Annals of Operations Research

, Volume 204, Issue 1, pp 11–32 | Cite as

Constraint Programming-based Column Generation



This paper surveys recent applications and advances of the Constraint Programming-based Column Generation framework, where the master subproblem is solved by traditional OR techniques, while the pricing subproblem is solved by Constraint Programming. This framework has been introduced to solve crew assignment problems, where complex regulations make the pricing subproblem demanding for traditional techniques, and then it has been applied to other contexts. The main benefits of using Constraint Programming are the expressiveness of its modeling language and the flexibility of its solvers. Recently, the Constraint Programming-based Column Generation framework has been applied to many other problems, ranging from classical combinatorial problems such as graph coloring and two dimensional bin packing, to application oriented problems, such as airline planning and resource allocation in wireless ad-hoc networks.


Column Generation Constraint Programming Integer linear programming 


  1. Achterberg, T. (2007). Constraint integer programming. PhD thesis, TU Berlin. Google Scholar
  2. Apt, K. R. (2003). Principles of constraint programming. Cambridge: Cambridge University Press. CrossRefGoogle Scholar
  3. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-price: column generation for solving huge integer programs. Operations Research, 46(3), 316–329. CrossRefGoogle Scholar
  4. Beldiceanu, N., Carlsson, M., & Rampon, J. X. (2005). Global constraint catalogue. Technical Report SICS-T2005:08, Swedish Institute of Computer Science. Google Scholar
  5. Capone, A., Carello, G., Filippini, I., Gualandi, S., & Malucelli, F. (2010). Solving a resource allocation problem in wireless mesh networks: a comparison between a CP-based and a classical column generation. Networks, 55(3), 221–233. doi:10.1002/net.20367. Google Scholar
  6. Chu, C., & Antonio, J. (1999). Approximation algorithms to solve real-life multicriteria cutting stock problems. Operations Research, 47(4), 495–508. CrossRefGoogle Scholar
  7. Ciriani, T. A., Colombani, Y., & Heipcke, S. (2003). Embedding optimisation algorithms with Mosel. 4OR, 1(2), 155–167. CrossRefGoogle Scholar
  8. Cortès, C., Gendreau, M., Rousseau, L.-M., Souyris, S., & Weintraub, A. (2012, to appear). Solving a technician dispatch problem using branch and price and constraint programming. European Journal of Operational Research. Google Scholar
  9. Cotè, M.-C., Gendron, B., & Rousseau, L.-M. (2012). Grammar-based column generation for personalized multi-activity shift scheduling. INFORMS Journal on Computing. doi:10.1287/ijoc.1120.0514. Google Scholar
  10. Demassey, S., Pesant, G., & Rousseau, L. M. (2006). A cost-regular based hybrid column generation approach. Constraints, 11(4), 315–333. CrossRefGoogle Scholar
  11. Desrosiers, J., Dumas, Y., Solomon, M. M., & Soumis, F. (1995). Time constrained routing and scheduling. In M. O. Ball, T. L. Magnanti, C. L. Monma, & G. L. Nemhauser (Eds.), Handbooks in operations research and management science: Vol. 8. Network routing (pp. 35–139). Amsterdam: Elsevier, North-Holland. CrossRefGoogle Scholar
  12. DIMACS (2002). Graph coloring instances.
  13. Easton, K., Nemhauser, G. L., & Trick, M. A. (2002). Solving the travelling tournament problem: a combined integer programming and constraint programming approach. In LNCS: Vol. 2740. Proc. of practice and theory of automated timetabling (pp. 100–112). Berlin: Springer. Google Scholar
  14. Fahle, T., & Sellmann, M. (2002). Cost based filtering for the constrained knapsack problem. Annals of Operations Research, 115(1), 73–93. CrossRefGoogle Scholar
  15. 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. CrossRefGoogle Scholar
  16. Gabteni, S., & Grönkvist, M. (2006). A hybrid column generation and constraint programming optimizer for the tail assignment problem. In LNCS: Vol. 3990. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 89–103). Berlin: Springer. CrossRefGoogle Scholar
  17. Gecode Team (2006). Gecode: generic constraint development environment.
  18. Gendron, B., Lebbah, H., & Pesant, G. (2005). Improving the cooperation between the master problem and the subproblem in constraint programming based column generation. In LNCS: Vol. 3524. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 217–227). Berlin: Springer. CrossRefGoogle Scholar
  19. Gilmore, P. C., & Gomory, R. E. (1961). A linear programming approach to the cutting-stock problem. Operations Research, 9(6), 849–859. CrossRefGoogle Scholar
  20. Grönkvist, M. (2004). A constraint programming model for tail assignment. In LNCS: Vol. 3011. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 142–156). Berlin: Springer. CrossRefGoogle Scholar
  21. Grönkvist, M. (2006). Accelerating column generation for aircraft scheduling using constraint propagation. Computers & Operations Research, 33(10), 2918–2934. CrossRefGoogle Scholar
  22. Gualandi, S. (2009). Enhancing constraint programming-based column generation for integer programs. 4OR, 7(3), 289–292. CrossRefGoogle Scholar
  23. Gualandi, S., & Malucelli, F. (2009). Constraint programming-based column generation: a survey. 4OR, 7(2), 113–137. CrossRefGoogle Scholar
  24. Gualandi, S., & Malucelli, F. (2012). Exact solution of graph coloring problems via constraint programming and column generation. INFORMS Journal on Computing, 24(1), 81–100. CrossRefGoogle Scholar
  25. Hansen, J., & Liden, T. (2005). Group construction for airline cabin crew: comparing constraint programming with branch and price. In LNCS: Vol. 3524. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 228–242). Berlin: Springer. CrossRefGoogle Scholar
  26. Harvey, W. D., & Ginsberg, M. L. (1995). Limited discrepancy search. In Proc. international joint conferences on artificial intelligence (pp. 607–615). Google Scholar
  27. Heisig, G., & Minner, S. (1999). ILOG OPL studio. OR Spektrum, 21(4), 419–427. CrossRefGoogle Scholar
  28. Junker, U., Karisch, S. E., Kohl, N., Vaaben, B., Fahle, T., & Sellmann, M. (1999). A framework for constraint programming based column generation. In LNCS: Vol. 1713. Proc. principles and practice of constraint programming (pp. 261–274). Berlin: Springer. Google Scholar
  29. Lübbecke, M. E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53(6), 1007–1023. CrossRefGoogle Scholar
  30. Marriott, K., Nethercote, N., Rafeh, R., Stuckey, P. J., De la Garcia, B. M., & Wallace, M. (2008). The design of the zinc modelling language. Constraints, 13(3), 229–267. CrossRefGoogle Scholar
  31. Martello, S., & Toth, P. (1990). Knapsack problems: algorithms and computer implementations. New York: Wiley Google Scholar
  32. Mehrotra, A., & Trick, M. A. (1996). A column generation approach for graph coloring. INFORMS Journal on Computing, 8(4), 344–354. CrossRefGoogle Scholar
  33. Michel, L., & Van Hentenryck, P. (2003). Comet in context. In PCK50: proceedings of the Paris C. Kanellakis memorial workshop on principles of computing & knowledge (pp. 95–107). New York: ACM. CrossRefGoogle Scholar
  34. Milano, M., & Wallace, M. (2006). Integrating operations research in constraint programming. 4OR, 4(3), 1–45. CrossRefGoogle Scholar
  35. Pisinger, D., & Sigurd, M. (2007). Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem. INFORMS Journal on Computing, 19(1), 36–51. CrossRefGoogle Scholar
  36. Puchinger, J., Stuckey, P. J., Wallace, M., & Brand, S. (2008). From high-level model to branch-and-price solution in G12. In LNCS: Vol. 5015. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 218–232). Berlin: Springer. CrossRefGoogle Scholar
  37. Ralphs, T. K., & Ladanyi, L. (2001). COIN/BCP user’s manual. Google Scholar
  38. Régin, J. C. (2002). Cost-based arc consistency for global cardinality constraints. Constraints, 7(3), 387–405. CrossRefGoogle Scholar
  39. Rossi, F., Van Beek, P., & Walsh, T. (2006). Handbook of constraint programming. Amsterdam: Elsevier. Google Scholar
  40. Rousseau, L. M. (2004). Stabilization issues for constraint programming based column generation. In LNCS: Vol. 3011. Proc. integration of AI and OR techniques in CP for combinatorial optimization problems (pp. 402–408). Berlin: Springer. CrossRefGoogle Scholar
  41. Rousseau, L. M., Gendreau, M., Pesant, G., & Focacci, F. (2004). Solving VRPTWs with constraint programming based column generation. Annals of Operations Research, 130(1), 199–216. CrossRefGoogle Scholar
  42. Rousseau, L. M., Gendreau, M., & Feillet, D. (2007). Interior point stabilization for column generation. Operations Research Letters, 35(5), 660–668. CrossRefGoogle Scholar
  43. Sadykov, R., & Wolsey, L. A. (2006). Integer programming and constraint programming in solving a multimachine assignment scheduling problem with deadlines and release dates. INFORMS Journal on Computing, 18(2), 209–217. CrossRefGoogle Scholar
  44. Sellmann, M., Zervoudakis, K., Stamatopoulos, P., & Fahle, T. (2002). Crew assignment via constraint programming: integrating column generation and heuristic tree search. Annals of Operations Research, 115(1), 207–225. CrossRefGoogle Scholar
  45. Wolsey, L. A. (1998). Integer programming. New York: Wiley. Google Scholar
  46. Yunes, T. H., Moura, A. V., & de Souza C. C. (2000). Solving very large crew scheduling problems to optimality. In Proc. ACM symposium on applied computing (Vol. 1, pp. 446–451). New York: ACM. Google Scholar
  47. Yunes, T. H., Moura, A. V., & de Souza C. C. (2005). Hybrid column generation approaches for urban transit crew management problems. Transportation Science, 39(2), 273–288. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Dipartimento di Elettronica ed InformazionePolitecnico di MilanoMilanoItaly

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