1. Chapter 3 Inventory Management, Supply Contracts and Risk Pooling Qi Xu Professor of Donghua University Tel: 021-62378860 E-mail: xuqi@dhu.edu.cn

2. Outline of the Presentation 3.1 Introduction to Inventory Management 3.2 Single Warehouse Inventory (1) EOQ (2) Demand Forecast (3) Supply Contracts (4) A multi-Period Inventory Model (5) Periodic Review Policy 3.3 Risk Pooling 3.4 Centralized vs. Decentralized Systems 3.5 Managing Inventory in the SC 3.6 Practical Issues in Inventory Management

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

4. Case: JAM Electronics: Service Level Crisis JAM Electronics is a Korean manufacturer of products such as industrial relays.The company has five manufacturing facilities in different countries in the Far East with headquarters in Seoul,South Korea. JAM produces about 2,500 different products, all of them manufactured in the Far East. Finished products are stored in a central warehouse in Korea and are shipped from there to different countries. Items sold in the US are transported by ship to the warehouse in Chicago.

5. Case: JAM Electronics Problems: the service level is at an all- time low. Only about 70% of all orders are delivered on time. Difficulty forecasting customer demand. Long lead time in the supply chain. The large number of SKUs handled by JAM USA.

6. Case: JAM Electronics

7. By the end of this chapter, you should be able to understand the following issues: How a firm can cope with huge variability in customer demand. What the relationship is between service and inventory levels. What an effective inventory management policy is.

8. 4.1 Inventory 4.1 Inventory Where do we hold inventory? Suppliers and manufacturers warehouses and distribution centers retailers Types of Inventory WIP raw materials finished goods Why do we hold inventory? Economies of scale Uncertainty in supply and demand Lead Time, Capacity limitations

9. Goals: Reduce Cost, Improve Service By effectively managing inventory: Xerox eliminated $700 million inventory from its supply chain Wal-Mart became the largest retail company utilizing efficient inventory management GM has reduced parts inventory and transportation costs by 26% annually

10. Goals: Reduce Cost, Improve Service 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 company was sharply off in its forecast of demand, resulting in inventory write downs” (WSJ, August 1993)

11. Understanding Inventory The inventory policy is affected by: Demand Characteristics Lead Time Number of Products Objectives Service level Minimize costs Cost Structure

12. Order costs Fixed Variable Holding Costs Insurance Maintenance and Handling Taxes Opportunity Costs Obsolescence

13. 4.2.1 EOQ: A Simple Model* A Case : Book Store Mug Sales Demand is constant, at 20 units a week (D for a year) Fixed order cost of $12.00, no lead time (k) Holding cost of 25% of inventory value annually (H) Mugs cost $1.00, sell for $5.00 Question How many(Q), when to order? EOQ illustrates the trade-offs between ordering and storage costs.

14. EOQ: A View of Inventory* Time Inventory Order Size Note: No Stockouts Order when no inventory Order Size determines policy Avg. Inven

15. EOQ: Calculating Total Cost* Purchase Cost Constant Holding Cost: (Avg. Inven) * (Holding Cost) Ordering (Setup Cost):Number of Orders * Order Cost Goal: Find the Order Quantity that Minimizes These Costs

16. EOQ:Total Cost* Total Cost Order Cost Holding Cost

17. EOQ: Optimal Order Quantity* Optimal Quantity = (2*Demand*Setup Cost)/holding cost Q=Sqrt((2*D*K)/H)=Sqrt(2*20*52*12)/25%)=316 So for our problem, the optimal quantity is 316

18. EOQ 总成本用如下公式表示： 等式右边的第一项表示的是库存持有成本。右边的第二项表示 的是订货成本或者生产准备成本， R/Q 表示每年向供货点发出 订货定单的次数。由此可见，如果 Q 增加，而每年的需求固定， 那么每年的订货的次数就相应减少。第三项是货物自身的成本， 它不影响最优订货批量和最优订购周期的确定。 为获得使总成本最低的最优订货批量 Q* ，总成本 TC 看作以 Q 为 自变量的函数，将 TC 函数对 Q 微分：

19. EOQ 令 为 0 ， 可求出最优的 Q * 为 每年的订货次数为 两次订货之间最佳的时间间隔为

20. EOQ: Important Observations * Tradeoff between set-up costs and holding costs when determining order quantity. Total Cost is not particularly sensitive to the optimal order quantity

21. The Effect of Demand Uncertainty Most companies 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 reality Recent technological advances have increased the level of demand uncertainty: Short product life cycles Increasing product variety

22. Outline 4.1 Introduction to Inventory Management 4.2 Single Warehouse Inventory (1) EOQ (2) Demand Forecast (3) Supply Contracts (4) A multi-Period Inventory Model (5) Periodic Review Policy 4.3 Risk Pooling 4.4 Centralized vs. Decentralized Systems 4.5 Managing Inventory in the SC 4.6 Practical Issues in Inventory Management

23. 4.2.2 Demand Forecast The three principles of all forecasting techniques: Forecasting is always wrong The longer the forecast horizon the worst is the forecast Aggregate forecasts are more accurate

24. Case: SnowTime Sporting Goods Fashion items have short life cycles, high variety of competitors SnowTime Sporting Goods New designs are completed One production opportunity Based 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. Case 2

25. Supply Chain Time Lines Jan 00 Jan 01Jan 02 Feb 00 Sep 00Sep 01 DesignProductionRetailing Feb 01 Production

26. SnowTime Demand Scenarios

27. SnowTime Costs The variable Production cost per unit (C): $80 Selling price per unit (S): $125 Salvage value per unit (V): $20 Fixed production cost (F): $100,000 To start production,the manufacturer has to invest $100,000 independent of the amount produced. Q is production quantity, D demand Profit = Revenue - Variable Cost - Fixed Cost + Salvage

28. SnowTime Scenarios Scenario One: Suppose you make 12,000 jackets and demand ends up being 13,000 jackets. Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000 Scenario Two: Suppose you make 12,000 jackets and demand ends up being 11,000 jackets. Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) = $ 335,000 Profit = Revenue - Variable Cost - Fixed Cost + Salvage

29. SnowTime Best Solution Find order quantity that maximizes weighted average profit. Question: Will this quantity be less than, equal to, or greater than average demand?

30. What to Make? Question: Will this quantity be less than, equal to, or greater than average demand? Average demand is 13,100 Look at marginal cost Vs. marginal profit if extra jacket sold, profit is 125-80 = 45 if not sold, cost is 80-20 = 60 So we will make less than average

31. SnowTime Expected Profit The quantity that maximizes average profit, is about 12,000.

32. SnowTime Expected Profit It indicates that producing 9,000 units or producing 16,000 units will lead to about the same average profit of $294,000.

33. SnowTime: Important Observations Tradeoff between ordering enough to meet demand and ordering too much Several quantities have the same average profit Average profit does not tell the whole story Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?

34. SnowTime Expected Profit

35. Probability of Outcomes When the production quantity is 16,000 units, the distribution of profit is not symmetrical. Losses of $220,000 happen about 11%, while profits of at least $410,000 happen 50%. When the production quantity is 9,000 units,the distribution has only two possible outcomes. Profit is either $200,000 with probability of about 11%,or $305,000 with probability of about 89%.

36. Key Insights 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, risk increases. In other words, the probability of large gains and of large losses increases

37. SnowTime Costs: The Effect of Initial Inventory 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, D demand Profit = Revenue - Variable Cost - Fixed Cost + Salvage

38. SnowTime Expected Profit

39. Initial Inventory Suppose that one of the jacket designs is a model produced last year. Some inventory is left from last year Assume the same demand pattern as before If only old inventory is sold, no setup cost Question: If there are 5000 units remaining, what should SnowTime do? What should they do if there are 10,000 remaining?

40. Initial Inventory and Profit

42. If the manufacturer does not produce any additional suits, no more than 5,000 units can be sold and no additional fixed cost will be incurred. However, it the manufacturer decides to produce, a fixed production cost is charged independent of the amount produced.

43. Initial Inventory and Profit Average profit excluding fixed production cost Average profit including fixed production cost

44. (1) there are 5000 units remaining If nothing is produced, average profit is equal to 625000. Production should increase inventory from 5,000 units to 12,000 units. Thus, average profit is equal to 771000 (from the figure). (2) there are 10,000 units remaining It is easy to see that there is no need to produce anything because the average profit associated with an initial inventory of 10,000 is larger than what we would achieve if we produce to increase inventory to 12,000 units. If we produce, the most we can make on average is a profit of$375,000. This is the same average profit that we will have if our initial inventory is about 8,500 units. Hence, if our initial inventory is below 8,5000 units, we produce to raise the inventory level to 12,000 units. If initial inventory is at least 8,5000 units,we should not produce anything. Analysis

45. (s, S) Policies For some starting 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 fixed costs associated with ordering, transportation, or manufacturing

46. Manufacturer Manufacturer DC Retail DC Stores Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Wholesale Price =$80 4.2.3 Supply Contracts Who takes the risk? What would the manufacturer like?

47. Demand Scenarios

48. Distributor Expected Profit

49. 470,000

50. Supply Contracts (cont.) Distributor optimal order quantity is 12,000 units Distributor expected profit is $470,000 Manufacturer profit is $440,000 Supply Chain Profit is $910,000 –Is there anything that the distributor and manufacturer can do to increase the profit of both?

51. Manufacturer Manufacturer DC Retail DC Stores Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Wholesale Price =$80 Supply Contracts (between manufacturer and retailer) In the previous strategy, the retailer takes all the risk and the manufacturer takes zero risk. This is why the retailer has to be very conservative with the amount he orders. If the retailer can transfer some of the risk to the manufacturer, the retailer may be willing to increase his order quantity and thus increase both his profit and the manufacturer profit.

52. Retailer Profit (Buy Back=$55)

53. $513,800 * 假定制造商同意以 55 美元的价格从零售商处购买销售不了的衣服， 则零售商愿意增加订货量到 14000 件，并获得 513800 美元的利润， 而制造商的平均利润增加到 471900

54. Manufacturer Profit (Buy Back=$55)

55. $471,900

56. Manufacturer Manufacturer DC Retail DC Stores Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Wholesale Price =$?? Supply Contracts Supply Contracts (between manufacturer’s wholesale price and retailer) What does wholesale price drive? How can manufacturer benefit from lower price?

57. Retailer Profit (Wholesale Price $70, Retailers back 15% to manufacturer )

58. Retailer Profit (Wholesale Price $70, RS 15%) $504,325

59. Manufacturer Profit (Wholesale Price $70, RS 15%)

60. $481,375

61. Supply Contracts Wholesale Price $70, RS 15%

62. Manufacturer Manufacturer DC Retail DC Stores Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Wholesale Price =$80 Supply Contracts What is the maximum profit that the supply chain can achieve? To answer this question, one needs to forget about the transfer of money from the retailer to the manufacturer.

63. Supply Chain Profit

64. Supply Chain Profit Supply Chain Profit (Global optimization) $1,014,500

65. Supply Contracts

66. Supply Contracts: Key Insights Effective supply contracts allow supply chain partners to replace sequential optimization by global optimization Buy Back and Revenue Sharing contracts achieve this objective through risk sharing

67. Supply Contracts: Case Study Example: Demand for a movie newly released video cassette typically starts high and decreases rapidly Peak demand last about 10 weeks Blockbuster purchases a copy from a studio for $65 and rent for $3 Hence, retailer must rent the tape at least 22 times before earning profit Retailers cannot justify purchasing enough to cover the peak demand In 1998, 20% of surveyed customers reported that they could not rent the movie they wanted

68. Supply Contracts: Case Study Starting in 1998 Blockbuster entered a revenue sharing agreement with the major studios Studio charges $8 per copy Blockbuster pays 30-45% of its rental income Even if Blockbuster keeps only half of the rental income, the breakeven point is 6 rental per copy The impact of revenue sharing on Blockbuster was dramatic Rentals increased by 75% in test markets Market share increased from 25% to 31% (The 2nd largest retailer, Hollywood Entertainment Corp has 5% market share)

69. Other Contracts Quantity Flexibility Contracts Supplier provides full refund for returned items as long as the number of returns is no larger than a certain quantity Sales Rebate Contracts Supplier provides direct incentive for the retailer to increase sales by means of a rebate paid by the supplier for any item sold above a certain quantity

70. 4.2.4 A Multi-Period Inventory Model Often, there are multiple reorder opportunities Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory

71. The DC holds inventory to: Satisfy demand during lead time Protect against demand uncertainty Balance fixed costs and holding costs

72. Reminder: The Normal Distribution Average = 30 Standard Deviation = 5 Standard Deviation = 10

73. The Multi-Period Continuous Review Inventory Model Normally distributed random demand Fixed order cost plus a cost proportional to amount ordered. Inventory cost is charged per item per unit time If an order arrives and there is no inventory, the order is lost The distributor has a required service level. This is expressed as the the likelihood that the distributor will not stock out during lead time. Intuitively, how will this effect our policy?

74. A View of (s, S) Policy Time Inventory Level S s 0 Lead Time Lead Time Inventory Position

75. The (s,S) Policy (s, S) Policy: Whenever the inventory position drops below a certain level, s, we order to raise the inventory position to level S. The reorder point is a function of: The Lead Time Average demand Demand variability Service level

76. Notation Notation AVG = average daily demand STD = standard deviation of daily demand LT = replenishment lead time in days h = holding cost of one unit for one day K = fixed 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.

77. Analysis Analysis The reorder point (s) has two components: To account for average demand during lead time: LT  AVG To account for deviations from average (we call this safety stock) z  STD   LT where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is 100%-SL. Since there is a fixed cost, we order more than up to the reorder point: Q=  (2  K  AVG)/h The total order-up-to level is: S=Q+s

78. Example Example The distributor has historically observed weekly demand of: AVG = 44.6STD = 32.1 Replenishment lead time is 2 weeks, and desired service level SL = 97% Average demand during lead time is: 44.6  2 = 89.2 Safety Stock is: 1.88  32.1   2 = 85.3 Reorder point is thus 175, or about 3.9 weeks of supply at warehouse and in the pipeline What is Reorder point? what is the order-up-to-level?

79. Example, Cont. Weekly inventory holding cost:.87 Therefore, Q=679 Order-up-to level thus equals: Reorder Point + Q = 176+679 = 855

80. 4.2.5 Periodic Review Suppose the distributor places orders every month What policy should the distributor use? What about the fixed cost?

81. Base-Stock Policy Inventory Level Time Base- stock Level 0 Inventory Position r r L L L

82. Periodic Review Policy Each review echelon, inventory position is raised to the base-stock level. The base-stock level includes two components: Average demand during r+L days (the time until the next order arrives): (r+L)*AVG Safety stock during that time: z *STD*  r+L

83. 4.3 Risk Pooling Example Consider these two systems: Some problems faced by ACME, a company that produces and distributes electronic equipment in the Northeast of the United States. (1)The current distribution system partitions the Northeast into two markets, each of which has a single warehouse. Retailers receive items directly from the warehouses; each retailer is assigned to a single market and receives deliveries from the corresponding warehouse. Supplier Warehouse One Warehouse Two Market One Market Two

84. Risk Pooling Example (cont’) (2)Replace the two warehouses with a single warehouse. The same service level,97%, be maintained regardless of the logistics strategy employed. This system allows ACME to achieve either the same service level of 97% with much lower inventory or a higher service level with the same amount of total inventory. Market Two Supplier Warehouse Market One

85. Risk Pooling Example (cont’) 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?

86. Risk Pooling Example (cont’) Compare the two systems: two products (A,B) maintain 97% service level $60 order cost $.27 weekly holding cost $1.05 transportation cost per unit in decentralized system, $1.10 in centralized system 1 week lead time

87. Table 1 Historical Data for Product A and B Risk Pooling Example The tables include weekly demand information for each product for the last eight weeks in each market area. Observe that Product B is a slow-moving product –the demand for Product B is fairly small relative to the demand for Product A.

88. Risk Pooling Example Table 2 Summary of Historical Data Product Average Demand Standard Deviation Demand Coefficient of Variation Market1 A39.313.20.34 Market1 B1.1251.361.21 Market2 A38.612.00.31 Market2 B1.251.581.26 Total A77.920.710.27 Total B2.3751.90.81

89. Risk Pooling Example Table 3 Inventory Levels Produc t AVG D Safety Stock Reorder point QOrder-up to level Market 1 A 39.325.865132197 Market 1 B 1.1252.5842529 Market 2 A 38.622.862131193 Market 2 B 1.25352429 Total A 77.939.35118186304 Total B 2.3753.6163339

90. Risk Pooling: Important Observations Centralizing inventory control reduces both safety stock and average inventory level for the same service level. This works best for High coefficient of variation, which increases required safety stock. Negatively correlated demand. Why? What other kinds of risk pooling will we see?

91. Risk Pooling: Types of Risk Pooling* Risk Pooling Across Markets Risk Pooling Across Products Risk Pooling Across Time Daily order up to quantity is: LT  AVG + z  AVG   LT 101211131415 Demands Orders

92. 4.4 To Centralize or not to Centralize What are the trade-offs that we need to consider in comparing centralized distribution systems with decentralized distribution systems? What is the effect on: Safety stock? Service level? Overhead? Lead time? Transportation Costs?

93. Centralized vs Decentralized system Safety stock. Clearly, safety stock decreases as a firm moves from a decentralized to a centralized system. Service level. When the centralized and decentralized systems have the same total safety stock, the service level provided by the centralized system is higher. Lead time. Since the warehouses are much closer to the customers in a decentralized system,response time is much lower.

94. The warehouse echelon inventory Supplier Warehouse Retailers 4.5 Managing Inventory in the SC (Centralized Systems*) The warehouse policy controls its echelon inventory position, that is, whenever the echelon inventory position for the W is below s, an order is placed to raise its echelon inventory position to S.

95. Centralized Distribution Systems* Question: How much inventory should management keep at each location? A good strategy: The retailer raises inventory to level S r each period The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to S s 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.

96. 4.6 Inventory Management: Best Practice Periodic inventory reviews Tight management of usage rates, lead times and safety stock ABC approach Reduced safety stock levels Shift more inventory, or inventory ownership, to suppliers Quantitative approaches

97. Changes In Inventory Turnover Inventory turnover ratio = annual sales/avg. inventory level Inventory turns increased by 30% from 1995 to 1998 Inventory turns increased by 27% from 1998 to 2000 Overall the increase is from 8.0 turns per year to over 13 per year over a five year period ending in year 2000.

98. Inventory Turnover Ratio

99. Factors that Drive Reduction in Inventory Top management emphasis on inventory reduction (19%) Reduce the Number of SKUs in the warehouse (10%) Improved forecasting (7%) Use of sophisticated inventory management software (6%) Coordination among supply chain members (6%) Others

100. Factors that Drive Inventory Turns Increase Better software for inventory management (16.2%) Reduced lead time (15%) Improved forecasting (10.7%) Application of SCM principals (9.6%) More attention to inventory management (6.6%) Reduction in SKU (5.1%) Others

101. Forecasting Recall the three rules Nevertheless, forecast is critical General Overview: Judgment methods Market research methods Time Series methods Causal methods

102. Judgment Methods Assemble the opinion of experts Sales-force composite combines salespeople’s estimates Panels of experts – internal, external, both Delphi method Each member surveyed Opinions are compiled Each member is given the opportunity to change his opinion

103. Market Research Methods Particularly valuable for developing forecasts of newly introduced products Market testing Focus groups assembled. Responses tested. Extrapolations to rest of market made. Market surveys Data gathered from potential customers Interviews, phone-surveys, written surveys, etc.

104. Time Series Methods Past data is used to estimate future data Examples include Moving averages – average of some previous demand points. Exponential Smoothing – more recent points receive more weight Methods for data with trends: Regression analysis – fits line to data Holt’s method – combines exponential smoothing concepts with the ability to follow a trend Methods for data with seasonality Seasonal decomposition methods (seasonal patterns removed) Winter’s method: advanced approach based on exponential smoothing Complex methods (not clear that these work better)

105. Causal Methods Forecasts are generated based on data other than the data being predicted Examples include: Inflation rates GNP Unemployment rates Weather Sales of other products

106. Selecting the Appropriate Approach: What is the purpose of the forecast? Gross or detailed estimates? What are the dynamics of the system being forecast? Is it sensitive to economic data? Is it seasonal? Trending? How important is the past in estimating the future? Different approaches may be appropriate for different stages of the product lifecycle: Testing and intro: market research methods, judgment methods Rapid growth: time series methods Mature: time series, causal methods (particularly for long-range planning) It is typically effective to combine approaches.