Freight Locomotive Rescheduling and Uncovered Train Detection during Disruptions

This paper discusses optimization of freight train locomotive rescheduling under a disrupted situation in the daily operations in Japan. In the light of the current framework of dispatching processes that passenger railway operators modify the entire timetables, the adjusted timetable is distributed to a freight train operator. We solve the locomotive rescheduling problem for the given adjusted timetable in which we change the assignment of the locomotives to the trains as required, considering a periodic inspection of the locomotives. The uncovered train detection problem that selects unassigned trains of less importance is solved if the rescheduling has failed. We formulate the two problems as integer programming problems derived from our network representation of the disrupted situation, and solve the problems by column generation. Our simple speeding-up technique named set-covering relaxation is applied to the rescheduling problem, which has set-partitioning constraints. The column generation subproblem reduced to a shortest path problem with the inspection constraint is solved in polynomial time. Numerical experiments using a real timetable, locomotive scheduling plan and major disruption data in the highest-frequency freight train operation area reveal that satisfactory solutions are obtained within around 30 seconds by a PC even for the cases with 72-hour goal for recovery. The set-covering relaxation speeds up the computation time by a factor of six at a maximum.