Resumen de Obnoxious facility location in multiple dimensional space

Pawel Kalczynski, Atsuo Suzuk, Zvi Drezner

• The obnoxious facility location problem in three dimensions is optimally solved by an exact method based on Apollonius spheres, and in three or more dimensions by a modifcation of the Big-Cube-Small-Cube (BCSC, Schobel and Scholz in Comput Oper Res 37:115–122, 2010) global optimization method to within a pre-specifed accuracy. In our implementation, no specifcally designed bounds are required.

  The general purpose bounds proposed in this paper do not employ derivatives of the functions. Such an approach can be used, for example, for locating multiple obnoxious facilities in two dimensional space, locating obnoxious facilities on the plane with demand points in three-dimensional space, or applying diferent distance norms. We concentrated mainly on three-dimensional problems which have the most practical applications. A four dimensional practical application is presented.

  We solved problems in a cube, part of a cube, a non-convex building, and locating a facility on the plane when demand points are in a three-dimensional space. We also solved problems in 4–6 dimensions to illustrate the efectiveness of the BCSC method.