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 an optimization framework 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 models provide a precise tradeoff 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. Special cases of our general models reduce to the classical notion of proportional fairness. Computationally, the underlying mixed-integer quadratic optimization models are challenging to solve naively for medium-sized instances. We propose several enhancements that facilitate a feasible solution, and develop a heuristic that does not require solving an optimization model. 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. 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 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.
Schmitt, C. & Singh, B (November, 2021). Balancing preferential access and fairness with an application to waste management: mathematical models, optimality conditions, and heuristics. Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen