Journal of Heuristics

, Volume 8, Issue 1, pp 59–81 | Cite as

Constraint Programming Based Column Generation for Crew Assignment

  • Torsten Fahle
  • Ulrich Junker
  • Stefan E. Karisch
  • Niklas Kohl
  • Meinolf Sellmann
  • Bo Vaaben


Airline crew assignment problems are large-scale optimization problems which can be adequately solved by column generation. The subproblem is typically a so-called constrained shortest path problem and solved by dynamic programming. However, complex airline regulations arising frequently in European airlines cannot be expressed entirely in this framework and limit the use of pure column generation. In this paper, we formulate the subproblem as a constraint satisfaction problem, thus gaining high expressiveness. Each airline regulation is encoded by one or several constraints. An additional constraint which encapsulates a shortest path algorithm for generating columns with negative reduced costs is introduced. This constraint reduces the search space of the subproblem significantly. Resulting domain reductions are propagated to the other constraints which additionally reduces the search space. Numerical results based on data of a large European airline are presented and demonstrate the potential of our approach.

airline crew assignment constraint satisfaction column generation shortest path constraint hybrid OR/CP methods 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Torsten Fahle
    • 1
  • Ulrich Junker
    • 2
  • Stefan E. Karisch
    • 3
  • Niklas Kohl
    • 4
  • Meinolf Sellmann
    • 1
  • Bo Vaaben
    • 4
  1. 1.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany
  2. 2.ILOG S.A.ValbonneFrance
  3. 3.Carmen Systems Ltd.MontrealCanada
  4. 4.Carmen ConsultingCopenhagen ØDenmark

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