A parts selection model with one-way substitution

This paper develops a parts selection model with one-way substitution. The problem horizon is assumed to be infinite and cost and demand parameters are assumed to be stationary over the problem horizon. The objective is to select a subset of parts from the available set of parts to minimize the average per-period cost. In addition to the purchase and inventory related costs, the authors assume that there is an overhead cost to manage the stock of parts which is a function of the number of parts kept in stock. The purchase price function used in the paper covers all the commonly used quantity discount models. Several analytical results are developed for the problem and an efficient dynamic programming algorithm is developed to find an optimal solution.