Despite the success of constraint programming (CP ) for scheduling, the much wider penetration of mixed integer programming (MIP ) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP ) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems.


Schedule Problem Mixed Integer Programming Constraint Programming Master Problem Linear Relaxation 
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  1. 1.
    Achterberg, T., Berthold, T.: Hybrid Branching. In: van Hoeve, W.-J., Hooker, J.N. (eds.) CPAIOR 2009. LNCS, vol. 5547, pp. 309–311. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  2. 2.
    Achterberg, T.: Conflict analysis in mixed integer programming. Discrete Optimization 4(1), 4–20 (2007); special issue: Mixed Integer ProgrammingMathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Achterberg, T.: Constraint Integer Programming. Ph.D. thesis, Technische Universität Berlin (2007)Google Scholar
  4. 4.
    Achterberg, T.: SCIP: Solving Constraint Integer Programs. Mathematical Programming Computation 1(1), 1–41 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Achterberg, T., Brinkmann, R., Wedler, M.: Property checking with constraint integer programming. ZIB-Report 07-37, Zuse Institute Berlin (2007)Google Scholar
  6. 6.
    Baptiste, P., Pape, C.L., Nuijten, W.: Constraint-based Scheduling. Kluwer Academic Publishers (2001)Google Scholar
  7. 7.
    Bartak, R., Salido, M.A., Rossi, F.: New trends on constraint satisfaction, planning, and scheduling: a survey. The Knowledge Engineering Review 25(3), 249–279 (2010)CrossRefGoogle Scholar
  8. 8.
    Beck, J.C., Refalo, P.: A hybrid approach to scheduling with earliness and tardiness costs. Annals of Operations Research 118, 49–71 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Beck, J.C.: Checking-Up on Branch-and-Check. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 84–98. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Beck, J.C., Fox, M.S.: Constraint directed techniques for scheduling with alternative activities. Artificial Intelligence 121(1-2), 211–250 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Berthold, T., Heinz, S., Lübbecke, M.E., Möhring, R.H., Schulz, J.: A Constraint Integer Programming Approach for Resource-Constrained Project Scheduling. In: Lodi, A., Milano, M., Toth, P. (eds.) CPAIOR 2010. LNCS, vol. 6140, pp. 313–317. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Berthold, T., Heinz, S., Pfetsch, M.E.: Nonlinear Pseudo-Boolean Optimization: Relaxation or Propagation? In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 441–446. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Berthold, T., Heinz, S., Vigerske, S.: Extending a CIP framework to solve MIQCPs. ZIB-Report 09-23, Zuse Institute Berlin (2009)Google Scholar
  14. 14.
    Debruyne, R., Bessière, C.: Some practicable filtering techniques for the constraint satisfaction problem. In: Proceedings of the Fifteenth International Joint Conference on Artificial Intelligence (IJCAI 1997), pp. 412–417 (1997)Google Scholar
  15. 15.
    Heinz, S., Beck, J.C.: Solving resource allocation/scheduling problems with constraint integer programming. In: Salido, M.A., Barták, R., Policella, N. (eds.) Proceedings of the Workshop on Constraint Satisfaction Techniques for Planning and Scheduling Problems (COPLAS 2011), pp. 23–30 (2011)Google Scholar
  16. 16.
    Heinz, S., Beck, J.C.: Reconsidering mixed integer programming and MIP-based hybrids for scheduling. ZIB-Report 12-05, Zuse Institute Berlin (2012)Google Scholar
  17. 17.
    Heinz, S., Schulz, J.: Explanations for the Cumulative Constraint: An Experimental Study. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 400–409. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Hooker, J.N.: Planning and Scheduling to Minimize Tardiness. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 314–327. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Hooker, J.N.: Integrated Methods for Optimization. Springer (2007)Google Scholar
  20. 20.
    Hooker, J.N.: Planning and scheduling by logic-based Benders decomposition. Operations Research 55, 588–602 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96, 33–60 (2003)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Koch, T., Achterberg, T., Andersen, E., Bastert, O., Berthold, T., Bixby, R.E., Danna, E., Gamrath, G., Gleixner, A.M., Heinz, S., Lodi, A., Mittelmann, H., Ralphs, T., Salvagnin, D., Steffy, D.E., Wolter, K.: MIPLIB 2010. Mathematical Programming Computation 3(2), 103–163 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Marques-Silva, J.P., Sakallah, K.A.: GRASP: A search algorithm for propositional satisfiability. IEEE Transactions on Computers 48(5), 506–521 (1999)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Martin, P., Shmoys, D.B.: A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem. In: Cunningham, W.H., Queyranne, M., McCormick, S.T. (eds.) IPCO 1996. LNCS, vol. 1084, pp. 389–403. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  25. 25.
    Milano, M., Van Hentenryck, P. (eds.): Hybrid Optimization: The Ten Years of CPAIOR. Springer (2010)Google Scholar
  26. 26.
    Schutt, A., Feydy, T., Stuckey, P., Wallace, M.: Explaining the cumulative propagator. Constraints, 1–33 (2010)Google Scholar
  27. 27.
    Wunderling, R.: Paralleler und objektorientierter Simplex-Algorithmus. Ph.D. thesis, Technische Universität Berlin (1996)Google Scholar
  28. 28.
    Yunes, T.H., Aron, I.D., Hooker, J.N.: An integrated solver for optimization problems. Operations Research 58(2), 342–356 (2010)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Stefan Heinz
    • 1
  • J. Christopher Beck
    • 2
  1. 1.Zuse Institute BerlinBerlinGermany
  2. 2.Department of Mechanical & Industrial EngineeringUniversity of TorontoTorontoCanada

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