Sliding-mode dead-beat control of perishable inventory systems with positive lead-time and uncertain demand

In this paper
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we propose a control-theoretic approach for the design of inventory management policy for systems with perishable goods. In the considered systems the deteriorating stock at a distribution center used to fulfill an unknown, time-varying demand is replenished with delay from a supply source. The challenging issue is to achieve a high service level with minimum costs when the replenishment orders are procured with lead-time delay spanning multiple review periods. In contrast to the classical stochastic approaches, we employ a formal design methodology based on discrete sliding-mode (DSM) control. The proposed DSM controller with the sliding plane selected for a dead-beat scheme ensures that a maximum service level is obtained in the system with arbitrary delay and any bounded demand pattern. The proposed strategy achieves a given service level with smaller holding costs and reduced order-to-demand variance ratio as compared to the classical order-up-to policy.