A Meta-Heuristic Approach for Hub Location-Routing Problem with Capacity and Balancing Decisions

Hub location-routing problem is a practical subject in the last decades. This study considers a many-to-many hub location-routing problem where the best locations of hubs and tours for each hub are determined with simultaneous pickup and delivery. First, an optimization model is proposed to minimize the total sum of fixed costs of locating hubs, the costs of handling, traveling, assigning, and transportation costs. To find practical solutions, the hubs have constrained capacity, in which single allocations can service every node to the hubs. What is more, the balancing requisites are imposed on the network by allocating the appropriate number of demand nodes to the hubs. Then the problem is solved using GAMS software for small-size instances of the problem. Due to the NP-hard nature of the problem, the proposed optimization model is solved by the Genetic Algorithm (GA) and Imperialist Competitive Algorithm (ICA). For the problem instances, the comparative results indicate that GA has a better performance compared to ICA, and incorporating capacity and balancing considerations can influence the reduction of costs of the investigated network.