Inventory Management And Risk Pooling

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Inventory Management And Risk Pooling

  1. 1. Inventory Management and Risk Pooling Chap 03 王仁宏 助理教授 國立中正大學企業管理學系 ©Copyright 2001 製商整合科技中心
  2. 2. Outline of the Presentation <ul><li>Introduction to Inventory Management </li></ul><ul><li>The Effect of Demand Uncertainty </li></ul><ul><ul><li>(s,S) Policy </li></ul></ul><ul><ul><li>Risk Pooling </li></ul></ul><ul><li>Centralized vs. Decentralized Systems </li></ul><ul><li>Practical Issues in Inventory Management </li></ul>
  3. 3. Supply Sources: plants vendors ports Regional Warehouses: stocking points Field Warehouses: stocking points Customers, demand centers sinks Production/ purchase costs Inventory & warehousing costs Transportation costs Inventory & warehousing costs Transportation costs Logistics Network
  4. 4. Case: JAM Electronics <ul><li>JAM produces about 2,500 different products in the Far East. </li></ul><ul><li>Central warehouse in Korea </li></ul><ul><li>70% service level for JAM USA </li></ul><ul><ul><li>difficulty forecasting customer demand </li></ul></ul><ul><ul><li>long lead time in supply chain to USA </li></ul></ul><ul><ul><li>large number of SKUs handled by JAM USA </li></ul></ul><ul><ul><li>low priority given the US subsidiary by headquarter in Seoul </li></ul></ul>
  5. 5. Inventory (1/2) <ul><li>Where do we hold inventory? </li></ul><ul><ul><li>Suppliers and manufacturers </li></ul></ul><ul><ul><li>warehouses and distribution centers </li></ul></ul><ul><ul><li>retailers </li></ul></ul><ul><li>Types of Inventory </li></ul><ul><ul><li>WIP </li></ul></ul><ul><ul><li>raw materials </li></ul></ul><ul><ul><li>finished goods </li></ul></ul>
  6. 6. Inventory (2/2) <ul><li>Why do we hold inventory? </li></ul><ul><ul><li>Uncertainty in customer demand </li></ul></ul><ul><ul><ul><li>short life cycle implies that historical data may not be available </li></ul></ul></ul><ul><ul><ul><li>many competing products in the marketplace </li></ul></ul></ul><ul><ul><li>Uncertainty in quantity and quality of the supply, supplier costs, and delivery times </li></ul></ul><ul><ul><li>Economies of scale offered by transportation companies </li></ul></ul>
  7. 7. Goals: Reduce Cost, Improve Service <ul><li>By effectively managing inventory: </li></ul><ul><ul><li>Xerox eliminated $700 million inventory from its supply chain </li></ul></ul><ul><ul><li>Wal-Mart became the largest retail company utilizing efficient inventory management </li></ul></ul><ul><ul><li>GM has reduced parts inventory and transportation costs by 26% annually </li></ul></ul>
  8. 8. Goals: Reduce Cost, Improve Service <ul><li>By not managing inventory successfully </li></ul><ul><ul><li>In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994) </li></ul></ul><ul><ul><li>In 1993, “Liz Claiborne said its unexpected earning decline is the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993) </li></ul></ul><ul><ul><li>In 1993, “Dell Computers predicts a loss; Stock plunges. Dell acknowledged that the company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993) </li></ul></ul>
  9. 9. Understanding Inventory <ul><li>The inventory policy is affected by: </li></ul><ul><ul><li>Demand Characteristics: known in advance or random </li></ul></ul><ul><ul><li>Lead Time </li></ul></ul><ul><ul><li>Number of Different Products Stored in the Warehouse </li></ul></ul><ul><ul><li>Length of Planning Horizon </li></ul></ul><ul><ul><li>Objectives </li></ul></ul><ul><ul><ul><li>Service level </li></ul></ul></ul><ul><ul><ul><li>Minimize costs </li></ul></ul></ul>
  10. 10. Cost Structure <ul><ul><li>Cost Structure </li></ul></ul><ul><ul><ul><li>order costs: </li></ul></ul></ul><ul><ul><ul><ul><li>cost of product </li></ul></ul></ul></ul><ul><ul><ul><ul><li>transportation costs </li></ul></ul></ul></ul><ul><ul><ul><li>holding costs: </li></ul></ul></ul><ul><ul><ul><ul><li>tax </li></ul></ul></ul></ul><ul><ul><ul><ul><li>insurance </li></ul></ul></ul></ul><ul><ul><ul><ul><li>obsolescence </li></ul></ul></ul></ul><ul><ul><ul><ul><li>opportunity cost </li></ul></ul></ul></ul>
  11. 11. EOQ: A Simple Model* <ul><li>Book Store Mug Sales </li></ul><ul><ul><li>Demand is constant, at 20 units a week </li></ul></ul><ul><ul><li>Fixed order cost of $12.00, no lead time </li></ul></ul><ul><ul><li>Holding cost of 25% of inventory value annually </li></ul></ul><ul><ul><li>Mugs cost $1.00, sell for $5.00 </li></ul></ul><ul><li>Question </li></ul><ul><ul><li>How many, when to order? </li></ul></ul>
  12. 12. EOQ: A View of Inventory* Time Inventory Order Size Note: • No Stockouts • Order when no inventory • Order Size determines policy Avg. Inven
  13. 13. EOQ: Calculating Total Cost* <ul><li>Purchase Cost Constant </li></ul><ul><li>Holding Cost: (Avg. Inven) * (Holding Cost) </li></ul><ul><li>Ordering (Setup Cost): Number of Orders * Order Cost </li></ul><ul><li>Goal: Find the Order Quantity that Minimizes These Costs: </li></ul>
  14. 14. EOQ:Total Cost* Total Cost Order Cost Holding Cost
  15. 15. EOQ: Optimal Order Quantity* <ul><li>Optimal Quantity = (2*Demand*Setup Cost)/holding cost </li></ul><ul><li>So for our problem, the optimal quantity is 316 </li></ul>
  16. 16. EOQ: Important Observations* <ul><li>Tradeoff between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit time </li></ul><ul><li>Total Cost is not particularly sensitive to the optimal order quantity </li></ul>b for b*EOQ 50% 80% 90% 100% 110% 120% 150% 200% Cost Increase 25% 2.5% 0.5% 0 0.4% 1.6% 8.0% 25%
  17. 17. The Effect of Demand Uncertainty (1/2) <ul><li>Most companies treat the world as if it were predictable: </li></ul><ul><ul><li>Production and inventory planning are based on forecasts of demand made far in advance of the selling season </li></ul></ul><ul><ul><li>Companies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents reality </li></ul></ul>
  18. 18. The Effect of Demand Uncertainty (1/2) <ul><li>Recent technological advances have increased the level of demand uncertainty: </li></ul><ul><ul><li>Short product life cycles </li></ul></ul><ul><ul><li>Increasing product variety </li></ul></ul><ul><li>The three principles of all forecasting techniques: </li></ul><ul><ul><li>Forecasting is always wrong </li></ul></ul><ul><ul><li>The longer the forecast horizon the worst is the forecast </li></ul></ul><ul><ul><li>Aggregate forecasts are more accurate </li></ul></ul>
  19. 19. Case: Swimsuit Production <ul><li>Fashion items have short life cycles, high variety of competitors </li></ul><ul><li>Swimsuit products </li></ul><ul><ul><li>New designs are completed </li></ul></ul><ul><ul><li>One production opportunity </li></ul></ul><ul><ul><li>Based on past sales, knowledge of the industry, and economic conditions, the marketing department has a probabilistic forecast </li></ul></ul><ul><ul><li>The forecast averages about 13,000, but there is a chance that demand will be greater or less than this. </li></ul></ul>
  20. 20. Swimsuit Demand Scenarios
  21. 21. Swimsuit Costs <ul><li>Production cost per unit (C): $80 </li></ul><ul><li>Selling price per unit (S): $125 </li></ul><ul><li>Salvage value per unit (V): $20 </li></ul><ul><li>Fixed production cost (F): $100,000 </li></ul><ul><li>Q is production quantity, D: demand </li></ul><ul><li>Profit = Revenue - Variable Cost - Fixed Cost + Salvage </li></ul>
  22. 22. Swimsuit Scenarios <ul><li>Scenario One: </li></ul><ul><ul><li>Suppose you make 12,000 jackets and demand ends up being 13,000 jackets. </li></ul></ul><ul><ul><li>Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000 </li></ul></ul><ul><li>Scenario Two: </li></ul><ul><ul><li>Suppose you make 12,000 jackets and demand ends up being 11,000 jackets. </li></ul></ul><ul><ul><li>Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) = $ 335,000 </li></ul></ul>
  23. 23. Swimsuit Best Solution <ul><li>Find order quantity that maximizes weighted average profit. </li></ul><ul><li>Question: Will this quantity be less than, equal to, or greater than average demand? </li></ul>
  24. 24. What to Make? <ul><li>Average demand is 13,100 </li></ul><ul><li>Look at marginal cost Vs. marginal profit </li></ul><ul><ul><li>if extra jacket sold, profit is 125-80 = 45 </li></ul></ul><ul><ul><li>if not sold, cost is 80-20 = 60 </li></ul></ul><ul><li>So we will make less than average </li></ul>
  25. 25. Swimsuit Expected Profit
  26. 26. Swimsuit Expected Profit
  27. 27. Swimsuit Expected Profit
  28. 28. Swimsuit : Important Observations <ul><li>Tradeoff between ordering enough to meet demand and ordering too much </li></ul><ul><li>Several quantities have the same average profit </li></ul><ul><li>Average profit does not tell the whole story </li></ul><ul><li>Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer? </li></ul>
  29. 29. Probability of Outcomes
  30. 30. Key Points from this Model <ul><li>The optimal order quantity is not necessarily equal to average forecast demand </li></ul><ul><li>The optimal quantity depends on the relationship between marginal profit and marginal cost </li></ul><ul><li>As order quantity increases, average profit first increases and then decreases </li></ul><ul><li>As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases </li></ul>
  31. 31. Initial Inventory <ul><li>Suppose that one of the jacket designs is a model produced last year. </li></ul><ul><li>Some inventory is left from last year </li></ul><ul><li>Assume the same demand pattern as before </li></ul><ul><li>If only old inventory is sold, no setup cost </li></ul><ul><li>Question: If there are 7000 units remaining, what should SnowTime do? What should they do if there are 10,000 remaining? </li></ul>
  32. 32. Initial Inventory and Profit
  33. 33. Initial Inventory and Profit
  34. 34. Initial Inventory and Profit
  35. 35. Initial Inventory and Profit
  36. 36. (s, S) Policies <ul><li>For some starting inventory levels, it is better to not start production </li></ul><ul><li>If we start, we always produce to the same level </li></ul><ul><li>Thus, we use an (s,S) policy. If the inventory level is below s , we produce up to S . </li></ul><ul><li>s is the reorder point, and S is the order-up-to level </li></ul><ul><li>The difference between the two levels is driven by the fixed costs associated with ordering, transportation, or manufacturing </li></ul>
  37. 37. A Multi-Period Inventory Model <ul><li>Often, there are multiple reorder opportunities </li></ul><ul><li>Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory </li></ul>
  38. 38. Case Study: Electronic Component Distributor <ul><li>Electronic Component Distributor </li></ul><ul><li>Parent company HQ in Japan with world-wide manufacturing </li></ul><ul><li>All products manufactured by parent company </li></ul><ul><li>One central warehouse in U.S. </li></ul>
  39. 39. Case Study:The Supply Chain
  40. 40. Demand Variability: Example 1
  41. 41. Demand Variability: Example 1
  42. 42. Reminder: The Normal Distribution Average = 30 Standard Deviation = 5 Standard Deviation = 10
  43. 43. The distributor holds inventory to: <ul><li>Satisfy demand during lead time </li></ul><ul><li>Protect against demand uncertainty </li></ul><ul><li>Balance fixed costs and holding costs </li></ul>
  44. 44. The Multi-Period Inventory Model <ul><li>Normally distributed random demand </li></ul><ul><li>Fixed order cost plus a cost proportional to amount ordered. </li></ul><ul><li>Inventory cost is charged per item per unit time </li></ul><ul><li>If an order arrives and there is no inventory, the order is lost </li></ul><ul><li>The distributor has a required service level. </li></ul><ul><li>Intuitively, what will a good policy look like? </li></ul>
  45. 45. A View of (s, S) Policy Time Inventory Level S s 0 Lead Time Lead Time Inventory Position
  46. 46. The (s,S) Policy <ul><li>(s, S) Policy: Whenever the inventory position drops below a certain level, s, we order to raise the inventory position to level S. </li></ul><ul><li>The reorder point is a function of: </li></ul><ul><ul><li>Lead Time </li></ul></ul><ul><ul><li>Average demand </li></ul></ul><ul><ul><li>Demand variability </li></ul></ul><ul><ul><li>Service level </li></ul></ul>
  47. 47. Notation <ul><li>AVG = average daily demand </li></ul><ul><li>STD = standard deviation of daily demand </li></ul><ul><li>LT = lead time in days </li></ul><ul><li>h = holding cost of one unit for one day </li></ul><ul><li>SL = service level (for example, 95%). </li></ul><ul><li>Also, the Inventory Position at any time is the actual inventory plus items already ordered, but not yet delivered. </li></ul>
  48. 48. Analysis <ul><li>The reorder point has two components: </li></ul><ul><ul><li>To account for average demand during lead time: LT  AVG </li></ul></ul><ul><ul><li>To account for deviations from average (we call this safety stock ) </li></ul></ul><ul><ul><li>z  STD   LT </li></ul></ul><ul><ul><li>where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is 100%-SL. </li></ul></ul>
  49. 49. Example <ul><li>The distributor has historically observed weekly demand of: AVG = 44.6 STD = 32.1 lead time is 2 weeks, </li></ul><ul><li>desired service level SL = 97% </li></ul><ul><li>Average demand during lead time is: 44.6  2 = 89.2 </li></ul><ul><li>Safety Stock is: 1.88  32.1   2 = 85.3 </li></ul><ul><li>Reorder point is thus 175, or about 3.9 weeks of supply at warehouse and in the pipeline </li></ul>
  50. 50. Model Two : Fixed Costs* <ul><li>In addition to previous costs, a fixed cost K is paid every time an order is placed. </li></ul><ul><li>We have seen that this motivates an (s,S) policy, where reorder point and order quantity are different. </li></ul><ul><li>The reorder point will be the same as the previous model, in order to meet meet the service requirement: s = LT  AVG + z  AVG   L </li></ul><ul><li>What about the order up to level? </li></ul>
  51. 51. Model Two : The Order-Up-To Level* <ul><li>We have used the EOQ model to balance fixed, variable costs: Q=  (2  K  AVG)/h </li></ul><ul><li>If there was no variability in demand, we would order Q when inventory level was at LT  AVG . Why? </li></ul><ul><li>There is variability, so we need safety stock z  AVG *  LT </li></ul><ul><li>The total order-up-to level is: S=max{Q, LT  AVG}+ z  AVG *  LT </li></ul>
  52. 52. Model Two : Example* <ul><li>Consider the previous example, but with the following additional info: </li></ul><ul><ul><li>fixed cost of $4500 when an order is placed </li></ul></ul><ul><ul><li>$250 product cost </li></ul></ul><ul><ul><li>holding cost 18% of product </li></ul></ul><ul><li>Weekly holding cost: h = (.18  250) / 52 = 0.87 </li></ul><ul><li>Order quantity Q=  (2  4500  44.6) / 0.87 = 679 </li></ul><ul><li>Order-up-to level: s + Q = 85 + 679 = 765 </li></ul>
  53. 53. Risk Pooling <ul><li>Consider these two systems: </li></ul>Market Two Supplier Warehouse One Warehouse Two Market One Market Two Supplier Warehouse Market One LT = 1 week 1500 products, 10000 accounts
  54. 54. Risk Pooling <ul><li>For the same service level, which system will require more inventory? Why? </li></ul><ul><li>For the same total inventory level, which system will have better service? Why? </li></ul><ul><li>What are the factors that affect these answers? </li></ul>
  55. 55. Risk Pooling Example <ul><li>Compare the two systems: </li></ul><ul><ul><li>two products </li></ul></ul><ul><ul><li>maintain 97% service level </li></ul></ul><ul><ul><li>$60 order cost </li></ul></ul><ul><ul><li>$0.27 weekly holding cost </li></ul></ul><ul><ul><li>$1.05 transportation cost per unit in decentralized system, $1.10 in centralized system </li></ul></ul><ul><ul><li>1 week lead time </li></ul></ul>
  56. 56. Risk Pooling Example
  57. 57. Risk Pooling Example Centralized Warehouse Product AVG STD CV s S Avg. Inven. % Dec. Market 1 A 39.3 13.2 .34 65 158 91 Market 2 A 38.6 12.0 .31 62 154 88 Market 1 B 1.125 1.36 1.21 4 26 15 Market 2 B 1.25 1.58 1.26 5 27 15 Centralized A 77.9 20.7 .27 118 226 132 26% B 2.375 1.9 .81 6 37 20 33%
  58. 58. Risk Pooling: Important Observations <ul><li>Centralizing inventory control reduces both safety stock and average inventory level for the same service level. </li></ul><ul><li>This works best for </li></ul><ul><ul><li>High coefficient of variation, which reduces required safety stock. </li></ul></ul><ul><ul><li>Negatively correlated demand. Why? </li></ul></ul><ul><li>What other kinds of risk pooling will we see? </li></ul>
  59. 59. Risk Pooling: Types of Risk Pooling* <ul><li>Risk Pooling Across Markets </li></ul><ul><li>Risk Pooling Across Products </li></ul><ul><li>Risk Pooling Across Time </li></ul><ul><ul><li>Daily order up to quantity is: </li></ul></ul><ul><ul><ul><li>LT  AVG + z  AVG   LT </li></ul></ul></ul>10 12 11 13 14 15 Demands Orders
  60. 60. To Centralize or not to Centralize <ul><li>What is the effect on: </li></ul><ul><ul><li>Safety stock? </li></ul></ul><ul><ul><li>Service level? </li></ul></ul><ul><ul><li>Overhead? </li></ul></ul><ul><ul><li>Lead time? </li></ul></ul><ul><ul><li>Transportation Costs? </li></ul></ul>
  61. 61. <ul><li>Centralized Decision </li></ul>Centralized Systems* Supplier Warehouse Retailers
  62. 62. Centralized Distribution Systems* <ul><li>Question: How much inventory should management keep at each location? </li></ul><ul><li>A good strategy: </li></ul><ul><ul><li>The retailer raises inventory to level S r each period </li></ul></ul><ul><ul><li>The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to S s </li></ul></ul><ul><ul><li>If there is not enough inventory in the warehouse to meet all demands from retailers, it is allocated so that the service level at each of the retailers will be equal. </li></ul></ul>
  63. 63. Inventory Management: Best Practice <ul><li>Periodic inventory review policy (59%) </li></ul><ul><li>Tight management of usage rates, lead times and safety stock (46%) </li></ul><ul><li>ABC approach (37%) </li></ul><ul><li>Reduced safety stock levels (34%) </li></ul><ul><li>Shift more inventory, or inventory ownership, to suppliers (31%) </li></ul><ul><li>Quantitative approaches (33%) </li></ul>
  64. 64. Inventory Turnover Ratio
  65. 65. Memo

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