Reaching Law Approach to the Sliding Mode Control of Periodic Review Inventory Systems

In this paper, a discrete-time sliding mode inventory management strategy based on a novel non-switching type reaching law is introduced. The proposed reaching law eliminates undesirable chattering, and ensures that the sliding variable rate of change is upper bounded by a design parameter which does not depend on the system initial conditions. This approach guarantees fast convergence with non-negative, upper limited supply orders, and ensures that the maximum stock level may be specified a priori by the system designer. Furthermore, a sufficient condition for 100% customers' demand satisfaction is derived. The inventory replenishment system considered in this paper involves multiple suppliers with different lead times and different transportation losses in the delivery channels. Note to Practitioners-This paper presents a new periodic review inventory management strategy which prevents from exceeding the available storage capacity, ensures smooth order evolution and helps attenuate the bullwhip effect. The strategy is scalable, computationally efficient, and easy to implement in any typical inventory replenishment system. The strategy explicitly accounts for transportation losses and different lead times of commodity suppliers.