Benders decomposition applied to a robust multiple allocation incomplete hub location problem

Abstract This paper focuses on a multiple allocation incomplete hub location problem in which a hub network can be partially interconnected by hub arcs, direct connections between non-hub nodes are allowed, and uncertainty is assumed for the data of origin-destination demands and hub fixed costs. This problem consists of locating hubs, activating hub arcs and routing the demand flows over the designed network such that the total cost is minimized. The total cost is composed of fixed setup costs for hubs and hub arcs, and of transportation costs. This problem has economical and social appeals for designers of public transportation systems and other hub networks. A robust optimization approach is chosen to address the data uncertainty considering that demand flows and fixed setup costs are not known with certainty in advance. The computational experiments on benchmark instances from the hub location literature showed that the proposed robust model renders better assurance of not violating budget constraints than the deterministic version. Further, two specialized Benders decomposition frameworks and an ILS-VND stochastic local search procedure are also devised to tackle larger problem instances with up to 100 nodes in reasonable computational times.