A Two-phase Approach for Real-world Train Unit Scheduling

A two-phase approach for the train unit scheduling problem is proposed. The first phase assigns and sequences train trips to train units temporarily ignoring some infrastructure details at train stations. The solutions of the first phase would be near-operable. The second phase focuses on satisfying the remaining constraints with respect to detailed station layouts. Real-world scenarios such as compatibility among traction types and time allowances for coupling/decoupling activities are considered, so that the solutions would be fully operable. The first phase is modeled as a large scale integer multi-commodity network flow (MCNF) problem. A branch-and-price integer linear programming approach is proposed. Preliminary experiments have shown that the approach would not yield solutions in reasonable time for problem instances exceeding about 1000 train trips. The train company collaborating in this research operates over 2400 train trips on a typical weekday. Hence, a heuristic has been designed for compacting the problem instance to a much smaller size before the ILP solver is applied. The process is iterative with evolving compaction based on the results from the previous iteration thereby converging to near optimal results. The second phase is modeled as a multidimensional matching problem with a mixed integer linear programming (MILP) formulation.