A multiobjective model for locating undesirable facilities

In this paper, we develop a multiobjective model to depict the tradeoffs involved when locating one or more undesirable facilities to service a region. We assume that the region requires a certain capacity of service, and that this capacity can be met by building a combination of different-sized facilities. Examples could include sanitary landfills, incinerators, and power-generating stations. Our objectives are to minimize the total cost of the facilities located, the total opposition to the facilities, and the maximum disutility imposed on any individual. Opposition and disutility are assumed to be nonlinearly decreasing functions of distance, and increasing functions of facility size. We formulate our model as a multiobjective mixed-integer program, and generate the set of efficient solutions using an enumeration algorithm. Our code can solve realistically sized problems on a microcomputer. We give an example to illustrate the tradeoffs between the three objectives, which are inevitable in such a location problem.This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada (OGP 25481), and by the Nova Fellowship of the Faculty of Business, University of Alberta.