An efficient Benders decomposition for the p-median problem

TL;DR

This paper introduces an efficient Benders decomposition approach for the p-median problem, providing a new compact formulation and demonstrating significant performance improvements over existing methods on benchmark instances.

Contribution

It develops a polynomial-time separation algorithm for Benders cuts and proposes a branch-and-Benders-cut method that outperforms current state-of-the-art techniques.

Findings

Outperforms existing methods by an order of magnitude on benchmarks

Provides a polynomial-time algorithm for Benders cut separation

Introduces a new compact formulation for the p-median problem

Abstract

The p-median problem is a classic discrete location problem with several applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most efficient formulation in the literature. We prove that the Benders cuts can be separated by a polynomial time algorithm. The Benders decomposition also leads to a new compact formulation for the p-median problem. We implement a branch-and-Benders-cut approach that outperforms state-of-the-art methods on benchmark instances by an order of magnitude.