Simultaneous capacity and production management of short-life-cycle, produce-to-stock goods under stochastic demand

This paper derives the optimal simultaneous capacity and production plan for a short-life-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 carry-over 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.