Annals of Operations Research

, Volume 218, Issue 1, pp 93–106 | Cite as

Optimizing the Simplon railway corridor

  • Ralf Borndörfer
  • Berkan Erol
  • Thomas Graffagnino
  • Thomas Schlechte
  • Elmar Swarat


This paper presents a case study of a railway timetable optimization for the very dense Simplon corridor, a major railway connection in the Alps between Switzerland and Italy. The key to deal with the complexity of this scenario is the use of a novel aggregation-disaggregation method. Starting from a detailed microscopic representation as it is used in railway simulation, the data is transformed by an automatic procedure into a less detailed macroscopic representation, that is sufficient for the purpose of capacity planning and amenable to state-of-the-art integer programming optimization methods. This macroscopic railway network is saturated with trains. Finally, the optimized timetable is re-transformed to the microscopic level in such a way that it can be operated without any conflicts among the train paths. Using this micro-macro aggregation-disaggregation approach in combination with integer programming methods, it becomes for the first time possible to generate a profit maximal and conflict free timetable for the complete Simplon corridor over an entire day by a simultaneous optimization of all trains requests. In addition, this also allows us to undertake a sensitivity analysis of various problem parameters.


Railway track allocation Network aggregation Case study Simplon corridor 



We thank Martin Grötschel, Gottfried Ilgmann and Klemens Polatschek for their important support in organizing und realizing this project, and in particular the Simplon case-study. Finally, we thank Daniel Hürlimann for his excellent support for the simulation tool OpenTrack. Furthermore, we want to thank four anonymous referees for improving the quality of the paper by their valuable comments.


  1. Borndörfer, R., & Schlechte, T. (2007). Models for railway track allocation. In C. Liebchen, R. K. Ahuja, & J. A. Mesa (Eds.), ATMOS 2007—7th workshop on algorithmic approaches for transportation modeling, optimization, and systems, Dagstuhl, Germany, 2007. Schloss Dagstuhl, Germany: Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI). ISBN 978-3-939897-04-0. Google Scholar
  2. Borndörfer, R., Grötschel, M., Lukac, S., Mitusch, K., Schlechte, T., Schultz, S., & Tanner, A. (2006). An auctioning approach to railway slot allocation. Competition and Regulation in Network Industries, 1(2), 163–196. Google Scholar
  3. Borndörfer, R., Grötschel, M., & Pfetsch, M. E. (2007). A column-generation approach to line planning in public transport. Transportation Science, 41(1), 123–132. CrossRefGoogle Scholar
  4. Borndörfer, R., Erol, B., & Schlechte, T. (2009). Optimization of macroscopic train schedules via TS-OPT. In I. Hansen, E. Wendler, U. Weidmann, M. Lüthi, J. Rodriguez, S. Ricci, & L. Kroon (Eds.), Proceedings of the 3rd international seminar on railway operations modelling and analysis—engineering and optimisation approaches, Zürich, Switzerland. Google Scholar
  5. Brännlund, U., Lindberg, P. O., Nou, A., & Nilsson, J.-E. (1998). Railway timetabling using Langangian relaxation. Transportation Science, 32(4), 358–369. CrossRefGoogle Scholar
  6. Cacchiani, V. (2007). Models and algorithms for combinatorial optimization problems arising in railway applications. PhD thesis, DEIS, Bologna. Google Scholar
  7. Cacchiani, V., Caprara, A., & Toth, P. (2008). A column generation approach to train timetabling on a corridor. 4OR, 6(2), 125–142. CrossRefGoogle Scholar
  8. Cai, X., & Goh, C. J. (1994). A fast heuristic for the train scheduling problem. Computers & Operations Research, 21(5), 499–510. ISSN 0305-0548. CrossRefGoogle Scholar
  9. Caimi, G. (2009). Algorithmic decision support for train scheduling in a large and highly utilised railway network. PhD thesis, ETH, Zurich. Google Scholar
  10. Caimi, G., Burkolter, D., & Herrmann, T. (2004). Finding delay-tolerant train routings through stations. In H. A. Fleuren, D. den Hertog, & P. M. Kort (Eds.), OR (pp. 136–143). ISBN 978-3-540-24274-1. Google Scholar
  11. Caprara, A., Fischetti, M., & Toth, P. (2002). Modeling and solving the train timetabling problem. Operations Research, 50(5), 851–861. CrossRefGoogle Scholar
  12. Caprara, A., Galli, L., & Toth, P. (2007). Solution of the train platforming problem. In C. Liebchen, R. K. Ahuja, & J. A. Mesa (Eds.), Dagstuhl seminar proceedings: Vol. 07001. ATMOS. Schloss Dagstuhl, Germany: Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI). Google Scholar
  13. Corman, F., D’Ariano, A., Pacciarelli, D., & Pranzo, M. (2010). Centralized versus distributed systems to reschedule trains in two dispatching areas. Public Transport, 2, 219–247. doi: 10.1007/s12469-010-0032-7. CrossRefGoogle Scholar
  14. Erol, B., Klemenz, M., Schlechte, T., Schultz, S., & Tanner, A. (2008). TTPLIB 2008—a library for train timetabling problems. In A. T. J. Allan, E. Arias, C. A. Brebbia, C. Goodman, & A. F. Rumsey (Eds.), Computers in railways XI. Southampton: WIT Press. Google Scholar
  15. Fischer, F., Helmberg, C., Janßen, J., & Krostitz, B. (2008). Towards solving very large scale train timetabling problems by Lagrangian relaxation. In M. Fischetti & P. Widmayer (Eds.), ATMOS 2008—8th workshop on algorithmic approaches for transportation modeling, optimization, and systems, Dagstuhl, Germany, 2008. Schloss Dagstuhl, Germany: Leibniz-Zentrum fuer Informatik. Google Scholar
  16. Gröger, T. (2002). Simulation der Fahrplanerstellung auf der Basis eines hierarchischen Trassenmanagements und Nachweis der Stabiliät der Betriebsabwicklung. PhD thesis, Veröffentlichungen d. Verkehrswiss. Inst. der Rheinisch-Westfälischen Techn. Hochsch, Aachen. Google Scholar
  17. Hansen, I., & Pachl, J. (2008). Railway, timetable & traffic. Hamburg: Eurailpress. Google Scholar
  18. Hürlimann, D. (2001). Object oriented modeling of infrastructure elements and business processes in railways. PhD thesis, ETH, Zürich. Google Scholar
  19. Jespersen-Groth, J., Potthoff, D., Clausen, J., Huisman, D., Kroon, L. G., Maróti, G., & Nielsen, M. N. (2009). Disruption management in passenger railway transportation. In Lecture notes in computer science: Robust and online large-scale optimization (pp. 399–421). Berlin: Springer. CrossRefGoogle Scholar
  20. Kettner, M., Sewcyk, B., & Eickmann, C. (2003). Integrating microscopic and macroscopic models for railway network evaluation. In Proceedings of the European transport conference, 2003. Washington: Association for European Transport. Google Scholar
  21. Liebchen, C. (2006). Periodic timetable optimization in public transport. Berlin: Springer. Google Scholar
  22. Lusby, R., Larsen, J., Ryan, D., & Ehrgott, M. (2006). Routing trains through railway junctions: a new set packing approach. Technical report, Informatics and Mathematical Modelling, Technical University of Denmark, DTU, Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby, 2006.
  23. Schlechte, T., Borndörfer, R., Erol, B., Graffagnino, T., & Swarat, E. (2011). Micro–macro transformation of railway networks. Journal of Rail Transport Planning & Management, 1(1), 38–48. CrossRefGoogle Scholar
  24. Siefer, T., & Radtke, A. (2005). Railway-simulation key for better operation and optimal use of infrastructure. In Proceedings of the 1st international seminar on railway operations modelling and analysis. Google Scholar
  25. Wendler, E. (1999). Analytische Berechnung der planmässigen Wartezeiten bei asynchroner Fahrplankonstruktion. Aachen: Verkehrswiss. Inst. der Rheinisch-Westfälischen Techn. Hochsch. Google Scholar
  26. Zwaneveld, P. J., Kroon, L. G., Romeijn, H. E., Salomon, M., Dauzere-Peres, S., Van Hoesel, S. P. M., & Ambergen, H. W. (1996). Routing trains through railway stations: model formulation and algorithms. Transportation Science, 30(3), 181–194. doi: 10.1287/trsc.30.3.181. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Ralf Borndörfer
    • 1
  • Berkan Erol
    • 1
  • Thomas Graffagnino
    • 2
  • Thomas Schlechte
    • 1
  • Elmar Swarat
    • 1
  1. 1.Zuse Institute Berlin (ZIB)Berlin-DahlemGermany
  2. 2.Infrastruktur – Fahrplan und NetzdesignSchweizerische Bundesbahnen SBB AGBern 65Switzerland

Personalised recommendations