Simultaneous Production and Capacity Management under Stochastic Demand for Perishable Goods

This paper derives the optimal simultaneous capacity and production plan for a high volatility, short life-cycle, produce-to-stock, product that requires (at least some) dedicated production capacity. Capacity can be reduced as well as added, at exogenously set unit prices. We show that a target interval policy is optimal in both the perishable goods and durable goods cases: 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. A detailed characterization of the target intervals is given for the case of perishable goods, assuming that demands increase stochastically at the beginning of the life-cycle and decrease thereafter. In the durable goods case, the target intervals depend on the initial stock level as well as the period. For both cases, optimal service rates are not necessarily constant over time. A numerical example illustrates the results.