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Inventory Management and Risk Pooling

Inventory Management and Risk Pooling. Designing & Managing the Supply Chain Chapter 3 Byung-Hyun Ha bhha@pusan.ac.kr. Outline. Introduction to Inventory Management Effect of Demand Uncertainty (s,S) Policy Supply Contracts Continuous/Periodic Review Policy Risk Pooling

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Inventory Management and Risk Pooling

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  1. Inventory Management and Risk Pooling Designing & Managing the Supply Chain Chapter 3 Byung-Hyun Ha bhha@pusan.ac.kr

  2. Outline • Introduction to Inventory Management • Effect of Demand Uncertainty • (s,S) Policy • Supply Contracts • Continuous/Periodic Review Policy • Risk Pooling • Centralized vs. Decentralized Systems • Managing Inventory in Supply Chain • Practical Issues in Inventory Management • Forecasting

  3. Case: JAM USA, Service Level Crisis • Background • Subsidiary of JAM Electronics (Korean manufacturer) • Established in 1978 • Five Far Eastern manufacturing facilities, each in different countries • 2,500 different products, a central warehouse in Korea for FGs • A central warehouse in Chicago with items transported by ship • Customers: distributors & original equipment manufacturers (OEMs) • Problems • Significant increase in competition • Huge pressure to improve service levels and reduce costs • Al Jones, inventory manage, points out: • Only 70% percent of all orders are delivered on time • Inventory, primarily that of low-demand products, keeps pile up

  4. Case: JAM USA, Service Level Crisis • Reasons for the low service level: • Difficulty forecasting customer demand • Long lead time in the supply chain • About 6-7 weeks • Large number of SKUs handled by JAM USA • Low priority given the U.S. subsidiary by headquarters in Seoul Monthly demand for item xxx-1534

  5. Inventory • Where do we hold inventory? • Suppliers and manufacturers / warehouses and distribution centers / retailers • Types of Inventory • Raw materials / WIP (work in process) / finished goods • Reasons of holding inventory • Unexpected changes in customer demand • 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 and capacity limitations even with no uncertainty • Economies of scale (transportation cost)

  6. Single Warehouse Inventory Example • Contents • Economy lot size model • News vendor model • Effect of demand uncertainty • Supply contract • Multiple order opportunities • Continuous review policy • Periodic review policy

  7. Single Warehouse Inventory Example • Key factors affecting inventory policy • Customer demand characteristics • Replenishment lead time • Number of products • Length of planning horizon • Cost structure • Order cost • Fixed, variable • Holding cost • Taxes, insurance, maintenance, handling, obsolescence, and opportunity costs • Service level requirements

  8. Economy Lot Size Model • Assumptions • Constant demand rate of D items per day • Fixed order quantities at Q items per order • Fixed setup cost K when places an order • Inventory holding cost h per unit per day • Zero lead time • Zero initial inventory & infinite planning horizon

  9. Economy Lot Size Model • Inventory level • Total inventory cost in a cycle of length T • Average total cost per unit of time (Q) Cycle time (T)

  10. Economy Lot Size Model • Trade-off between order cost and holding cost Total Cost Holding Cost Order Cost

  11. Economy Lot Size Model • Optimal order quantity • Economic order quantity (EOQ) • Important insights • Tradeoff between setup 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 sensitive to the optimal order quantity

  12. 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

  13. Effect of Demand Uncertainty • 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 • News vendor model • Incorporating demand uncertainty and forecast demand into analysis • Characterizing impact of demand uncertainty on inventory policy

  14. Case: Swimsuit Production • Fashion items have short life cycles, high variety of competitors • Swimsuit production • 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

  15. Case: Swimsuit Production • Information • Production cost per unit (C) = $80 • Selling price per unit (S) = $125 • Salvage value per unit (V) = $20 • Fixed production cost (F) = $100,000 • Production quantity (Q)

  16. Case: Swimsuit Production • Possible scenarios • Make 10,000 swimsuits, demand ends up being 12,000 • Profit = 125(10,000) - 80(10,000) - 100,000 = $350,000 • Make 10,000 swimsuits, demand ends up being 8,000 • Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = $140,000 • …

  17. Swimsuit Production Solution • Problem • Find optimal order quantity Q* that maximizes expected profit • Notation • di – ith possible demand where di < di+1 • (d1, d2, d3, d4, d5, d6) = (8K, 10K, 12K, 14K, 16K, 18K) • pi – probability that ith possible demand occurs • (p1, p2, p3, p4, p5, p6) = (0.11, 0.11, 0.28, 0.22, 0.18, 0.10) • ES(Q) – expected sales when producing Q • EI(Q) – expected left over inventory when producing Q • EP(Q) – expected profit when producing Q • Expected profit • EP(Q) = SES(Q) – CQ – F + VEI(Q)

  18. Swimsuit Production Solution • Expected sales • Case 1: Q  d1 • Case 2: dk < Q  dk+1, k=1,…,5 • Case 3: d6  Q • Expected left over inventory (why?) • EI(Q) = Q – ES(Q)

  19. Swimsuit Production Solution • Quantity that maximizes average profit

  20. Swimsuit Production Solution • Question • Average demand is 13,000 • Will optimal quantity be less than, equal to, or greater than average demand? • Note that fixed production cost is sunk cost • We have to pay in all cases

  21. Swimsuit Production Solution • Look at marginal cost vs. marginal profit • If extra swimsuit sold, profit is 125-80 = 45 • If not sold, cost is 80-20 = 60 • In case of Scenario Two (make 10,000, demand 8,000) • Profit = 125(8,000) - 80(10,000) - 100,000 + 20(2,000) = 125(8,000) - 80(8,000 + 2,000) - 100,000 + 20(2,000) = 45(8,000) - 60(2,000) - 100,000 = $140,000 • That is, • EP(Q) = SES(Q) – CQ – F + VEI(Q) = SES(Q) – C{ES(Q) + EI(Q)} – F + VEI(Q) = (S – C)ES(Q) – (C – V)EI(Q) – F • So we will make less than average

  22. Swimsuit Production Solution • 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?

  23. Swimsuit Production Solution • Risk and reward Consult Ch13 of Winston, “Decision making under uncertainty”

  24. Case: Swimsuit Production • Key insights • 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 (the probability of large gains and of large losses increases)

  25. Case: Swimsuit Production • Initial inventory • Suppose that one of the swimsuit 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 5,000 units remaining, what should Swimsuit production do?

  26. Case: Swimsuit Production • Analysis for initial inventory and profit • Solid line: average profit excluding fixed cost • Dotted line: same as expected profit including fixed cost • Nothing produced • 225,000 (from the figure) + 80(5,000) = 625,000 • Producing • 371,000 (from the figure) + 80(5,000) = 771,000 • If initial inventory was 10,000?

  27. Case: Swimsuit Production • Initial inventory and profit

  28. Case: Swimsuit Production • (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

  29. Supply Contracts • Assumptions for Swimsuit production • In-house manufacturing  Usually, manufactures and retailers • Supply contracts • Pricing and volume discounts • Minimum and maximum purchase quantities • Delivery lead times • Product or material quality • Product return policies

  30. Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Manufacturer DC Manufacturer Retail DC Stores Supply Contracts • Condition Wholesale Price =$80

  31. Demand Scenario and Retailer Profit

  32. Demand Scenario and Retailer Profit • Sequential supply chain • Retailer optimal order quantity is 12,000 units • Retailer expected profit is $470,700 • Manufacturer profit is $440,000 • Supply Chain Profit is $910,700 • Is there anything that the distributor and manufacturer can do to increase the profit of both? • Global optimization?

  33. Buy-Back Contracts • Buy back=$55 retailer manufacturer

  34. Buy-Back Contracts • Sequential supply chain • Retailer optimal order quantity is 12,000 units • Retailer expected profit is $470,700 • Manufacturer profit is $440,000 • Supply chain profit is $910,700 • With buy-back contracts • Retailer optimal order quantity is 14,000 units • Retailer expected profit is $513,800 • Manufacturer expectedprofit is $471,900 • Supply chain profit is $985,700 • Manufacture sharing some of risk!

  35. Revenue-Sharing Contracts • Wholesale price from $80 to $60, RS 15% • Supply chain profit is $985,700 retailer manufacturer

  36. Other Types of Supply Contracts • Quantity-flexibility contracts • Supplier providing full refund for returned (unsold) items up to a certain quantity • Sales rebate contracts • Direct incentive to retailer by supplier for any item sold above a certain quantity • … • Consult Cachon 2002

  37. Global Optimization • What is the most profit both the supplier and the buyer can hope to achieve? • Assume an unbiased decision maker • Transfer of money between the parties is ignored • Allowing the parties to share the risk! • Marginal profit=$90, marginal loss=$15 • Optimal production quantity=16,000 • Drawbacks • Decision-making power • Allocating profit

  38. Global Optimization • Revised buy-back contracts • Wholesale price=$75, buy-back price=$65 • Global optimum • Equilibrium point! • No partner can improve his profit by deciding to deviate from the optimal decision • Consult Ch14 of Winston, “Game theory” • 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

  39. 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

  40. 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)

  41. Multiple Order Opportunities • Situation • Often, there are multiple reorder opportunities • A central distribution facility which orders from a manufacturer and delivers to retailers • The distributor periodically places orders to replenish its inventory • Reasons why DC holds inventory • Satisfy demand during lead time • Protect against demand uncertainty • Balance fixed costs and holding costs

  42. Continuous Review Inventory Model • Assumptions • 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 • expressed as the likelihood that the distributor will not stock out during lead time. • (s, S) Policy • Whenever the inventory position drops below a certain level (s) we order to raise the inventory position to level S

  43. Reminder: The Normal Distribution

  44. A View of (s, S) Policy

  45. (s, S) Policy • Notations • 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%) • The probability of stocking out is 100% - SL (for example, 5%) • Policy • s = reorder point, S = order-up-to level • Inventory Position • Actual inventory + (items already ordered, but not yet delivered)

  46. (s, S) Policy - 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LTwhere z is chosen from statistical tables to ensure that the probability of stock-outs during lead-time is100% - 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

  47. (s, S) Policy - Example • The distributor has historically observed weekly demand of: AVG = 44.6 STD = 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 • Weekly inventory holding cost: .87 • Therefore, Q=679 • Order-up-to level thus equals: • Reorder Point + Q = 176+679 = 855

  48. Periodic Review • Periodic review model • Suppose the distributor places orders every month • What policy should the distributor use? • What about the fixed cost? • Base-Stock Policy

  49. Periodic Review • Base-Stock 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

  50. Risk Pooling • Consider these two systems: • 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?

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