PLAISANCE : A tool for scheduling trains drivers for French railways
Résumé
In this paper, we describe a method to solve the passenger crew scheduling problem for SNCF (the French national railway company). From rolling-stock rosters and a limited number of train drivers in several depots, the objective of the problem we address is to build duties to minimize a total certain cost in the week. Several models for the cost function are proposed in this article. We first generate a set of shifts according to regulation rules using a depth-first search algorithm. Then an iterative procedure based on a Lagrangian relaxation is used to solve the resulting set covering problem. This procedure relies on a three-step algorithm based on a method developed by Caprara et al. : a subgradient method, a constructive heuristic and a fixation technique to select efficient shifts. The algorithm has been implemented in a proprietary software module named PLAISANCE. Numerical experiments have been performed on several real-life instances with up to 2,900 passenger trains to schedule in a week. The results correspond to the business requirements and prove the effectiveness of the described method.