Semi-obnoxious single facility location in Euclidean space

This paper deals with the problem of determining within a bounded region the location for a new facility that serves certain demand points. For that purpose, the facility planners have two objectives. First, they attempt to minimize the undesirable effects introduced by the new facility by maximizing its minimum Euclidean distance with respect to all demand points (maximin). Secondly, they want to minimize the total transportation cost from the new facility to the demand points (minisum). Typical examples for such “semi-obnoxious” facilities are power plants that, as polluting agents, are undesirable and should be located far away from demand points, while cost considerations force planners to have the facility in close proximity to the customers. We describe the set of efficient solutions of this bi-criterion problem and propose an efficient algorithm for its solution.