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OR Spectrum

, 31:727 | Cite as

Branching strategies to improve regularity of crew schedules in ex-urban public transit

  • Ingmar SteinzenEmail author
  • Leena Suhl
  • Natalia Kliewer
Regular Article

Abstract

We discuss timetables in ex-urban bus traffic that consist of many trips serviced every day together with some exceptions that do not repeat daily. Traditional optimization methods for vehicle and crew scheduling in such cases usually produce schedules that contain irregularities which are not desirable especially from the point of view of the bus drivers. We propose a solution method which improves regularity while partially integrating the vehicle and crew scheduling problems. The approach includes two phases: first we solve the LP relaxation of a set covering formulation, using column generation together with Lagrangean relaxation techniques. In a second phase, we generate integer solutions using a new combination of local branching and various versions of follow-on branching. Numerical tests with artificial and real instances show that regularity can be improved significantly with no or just a minor increase of costs.

Keywords

Column Generation Crew Schedule Vehicle Schedule Regular Chain Regular Pair 
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.

References

  1. Borndoerfer R, Loebel A, Weider S (2004) A bundle method for integrated multi-depot vehicle and duty scheduling in public transit. Technical report ZR-04-14, ZIB, Zuse Institute Berlin, Berlin, GermanyGoogle Scholar
  2. Dallaire A, Fleurent C, Rousseau J-M (2004) Dynamic constraint generation in crewopt, a column generation approach for transit crew scheduling. Technical report, GIRO Inc., Montreal, CanadaGoogle Scholar
  3. Fischetti M, Lodi A (2003) Local branching. Math Program 84: 23–47CrossRefGoogle Scholar
  4. Fischetti M, Lodi A, Martello S, Toth P (1989) The fixed job schedule problem with working-time constraints. Oper Res 37(3): 395–403CrossRefGoogle Scholar
  5. GIRO (2007) Hastus transit scheduling and operations. Available at http://www.giro.ca/en/products/hastus/index.htm, July 2007.
  6. Guo Y, Suhl L, Thiel MP (2005) Solving the airline crew recovery problem by a genetic algorithm with local improvement. Oper Res Int J 5Google Scholar
  7. Huisman D (2005) Random data instances for multiple-depot vehicle and crew scheduling. Available at http://www.few.eur.nl/few/people/huisman/instances.htm, April
  8. Huisman D (2004) Integrated and dynamic vehicle and crew scheduling. Ph.D thesis, Tinbergen Institute, Erasmus University RotterdamGoogle Scholar
  9. Huisman D (2007) A column generation approach to solve the crew re-scheduling problem. Eur J Oper Res 180: 163–173CrossRefGoogle Scholar
  10. Klabjan D, Johnson E, Nemhauser G, Gelman E, Ramaswamy S (2001) Airline crew scheduling with regularity. Transp Sci 35: 359–374CrossRefGoogle Scholar
  11. Lettovsky L, Johnson E, Nemhauser G (2000) Airline crew recovery. Transp Sci 34: 337–348CrossRefGoogle Scholar
  12. Medard C, Sawhney N (2007) Airline crew scheduling: From planning to operations. Eur J Oper Res 183: 1013–1027CrossRefGoogle Scholar
  13. Nissen R, Haase K (2006) Duty-period-based network model for crew rescheduling in european airlines. J Sched 9: 255–278CrossRefGoogle Scholar
  14. Ryan DM, Foster B (1981) An integer programming approach to scheduling. In: Wren A (ed), Computer scheduling of public transport: urban passenger vehicle and crew scheduling. North-Holland, Amsterdam, pp 269–280Google Scholar
  15. Steinzen I (2007) Topics in integrated vehicle and crew scheduling in public transit. Ph.D thesis, DSOR Lab, University of PaderbornGoogle Scholar
  16. Steinzen I, Gintner V, Suhl L (2007) Local Branching und Branching-Strategien fuer Umlauf- und Dienstplanung im Regionalverkehr mit unregelmaessigen Fahrplaenen. In: Guenther H-O, Mattfeld D, Suhl L(eds) Management logistischer Netzwerke: Entscheidungsunterstuetzung, Informationssysteme und OR-Tools. Physica-Verlag, Heidelberg, pp 407–424CrossRefGoogle Scholar
  17. Tajima A, Misono S (1997) Airline crew-scheduling with many irregular flights. In: Leong H, Imai H, Jain S (eds) Lecture notes in computer science: proceedings of the 8th international symposium on algorithms and computation—ISAAC97. Springer, Heidelberg, pp 2–11Google Scholar
  18. Vance PH, Atamtuerk A, Barnhart C, Gelman F, Johnson E, Krishna A, Mahidhara D, Rebello R (1997) A heuristic branch-and-price approach for the airline crew pairing problem. Technical report LEC-97-06, Georgia Institute of Technology, Atlanta, USAGoogle Scholar
  19. Vanderbeck F (1994) Decomposition and column generation for integer programs. Ph.D thesis, Universite Catholique de LouvainGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.International Graduate School of Dynamic Intelligent SystemsUniversity of PaderbornPaderbornGermany
  2. 2.Decision Support and OR LabUniversity of PaderbornPaderbornGermany

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