Crew Pairing for a Regional Carrier

  • Guy Desaulniers
  • Jacques Desrosiers
  • Arielle Lasry
  • Marius M. Solomon
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 471)


This paper addresses the problem of generating valid crew pairings in the context of a regional air carrier. The classical column generation solution approach based on extensive enumeration of all valid duties is impractical in this context where duties comprise ten to twelve legs. In order to alleviate this difficulty, we propose an alternative approach which takes into account all work rules and air traffic regulations during the construction of valid crew pairings. Two network structures compatible with this approach are described. The first is a leg-on-node model while the second involves a leg-on-arc representation. Computational results obtained with the GENCOL optimizer on problems varying from 63 to 986 legs lead us to conclude that the leg-on-arc representation is substantially more efficient. In addition, we study the cost impact of three changes in the operating scenario. Finally, we illustrate how bounded perturbation variables virtually eliminate degeneracy, hence significantly decreasing CPU time.


Column Generation Master Problem Linear Relaxation Crew Schedule Connection Time 
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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  1. Anbil, R./Gelman, E./Patty, B./Tanga, R. (1991): Recent Advances in Crew Pairing Optimization at American Airlines. Interfaces 21, 62–74.CrossRefGoogle Scholar
  2. Ball, M./Roberts, A. (1985): A Graph Partitioning Approach to Airline Crew Scheduling. Transportation Science 19, 107–126.CrossRefGoogle Scholar
  3. Barnhart, C./Johnson, E.L./Anbil, R./Hatay, L. (1994): A Column Generation Technique for the Long-Haul Crew Assignment Problem. in: Ciriani, T.A./Leachman, R.C.(eds.): Optimization in Industry 2. (John Wiley) New York, 7–22.Google Scholar
  4. Chu, H.D./Gelman, E./Johnson, E. (1997): Solving Large Scale Crew Scheduling Problems. European Journal of Operational Research 97, 260–268.CrossRefGoogle Scholar
  5. Crainic, T.G./Rousseau, J.-M. (1987): The Column Generation Principle and the Airline Crew Scheduling Problem. INFOR 25, 136–151.Google Scholar
  6. Dantzig, G.B./Wolfe, P. (1960): Decomposition Principle for Linear Programming. Operations Research 8, 101–111.CrossRefGoogle Scholar
  7. Desaulniers, G./Desrosiers, J./Ioachim, I./Solomon, M.M./Soumis, F./Villeneuve, D. (1998): A Unified Framework for Deterministic Time Constrained Vehicle Routing and Crew Scheduling Problems. in: Crainic, T./Laporte, G. (eds.): Fleet Management and Logistics.Google Scholar
  8. Desaulniers, G./Desrosiers, J./Dumas, Y./Marc, S./Rioux, B./ Solomon, M.M./Soumis, F. (1997): Crew Pairing at Air France. European Journal of Operational Research 97, 245–259.CrossRefGoogle Scholar
  9. Desrochers, M./Desrosiers, J./Solomon, M.M. (1992): A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows. Operations Research 40, 342–354.CrossRefGoogle Scholar
  10. Desrochers, M./Soumis, F. (1988): A Reoptimization Algorithm for the Shortest Path Problem with Time Windows. European Journal of Operational Research 35, 242–254.CrossRefGoogle Scholar
  11. Desrosiers, J./Dumas, Y./Solomon, M.M./Soumis, F. (1995): Time Constrained Routing and Scheduling. in: Ball, M.O./Magnanti, T.L./ Monma, C.L./Nemhauser, G.L. (eds.): Network Routing, Handbooks in O.R. & M.S. 8, (Elsevier) Amsterdam, 35–139.Google Scholar
  12. du Merle, O./Villeneuve, D./Desrosiers, J./Hansen, P. (1997): Stabilized Column Generation. Les Cahiers du GERAD, G-98–06, École des Hautes Études Commerciales, Montréal, Canada, H3T 2A7.Google Scholar
  13. Etschmaier, M.M./Mathaisel, D.F.X. (1985): Airline Scheduling: An Overview. Transportation Science 19, 127–138.Google Scholar
  14. Gershkoff, L. (1989): Optimizing Flight Crew Schedules. Interfaces 19, 29–43.CrossRefGoogle Scholar
  15. Graves, G.W./McBride, R.D./Gershkoff, I./Anderson, D./ Mahidara, D. (1993): Flight Crew Scheduling. Management Science 39, 736–745.CrossRefGoogle Scholar
  16. Hoffman, K.L./Padberg, M. (1993): Solving Airline Crew Scheduling Problems by Branch-and-Cut. Management Science 39, 657–682.CrossRefGoogle Scholar
  17. Lavoie, S./Minoux, M./Odier, E. (1988): A New Approach for Crew Pairing Problems by Column Generation with an Application to Air Transportation. European Journal of Operational Research 35, 45–58.CrossRefGoogle Scholar
  18. Salkin, H.M. (1975): Integer Programming (Addison-Wesley) Reading, Mass.Google Scholar
  19. Wedelin, D. (1995): An Algorithm for Large Scale 0–1 Integer Programming with Applications to Airline Crew Scheduling. Annals of Operations Research 57, 283–301.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Guy Desaulniers
    • 1
  • Jacques Desrosiers
    • 2
  • Arielle Lasry
    • 3
  • Marius M. Solomon
    • 4
  1. 1.École Polytechnique and GERADMontréalCanada
  2. 2.École des Hautes Études Commerciales and GERADMontréalCanada
  3. 3.Numetrix LimitedTorontoCanada
  4. 4.Northeastern University and GERADBostonUSA

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