Rescheduling in passenger railways: the rolling stock rebalancing problem

This paper addresses the Rolling Stock Rebalancing Problem (RSRP) which arises within a passenger railway operator when the rolling stock has to be rescheduled due to changing circumstances. RSRP is relevant both in the short-term planning stage and in the real-time operations. RSRP has as input a timetable and a rolling stock circulation where the allocation of the rolling stock among the stations at the start or at the end of a certain planning period does not match with the allocation before or after that planning period. The problem is then to modify the input rolling stock circulation in such a way that the number of remaining off-balances is minimal. If all off-balances have been solved, then the obtained rolling stock circulation can be implemented in practice. For practical usage of solution approaches for RSRP, it is important to solve the problem quickly. Since we prove that RSRP is NP-hard, we focus on heuristic solution approaches: we describe two heuristics and compare them with each other on (variants of) real-life instances of NS, the main Dutch passenger railway operator. Finally, to get further insight in the quality of the proposed heuristics, we also compare their outcomes with optimal solutions obtained by solving an existing rolling stock circulation model.