Simultaneous Capacity and Production Management of Short-Life-Cycle, Produce-to-Stock Goods Under Stochastic Demand

Alexandar Angelus · Evan L. Porteus

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Supply Chain and Inventory Management Management and Optimization Techniques Operations Management Techniques

Abstract

This paper derives the optimal simultaneous capacity and production plan for a shortlife-cycle, produce-to-stock good under stochastic demand. Capacity can be reduced as well as added, at exogenously set unit prices. In both cases studied, with and without carryover of unsold units, a target interval policy is optimal: There is a (usually different) target interval for each period such that capacity should be changed as little as possible to bring the level available into that interval. Our contribution in the case of no carry-over, is a detailed characterization of the target intervals, assuming demands increase stochastically at the beginning of the life cycle and decrease thereafter. In the case of carry-over, we establish the general result and show that capacity and inventory are economic substitutes: The target intervals decrease in the initial stock level and the optimal unconstrained base stock level decreases in the capacity level. In both cases, optimal service rates are not necessarily constant over time. A numerical example illustrates the results.

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References

2011Supermodularity and Complementarity 1983Production and inventory management 1982Operations Research and Capacity Expansion Problems: A Survey 1998Investment Strategies for Flexible Resources 1961Capacity Expansion and Probabilistic Growth 1986An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion 1986An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion 1999Multi-resource investment strategies: Operational hedging under demand uncertainty

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