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Optimizing the Simplon railway corridor

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Abstract

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.

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Notes

  1. In Switzerland trains are usually running on the left side.

  2. The “n” in the second 24h request is a reminder that freight trains drive more frequently at night.

  3. There is no general relation between problem size and solution time as one can see by a comparison of the 6s-discretization runs.

References

  • 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. http://drops.dagstuhl.de/opus/volltexte/2007/1170.

    Google Scholar 

  • 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. http://opus.kobv.de/zib/volltexte/2005/878.

    Google Scholar 

  • Borndörfer, R., Grötschel, M., & Pfetsch, M. E. (2007). A column-generation approach to line planning in public transport. Transportation Science, 41(1), 123–132. http://opus.kobv.de/zib/volltexte/2005/852/.

    Article  Google Scholar 

  • 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 

  • Brännlund, U., Lindberg, P. O., Nou, A., & Nilsson, J.-E. (1998). Railway timetabling using Langangian relaxation. Transportation Science, 32(4), 358–369.

    Article  Google Scholar 

  • Cacchiani, V. (2007). Models and algorithms for combinatorial optimization problems arising in railway applications. PhD thesis, DEIS, Bologna.

  • Cacchiani, V., Caprara, A., & Toth, P. (2008). A column generation approach to train timetabling on a corridor. 4OR, 6(2), 125–142.

    Article  Google Scholar 

  • Cai, X., & Goh, C. J. (1994). A fast heuristic for the train scheduling problem. Computers & Operations Research, 21(5), 499–510. ISSN 0305-0548. http://dx.doi.org/10.1016/0305-0548(94)90099-X.

    Article  Google Scholar 

  • Caimi, G. (2009). Algorithmic decision support for train scheduling in a large and highly utilised railway network. PhD thesis, ETH, Zurich.

  • 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 

  • Caprara, A., Fischetti, M., & Toth, P. (2002). Modeling and solving the train timetabling problem. Operations Research, 50(5), 851–861.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • 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. http://opus.kobv.de/zib/volltexte/2008/1102/.

    Google Scholar 

  • 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. http://drops.dagstuhl.de/opus/volltexte/2008/1585.

    Google Scholar 

  • 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.

  • Hansen, I., & Pachl, J. (2008). Railway, timetable & traffic. Hamburg: Eurailpress.

    Google Scholar 

  • Hürlimann, D. (2001). Object oriented modeling of infrastructure elements and business processes in railways. PhD thesis, ETH, Zürich.

  • 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.

    Chapter  Google Scholar 

  • 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 

  • Liebchen, C. (2006). Periodic timetable optimization in public transport. Berlin: Springer.

    Google Scholar 

  • 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. http://www2.imm.dtu.dk/pubdb/p.php?4961

  • 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.

    Article  Google Scholar 

  • 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 

  • Wendler, E. (1999). Analytische Berechnung der planmässigen Wartezeiten bei asynchroner Fahrplankonstruktion. Aachen: Verkehrswiss. Inst. der Rheinisch-Westfälischen Techn. Hochsch.

    Google Scholar 

  • 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. http://transci.journal.informs.org/cgi/content/abstract/30/3/181.

    Article  Google Scholar 

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Acknowledgements

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.

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Authors and Affiliations

  1. Zuse Institute Berlin (ZIB), Takustr. 7, 14195, Berlin-Dahlem, Germany

    Ralf Borndörfer, Berkan Erol, Thomas Schlechte & Elmar Swarat

  2. Infrastruktur – Fahrplan und Netzdesign, Schweizerische Bundesbahnen SBB AG, Mittelstrasse 43, 300, Bern 65, Switzerland

    Thomas Graffagnino

Authors
  1. Ralf Borndörfer
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  2. Berkan Erol
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  3. Thomas Graffagnino
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  4. Thomas Schlechte
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  5. Elmar Swarat
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Corresponding author

Correspondence to Thomas Schlechte.

Additional information

This research was funded by the German Federal Ministry of Economics and Technology (BMWi), project Trassenbörse, grant 19M7015B.

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Borndörfer, R., Erol, B., Graffagnino, T. et al. Optimizing the Simplon railway corridor. Ann Oper Res 218, 93–106 (2014). https://doi.org/10.1007/s10479-012-1260-9

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