A multi-layer congested facility location problem with consideration of impatient customers in a queuing system

This study presents a novel multi-objective model for a facility location-allocation problem with congestion in a multi-layer network. The proposed model contemplates the existence of impatient customers within a classical queuing system, namely M/M/1. The network is configured by determining the optimal number of facilities in each layer and allocation of customers to the facilities in a hierarchy facilities problem. Regarding the first objective function of the model, we minimize the sum of aggregate costs related to the customers' waiting times, as well as the costs imposed by the impatience of the customers. In the second objective function, the costs associated with the sum of aggregate idleness of facilities are minimized. The proposed multi-objective multi-layer facility location-allocation (MLFLA) problem is solved by an evolutionary approach according to the Pareto envelope-based selection algorithm II (PESA-II). Parameters of the algorithm are tuned by Taguchi method. Then, the performance of the algorithm is reported by four performance metrics introduced for multi-objective optimization problems. The computational run times of 10 test problems demonstrate that the solution methodology is capable of solving the problem with large network sizes.