A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem

TL;DR

This paper introduces a branch-and-price method and heuristics for the Continuous Multifacility Monotone Ordered Median Problem, demonstrating improved performance over traditional formulations in medium-sized instances.

Contribution

The paper presents a novel branch-and-price algorithm and two heuristics specifically designed for the continuous multifacility ordered median problem, with detailed implementation and performance analysis.

Findings

Branch-and-price outperforms compact formulations on medium-sized instances.

Matheuristics provide good solutions for larger instances.

Extensive computational experiments validate the effectiveness of the proposed methods.

Abstract

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest facility among the $p$ selected, also in a continuous space. We propose a new branch-and-price procedure for this problem, and two mathehuristics. One of them is a decomposition-based procedure and the other an aggregation-based heuristic. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performance in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.