Inventory Problem Revisited

Abstract

The paper is basically a review work. The purpose of the paper is to highlight most meaningful approach to Inventory problem. In fact, it establishes that inventory problem is a continuous or discrete optimal control problem. To be more precise, it is to be treated as a continuous- discrete optimal control problem. The paper reviews all types of dynamic inventory problems, their nature and the methodologies for their solutions. In the process of sequential development of realistic approaches to inventory problems, the very purpose of inventory problems is challenged. It no longer remains a cost minimization or profit maximization of inventory at hand. Rather it reduces to a control theoretic optimization of net cost or profit expressed as a functional, with respect to the given control. The control may be taken as the current inventory in case of a discrete model and updating of the current inventory in case of a continuous or a continuous-discrete model. Lastly the paper suggests some open problems, based on which, some additional contributions to the literature of Inventory models could be made in future.