Multiproduct purchase scheduling with limited budget and/or group discounts

Abstract

A grouping scheme is employed whereby the products are ranked by the ratio of the inventory carrying cost per period and the order placing cost, and are assigned to the groups so that the products belonging to a group are consecutive in their rank-order. The product to group assignment is achieved using a “shortest-path” approach. We show that the above grouping scheme minimizes the total cost composed of the order placing cost, inventory carrying cost and purchase cost with group discounts. We also establish a powerful and somewhat surprising result that the composition of the optimal groups is not affected even if a limit is placed on the purchase budget.