عنوان مقاله [English]
In the real world, we consider the location of facilities that communicate with each other that known as hierarchical location. Nowday the major problem in many service and industrial centers is providing new service centers and facilities in new places and allocate customers to use this facility. As in the healthcare system there is hierarchical structure and different layers in this model can provide the customer٬s needs, so in this paper, a multi-location programming model is proposed for modeling hierarchical systems with two layers. Although utility systems are commonly used as a hierarchical system, spatial problems for single-level systems have been investigated. Hierarchical systems must decide on the locations of their interactions in a multi-layer configuration. The primary objective in a typical hierarchical facility location problem is to determine the location of facilities in a multi-level network in a way to serve the customers at the lowest level of hierarchy This further acknowledges the need to focus on solving relocation hierarchical facility location problem using innovative approaches such as dynamic time elements. Hierarchical facility location models have been widely applied in public facility location problems. The hierarchical structures use almost in public and private sections.
In this paper, we present the hierarchical facility location-allocation with two layers, Because of demand congestion in service networks, an M/M/1/K queuing system is considered. We assume that the capacity of each facility is limited. In this paper servers of each level offer a different service and users can go to the higher level server without a low-level server refers them to it. We formulate the problem as nonlinear integer-programming models and proposed four algorithm (including a multi-objective Non-Dominated Sorting Genetic algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO)) to solve them. The parameters of the proposed algorithms are based on the Taguchi test design method. At the end, some numerical examples are generated to analyze and to statistically compare the performance of the proposed solving algorithms.