Constraint Programming Contribution to Benders Decomposition: A Case Study

  • Thierry Benoist
  • Etienne Gaudin
  • Benoit Rottembourg
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2470)


The aim of this paper is to demonstrate that CP could be a better candidate than MIP for solving the master problem within a Benders decomposition approach. Our demonstration is based on a case study of a workforce scheduling problem encountered in a large call center of Bouygues Telecom, a French mobile phone operator. Our experiments show that CP can advantageously replace MIP for the implementation of the master problem due to its greater ability to efficiently manage a wide variety of constraints such as the ones occurring in time tabling applications.


Call Center Constraint Programming Master Problem Global Constraint Bender Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [I]
    J. F. Benders. Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4:238–252, 1962.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    A. M. Geoffiïon and G. W. Graves. Multicomodity distribution system design by Benders decomposition. Management Science, 20:822–844, 1974.CrossRefGoogle Scholar
  3. [3]
    M. Minoux. Network Synthesis and Optimum Network Design Problems: Models, Solution Methods and Applications. Network, 19:313–360, 1989.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    N. Kagan and R. N. Adams. A Benders’ Decomposition Approach To The Multi-Objective Distribution Planning Problem. International Journal of Electrical Power & Energy Systems, 15(5):259–271,1993.Google Scholar
  5. [5]
    R.M. Wollmer. Two stage linear programming under uncertainty with 0-1 first stage variables. Mathematical Programming, 19:279–288, 1980.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    J.N. Hooker and G. Ottosson. Logic-based Benders decomposition. Mathematical Programming, to appear in November 2001.Google Scholar
  7. [7]
    A. Eremin and M. Wallace. Hybrid Benders decomposition algorithms in constraint logic programming. CP 2001, LNCS, 2239:1–15, 2001.Google Scholar
  8. [8]
    E. S. Thornsteinsson. Branch-and-Check: a Hybrid Framework Integrating Mixed Integer Programming and Constraint Logic Programming. In Proceedings of CP-01, Lecture Notes in Computer Science, 2239:16–30. Springer-Verlag, November 2001.Google Scholar
  9. [9]
    V. Jain, I. E. Grossmann. Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems. In Informs Journal On Computing, 13:258–276, 2001.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    C. Berge and A. Ghouila-Houri. Programming, Games and Transportation Networks. Wiley, New York, 1962.Google Scholar
  11. [II]
    V. Chvatal. Linear Programming. W. H. Freeman, New York, 1983.MATHGoogle Scholar
  12. [12]
    XPRESS-MP., 2002.
  13. [13]
    F. Laburthe and the OCRE project team. CHOCO: Implementing a CP kernel. CP 2000 Workshop Program, 2000.Google Scholar
  14. [14]
    Y. Caseau, F.-X. Josset, F. Laburthe. Claire: Combining Sets, Search and Rules to Better Express Algorithms. Proceeding of ICLP’99, MIT Press, New Mexico, 1999.Google Scholar
  15. [15]
    N. Beldiceanu and E. Contejean. Introducing Global Constraints in CHIP. Mathematical and Computer Modeling, 20(2):97–123, 1994.MATHCrossRefGoogle Scholar
  16. [16]
    A. Bockmayr, N. Pisaruk and A. Aggoun. Network Flow Problems in Constraint Programming. CP 2001, LNCS, 2239:196–210, 2001.Google Scholar
  17. [17]
    R.K. Ahuja, T.L. Magnanti and J.B. Orlin. Network Flows: theory, algorithms and applications. Prentice Hall, 1993.Google Scholar
  18. [18]
    P. Van Hentenryck. Constraint Satisfaction in Logic Programming. The MIT Press, 1989.Google Scholar
  19. [19]
    A.V. Goldberg and R.E. Tarjan. A new approach to the maximum flow problem. Proceedings of the 18 th ACMsymposium on Theory of Computing, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thierry Benoist
    • 1
  • Etienne Gaudin
    • 1
  • Benoit Rottembourg
    • 1
  1. 1.Bouygues e-lab1 av. Eugène FreyssinetSt Quentin en Yvelines CedexFrance

Personalised recommendations