Document Type : Research Paper


Overally location problem could be classified as desirable facility location and undesirable facility location. In the undesirable facility location problem contrary to desirable location, facilities are located far from service receiver facilities as much as possible. The problem of locating such facilities is discussed in this paper. This research is focused on the “not in my backyard” (NIMBY) which refers to the social phenomena in which residents are opposed to locate undesirable facilities around their houses. Examples of such facilities include electric transmission lines and recycling centers. Due to the opposition typically encountered in constructing an undesirable facility, the facility planner should understand the nature of the NIMBY phenomena and consider it as a key factor in the determining facility location. A integer linear model of this problem and a Lagrange relaxation method are proposed in this research. This method relaxes up the hard constraints and adds the constraints to the objective function with a Lagrangian multiplier. To show that the Lagrangian relaxation method is computationally powerful exact solution algorithm and is capable to solve the medium-size problems, the performance of the proposed algorithm is examined by applying it to several test problems.


[1] E. Melachrinoudis, 1984. Determining an optimum location for an undesirable facility in a workroom environment, Appl. Math. Model., 9, 365-369.
[2] A. Mehrez, Z. Sinuany-stern, A. Stulman, 1985. The one-dimensional single facility maximin distance location problem, Comput. Ops. Res., 12, 51-60.
[3] O. Berman, Z. Drezner, 2000. A note on the location of an obnoxious facility on a network, Eur. J. Oper. Res., 120, 215-217.
[4] S.E. Mousavi, M. Heydar, S.M.H. Mojtahedi, S.M. Mousavi, 2008. A fuzzy multi objective decision making approach for locating undesirable facilities and hazardous materials, Proceedings of the 2008 IEEE ICMIT, 1094-1098.
[5] B. D. Song, J. R. Morrison, Y. D. Ko, 2013. Efficient location and allocation strategies for undesirable facilities considering their fundamental properties, Comput. Ind. Eng., 65, 475–484.
[6] L.A.Wolsey,1998. Integer Programming, John Wiley & Sons, INC.
[7] M. Colebrook, J. Gutierrez, J. Sicilia, 2005. A new bound and an O(mn) algorithm for the undesirable1-median problem (maxian) on networks, Computers & Operations Research, 32, 309–325.
[8] E. Erkut and S. Neuman, 1989. Analytical models for locating undesirable facilities, European Journal of Operational Research, 40, 275-291.
[9] L. Giannikos, 1998. A multi-objective programming model for locating treatment sites and routing hazardous wastes, European Journal of Operational Research, 104, 333–342.
[10] S. Ratick, A. White,1988. A Risk-Sharing Model for Locating Noxious Facilities. Envrionment and Planning B, 15, 165–179.
[11] J. Brimberg and H. Juel, 1998, On Locating a Semi-desirable Facility on the Continuous Plane, Int. Trans. Opl. Res., 51, 59-66.
[12] E. Carrizosa and F. Plastria, 1999, Location of Semi-obnoxious Facilities, Studies in Locational Analysis,12 , 1-27.
[13] E. Melachrinoudis and T.P. Cullinane, 1985, Locating an Undesirable Facility within a Geographical Region Using the Maximin Criterion, Journal of Regional Science, 25, 115-127.
[14] E. Melachrinoudis and T.P. Cullinane, 1986, Locating an Obnoxious Facility within a Polygonal Region, Annals of Operations Research, 6, 137-145.
[15] E. Melachrinoudis and Z. Xanthopulos 2003, Semi-obnoxious Single Facility Location in Euclidean Space, Computers & Operations Research, 30, 2191-2209.
[16] F. Plastria, 1996, Optimal Location of Undesirable Facilities: A Selective Overview, Belgian Journal of Operations Research, Statistics and Computer Science, 36, 109-127.
[17] J. Rakas, D. Teodorovi, T. Kim, 2004, Multi-objective modeling for determining location of undesirable facilities, Transportation Research Part D, 9, 125-138.
  میرحسنی،سید علی، 1393، برنامه ریزی تصادفی، انتشارات دانشگاه صنعتی امیرکب