Skip to main content
SpringerLink
Log in

Advanced Column Generation Techniques for Crew Pairing Problems

  • Conference paper
Modeling, Simulation and Optimization of Complex Processes

  • 1401 Accesses

Summary

Crew pairing problems are often solved using column generation in a branch-and-price framework. The main idea of this approach consists of solving linear programming relaxations for a subset of variables and employing pricing for introducing additional variables with negative reduced costs. Since the dual variables are not bounded, this leads to instability in the standard implementation of this method. Therefore, a so-called stabilized column generation with respective control parameters is suggested to overcome this problem by reducing the number of redundant variables. In this paper we report about possible realizations of this principle and show that the performance of algorithms can be improved significantly.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P. Alefragis, C. Goumopoulos, E. Housos, P. Sanders, T. Takkula, and D. Wedelin. Parallel Crew Scheduling in PAROS. In Proceedings of Euro-Par'98 Parallel Processing: 4th International Euro-Par Conference, 1998.

    Google Scholar 

  2. C. Barnhart, E. L. Johnson, G. L. Nemhauser, M. W. P. Savelsbergh, and P. H. Vance. Branch-and-price: Column Generation for Solving Huge Integer Programs. Operations Research, 46:316–329, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Desrosiers, Y. Dumas, M. M. Solomon, and F. Soumis. Handbooks in Operations Research and Management Science, volume 8, chapter Time Constrained Routing and Scheduling, pages 35–139. North-Holland, 1993.

    MathSciNet  Google Scholar 

  4. O. du Merle, D. Villeneuve, J. Desrosiers, and P. Hansen. Stabilized Column Generation. Discrete Mathematics, 194:229–237, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  5. N. Guerinik and M. V. Caneghem. Solving Crew Scheduling Problems by Constraint Programming. In Proceedings of the ist Conference of Principles and Practice of Constraint Programming, pages 481–498, 1995.

    Google Scholar 

  6. T. Gustafsson. A Heuristic Approach to Column Generation for Airline Crew Scheduling. PhD thesis, Chalmers University of Technology, 1999.

    Google Scholar 

  7. I. Ioachim, S. GAlinas, F. Soumis, and J. Desrosiers. A Dynamic Programming for the Shortest Path Problem with Time Windows and Linear Node Costs. Networks, 31, 1997.

    Google Scholar 

  8. B. Jaumard, F. Semet, and T. Vovor. A Two-Phase Resource Constrained Shortest Path Algorithm for Acyclic Graphs. Technical report, Les Cahiers du GERAD, 1999.

    Google Scholar 

  9. J. E. Kelley. The Cutting Plane Method for Solving Convex Program. Journal of SIAM, 8:703–712, 1960.

    MathSciNet  Google Scholar 

  10. D. Klabjan and K. Schwan. Airline Crew Pairing Generation in Parallel. Technical report, The Logistics Institute, Georgia institute of Technology, 1999.

    Google Scholar 

  11. R. E. Marsten, W. W. Hogan, and J. W. Blankenship. The Boxstep Method for Large-Scale Optimization. Operations Research, 23(3):389–405, 1975.

    MathSciNet  MATH  Google Scholar 

  12. P. J. Neame. Nonsmooth Dual Methods in Integer Programming. PhD thesis, The University of Melbourne, 1999.

    Google Scholar 

  13. P. H. Vance, A. Atamtürk, C. Barnhart, E. Gelman, E. L. Johnson, A. Krishna, D. Mahidhara, and R. Rebello. A Heuristic Branch-and-Price Approach for the Airline Crew Pairing Problem, 1997.

    Google Scholar 

  14. R. Wunderling. SoPlex, The Sequential Object-Oriented Simplex Class Library. ZIB, 1997.

    Google Scholar 

  15. T. H. Yunes, A. V. Moura, and C. C. de Souza. Practical Aspects of Declarative Languages, volume 1753 of Lecture notes in computer science, chapter A Hybrid Approach for Solving Large Scale Crew Scheduling Problems, pages 293–307. Springer, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Tran Van Hoai & Hans Georg Bock

  2. Institute for Computer Science, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Gerhard Reinelt

Authors
  1. Tran Van Hoai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gerhard Reinelt
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hans Georg Bock
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Hans Georg Bock  & Ekaterina Kostina  & 

  2. Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Xuan Phu

  3. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 68120, Heidelberg, Germany

    Rolf Rannacher

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Van Hoai, T., Reinelt, G., Bock, H.G. (2005). Advanced Column Generation Techniques for Crew Pairing Problems. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_16

Download citation

Publish with us

Policies and ethics

Search

Navigation