An Integer Programming Model to Assign Train Drivers to Good Positions in Basic Turni

We are reporting on a project on duty rostering of a train operating company in Germany. There, in the past, rostering took place on a purely individual basis. As the goal of the project, the train drivers should work according to a set of 25 essentially fixed basic turni. These plans took into effect from January 2024 on. In this extended abstract, we are focusing on a specific task that had to be resolved within the transition process. In particular, the fixed turni are intended to repeat periodically, most of them after 17 weeks. In particular, for that one turnus is equipped with train drivers in a balanced way, 17 employees have to be assigned to this turnus, each of them to one of the 17 different weeks of the turnus to start. To cover each day of the week, the weeks of the turnus typically differ in their number of working days. Since the holidays of the train drivers had been already planned in advance, depending on the starting week, during the entire year, a smaller or larger number of working days of the turnus could be erased by the individual holidays. In order to preserve as many working days as necessary, a straightforward mixed-integer linear optimization problem has been designed and solved, to decide which train driver should start to work in which week of the turnus. The solution of this optimization run has been finally applied in practice.