Technical Note—A One-Product Production/Inventory Problem under Continuous Review Policy

Bezalel Gavish and Stephen C. Graves
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Bezalel Gavish: University of Rochester, Rochester, New York
Stephen C. Graves: Massachusetts Institute of Technology, Cambridge, Massachusetts

Operations Research, 1980, vol. 28, issue 5, 1228-1236

Abstract: A single production facility is dedicated to producing one type of product with completed units going directly into inventory. The demand for the product is governed by a Poisson process and is supplied directly to inventory when available, or is backordered until it is produced by the production facility. Relevant costs are a linear inventory holding cost, a linear backorder cost, a fixed setup cost for initiating a production run. The objective is to find a control policy to minimize the expected cost per time unit. It is shown that the problem may be modeled as an M / D /1 queueing system with the optimal policy being a two-critical-number policy. Cost expressions are derived as functions of the policy parameters, and based on a convexity property of these cost expressions, an efficient search procedure is proposed for finding the optimal policy. In computational tests that were performed on an IBM 360/65, optimal policies were computed in less than 1/8 second of CPU time.

Date: 1980
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