A DISCRETE EOQ PROBLEM WITH MAXIMUM ORDER SIZE COSTS

摘要

The Economic Order Quantity (EOQ) problem is a fundamental problem in supply and inventory management. An optimal solution to this problem in a closed form exists under the assumption that time and the product are continuously divisible. This paper studies problem D-EOQ, in which time and the product are discrete. Furthermore, in the objective function, there is a fixed cost for each order and a fixed cost for each product unit in an order of the maximum size. It is shown that the continuous relaxation of problem D-EOQ provides a solution that can be up to 50% worse than the optimal solution and this worst-case error bound is tight. Properties of an optimal solution of the problem D-EOQ are established. These properties allow to solve many special cases in polynomial time and can be used to derive a polynomial time algorithm for the general case of the problem D-EOQ.