Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions

Christian Schmitt () and Bismark Singh ()
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Christian Schmitt: Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, 91058 Bavaria, Germany
Bismark Singh: School of Mathematical Sciences, University of Southampton, Southampton S017 1BJ, United Kingdom

INFORMS Journal on Computing, 2024, vol. 36, issue 5, 1150-1167

Abstract: Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them, fairness between the usage of facilities becomes especially important. Limited research exists on this notion of fairness. To close this gap, we develop a series of optimization models for the allocation of populations of users to facilities such that access for users is balanced with a fair utilization of facilities. The optimality conditions of the underlying nonconvex quadratic models state the precise balance between accessibility and fairness. We define new classes of fairness and a metric to quantify the extent to which fairness is achieved in both optimal and suboptimal allocations. We show that a continuous relaxation of our central model is sufficient to achieve a perfect extent of fairness, while a special case reduces to the classical notion of proportional fairness. Our work is motivated by pervasive ecological challenges faced by the waste management community as policymakers seek to reduce the number of recycling centers in the last few years. As a computational case study, applying our models on data for the state of Bavaria in Germany, we find that even after the closure of a moderate number of recycling centers, large degrees of access can be ensured, provided that the closures are conducted optimally. Fairness, however, is impacted more, with facilities in rural regions shouldering larger loads of visiting populations than those in urban regions.

Keywords: quadratic combinatorial optimization; KKT optimality conditions; fairness; waste management; facility location problems (search for similar items in EconPapers)
Date: 2024
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