Optimal control of an inventory system with ameliorating and deteriorating items

This paper is concerned with the development of a production inventory model for both ameliorating and deteriorating items. Given an inventory goal level and a production goal rate set by the production facility, and given penalties for the inventory level and for the production rate to deviate from their respective targets, a system total cost objective function is derived. We seek the optimal production rate, that is the production rate that minimizes this performance measure, while satisfying the system dynamics. The resulting problem is an optimal control problem with mixed inequality constraints, in which the inventory level is the state variable and the production rate is the control variable. The necessary optimality conditions are derived using Pontryagin maximum principle. This paper generalizes some of the models available in the literature. M.S.C. 2000: 49J15, 90B30.