Comparison of four models for dispersing facilities

Given a set of candidate points in some space, this paper considers the problem of selecting a dispersed subset. Possible applications include the location of mutually undesirable facilities. Four different models of dispersal are considered. Mathematical programming formulations are given, and an implicit enumeration procedure, which solves all four problems in parallel, is developed. A simple heuristic is also developed which gives very good solutions. Computational experience with the four models is reported in detail, in which the solutions of the models are compared with an emphasis on similarities and differences. Possible extensons of the models are also considered, to incorporate minimum distance separation constraints and existing facility points.