The Periodic Joint Replenishment Problem is Strongly NP-Hard

TL;DR

This paper proves that the periodic joint replenishment problem, a key issue in supply chain management, is strongly NP-hard, resolving a long-standing open question about its computational complexity.

Contribution

The paper establishes the strong NP-hardness of the periodic joint replenishment problem, settling a long-standing open problem in supply chain optimization.

Findings

The problem is strongly NP-hard.

Previous heuristic and approximation algorithms cannot guarantee optimal solutions.

The complexity status of the problem is now definitively known.

Abstract

In this paper we study the long-standing open question regarding the computational complexity of one of the core problems in supply chains management, the periodic joint replenishment problem. This problem has received a lot of attention over the years and many heuristic and approximation algorithms were suggested. However, in spite of the vast effort, the complexity of the problem remained unresolved. In this paper, we provide a proof that the problem is indeed strongly NP-hard.