Optimal control of a production inventory system with deteriorating items

This paper is concerned with the problem of controlling the production rate of a production inventory system with deteriorating items. Under reasonable conditions. we derive the closed form optimal control of a cost minimization problem and a profit maximization problem. The derived analytical solutions yield good insight on how production Planning tasks can be carried Out. In addition. they also provide guidelines for further study and development of numerical methods for more complex systems involving more general exogenous functions.