The Order Up-To Model

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Medtronic’s InSync pacemaker supply chain and objectives
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Supply chain:  One distribution center (DC) in Mounds View, MN.  About 500 sales territories throughout the country. Consider Susan Magnotto’s territory in Madison, Wisconsin.
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Objective:  Because the gross margins are high, develop a system to minimize inventory investment while maintaining a very high service target, e.g., a 99.9% in-stock probability or a 99.9% fill rate.

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Timing in the order up-to model
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Time is divided into periods of equal length, e.g., one hour, one month. During a period the following sequence of events occurs:  A replenishment order can be submitted.  Inventory is received.  Random demand occurs. Lead times:  An order is received after a fixed number of periods, called the lead time.  Let l represent the length of the lead time.

An example with l = 1

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Order up-to model vs. newsvendor model
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Both models have uncertain future demand, but there are differences…
Newsvendor
Inventory obsolescence Number of replenishments Demand occurs during replenishment After one period One (maybe two or three with some reactive capacity) No

Order up-to
Never Unlimited

Yes

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Newsvendor applies to short life cycle products with uncertain demand and the order up-to applies to long life cycle products with uncertain, but stable, demand.

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The Order Up-To Model: Choosing a demand distribution/forecast

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InSync demand and inventory at the DC
700 600 500 400 300 200 100 0

Average monthly demand = 349 units Standard deviation of monthly demand = 122.28 Average weekly demand = 349/4.33 = 80.6 Standard deviation of weekly demand = 122.38 / 4.33  58.81 (The evaluations for weekly demand assume 4.33 weeks per month and demand is independent across