On the Optimality of Generalized (s,S) Policies.

by E. L. Porteus

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Demonstration that a generalized (s,S) policy is optimal in a standard inventory model with a concave increasing ordering cost function rather than a linear one with setup cost. The ordering policy function as used here specifies the level of inventory after ordering as a function of the level of inventory before ordering. A generalization of K-convex and quasiconvex functions to quasi-K convex functions is required in the process; moreover, the probability densities of demand must be one-sided Polya densities. It is shown that some assumptions are crucial, others are not. For example, the cost functions, discount factors, and probability densities of demand can be time-dependent. 31 pp. Ref.

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