عنوان مقاله [English]
Most of the studies, which deal with the congested facility location problems, assumed that each customer must be only served by a facility, such that if the corresponding facility is out of service, the customers request will not be covered by other facilities. Considering backup facilities for customers help mathematical model to cope with the real-world situations; however, the common queue models will not be suitable any longer for analyzing the service system. In these situations, a common queueing system is hyper-cube queue models, in which the states of the queue are represented by a binary vector, showing the availability (i.e., 1) and unavailability or busyness (i.e., 0) of the facilities. In this paper, we use the concept of hypercube queue system in modelling emergency facility location problem with mobile servers. The proposed model aims to select a number of facilities from a number of candidate sites in a way that total expected waiting time for customers is minimized. It is assumed that each customers demand is provided by the closest free facility, and his or her arrival (call for service) process is considered to be Poisson process. Furthermore, in each facility, a single server with exponentially distributed service times is established. All previous studies on the applications of hyper-cube queue models in location problems considered the structure of queue model in terms of steady-state equations in the body of the proposed heuristic algorithms. For the first time, the steady-state equations of the hyper-cube queue model are included in the mathematical model; hence, the optimal solution can be found by solving the proposed model. Moreover, since the problem is NP-hard, a genetic algorithm is developed to solve large-scale problems. In order to evaluate the accuracy of the proposed model and the effectiveness of the proposed algorithm, a number of numerical examples are presented and analyzed. The results of the numerical examples demonstrate the acceptable performance of the proposed genetic algorithm.