Scheduling direct and indirect trains and containers in an intermodal setting

The focus of our research is on rail transportation of intermodal containers. We address the problem of determining day-of-week schedules for both direct and indirect (via a hub) trains and allocating containers to these trains for the rail (linehaul) portion of the intermodal trip. The goal is to minimize operating costs, including a fixed charge for each train, variable transportation and handling costs for each container and yard storage casts, while meeting on-time delivery requirements. We formulate the problem as an integer program and develop a novel decomposition procedure to find near-optimal solutions. We also develop a method to provide relatively tight bounds on the objective function values. Finally, we compare our solutions to those obtained with heuristics designed to mimic current operations, and show that a savings of between 5 and 20% can be gained from using our solution procedure.