High performance integer optimization for crew scheduling

  • Peter Sanders
  • Tuomo Takkula
  • Dag Wedelin
Track C1: (Industrial) End-user Applications of HPCN
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1593)


Performance aspects of a Lagrangian relaxation based heuristic for solving large 0–1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Göteborg, Sweden, based on distributing the variables and a new sequential active set strategy which requires less work and is better adapted to the memory hierachy properties of modern RISC processors. The active set strategy can even be parallelized on networks of workstations.


Lagrangian Relaxation Crew Schedule Global Iteration Innermost Loop Good Load Balance 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Alefragis, C. Goumopoulos, E. Housos, P. Sanders, T. Takkula, and D. Wedelin. Parallel crew scheduling in PAROS. In EUROPAR'98, Lecture Notes in Computer Science, 1998. to appear.Google Scholar
  2. 2.
    E. Andersson, E. Housos, N. Kohl, and D. Wedelin. OR in the Airline Industry, chapter Crew Pairing Optimization, Kluwer Academic Publishers, Boston, London, Dordrecht, 1997.Google Scholar
  3. 3.
    C. Barnhart and R. G. Shenoi. An alternate model and solution approach for the long-haul crew pairing problem. Jul 1996.Google Scholar
  4. 4.
    A. Caprara, M. Fischetti, and P. Toth. A heuristic algorithm for the set covering problem. In Lecture Notes in Computer Science, pages 72–84, 1996.Google Scholar
  5. 5.
    The Carmen System, version 5.1. Carmen Systems AB, Göteborg, Sweden.Google Scholar
  6. 6.
    S. Ceria, P. Nobili, and A. Sassano. A Lagrangian-based heuristic for large-scale set covering problems. Technical report, Dipartimento di Informatica e Sistemistica, Università di Roma, La Sapienza, Italy, 1995.Google Scholar
  7. 7.
    T. H. Cormen, C. E. Leiserson, and R. L. Rivest. Introduction to Algorithms. McGraw-Hill, 1990.Google Scholar
  8. 8.
    G. Desaulniers, J. Desrosiers, Y. Dumas, S. Marc, B. Rioux, M. Solomon, and F. Soumis. Crew pairing at Air France. European Journal of Operational Research, 97:245–259, 1997.CrossRefzbMATHGoogle Scholar
  9. 9.
    M. L. Fisher. The Lagrangian relaxation method for solving integer programming problems. Management Sciences, 27(1):1–18, 1981.zbMATHGoogle Scholar
  10. 10.
    C. Goumopoulos, P. Alefragis, and E. Housos. Parallel algorithms for airline crew planning on networks of workstations. In International Conference on Parallel Processing, Minneapolis, 1998.Google Scholar
  11. 11.
    C. Goumopoulos, E. Housos, and O. Liljenzin. Parallel crew scheduling on work-station networks using PVM. In Euro PVM-MPI, number 1332 in LNCS, Cracow, Poland, 1997.Google Scholar
  12. 12.
    K. L. Hoffman and M. Padberg. Solving airline crew scheduling problems by branch-and-cut. Management Science, 39(6):657–682, 1993.CrossRefzbMATHGoogle Scholar
  13. 13.
    S. Lavoie, M. Minoux, and E. Odier. A new approach for crew pairing problems by column generation with an application to air transportation. European Journal of Operations Research, 35:45–58, 1988.CrossRefzbMATHGoogle Scholar
  14. 14.
    R. Marsten. RALPH: Crew Planning at Delta Air Lines. Technical Report. Cutting Edge Optimization, 1997.Google Scholar
  15. 15.
    J. Motwani and P. Raghavan. Randomized algorithms. Cambridge University Press, 1995.Google Scholar
  16. 16.
    M. Snir, S. W. Otto, S. Huss-Lederman, D. W. Walker, and J. Dongarra. MPI—the Complete Reference. MIT Press, 1996.Google Scholar
  17. 17.
    P. H. Vance. Crew Scheduling, Cutting Stock, and Column Generation: Solving Huge Integer Programs. PhD thesis, Georgia Institute of Technology, August 1993.Google Scholar
  18. 18.
    D. Wedelin. An algorithm for large scale 0–1 integer programming with application to airline crew scheduling. Annals of Operations Research, 57:283–301, 1995.CrossRefMathSciNetzbMATHGoogle Scholar
  19. 19.
    A. Wool and T. Grossman. Computational experience with approxima-tion algorithms for the set covering problem. Technical Report CS94-25, Weizmann Institute of Science, Faculty of Mathematical Sciences, Jan. 1, 1994.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Peter Sanders
    • 1
  • Tuomo Takkula
    • 2
  • Dag Wedelin
    • 2
  1. 1.Max-Planck-Institute for Computer ScienceSaarbrückenGermany
  2. 2.Chalmers University of Technology, Computing ScienceGöteborgSweden

Personalised recommendations