inventory?,Trade-off between: Using on-hand inventory to meet demand and avoid paying fixed production cost: need sufficient invent
36、ory stock Paying the fixed cost of production and not have as much inventory,Initial Inventory Solution,FIGURE 2-8: Profit and the impact of initial inventory,Example Swimsuit production,225000,Manufacturer Initial Inventory = 5,000,If nothing is produced, average profit = 225,000 (from the figure)
37、+ 5,000 x 80 = 625,000 (125 5000=625000) If the manufacturer decides to produce Production should increase inventory from 5,000 units to 12,000 units. Average profit = 371,000 (from the figure) + 5,000 80 = 771,000,Example Swimsuit production,Trade-off between Produced and not Produced,Example Swims
38、uit production,Let X is the trade-off point,No need to produce anything average profit profit achieved if we produce to increase inventory to 12,000 units If we produce, the most we can make on average is a profit of $371,000. Same average profit with initial inventory of 8,245 units and not produci
39、ng anything. If initial inventory produce to raise the inventory level to 12,000 units. If initial inventory is at least 8,245 units, we should not produce anything (s, S) policy or (min, max) policy,Manufacturer Initial Inventory = 10,000,Example Swimsuit production,(s, S) Policies,For some startin
40、g inventory levels, it is better to not start production If we start, we always produce to the same level Thus, we use an (s,S) policy. If the inventory level is below s, we produce up to S. s is the reorder point, and S is the order-up-to level The difference between the two levels is driven by the
41、 fixed costs associated with ordering, transportation, or manufacturing,2.2.5. Multiple Order Opportunities1,REASONS To balance annual inventory holding costs and annual fixed order costs. To satisfy demand occurring during lead time. To protect against uncertainty in demand.,2.2.5. Multiple Order O
42、pportunities2,TWO POLICIES Continuous review policy(持續檢視政策) inventory is reviewed continuously an order is placed when the inventory reaches a particular level or reorder point. inventory can be continuously reviewed (computerized inventory systems are used) Periodic review policy(週期檢視政策) inventory
43、is reviewed at regular intervals appropriate quantity is ordered after each review. it is impossible or inconvenient to frequently review inventory and place orders if necessary.,2.2.6. Continuous Review Policy Assumptions,Daily demand is random and follows a normal distribution. Every time the dist
44、ributor places an order from the manufacturer, the distributor pays a fixed cost, K, plus an amount proportional to the quantity ordered. Inventory holding cost is charged per item per unit time. Inventory level is continuously reviewed, and if an order is placed, the order arrives after the appropr
45、iate lead time. If a customer order arrives when there is no inventory on hand to fill the order (i.e., when the distributor is stocked out), the order is lost.(不考慮缺貨) The distributor specifies a required service level.,The (Q,R) Policy,(Q,R ) Policy: Whenever the inventory position drops below a ce
46、rtain level, R, we order to raise the inventory position to level Q. The reorder point (R) is a function of: The Lead Time Average demand Demand variability Service level,Notation,AVG = average daily demand STD = standard deviation of daily demand L = replenishment lead time in days h = holding cost
47、 of one unit for one day K = fixed cost (setup cost) = service level. This implies that the probability of stocking out is 1 - Also, the Inventory Position at any time is the actual inventory plus items already ordered, but not yet delivered.,Analysis1,The reorder point - (R) has two components: 1.
48、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 stock-outs during leadtime is 100%-SL.,Analysis2,reorder point - (R): The total order-up-to level is (S)(倉
49、庫容量): The average inventory level is:,Service Level & Safety Factor, z,z is chosen from statistical tables to ensure that the probability of stock-outs during lead time is exactly 1 - ,Inventory Level Over Time,Inventory level before receiving an order =,Inventory level after receiving an order =,Average Inventory =,FIGURE 2-9: Inventory level as a function of time in a (Q,R) policy,Continuous Review Policy Example1,A distributor of TV sets that orders from a manufacturer and sells to retailers Fixed