Fairness in Maximal Covering Location Problems

TL;DR

This paper introduces a flexible mathematical framework for incorporating fairness into maximal covering location problems, using advanced optimization techniques and fairness measures, supported by extensive computational experiments.

Contribution

It develops a novel optimization model that integrates fairness into location problems using ordered weighted averaging and $$-fairness operators, with reformulations for efficient solving.

Findings

Models effectively incorporate fairness in location problems.

Reformulations enable solving complex mixed integer problems.

Computational results validate the approach's practicality.

Abstract

This paper provides a general mathematical optimization based framework to incorporate fairness measures from the facilities' perspective to Discrete and Continuous Maximal Covering Location Problems. The main ingredients to construct a function measuring fairness in this problem are the use of: (1) ordered weighted averaging operators, a family of aggregation criteria very popular to solve multiobjective combinatorial optimization problems; and (2) $\alpha$-fairness operators which allow to generalize most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are firstly formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained on an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.