Benders decomposition applied to profit maximizing hub location problem with incomplete hub network

This paper addresses a profit maximizing multiple allocation hub network design problem, which is a hub location problem with incomplete hub network, aiming to determine the quantity and location of the hubs, allocate demand nodes to these hubs, establish the network topology, and route the demand flows to satisfy the demands between the origin and destination pairs that were selected to be served in order to obtain the highest profit. This problem also considers the multiple allocation strategy, does not allow direct connections between non-hub nodes, does not impose capacity constraints, and assumes that there are fixed costs involved in installing hubs and installing hub arcs. A new formulation for the problem is presented and it is proved that this formulation is stronger than another one in the literature, which models the same problem. Several versions of the Benders decomposition method, combining the generation of Pareto-optimal cuts, multiple cuts strategies, and Benders branch-and-cut scheme, are proposed and analyzed through extensive computational experiments on benchmark instances. The best-proposed Benders decomposition versions were compared with the CPLEX solver, with and without the activation of its Benders decomposition algorithm. The results showed that these algorithms perform much better than the solver versions. The proposed Benders decomposition approach can solve benchmark instances with up to 150 nodes.