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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.