In this work, a semi-obnoxious facility must be located in the Euclidean plane to give service to a group of customers. Simultaneously, a set of populated areas, with shapes approximated via polygons, must be protected from the negative effects derived from that facility. The problem is formulated as a margin maximization model, following a strategy successfully used in Support Vector Machines. Necessary optimality conditions are studied and a finite dominating set of solutions is obtained, leading to a polynomial algorithm.
Technical Report MOSI/20, MOSI Department, Vrije Universiteit Brussel, October 2006