OPTIMAL POLICIES FOR TWO PRODUCT INVENTORY SYSTEMS, WITH AND WITHOUT SETUP COSTS.
CORNELL UNIV ITHACA N Y DEPT OF INDUSTRIAL ENGINEERING AND OPERATIONS RESEARCH
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For the case of no setup cost, the structure of the transient portion of the optimal N period policy for two product inventory systems is obtained, the recurrent portion having been obtained by Veinott. The function L, the expected holding and shortage cost this period, is assumed to satisfy conditions roughly equivalent to a having a unique minimum and b being quasiconvex in each dimension with the relative minimum decreasing as the other value increases. The policy is do not order the overstocked product and order less of the other product than would be ordered if there were no overstocked product. The policy is stationary, depending neither on N nor on the number of periods remaining. For the setup cost case, the optimal N period policy is obtained under strong assumptions on L and the optimal one period policy under a and b. Bounds analogous to those of Veinott and Wagner are obtained. The apparent inappropriateness of K-convexity is discussed. Author
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