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This paper considers a system in which an order is placed every T periods to bring the inventory position up to the base stock S. It accepts demand until the inventory position reaches a sales rejection threshold M. The objective is to find the optimal values of S and M which minimize the long-run average cost per period. It establishes the stationary distribution of the system and develops structural properties of the optimal solution that facilitate computation. In particular, it shows that in an optimal solution, the optimal value of M is non-negative under some reasonable conditions. Hence, in the model a mixture of backorders and lost sales may occur. Additionally, the paper compares the system against traditional systems in which demand during stockouts is either fully backordered or lost.
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