Companies running a 24/7 business (such as railroad operators) also need employees around the clock. Duties at very irregular times (overnight or weekends), a low number of breaks (especially on weekends), and mainly a lack of long-term stability in scheduling plans leads to dissatisfaction and, in the long run, health problems and resignations. When it came to negotiations between the labor union and the management, we were hired as consultants to accompany the process with our scientific background in mathematical optimization.

During this project we developed an optimization model to create feasible working plans for crews. In a second step we evaluated the long-term stability of our plans using Monte-Carlo simulation methods.

The main difficulty was the inherent complexity of the problem. To be feasible, a working plan has to fulfill many complex labor regulations. The resulting optimization model is by far to large to be solved directly even with a state-of-the-art solver. Hence we developed several decomposition rules to break the large problem into a set of smaller ones (using moving horizon and other
techniques), and combined the individual solutions into a global solution for the entire problem.

Partners

•  TU Darmstadt

Industrial partners / Funding

• DB Regio AG, Frankfurt.

Related talks

• Schichtplanung bei der Deutschen Bahn, International Conference on Operations Research OR 2008, Augsburg, Germany, 3.9.2008