Approximation Approaches for Inventory Systems with General Production/Ordering Cost Structures

Abstract

The production/ordering cost structure is fundamental to determining an optimal inventory control policy. For example, it is well known that a base‐stock policy is optimal for inventory systems with linear production costs, whereas an ( s, S) policy is optimal if both linear and fixed costs exist. However, many of the cost structures that have arisen from the practice are quite complex and make the optimal policies too complicated for managers to implement. In this study, we propose several easy‐to‐implement and efficient heuristic policies for inventory systems with general production costs, which include multiple linear pieces and fixed costs, suggesting a wide application to many practical problems that were previously difficult to solve. We establish the worst‐case performance bounds on the proposed heuristic policies by using the concept of K‐approximate convexity. Our extensive numerical studies, which are designed to reflect practical inventory control applications, evaluate the performance of the heuristic policies and show that the best heuristic policy we propose performs extremely well. We also try to provide explanations for the performance of different heuristic policies.