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 station infrastructure details. Real-world scenarios such as compatibility among traction types and banned/restricted locations and time allowances for coupling/ decoupling are considered. Its solutions would be near-operable. The second phase focuses on satisfying the remaining station detail requirements, such that the solutions would be fully operable. The first phase is modeled as an integer fixed-charge multicommodity flow (FCMF) problem. A branch-and-price approach is proposed to solve it. Experiments have shown that it is only capable of handling problem instances within about 500 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 branch-and-price 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. A column-and-dependentrow generation method for it is under development.