An extended version of a Branch-Price-and-Cut Procedure for the Discrete Ordered Median Problem

TL;DR

This paper introduces an advanced branch-price-and-cut algorithm to efficiently solve the Discrete Ordered Median Problem, a complex set partitioning problem with an exponential number of variables, improving solution times for small to medium instances.

Contribution

It extends existing methods by developing a column generation approach combined with branch-price-and-cut for the DOMP, enabling optimal solutions within reasonable computational times.

Findings

Effective solution of small to medium DOMP instances

Column generation approach improves relaxation bounds

Branch-price-and-cut achieves optimality efficiently

Abstract

The Discrete Ordered Median Problem (DOMP) is formulated as a set partitioning problem using an exponential number of variables. Each variable corresponds to a set of demand points allocated to the same facility with the information of the sorting position of their corresponding costs. We develop a column generation approach to solve the continuous relaxation of this model. Then, we apply a branch-price-and-cut algorithm to solve to optimality small to moderate size of DOMP in competitive computational time.