Models and Algorithms for Intermodal Transportation and Equipment Selection.

A classical problem in transportation is a combined format problem involving several types of transportation such as truck and train that operate on both flexible and fixed schedules. This is the intermodal transportation problem: a problem closely related to Less-Than-Load transportation where consolidation points are required in the transportation network with the side constraint that multiple types of equipment may be operated within the network. We consider an intermodal transportation problem that also incorporates the problem of equipment selection. This problem is inspired by the requirements of a leading European construction group currently delivering a product from a handful of factories via a trucking network to several destinations. The company is considering opportunities to expand the network to an intermodal transportation network by adding rail and/or barge links as well as buying the necessary equipment. We model this network design problem as a capacitated multi-commodity network flow problem, with flow variables creating a distribution schedule from factories to destinations such that demands at the destinations are satisfied. Flow variables are binary, ensuring that flow cannot be split. The resulting model is large scale due to the time step; has weak bounds due to the flow bundling constraints; and also contains SOS1 constraints. To address these issues, we propose a reduction preprocessing approach and a branch-and-cut step to improve the bounds. We exploit the structure created by the time step and SOS1 constraints to generate a Benders decomposition approach that elicits a 2-stage stochastic programming solution.