Inventory management through one step ahead optimal control based on linear programming

Abstract

A one step ahead optimal strategy is proposed for the inventory control and management problem, and rewritten as a linear programming problem, permitting practical implementation. Important novel aspects of the proposed solution are that it uses economic value added (EVA), a comprehensive performance index commonly used in business management, instead of regulation to a set point or to a interval of stock values; it does not require knowledge or prediction of the demand distribution; it achieves good efficiency with respect to a globally optimal value, defined in this paper, and no significant bullwhip effect, while being robust to demand and lead time variations. The proposed one step ahead optimal controller is compared with the classical (s, S) controller, as well as with a representative of the inventory and order-based production controller family. In order to make a fair comparison, this paper also proposes a tuning method for the latter two controllers. Numerical experiments based on average performance of the three controllers for a set of normally distributed demands show the superiority of the proposed one step ahead optimal controller, in terms of EVA as well as in terms of other measures proposed in the paper.