Abstract
This paper considers the problem of locating semi-obnoxious facilities assuming that demand points within a certain distance from an open facility are expropriated at a given price. The objective is to locate the facilities so as to minimize the total weighted transportation cost and expropriation cost. Models are developed for both single and multiple facilities. For the case of locating a single facility, finite dominating sets are determined for the problems on a plane and on a network. An efficient algorithm is developed for the problem on a network. For the case of locating multiple facilities, a branch-and-bound procedure using Lagrangian relaxation is proposed and its efficiency is tested with computational experiments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agar MC and Salhi S (1998). Lagrangian heuristics applied to a variety of large capacitated plant location problems. J Opl Res Soc 49: 1072–1084.
Beasley JE (1993). Lagrangian relaxation. In: Reeves CR (ed). Modern Heuristic Techniques for Combinatorial Problems. John Wiley & Sons, Inc., New York, pp 243–303.
Berman O, Drezner Z and Wesolowsky GO (2003). The expropriation location problem. J Opl Res Soc 54: 769–776.
Berman O and Krass D (2002). The generalized maximal covering location problem. Comput Opns Res 26: 563–581.
Berman O and Wang Q (forthcoming). Locating semi-obnoxious facilities with expropriation. Comput Opns Res, Special Issue on Location, in press.
Brimberg J and Juel H (1998). A bicriteria model for locating a semi-desirable facility in the plane. Eur J Opl Res 106: 144–151.
Cornuejols G, Fisher ML and Nemhauser GL (1977). Location of bank accounts to optimize float: an analytical study of exact and approximate algorithms. Mngt Sci 23: 789–810.
Church RL and Garfinkel RS (1978). Locating an obnoxious facility on a network. Transport Sci 12: 107–118.
Church RL and Revelle C (1974). The maximal covering location problem. Papers Regional Sci Assoc 32: 101–118.
Erkut E and Neuman S (1989). Analytical models for locating undesirable facilities. Eur J Opl Res 40: 275–291.
Melachrinoudis E (1999). Bicriteria location of a semi-obnoxious facility. Comput Indust Eng 37: 581–593.
Narula SC, Ogbu VI and Samuelsson HM (1977). An algorithm for the p-median problem. Opns Res 25: 709–712.
Acknowledgements
This research was supported by a grant from the National Sciences and Engineering Research Council of Canada. We are grateful to two anonymous referees for their constructive comments and suggestions which helped us to improve the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Berman, O., Wang, Q. Locating semi-obnoxious facilities with expropriation: minisum criterion. J Oper Res Soc 58, 378–390 (2007). https://doi.org/10.1057/palgrave.jors.2602151
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1057/palgrave.jors.2602151