Siting Facilities along a Line when Equity of Service is Desirable

The problem where a number of facilities need to be sited along a line is often encountered in practice. In this paper, we consider the case where the objective is to achieve equity of service, which we accomplish by minimizing the maximum distance between two adjacent facilities. We also consider a stronger variation where the objective is not only to minimize the maximum distance, but also to hierarchically minimize the second maximum distance and so on. We then assume that there is a cost for siting a facility at a given point, and consider bicriteria extensions where the objective is to simultaneously achieve cost efficiency and service equity. Only the first among these various cases has thus far been addressed in the literature. We provide simple and effective solutions for all of them (indicating where and how solutions can be obtained using available methods).