A comparison of formulations and solution methods for the Minimum-Envy Location Problem. Additional results

TL;DR

This paper introduces a new equity-based criterion for facility location problems, focusing on minimizing total envy among demand points with strict preferences, and compares various integer linear programming formulations through extensive computational testing.

Contribution

It proposes a novel total envy criterion for location problems and evaluates multiple ILP formulations to model this approach.

Findings

Different formulations show varying computational performances.

Some formulations effectively solve small instances, others scale poorly.

The new envy criterion provides a fresh perspective on equitable facility placement.

Abstract

We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances.