Integrating Timetabling and Crew

We investigate to what degree we can integrate a Train Timetabling / Engine Scheduling Problem with a Crew Scheduling Problem. In the Timetabling Problem we design a timetable for the desired lines by fixing the departure and arrival times. Also, we allocate time-slots in the network to secure a feasible timetable. Next, we assign engines in the Engine Scheduling Problem to the lines in accordance with the timetable. The overall integration is achieved by obtaining an optimal solution for the Timetabling / Engine Scheduling Problem. We exploit the fact that numerous optimal, and near optimal solutions exists. We consider all solutions that can be obtained from the optimal engine schedule by altering the timetable, while keeping the order of demands in the schedules intact. The Crew Scheduling model is allowed to re-time the service of demands if the additional cost is outweighed by the crew savings. This information is implemented in a mathematical model for the Crew Scheduling Problem. The model is solved using a column generation scheme. Hereby it is possible for the Crew Scheduling algorithm to adjust the timetable and achieve a better overall solution. We perform computational experiments based on a case at a freight railway operator, DB Schenker Rail Scandinavia, and show that significant cost savings can be achieved.