Solving a new bi-objective hierarchical hub location problem with an M∕M∕c queuing framework

This paper presents a bi-objective hierarchical hub location problem with hub facilities as servicing centers. The objectives are to minimize the total cost (i.e., fixed cost of establishing hub facilities and transportation cost) and the maximum route length, simultaneously. Hub facilities are categorized as central and local ones. The queuing frameworks for these types of facilities are considered as M∕M∕c and M∕M∕1, respectively. Moreover, density functions for the traveling time and number of entities are assumed to be Exponential and Poisson functions. The presented mathematical model is solved by a new game theory variable neighborhood fuzzy invasive weed optimization (GVIWO) as introduced in this paper. To evaluate the efficiency of this proposed algorithm, some experiments are conducted and the related results are compared with the non-dominated sorting genetic algorithm (NSGA-II) and hybrid simulated annealing (HSA) algorithm with respect to some comparison metrics. The results show that the proposed GVIWO algorithm outperforms the NSGA-II and HSA. Finally, the conclusion is provided.