Multiple allocation tree of hubs location problem for non-complete networks

We study the Multiple Allocation Tree of Hubs Location Problem where a tree topology is required among the hubs and transportation cost of sending flows between OD pairs is minimized. Unlike most studies in the literature that assume a complete network with costs satisfying the triangle inequality to formulate the problem, we define the problem on non-complete networks and develop a modeling approach that does not require any specific cost and network structure. The proposed approach may provide more flexibility in modeling several characteristics of real-life hub networks. Moreover, the approach may produce better solutions than the classical approach, which may result from the differences in the selected hubs, the flow routes between origin-destination points, and the assignment of non-hub nodes to hub nodes. We solve the proposed model using CPLEX-based branch-and-bound algorithm and Gurobi-based branch-and-bound algorithm with Norel heuristic and develop Benders decomposition-based heuristic algorithms using two acceleration strategies, namely, strong cut generation and cut disaggregation. We conduct computational experiments using problem instances defined on non-complete networks with up to 500 nodes. The results indicate that the Benders-type heuristics are especially effective in finding good feasible solutions for large instances.