Multimodal Hub Network Design With Flexible Routes

This paper introduces a multimodal hub network design problem with flexible routes. Routes are flexible in the sense that they may contain a mix of hub and non-hub nodes. Nonetheless, commodity transfers can only occur at hubs, while transportation costs are flow-dependent, i.e., scale economies stem from the transport technology chosen to operate the routes. We propose a mixed integer mathematical program, and two metaheuristics based on the adaptive large neighborhood search paradigm to solve the problem. Extensive computational experiments show the performance of the formulation and of the devised algorithms in solving benchmark instances with up to 50 nodes.