Equitable service by a facility: Minimizing the Gini coefficient

In this paper, we investigate the location of facilities with equity considerations, namely, minimizing the Gini coefficient of the Lorenz curve based on service distances. Properties of the Gini coefficient in the context of location analysis are investigated both for demand originating at points and demand generated in an area. An algorithm that finds the optimal location of one facility in a bounded area in the plane when demand is generated at a set of demand points, is constructed. Randomly generated problems with up to 10,000 demand points are successfully solved in a reasonable computer time.