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A Cycle Based Optimization Model for the Cyclic Railway Timetabling Problem

  • Leon Peeters
  • Leo Kroon
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 505)

Abstract

The paper presents an optimization model for cyclic railway timetabling that extends the feasibility model by Schrijver and Steenbeek (1994). We use a mixed integer non-linear programming formulation for the problem, where the integer variables correspond to cycles in the graph induced by the constraints. Objective functions are proposed for minimizing passengers’ travel time, maximizing the robustness of the timetable, and minimizing the number of trains needed to operate the timetable. We show how to approximate the non-linear part of the formulation, thereby transforming it into a mixed integer linear programming problem. Furthermore, we describe preprocessing procedures that considerably reduce the size of the problem instances. The usefulness and practical applicability of the formulation and the objective functions is illustrated by several variants of an instance representing the Dutch intercity train network.1

Keywords

Mixed Integer Linear Program Cycle Basis Constraint Graph Buffer Time Quadratic Objective Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. Goverde, R.M.P. (1999). Improving punctuality and transfer reliability by railway timetable optimization. In P.H.L. Bovy (Ed.), Proceedings TRAIL 5th Annual Congress, 2, Delft.Google Scholar
  2. Hassin, R. (1996). A flow algorithm for network synchronization. Operations Research 44, 570–579.CrossRefGoogle Scholar
  3. Hurkens, C. (1996). Een polyhedrale aanpak van treinrooster problemen (A polyhedral approach to railway timetabling problems). Unpublished. In Dutch.Google Scholar
  4. ILOG (2001). ILOG CPLEX. http://www.Ilog.Com/products/cplex/, 07.04.2001.
  5. Kroon, L.G. and L.W.P. Peeters (1999). A variable running time model for cyclic railway timetabling. Erasm management report series 28–1999, Erasm, Rotterdam, The Netherlands.Google Scholar
  6. Lindner, T. (2000). Train Schedule Optimization in Public Rail Transport. Ph.D. thesis, Technical University Braunschweig, Braunschweig, Germany.Google Scholar
  7. Nachtigall, K. (1999). Periodic Network Optimization and Fixed Interval Timetables. Habilitation thesis, University Hildesheim.Google Scholar
  8. Odijk, M.A. (1996). A constraint generation algorithm for the construction of periodic railway timetables. Transportation Research B 30, 455–464.CrossRefGoogle Scholar
  9. Odijk, M.A. (1997). Railway Timetable Generation. Ph.D. thesis, Delft University of Technology, Delft, The Netherlands.Google Scholar
  10. Peeters, L.W.P. (1999). An optimization approch to railway timetabling. In P.H.L. Bovy (Ed.), Proceedings TRAIL 5th Annual Congress, 1, Delft.Google Scholar
  11. Rockafellar, R.T. (1984). Network Flows and Monotropic Optimization. Wiley, New York.Google Scholar
  12. Schrijver, A. (1986). Theory of Linear and Integer Programming. Wiley, New York.Google Scholar
  13. Schrijver, A. and A. Steenbeek (1994). Dienstregelingontwikkeling voor Railned (Timetable construction for Railned). Technical report, CWI, Center for Mathematics and Computer Science, Amsterdam. In Dutch.Google Scholar
  14. Serafini, P. and W. Ukovich (1989). A mathematical model for periodic event scheduling problems. SIAM Journal of Discrete Mathematics 2, 550–581.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Leon Peeters
    • 1
  • Leo Kroon
    • 1
  1. 1.Erasmus University RotterdamDR RotterdamThe Netherlands

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