Dead-Beat and reaching law based sliding mode control laws for perishable inventories with transportation losses

Abstract

Abstract This paper describes discrete sliding mode (SM) supply management strategies for inventory systems with perishable goods and transportation losses. In the considered systems, the stock used to satisfy the unknown, bounded and time-varying demand is replenished with some delay from a distant supply source. The on-hand stock deterioration during lead-time delay, as well as commodity losses in supply process are explicitly taken into account. Two supply management strategies are proposed. The first one ensures fast reaction to the imposed demand variations, but may result in excessive control signal magnitude at the beginning of the inventory management process. Therefore, in order to conform to supplier limitations we also develop an alternative control strategy based on the concept of the reaching law. That strategy helps reduce the initial supply rate and satisfy the supplier limitations. A number of desirable properties of both proposed strategies are formulated and formally proved. These properties include full customer demand satisfaction and elimination of the risk of exceeding the warehouse capacity.