Bi-objective optimization approach to a multi-layer location-allocation problem with jockeying

Multi-layer congested facility location problems (MLCFLPs) have been receiving increased attention over the past few years. In MLCFLPs, each layer includes several facilities that can provide different service. Reducing the total idle times in each layer's facilities' queues is of the utmost importance - especially when the network includes multiple identical collaborative facilities or when the organizers desire to apply severe dispatching rules in queue monitoring. As a new provision in this field of research, this study addresses a novel MLCFLP that includes a classical queuing system with jockeying, which allows the applicants/customers to receive service from the other layers of the network. Regarding the optimization approach, two objective functions are considered: (1) the minimization of the sum of waiting and traveling times, and (2) the minimization of facilities' maximum idleness probability. To find Pareto optimal solutions, an augmented-constraint method is utilized for solving the problem. Since the MLCFLP is NP-hard, in medium- and large-scale problems the MLCFLP is solved by a non-dominated sorting genetic algorithm (NSGA-II). Considering that the quality of meta-heuristic algorithms is critically related to their initial parameters, the Taguchi approach is used to calibrate the parameters of the NSGA-II. Four standard performance metrics are employed to evaluate the algorithms. We examine the effect of jockeying in a simulated manufacturing system as an example of a real-world problem. Several numerical experiments are introduced to evaluate the applicability of the model along different scales. The results demonstrate that in small-scale problems, the augmented epsilon-constraint method is a satisfactory solution. However, in the medium and larger-scale experiments, the NSGA-II provides optimal solutions with significantly lower computational times.