A finite-horizon, stochastic optimal control policy for a production–inventory system with backlog-dependent lost sales

This article considers a problem of optimal production control of a one-product-type production–inventory system. The demand is a discrete-time stochastic process, while production of a limited capacity is continious in time. The dynamics of the inventory over a finite time horizon are investigated and an optimal feedback strategy for production control under a backlog-dependent lost sales effect is developed. This strategy is called a target level strategy since, contrary to the existing production–inventory control strategies, it determines an optimal target inventory level as a function of time period and the initial stock at that period. Numerical examples illustrate the applicability of the developed solutions.