Scheduling direct and indirect trains and containers in an intermodal setting

The focus of our research is on rail transportation of intermodal container s. We address the problem of determining day-of-week schedules for both dir ect and indirect (via a hub) trains and allocating containers to these trai ns for the rail (linehaul) portion of the intermodal trip. The goal is to m inimize 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 nea r-optimal solutions. We also develop a method to provide relatively tight b ounds on the objective function values. Finally, eve compare? our solutions to those obtained with heuristics designed to mimic current operations, an d show that a savings of between 5 and 20% can be gained from using our sol ution procedure.