A fractional model for locating semi-desirable facilities on networks

In this paper, we address the problem of locating a series of facilities on a network maximizing the average distance to population centers (assumed to be distributed in the plane) per unit transportation cost (a function of the network distances to users). A finite dominating set is constructed, allowing the resolution of the problem by standard integer programming techniques. We also discuss some extensions of the model (including, in particular, the Weber problem with attaction and repulsion in networks), for which ϵ-dominating sets are derived.