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Dr. A. K. Dey1 Inventory Management, Supply Contracts and Risk Pooling Dr. A. K. Dey

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2 Outline of the Presentation Introduction to Inventory Management The Effect of Demand Uncertainty (s,S) Policy Periodic Review Policy Supply Contracts Risk Pooling Centralized vs. Decentralized Systems Practical Issues in Inventory Management

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Dr. A. K. Dey3 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

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Dr. A. K. Dey4 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

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Dr. A. K. Dey5 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)

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Dr. A. K. Dey6 Understanding Inventory 1. The inventory policy is affected by: Demand Characteristics Lead Time Number of Products Objectives Service level Minimize costs Cost Structure

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Dr. A. K. Dey7 Cost Structure Order costs Fixed Variable Holding Costs Insurance Maintenance and Handling Taxes Opportunity Costs Obsolescence

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Dr. A. K. Dey8 EOQ: A Simple Model 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 value annually Mugs cost $1.00, sell for $5.00 Question How many, when to order?

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Dr. A. K. Dey9 EOQ: A View of Inventory Note: No Stockouts Order when no inventory Order Size determines policy Inventory Order Size Avg. Inven Time

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Dr. A. K. Dey10 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:

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Dr. A. K. Dey11 EOQ: Total Cost

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Dr. A. K. Dey12 EOQ: Optimal Order Quantity Optimal Quantity = [(2*Demand*Setup Cost)/holding cost] So for our problem The optimal quantity is 316

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Dr. A. K. Dey13 EOQ: Important Observations 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 Total Cost is not particularly sensitive to the optimal order quantity

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Dr. A. K. Dey14 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

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Dr. A. K. Dey15 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

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Dr. A. K. Dey16 Swim Suit Sporting Goods Fashion items have short life cycles, high variety of competitors Swim Suit 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.

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Dr. A. K. Dey17 Supply Chain Time Lines Jan 00Jan 01Jan 02 Feb 00 Sep 00Sep 01 DesignProductionRetailing Feb 01 Production

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Dr. A. K. Dey18 Swim Suit Demand Scenarios

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Dr. A. K. Dey19 Swim Suit 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, D demand Profit = Revenue - Variable Cost - Fixed Cost + Salvage

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Dr. A. K. Dey20 Swim Suit Scenarios DemandProbability 80000.110 100000.110 120000.275 140000.225 160000.185 180000.095 Average13100

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Dr. A. K. Dey21 Key questions What is the best production quantity? How much is the profit if there is no beginning inventory, manufacturer produces 12000 swimsuits while the demand is 13000 swimsuits? Calculate the profit if the company produces 12000 swimsuits and the demand is for 11000 swimsuits.

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Dr. A. K. Dey22 Swim Suit 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

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Dr. A. K. Dey23 Key questions What is the weighted average profit if the company makes 9000 swimsuits? And if it makes 16000 swim suits?

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Dr. A. K. Dey24 Weighted Average Profit for 9000 Swim Suits Make 9000 Swim Suits DemandProb Revenue 125 Variable cost 80 Fixed Cost Salvage Value 20 Profit Weighted Average 80000.1110000007200001000002000020000022000 100000.111125000720000100000030500033550 120000.2751125000720000100000030500083875 140000.2251125000720000100000030500068625 160000.1851125000720000100000030500056425 180000.0951125000720000100000030500028975 Total Expected Profit293450

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Dr. A. K. Dey25 Weighted Average Profit for 16000 Swim Suits Make 16000 Swim Suits DemandProb Revenue 125 Variable cost 80 Fixed Cost Salvage Value 20 Profit Weighted Average 80000.1110000001280000100000160000-220000-24200 100000.1112500001280000100000120000-10000-1100 120000.275150000012800001000008000020000055000 140000.225175000012800001000004000041000092250 160000.185200000012800001000000620000114700 180000.09520000001280000100000062000058900 Total Expected Profit295550

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Dr. A. K. Dey26 Swim Suit Best Solution Find order quantity that maximizes weighted average profit. Question: Will this quantity be less than, equal to, or greater than average demand?

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Dr. A. K. Dey27 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

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Dr. A. K. Dey28 Swim Suit Expected Profit

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Dr. A. K. Dey29 Swim Suit Expected Profit – same for 9000 & 16000

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Dr. A. K. Dey30 Effect of Initial Inventory Suppose the beginning inventory is 5000 swimsuits If does not produce – max 5000 swimsuits can be sold If starts production, fixed cost will be charged Assuming same demand pattern Should the manufacturer start production? If yes, how many swimsuits should be produced?

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Dr. A. K. Dey31 Expected profit 771000 Initial Inventory 5000 Swim Suits, Make 7000 more to have 12000 to sell DemandProb Revenue 125 Variable cost 80 Fixed Cost Salvage Value 20 Profit Weighted Average 80000.1110000005600001000008000042000046200 100000.1112500005600001000004000063000069300 120000.27515000005600001000000840000231000 140000.22515000005600001000000840000189000 160000.18515000005600001000000840000155400 180000.0951500000560000100000084000079800 Total Expected Profit770700

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Dr. A. K. Dey32 Initial Inventory 10000 Swim Suits, Make 2000 more to have 12000 to sell DemandProb Revenu 125 Variabl cost 80 Fixed Cost Salvag Value 20 Profit Weighte Average 80000.1110000001600001000008000082000090200 100000.111250000160000100000400001030000113300 120000.275150000016000010000001240000341000 140000.225150000016000010000001240000279000 160000.185150000016000010000001240000229400 180000.095150000016000010000001240000117800 Total Expected Profit1170700 If only 10000 swimsuits are sold revenue and profit will be 1250000! Why produce more?

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Dr. A. K. Dey33 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

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