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.

Facility location problem is a branch of operations research and computational geometry. It covers the best allocation of facilities to minimize transportation costs by considering the factors involved (e. g., avoiding the placement of dangerous materials near the premises and the facilities of competitors). Given the unique customer characteristics and the fi, erce market competition of business-to-consumer e-commerce, the expected value model and chance-constrained model for uncertain Facility location problems were constructed. Owing to the intricacies of the competitive market, supply capacity, delivery cost, and customer demand were assumed as uncertain variables. The deterministic equivalent forms of the models were discussed using the inverse uncertainty distribution method. A hybrid algorithm was proposed to solve these models. Some numerical experiments were used to verify the effectiveness of the proposed models and method.

Introduction: The Voronoi game is a simple geometric model for competitive Facility location problem which is played by two players, White and Black, in a continuous space (one-dimensional or two-dimensional). In the one-round game, White places all his n points. After that, Black places the same number of points on the game space. The players Cannot change or reuse a point that was placed before. At the end of the game, the Voronoi diagram of all 2n points is constructed and a player who obtains the larger total area is the winner...

location theory is an interstice field of optimization and operations research. In the classic location problem, the goal is finding the location of one or more facilities such that some criteria such as transportation cost, the sum of distances passed by clients, total service time and cost of servicing are minimized. In this paper, we consider the goal location problem. In the goal location problem, the ideal is locating the Facility in the distances ri, from the i-th client. However, in the most instances, the solution of this problem doesn’ t exist. Therefore, we consider the minimizing of distances between clients and ideal point. The minimizing sum of square errors and minimizing absolute errors under Lp norm are considered as the objective function. We use the Weiszfeld like, Gauss-Newton and imperialist competitive algorithms for solving the problem. Then we compare the results which obtained by these methods for some test problems.

In 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 study. This research is focused on the ‘ not in my backyard’ (NIMBY) phrase 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 determining Facility location. Because of the adverse effects of these facilities, coupled with the uncertainty in the real world, it is estimated taking into account the potential uncertainty. This problem has been considered in the discrete space. The mathematical model is presented and methods to deal with uncertainty and stochastic programing problems modeling and methods used in the study are presented. According to the NP-hard problem, Simulated Annealing suggested for solving problems in large-scale. Numerical experiments to evaluate and validate the mathematical modeling and proposed algorithm are considered and operation of the proposed algorithm to solve various problems with genetic algorithms available in the literature about the problem is compared.

Network location models comprise one of the main categories of location models. These models have various applications in regional and urban planning as well as in transportation, distribution, and energy management. In a network location problem, nodes represent demand points and candidate locations to locate the facilities. If the links network is unchangeably determined, the problem will be an FLP (Facility location Problem). However, if links can be added to the network at a reasonable cost, the problem will then be a combination of Facility location and NDP (Network Design Problem). In previous studies, capacity of facilities was considered to be a constraint while capacity of links was not considered at all. The proposed MIP model considers capacity of facilities and links as decision variables. This approach increases the utilization of facilities and links, and prevents the construction of links and Facility locations with low utilization. Furthermore, Facility location cost (link construction cost) in the proposed model is supposed to be a function of the associated Facility (link) capacity. Computational experiments as well as sensitivity analyses performed indicate the efficiency of the model.