36 / 2024-04-16 15:17:38

A Unified Approximation Scheme for a Class of Operations Management Problems

dynamic programming,approximation algorithm

In this study, we propose the concept of weak K-convexity, which generalizes many variations of convexity in the literature. We show its equivalence with K-approximate convexity and establish a new preservation result of weak K-convexity applicable in dynamic programming settings. These findings imply the existence of a well-structured heuristic policy with a worst-case performance bound of O(TK) for a class of periodic-review inventory control or joint pricing and inventory control problems with T periods. Our numerical studies demonstrate the effectiveness of the proposed heuristic policy.