Solving a hub location-routing problem with a queue system under social responsibility by a fuzzy meta-heuristic algorithm

This paper presents a new multi-objective mathematical model for the hub location and routing problem under uncertainty in flows, costs, times, and number of job opportunities. This model aims at minimizing the total transportation cost consisting of routing and fixed cost and maximizing the employment and regional development as social responsibility. An M/M/c/K queue system is applied to estimate the waiting time at hub nodes and maximize the responsiveness. Also, a fuzzy queuing method is applied to model the uncertainties in this network. A powerful evolutionary meta-heuristic algorithm based on fuzzy invasive weed optimization, variable neighborhood search, and game theory is developed to solve the introduced model and obtain near-optimal Pareto solutions. Many experiments as well as a real transportation case-study show the superiority of the proposed approaches compared to the state-of-the-art algorithm.