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.
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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.
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.
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.
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.
Bessière, C. (1994). “Arc-Consistency and Arc-Consistency Again.” Artificial Intelligence 65, 179–190.
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.
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.
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.” Software—Practice and Experience 28(1), 49–76.
Caprara, A., P. Toth, D. Vigo, and M. Fischetti. (1998b). “Modeling and Solving the Crew Rostering Problem.” Operations Research 46(6), 820–830.
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.
Chu, H.D., E. Gelman, and E.L. Johnson. (1997). “Solving Large Scale Crew Scheduling Problems.” European Journal of Operational Research 97, 260–268.
Cormen, T.H., C.E. Leierson, and R.L. Riverste. (1990). Introduction to Algorithms. New York: McGraw-Hill.
Dantzig, G.B. and P. Wolfe. (1961). “The Decomposition Algorithm for Linear Programs.” Econometrica 29(4), 767–778.
Day, P.R. and D.M. Ryan. (1997). “Flight Attendant Rostering for Short-Haul Airline Operations.” Operations Research 45(5), 649–661.
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.
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.
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.
Gilmore, P.C. and R.E. Gomory. (1961). “A Linear Programming Approach to the Cutting Stock Problem.” Operations Research 9, 849–859.
Hoffman, K.L. and M. Padberg. (1993). “Solving Airline Crew Scheduling Problems by Branch-and-Cut.” Management Science 39(6), 657–682.
Hooker, J. (1999). “Unifying Optimization and Constraint Satisfaction.” Invited talk at IJCAI '99. Slides available at http://ba.gsia.cmu.edu/jnh/ijcai.ppt.
ILOG PLANNER 3.3. (1999). Reference manual and user manual. ILOG.
ILOG SOLVER 4.4. (1999). Reference manual and user manual. ILOG.
Kohl, N. and S.E. Karisch. (1999). “Airline Crew Assignment: Modeling and Optimization.” Carmen Report.
Mackworth, A.K. (1977). “Consistency in Networks of Relations.” Artificial Intelligence 8(1), 99–118.
Montanari, U. (1974). “Networks of Constraints: Fundamental Properties and Applications.” Information Science 7(2), 95–132.
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.
PARROT. (1997). Executive Summary. ESPRIT 24 960.
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.
Rushmeier, R.A., K.L. Hoffman, and M. Padberg. (1995). “Recent Advances in Exact Optimization of Airline Scheduling Problems.” Technical Report, George Mason University.
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.
Van Hentenryck, P., Y. Deville, and C.M. Teng. (1992). “A Generic Arc-Consistency Algorithm and its Specializations.” Artificial Intelligence 57, 291–321.
Yu, G. (ed.). (1998). Operations Research in the Airline Industry, International Series in Operations Research and Management Science, Vol. 9. Dordrecht: Kluwer Academic Publishers.
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Fahle, T., Junker, U., Karisch, S.E. et al. Constraint Programming Based Column Generation for Crew Assignment. Journal of Heuristics 8, 59–81 (2002). https://doi.org/10.1023/A:1013613701606
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DOI: https://doi.org/10.1023/A:1013613701606