Dead-beat and reaching-law-based sliding-mode control of perishable inventory systems

Abstract. In this paper we consider the problem of efficient control of inventory systems with perishable goods. In the analyzed setting the deteriorating stock at a distribution center used to fulfill unknown, time-varying demand is replenished with delay from a supply source. The challenging issue is to achieve the high service level with minimum costs when the replenishment orders are procured with lead-time delay spanning multiple review periods. On the contrary to the typical heuristic approaches, we apply formal methodology based on discrete-time sliding-mode (SM) control. The proposed SM controller with the sliding plane selected for a dead-beat scheme ensures that the maximum service level is obtained in the system with arbitrary delay and any bounded demand pattern. In order to account for the supplier capacity limitations in the systems with input constraints, we also develop an alternative control strategy based on reaching law. Both controllers achieve a given service level with smaller holding costs and reduced order-to-demand variance ratio as compared to the classical order-up-to policy.