Periodic Review Production Models with Variable Capacity, Random Yield, and Uncertain Demand

Yunzeng Wang and Yigal Gerchak
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Yunzeng Wang: Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Yigal Gerchak: Department of Management Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L-3G1

Management Science, 1996, vol. 42, issue 1, 130-137

Abstract: We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs (production, holding, and shortage costs), we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero; otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.

Keywords: inventory and production policies; stochastic dynamic programming; periodic review models (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:42:y:1996:i:1:p:130-137

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