Railway Rolling Stock Planning: Robustness Against Large Disruptions

In this paper we describe a two-stage optimization model for determining robust rolling stock circulations for passenger trains. Here robustness means that the rolling stock circulations can better deal with large disruptions of the railway system. The two-stage optimization model is formulated as a large Mixed-Integer Linear Programming model. We first use Benders decomposition to determine optimal solutions for the LP-relaxation of this model. Then we use the cuts that were generated by the Benders decomposition for computing heuristic robust solutions for the two-stage optimization model. We call our method Benders heuristic. We evaluate our approach on the real-life rolling stock planning problem of Netherlands Railways (NS), the main operator of passenger trains in the Netherlands. The computational results show that, thanks to Benders decomposition, the LP-relaxation of the two-stage optimization problem can be solved in short time for a representative number of disruption scenarios. In addition, they demonstrate that the robust rolling stock circulation computed heuristically has total costs that are close to the LP lower bounds. Finally, we discuss the practical effectiveness of the robust rolling stock circulation: when a large number of disruption scenarios were applied to these robust circulations and to the non-robust optimal circulations, the former appeared to be much more easily recoverable than the latter.