Non-switching reaching law based discrete time quasi-sliding mode control with application to warehouse management problem

In this paper a new non-switching type reaching law for sliding mode control of discrete time systems is introduced and applied to the problem of periodic review inventory management. The considered inventory is refilled by multiple suppliers through delivery channels subject to non-negligible commodity losses. The reaching law proposed in this paper is inspired by the earlier work of Gao, Wang and Homaifa, however, in this paper the original formulation is essentially modified in order to avoid undesirable switching, and to ensure good dynamic performance with limited commodity orders. These improvements are obtained by the application of a modified definition of the quasi-sliding mode, and also by the introduction of an adjustable, state dependent sliding variable decrease rate factor. The sliding mode inventory management strategy proposed in this paper ensures full customer demand satisfaction and enables the designer to specify upper limit of the on-hand stock level.