Equity Maximizing Facility Location Schemes

A plethora of methods exists for finding cost minimizing facility locations. However, it is generally true that once optimal locations have been found, the benefits derived from the facilities will not be distributed equally across customers due to differences in travel costs. Though some schemes aimed at providing more equitable facility locations have been proposed, none of these schemes are fully satisfactory in that there are always customers who are winners or losers with respect to the cost of travel. In this paper, we address the equity question using taxes (in the case of a central authority) or side payments (in the case of cooperating authorities) to redress benefit inequities. We show that the usual distance minimizing facility location formulations are still optimal, providing a very simple tax or side payment scheme is used to equalize benefits for all customers in the system. In the event that taxes or side payments cannot be utilized, our analysis leads to a natural method for locating facilities to minimize inequities. For the case of a single facility, the complexity of our approach is O(n⁴), where n is the number of customer demand points (nodes) in the service network.