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Inventory Management, Supply Contracts and Risk Pooling. Phil Kaminsky kaminsky@ieor.berkeley.edu. February 1, 2007. Issues. Inventory Management The Effect of Demand Uncertainty (s,S) Policy Periodic Review Policy Supply Contracts Risk Pooling Centralized vs. Decentralized Systems
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InventoryManagement, Supply Contracts and Risk Pooling Phil Kaminskykaminsky@ieor.berkeley.edu February 1, 2007
Issues • 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
Customers, demand centers sinks Field Warehouses: stocking points Sources: plants vendors ports Regional Warehouses: stocking points Supply Inventory & warehousing costs Production/ purchase costs Transportation costs Transportation costs Inventory & warehousing costs
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
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
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)
Understanding Inventory • The inventory policy is affected by: • Demand Characteristics • Lead Time • Number of Products • Objectives • Service level • Minimize costs • Cost Structure
Cost Structure • Order costs • Fixed • Variable • Holding Costs • Insurance • Maintenance and Handling • Taxes • Opportunity Costs • Obsolescence
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?
EOQ: A View of Inventory* Note: • No Stockouts • Order when no inventory • Order Size determines policy Inventory Order Size Avg. Inven Time
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:
EOQ:Total Cost* Total Cost Holding Cost Order Cost
EOQ: Optimal Order Quantity* • Optimal Quantity = (2*Demand*Setup Cost)/holding cost • So for our problem, the optimal quantity is 316
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
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
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
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.
Jan 00 Jan 01 Jan 02 Design Production Retailing Feb 00 Sep00 Feb01 Sep01 Production Supply Chain Time Lines
SnowTime 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
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
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?
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
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?
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
SnowTime Costs: 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
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 7000 units remaining, what should SnowTime do? What should they do if there are 10,000 remaining?
Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Manufacturer DC Manufacturer Retail DC Stores Supply Contracts Wholesale Price =$80
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?
Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Manufacturer DC Manufacturer Retail DC Stores Supply Contracts Wholesale Price =$80
Retailer Profit (Buy Back=$55) $513,800
Manufacturer Profit (Buy Back=$55) $471,900
Fixed Production Cost =$100,000 Variable Production Cost=$35 Selling Price=$125 Salvage Value=$20 Manufacturer DC Manufacturer Retail DC Stores Supply Contracts Wholesale Price =$??
