Skip to main content
Springer Nature Link
Log in

The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond

  • Conference paper
Algorithmic Methods for Railway Optimization

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4359))

  • 3294 Accesses

Abstract

In the planning process of railway companies, we propose to integrate important decisions of network planning, line planning, and vehicle scheduling into the task of periodic timetabling. From such an integration, we expect to achieve an additional potential for optimization.

Models for periodic timetabling are commonly based on the Periodic Event Scheduling Problem (PESP). We show that, for our purpose of this integration, the PESP has to be extended by only two features, namely a linear objective function and a symmetry requirement. These extensions of the PESP do not really impose new types of constraints. Indeed, practitioners have already required them even when only planning timetables autonomously without interaction with other planning steps. Even more important, we only suggest extensions that can be formulated by mixed integer linear programs.

Moreover, in a selfcontained presentation we summarize the traditional PESP modeling capabilities for railway timetabling. For the first time, also special practical requirements are considered that we proove not being expressible in terms of the PESP.

Supported by the DFG Research Center “Mathematics for key technologies” in Berlin.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bollobás, B.: Modern Graph Theory (2nd printing). Graduate Texts in Mathematics, vol. 184. Springer, Heidelberg (2002)

    Google Scholar 

  2. Borndörfer, R., Grötschel, M., Pfetsch, M.E.: A path-based model for line planning in public transport. Technical Report 05-18, Zuse Institute, Berlin (2005)

    Google Scholar 

  3. Borndörfer, R., Löbel, A., Weider, S.: Integrierte Umlauf- und Dienstplanung im öffentlichen Nahverkehr. In: HEUREKA 2002: Optimierung in Transport und Verkehr, Tagungsbericht, number 002/72. FGSV Verlag. German (2002)

    Google Scholar 

  4. Bussieck, M.R., Winter, T., Zimmermann, U.: Discrete optimization in public rail transport. Mathematical Programming B 79, 415–444 (1997)

    Google Scholar 

  5. Claessens, M.T., van Dijk, N.M., Zwanefeld, P.J.: Cost optimal allocation of rail passenger lines. European Journal of Operational Research 110(3), 474–489 (1998)

    Article  MATH  Google Scholar 

  6. Engelhardt-Funke, O., Kolonko, M.: Analysing stability and investments in railway networks using advanced evolutionary algorithms. International Transactions in Operational Research 11, 381–394 (2004)

    Article  MATH  Google Scholar 

  7. Grötschel, M., Löbel, A., Völker, M.: Optimierung des Fahrzeugumlaufs im öffentlichen Nahverkehr (In German). In: Hoffmann, K.H., Jäger, W., Lohmann, T., Schunck, H. (eds.) Mathematik - Schlüsseltechnologie für die Zukunft, Springer, Heidelberg (1997)

    Google Scholar 

  8. Haase, K., Desaulniers, G., Desrosiers, J.: Simultaneous vehicle and crew scheduling in urban mass transit systems. Transportation Science 35(3), 286–303 (2001)

    Article  MATH  Google Scholar 

  9. Krista, M.: Verfahren zur Fahrplanoptimierung am Beispiel der Synchronzeiten. Ph.D. thesis, Technische Universität Braunschweig. German (1997)

    Google Scholar 

  10. Kroon, L.G., Peeters, L.W.P.: A variable trip time model for cyclic railway timetabling. Transportation Science 37, 198–212 (2003)

    Article  Google Scholar 

  11. Leuschel, I.: Der Fernverkehrsfahrplan 2003 der Deutschen Bahn AG (In German). Eisenbahntechnische Rundschau 51(7–8), 452–464 (2002)

    Google Scholar 

  12. Liebchen, C.: Finding short integral cycle bases for cyclic timetabling. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 715–726. Springer, Heidelberg (2003)

    Google Scholar 

  13. Liebchen, C.: Symmetry for periodic railway timetables. Electronic Notes in Theoretical Computer Science 92, 34–51 (2004)

    Article  Google Scholar 

  14. Liebchen, C., Peeters, L.: Some practical aspects of periodic timetabling. In: Chamoni, P., Leisten, R., Martin, A., Minnemann, J., Stadtler, H. (eds.) Operations Research 2001, Springer, Heidelberg (2002)

    Google Scholar 

  15. Liebchen, C., Proksch, M., Wagner, F.H.: Performance of algorithms for periodic timetable optimization (to appear). In: Hickman, M. (ed.) Computer-Aided Transit Scheduling— Proceedings of the Ninth International Workshop on Computer-Aided Scheduling of Public Transport. Lecture Notes in Economics and Mathematical Systems, Springer, Heidelberg (2005)

    Google Scholar 

  16. Lindner, T.: Train Schedule Optimization in Public Rail Transport. Ph.D. thesis, Technische Universität Braunschweig (2000)

    Google Scholar 

  17. Rhein-Main Verkehrsverbund: Fahrplanbuch Gesamtausgabe (gültig ab 14. Dezember 2003) (2003)

    Google Scholar 

  18. Nachtigall, K.: A branch and cut approach for periodic network programming. Hildesheimer Informatik-Berichte 29, Universität Hildesheim (1994)

    Google Scholar 

  19. Nachtigall, K.: Cutting planes for a polyhedron associated with a periodic network. Institutsbericht IB 112-96/17, Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V (July 1996)

    Google Scholar 

  20. Nachtigall, K.: Periodic Network Optimization and Fixed Interval Timetables. Habilitation thesis, Universität Hildesheim (1998)

    Google Scholar 

  21. Nachtigall, K., Voget, S.: A genetic algorithm approach to periodic railway synchronization. Computers and Operations Research 23(5), 453–463 (1996)

    Article  MATH  Google Scholar 

  22. Nielsen, M.N., Hove, B., Clausen, J.: Constructing periodic timetables using MIP—a case study from DSB S-train. International Journal of Operations Research, 1 (2005)

    Google Scholar 

  23. Odijk, M.A.: Construction of periodic timetables, Part 1: A cutting plane algorithm. Technical Report 94-61, TU Delft (1994)

    Google Scholar 

  24. Odijk, M.A.: A constraint generation algorithm for the construction of periodic railway timetables. Transportation Research B 30(6), 455–464 (1996)

    Article  Google Scholar 

  25. Peeters, L.W.P.: Personal Communication (2000)

    Google Scholar 

  26. Peeters, L.W.P.: Cyclic Railway Timetable Optimization. Ph.D. thesis, Erasmus Universiteit Rotterdam (2003)

    Google Scholar 

  27. S-Bahn Berlin GmbH: S-Bahn Fahrplan (gültig ab 16. Juni 2003) (2003)

    Google Scholar 

  28. Schrijver, A.: Theory of Linear and Integer Programming, 2nd edn. Wiley, Chichester (1998)

    MATH  Google Scholar 

  29. Schrijver, A., Steenbeek, A.G.: Dienstregelingontwikkeling voor Nederlandse Spoorwegen N.S. Rapport Fase 1, Centrum voor Wiskunde en Informatica (Oktober 1993)

    Google Scholar 

  30. Serafini, P., Ukovich, W.: A mathematical model for periodic scheduling problems. SIAM Journal on Discrete Mathematics 2(4), 550–581 (1989)

    Article  MATH  Google Scholar 

  31. van den Berg, J.H.A., Odijk, M.A.: DONS: Computer aided design of regular service timetables. In: Murthy, T.K.S., Mellitt, B., Brebbia, C.A., Sciutto, G., Sone, S. (eds.) Computers in Railways IV (COMPRAIL)—vol. 2: Railway Operations. WIT Press (1994)

    Google Scholar 

  32. Völker, M.: Ein multikriterieller Algorithmus zur automatisierten Bus-liniennetzplanung. Lecture on the OR Workshop Optimierung im öffentlichen Nahverkehr (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TU Berlin, Institut für Mathematik, Straße des 17. Juni 136, D-10623 Berlin,  

    Christian Liebchen & Rolf H. Möhring

Authors
  1. Christian Liebchen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rolf H. Möhring
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Frank Geraets Leo Kroon Anita Schoebel Dorothea Wagner Christos D. Zaroliagis

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Liebchen, C., Möhring, R.H. (2007). The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables — and Beyond. In: Geraets, F., Kroon, L., Schoebel, A., Wagner, D., Zaroliagis, C.D. (eds) Algorithmic Methods for Railway Optimization. Lecture Notes in Computer Science, vol 4359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74247-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74247-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74245-6

  • Online ISBN: 978-3-540-74247-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics