Undesirable facility location using Lagrangian relaxation method

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.