Skip to main content
Log in

Combining column generation and constraint programming to solve the tail assignment problem

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Within the area of short term airline operational planning, Tail Assignment is the problem of assigning flight legs to individual identified aircraft while satisfying all operational constraints, and optimizing some objective function. In this article, we propose that Tail Assignment should be solved as part of both the short and the long term airline planning. We further present a hybrid column generation and constraint programming solution approach. This approach can be used to quickly produce solutions for operations management, and also to produce close-to-optimal solutions for long and mid term planning scenarios. We present computational results which illustrate the practical usefulness of the approach.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahuja, R. K., Liu, J., Goodstein, J., Mukherjee, A., Orlin, J. B., & Sharma, D. (2003). Solving multi-criteria combined through fleet assignment models. In T. A. Ciriani, G. Fasano, S. Gliozzi, & R. Tadei (Eds.), Operations research in space and air (pp. 233–256). Dordrecht: Kluwer Academic.

    Google Scholar 

  • Barnhart, C., Boland, N. L., Clarke, L. W., Johnson, E. L., Nemhauser, G. L., & Shenoi, R. G. (1998a). Flight string models for aircraft fleeting and routing. Transportation Science, 32(3), 208–220.

    Article  Google Scholar 

  • Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998b). Branch-and-Price: Column generation for solving huge integer programs. Operations Research, 46(3), 316–329.

    Article  Google Scholar 

  • Berge, M. E., & Hopperstad, C. A. (1993). Demand driven dispatch: a method for dynamic aircraft capacity assignment, Models and Algorithms. Operations Research, 41(1), 153–168.

    Article  Google Scholar 

  • Clarke, L. W., Johnson, E. L., Nemhauser, G. L., & Zhu, Z. (1997). The aircraft rotation problem. Annals of Operations Research, 69, 33–46.

    Article  Google Scholar 

  • Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8, 101–111.

    Article  Google Scholar 

  • Dash Optimization Ltd.: (2002). Xpress-Optimizer Reference Manual, release 14.

  • Desaulniers, G., Desrosiers, J., & Solomon, M. M. (1999). Accelerating strategies in column generation methods for vehicle routing and crew scheduling problems. Les Cahiers du GERAD G-99-36, GERAD.

  • Desrochers, M., & Soumis, F. (1988). A generalized permanent labelling algorithm for the shortest path problem with time windows. INFOR, 26(3), 191–212.

    Google Scholar 

  • du Merle, O., Villeneuve, D., Desrosiers, J., & Hansen, P. (1999). Stabilized column generation. Discrete Mathematics, 194, 229–237.

    Article  Google Scholar 

  • Elf, M., Jünger, M., & Kaibel, V. (2003). Rotation planning for the continental service of a European airline. In W. Jager & H. J. Krebs (Eds.), Mathematics—key technologies for the future. Joint projects between universities and industry (pp. 675–689). Berlin: Springer.

    Google Scholar 

  • Even, S., Itai, A., & Shamir, A. (1976). On the complexity of timetable and multicommodity flow problems. SIAM Journal on Computing, 5(4), 691–703.

    Article  Google Scholar 

  • Fahle, T., Junker, U., Karisch, S. E., Kohl, N., Sellmann, M., & Vaaben, B. (2002). Constraint programming based column generation for crew assignment. Journal of Heuristics, 8(1), 59–81.

    Article  Google Scholar 

  • Foster, B. A., & Ryan, D. M. (1981). An integer programming approach to scheduling. In A. Wren (Ed.), Computer scheduling in public transport (pp. 269–280). Amsterdam: North-Holland.

    Google Scholar 

  • Gamache, M., Soumis, F., Marquis, G., & Desrosiers, J. (1999). A column generation approach for large-scale aircrew rostering problems. Operations Research, 47(2), 247–263.

    Article  Google Scholar 

  • Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of np-completeness. San Fransisco: Freeman.

    Google Scholar 

  • Gopalan, R., & Talluri, K. T. (1998). The aircraft maintenance routing problem. Operations Research, 46(2), 260–271.

    Article  Google Scholar 

  • Grönkvist, M. (2003). Tail assignment—a combined column generation and constraint programming approach. Lic. thesis, Department of Computing Science, Chalmers University of Technology, Gothenburg, Sweden.

  • Grönkvist, M. (2004). A Constraint programming model for tail assignment. In Lecture notes in computer science: Vol. 3011. Proceedings of CPAIOR’04 (pp. 142–156). Berlin: Springer.

    Google Scholar 

  • Grönkvist, M. (2005). The Tail Assignment Problem. Ph.D. thesis, Department of Computing Science, Chalmers University of Technology, Gothenburg, Sweden.

  • Grönkvist, M. (2006). Accelerating column generation for aircraft scheduling using constraint propagation. Computers & Operations Research, 33(10), 2918–2934.

    Article  Google Scholar 

  • Hane, C. A., Barnhart, C., Johnson, E. L., Marsten, R. E., Nemhauser, G. L., & Sigismondi, G. (1995). The fleet assignment problem: solving a large-scale integer program. Mathematical Programming, 70, 211–232.

    Google Scholar 

  • Hjorring, C. A. (2004). Solving larger crew pairing problems. In Proceedings of TRISTAN V: the fifth triennial symposium on transportation analysis. Le Gosier, Guadeloupe.

  • ILOG Inc.: (2001). ILOG CPLEX 7.5 Reference Manual.

  • Jarrah, A. I., & Strehler, J. C. (2000). An optimization model for assigning through flights. IIE Transactions, 32(3), 237–244.

    Google Scholar 

  • Jarrah, A. I., Goodstein, J., & Narasimhan, R. (2000). An efficient airline re-fleeting model for the incremental modification of planned fleet assignments. Transportation Science, 34(4), 349–363.

    Article  Google Scholar 

  • Kabbani, N. M., & Patty, B. W. (1992). Aircraft routing at American airlines. In Proceedings of the thirty-second annual symposium of AGIFORS.

  • Lübbecke, M. E., & Desrosiers, J. (2002). Selected topics in column generation. Les Cahiers du GERAD G-2002-64, Department of Mathematical Optimization, Braunschweig University of Technology, and GERAD. Submitted to Operations Research.

  • Martins, E. Q. V., & dos Santos, J. L. E. (1999). The labelling algorithm for the multiobjective shortest path problem. (Technical report). Departamento de Matemática, Universidade de Coimbra, Coimbra, Portugal.

  • Rannou, B. (1986). A new approach to crew pairing optimization. Presentation at 26th AGIFORS Annual Symposium, Bowness-on-Windermere, England.

  • Régin, J. C. (1994). A filtering algorithm for constraints of difference in CSPs. In Proceedings of AAAI-94 (pp. 362–367).

  • Rosenberger, J. M., Johnson, E. L., & Nemhauser, G. L. (2004). A robust fleet-assignment model with hub isolation and short cycles. Transportation Science, 38, 3.

    Article  Google Scholar 

  • Rousseau, L. M., Gendreau, M., & Pesant, G. (2002). Solving small VRPTWs with constraint programming based column generation. In Proceedings of CPAIOR’02.

  • Schaefer, A. J., Johnson, E. L., Kleywegt, A. J., & Nemhauser, G. L. (2001). Airline crew scheduling under uncertainty. tech. rep. (Technical Report). Georgia Institute of Technology, Atlanta, GA, USA.

  • Talluri, K. T. (1998). The four-day aircraft maintenance problem. Transportation Science, 32, 43–53.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mattias Grönkvist.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gabteni, S., Grönkvist, M. Combining column generation and constraint programming to solve the tail assignment problem. Ann Oper Res 171, 61–76 (2009). https://doi.org/10.1007/s10479-008-0379-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-008-0379-1

Keywords

Navigation