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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
Article

Abstract

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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References

  1. Andersson, E., E. Housos, N. Kohl, and D. Wedelin. (1998). “Crew Pairing Optimization.” In G. Yu (ed.), Operations Research in the Airline Industry, International Series in Operations Research and Management Science, Vol. 9. Dordrecht: Kluwer Academic Publishers, pp. 228–258.Google Scholar
  2. Barnhart, C., E.L. Johnson, G.L. Nemhauser, M.W.P. Savelsbergh, and P.H. Vance. (1998). “Branch-and-Price: Column Generation for Solving Huge Integer Programs.” Operations Research 46(3), 316–329.Google Scholar
  3. Barnhart C. and R.G. Shenoi. (1998). “An Approximate Model and Solution Approach for the Long-Haul Crew Pairing Problem.” Transportation Science 32(3), 221–231.Google Scholar
  4. Beringer, H. and B. De Backer. (1995). “Combinatorial Problem Solving in Constraint Logic Programming with Cooperative Solvers.” In C. Beierle and L. Plumer (eds.), Logic Programming: Formal Methods and Practical Applications. Amsterdam: Elsevier, pp. 245–272.Google Scholar
  5. Bessière, C. (1994). “Arc-Consistency and Arc-Consistency Again.” Artificial Intelligence 65, 179–190.Google Scholar
  6. Bockmayr, A. and T. Kasper. (1998). “Branch and Infer: A Unifying Framework for Integer and Finite Domain Constraint Programming.” INFORMS Journal on Computing 10(3), 287–300.Google Scholar
  7. Caprara, A., M. Fischetti, and P. Toth. (1996). “A Heuristic Algorithm for the Set Covering Problem.” In Integer Programming and Combinatorial Optimization, 5th International IPCO Conference Proceedings. Berlin: Springer, pp. 1–15.Google Scholar
  8. Caprara, A., F. Focacci, E. Lamma, P. Mello, M. Milano, P. Toth, and D. Vigo. (1998a). “Integrating Constraint Logic Programming and Operations Research Techniques for the CrewRostering Problem.” SoftwarePractice and Experience 28(1), 49–76.Google Scholar
  9. Caprara, A., P. Toth, D. Vigo, and M. Fischetti. (1998b). “Modeling and Solving the Crew Rostering Problem.” Operations Research 46(6), 820–830.Google Scholar
  10. Cavique, L., C. Rego, and I. Themido. (1999). “Subgraph Ejection Chains and Tabu Search for the Crew Scheduling Problem.” Journal of the Operational Research Society 50, 608–616.Google Scholar
  11. Chu, H.D., E. Gelman, and E.L. Johnson. (1997). “Solving Large Scale Crew Scheduling Problems.” European Journal of Operational Research 97, 260–268.Google Scholar
  12. Cormen, T.H., C.E. Leierson, and R.L. Riverste. (1990). Introduction to Algorithms. New York: McGraw-Hill.Google Scholar
  13. Dantzig, G.B. and P. Wolfe. (1961). “The Decomposition Algorithm for Linear Programs.” Econometrica 29(4), 767–778.Google Scholar
  14. Day, P.R. and D.M. Ryan. (1997). “Flight Attendant Rostering for Short-Haul Airline Operations.” Operations Research 45(5), 649–661.Google Scholar
  15. Desaulniers, G., J. Desrosiers, Y. Dumas, S. Marc, B. Rioux, M.M. Solomon, and F. Soumis. (1997). “CrewPairing at Air France.” European Journal of Operational Research 97, 245–259.Google Scholar
  16. Desrosiers, J., Y. Dumas, M.M. Solomon, and F. Soumis. (1995). “Time Constrained Routing and Scheduling.” In Ball, Magnanti, Monma, and Nemhauser (eds.), Network Routing, Handbooks in Operations Research and Management Science, Vol. 8. Amsterdam: North-Holland, pp. 35–139.Google Scholar
  17. Gamache, M., F. Soumis, D. Villeneuve, J. Desrosiers, and E. Gélinas. (1998). “The Preferential Bidding System at Air Canada.” Transportation Science 32(3), 246–255.Google Scholar
  18. Gilmore, P.C. and R.E. Gomory. (1961). “A Linear Programming Approach to the Cutting Stock Problem.” Operations Research 9, 849–859.Google Scholar
  19. Hoffman, K.L. and M. Padberg. (1993). “Solving Airline Crew Scheduling Problems by Branch-and-Cut.” Management Science 39(6), 657–682.Google Scholar
  20. Hooker, J. (1999). “Unifying Optimization and Constraint Satisfaction.” Invited talk at IJCAI '99. Slides available at http://ba.gsia.cmu.edu/jnh/ijcai.ppt.Google Scholar
  21. ILOG PLANNER 3.3. (1999). Reference manual and user manual. ILOG.Google Scholar
  22. ILOG SOLVER 4.4. (1999). Reference manual and user manual. ILOG.Google Scholar
  23. Kohl, N. and S.E. Karisch. (1999). “Airline Crew Assignment: Modeling and Optimization.” Carmen Report.Google Scholar
  24. Mackworth, A.K. (1977). “Consistency in Networks of Relations.” Artificial Intelligence 8(1), 99–118.Google Scholar
  25. Montanari, U. (1974). “Networks of Constraints: Fundamental Properties and Applications.” Information Science 7(2), 95–132.Google Scholar
  26. Nuijten, W.P.M. and E.H.L. Aarts. (1996). “A Computational Study of Constraint Satisfaction for Multiple Capacitated Job Shop Scheduling.” European Journal of Operational Research 90(2), 269–284.Google Scholar
  27. PARROT. (1997). Executive Summary. ESPRIT 24 960.Google Scholar
  28. Rodosek, R., M. Wallace, and M.T. Haijan. (1999). “A New Approach to Integrating Mixed Integer Programming and Constraint Logic Programming.” Annals of Operations Research 86, 63–87.Google Scholar
  29. Rushmeier, R.A., K.L. Hoffman, and M. Padberg. (1995). “Recent Advances in Exact Optimization of Airline Scheduling Problems.” Technical Report, George Mason University.Google Scholar
  30. Ryan, D.M. (1992). “The Solution of Massive Generalized Set Partitioning Problems in Aircrew Rostering.” Journal of the Operational Research Society 43(5), 459–467.Google Scholar
  31. Van Hentenryck, P., Y. Deville, and C.M. Teng. (1992). “A Generic Arc-Consistency Algorithm and its Specializations.” Artificial Intelligence 57, 291–321.Google Scholar
  32. Yu, G. (ed.). (1998). Operations Research in the Airline Industry, International Series in Operations Research and Management Science, Vol. 9. Dordrecht: Kluwer Academic Publishers.Google Scholar

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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