A note on equity across groups in facility location

An equity model between groups of demand points is proposed. The set of demand points is divided into two or more groups. For example, rich and poor neighborhoods and urban and rural neighborhoods. We wish to provide equal service to the different groups by minimizing the deviation from equality among groups. The distance to the closest facility is a measure of the quality of service. Once the facilities are located, each demand point has a service distance. The objective function, to be minimized, is the sum of squares of differences between all pairs of service distances between demand points in different groups. The problem is analyzed and solution techniques are proposed for the location of a single facility in the plane. Computational experiments for problems with up to 10,000 demand points and rectilinear, Euclidean, or general 𝓁p distances illustrate the efficiency of the proposed algorithm.