Bender’s Cuts Guided Large Neighborhood Search for the Traveling Umpire Problem

  • Michael A. Trick
  • Hakan Yildiz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4510)

Abstract

This paper introduces the use of Bender’s Cuts to guide a Large Neighborhood Search to solve the Traveling Umpire Problem, a sports scheduling problem inspired by the real-life needs of the officials of a sports league. At each time slot, a Greedy Matching heuristic is used to construct a schedule. When an infeasibility is recognized Bender’s cuts are generated, which guides a Large Neighborhood Search to ensure feasibility and to improve the solution.

Keywords

Integer Program Travel Salesman Problem Constraint Program Large Neighborhood Major League Baseball 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Challenge Traveling Tournament Instances (January 2007), http://mat.gsia.cmu.edu/TOURN/
  2. 2.
    Dawande, M.W., Hooker, J.N.: Inference-Based Sensitivity Analysis for Mixed Integer/Linear Programming. Operations Research 48(4), 623–634 (2000)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Easton, K., Nemhauser, G.L., Trick, M.A.: The Traveling Tournament Problem: Description and Benchmarks. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–585. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Harjunkoski, I., Grossmann, I.E.: Decomposition Techniques for Multistage Scheduling Problems Using Mixed-integer and Constraint Programming Methods. Computers and Chemical Engineering 26, 1533–1552 (2002)CrossRefGoogle Scholar
  5. 5.
    Hooker, J.N.: Planning and Scheduling by Logic-based Benders Decomposition. Operations Research (to appear)Google Scholar
  6. 6.
    Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Mathematical Programming 96, 33–60 (2003)MATHMathSciNetGoogle Scholar
  7. 7.
    ILOG Inc., ILOG OPL Studio 3.7 Language Manual (2003)Google Scholar
  8. 8.
    Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP-CP models for a class of optimization problems. INFORMS Journal on Computing 13(4), 258–276 (2001)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Rasmussen, R.V., Trick, M.A.: A Benders approach for the constrained minimum break problem. European Journal of Operational Research 177, 198–213 (2007)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Traveling Umpire Problem (January 2007), http://www.andrew.cmu.edu/user/hakanyil/TUP/
  11. 11.
    Trick, M.A.: Integer and Constraint Programming Approaches for Round-Robin Tournament Scheduling. In: Burke, E.K., De Causmaecker, P. (eds.) PATAT 2002. LNCS, vol. 2740, pp. 63–77. Springer, Heidelberg (2003)Google Scholar
  12. 12.
    Yildiz, H., Trick, M.: The Traveling Umpire Problem. Invited Talk. In: Informs Annual Conference, Pittsburgh, PA (November 2006)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Michael A. Trick
    • 1
  • Hakan Yildiz
    • 1
  1. 1.Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA ,15213USA

Personalised recommendations