Title: Equitable Facility Location

Abstract: Facility location is one of the most common applications of combinatorial optimization. Models that minimize the mean distance between a “customer” and their assigned facility behave well computationally and make sense from a modeling perspective in many contexts. However, if equity is a concern, the mean is not an ideal metric. Many equitable facility location models have been developed in the literature, but they tend not to scale well computationally because nonlinear optimization models with integer variables are very hard to solve. Historically applied to incomes, equally distributed equivalents (EDEs) provide more accurate measures of the experience of a population than the population mean by penalizing values on the “bad” end of the distribution; i.e., very low incomes pull the EDE below the mean.  We develop a computationally scalable facility location model that minimizes the Kolm-Pollak EDE, a metric that is applied in the Environmental Justice literature to compare exposure to environmental harms, such as air pollution, across demographic groups. We apply our methods to food deserts and election polling locations, demonstrating that optimizing over the Kolm-Pollak EDE, rather than the mean, can lead to big gains in equity while still resulting in near-optimal average distances.