Locomotive scheduling

We developed a new model for a strategic locomotive scheduling problem arising at the Deutsche Bahn AG. The main goal is to generate feasible schedules of the locomotives, which are cyclic sequences of trips and deadhead trips. The main objective is to reduce operating expenses, that is, to use as few locomotives as possible to pull all trains. On a subordinate level the locomotives
are supposed to be scheduled in such a way that the deadhead trips are a short as possible.

The model is based on a multi-commodity min-cost flow formulation that is also used for public bus scheduling problems. However, several new aspects have to be additionally taken into account, such as cyclic departures of the trains, time windows on starting and arrival times, network-load dependent travel times, and a transfer of cars between trains. The model is formulated as an integer
linear programming problem (ILP). The formulation is improved by preprocessing and additional cutting planes. Solutions are obtained using a randomized greedy heuristic in combination with commercial ILP solvers.


  • TU Darmstadt,
  • Deutsche Bahn AG, Frankfurt
  • Université Libre de Bruxelles, Belgium

Industrial partners

  • Deutsche Bahn AG, Frankfurt.

Related talks

  • Locomotive and Wagon Scheduling in Freight Transport, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways ATMOS, Zürich, Switzerland, 14.9.2006.

Related publications

  • Prasanna Balaprakash, Armin Fügenschuh, Henning Homfeld, Michael Schoch, Thomas Stützle, Zhi Yuan, Iterated Greedy Algorithms for a Real-World Cyclic Train Scheduling Problem , Maria J. Blesa Aguilera (Ed.), Proceedings of the 5th
  • International Workshop on Hybrid Metaheuristics, Lecture Notes in Computer Science, Vol. 5296, pp. 21 – 31, 2008. Armin Fügenschuh, Henning Homfeld, Andreas Huck, Alexander Martin, Zhi Yuan, Scheduling Locomotives and Car Transfers in Freight Transport , Transportation Science, Vol. 42, No. 4, pp. 1 – 14, 2008.
  • Armin Fügenschuh, Henning Homfeld, Andreas Huck, Alexander Martin, Locomotive and Wagon Scheduling in Freight Transport , Rico Jacob, Matthias Müller-Hannemann (Eds.), e-Proceedings of the ATMOS06, 2006

This website uses cookies. There are two types of cookies: The first type supports the basic functionality of our website. The second allows us to improve our content for you by saving and analyzing pseudonymised user data. Since this second type is technically not required to run the website, you can withdraw your consent to those cookies at any time. For more information please visit our pages on data protection.


These cookies are needed for a smooth operation of our website.


For statistical reasons, we use the platform Matomo to analyse the user flow with the help of website users‘ pseudonymised data. This allows us to optimize website content.

Name Purpose Lifetime Type Provider
_pk_id Used to store a few details about the user such as the unique visitor ID. 13 months HTML Matomo
_pk_ref Used to store the attribution information, the referrer initially used to visit the website. 6 months HTML Matomo
_pk_ses Short lived cookie used to temporarily store data for the visit. 30 minutes HTML Matomo