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We consider the problem of finding the optimal solution from the class of single critical number order policies for an m-period lifetime perishable product. The objective function is expected cost per period, Accordingly, the steady-state characteristics of the inventory process induced by the order restriction are analyzed. We demonstrate the existence of an invariant measure for an inventory related process, which provides information sufficient for cost minimization. Particular results for the two- and three-period-lifetime cases are given.
Morris A. Cohen (Sun,) studied this question.