A capacitated hub location problem in freight logistics multimodal networks

In this paper we deal with a capacitated hub location problem arising in a freight logistics context; in particular, we have the need of locating logistics platforms for containers travelling via road and rail. The problem is modelled on a weighed multimodal network. We give a mixed integer linear programming model for the problem, having the goal of minimizing the location and shipping costs. The proposed formulation presents some novel features for modelling capacity bounds that are given both for the candidate hub nodes and the arcs incident to them; further, the containerised origin-destination (\(o-d)\) demand can be split among several platforms and different travelling modes. Note that here the network is not fully connected and only one hub for each \(o-d\) pair is used, serving both to consolidate consignments on less transport connections and as reloading point for a modal change. Results of an extensive computational experimentation performed with randomly generated instances of different size and capacity values are reported. In the test bed designed to validate the proposed model all the instances up to 135 nodes and 20 candidate hubs are optimally solved in few seconds by the commercial solver CPLEX 12.5.