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The sport teams grouping problem

Author

Listed:
  • Túlio A. M. Toffolo

    (KU Leuven
    Federal University of Ouro Preto)

  • Jan Christiaens

    (KU Leuven)

  • Frits C. R. Spieksma

    (KU Leuven)

  • Greet Vanden Berghe

    (KU Leuven)

Abstract

The sport teams grouping problem (STGP) concerns the assignment of sport teams to round-robin tournaments. The objective is to minimize the total travel distance of the participating teams while simultaneously respecting fairness constraints. The STGP is an NP-Hard combinatorial optimization problem highly relevant in practice. This paper investigates the performance of some complimentary optimization approaches to the STGP. Three integer programming formulations are presented and thoroughly analyzed: two compact formulations and another with an exponential number of variables, for which a branch-and-price algorithm is proposed. Additionally, a meta-heuristic method is applied to quickly generate feasible high-quality solutions for a set of real-world instances. By combining the different approaches’ results, solutions within 1.7% of the optimum values were produced for all feasible instances. Additionally, to support further research, the considered STGP instances and corresponding solutions files were shared online.

Suggested Citation

  • Túlio A. M. Toffolo & Jan Christiaens & Frits C. R. Spieksma & Greet Vanden Berghe, 2019. "The sport teams grouping problem," Annals of Operations Research, Springer, vol. 275(1), pages 223-243, April.
    • Handle: RePEc:spr:annopr:v:275:y:2019:i:1:d:10.1007_s10479-017-2595-z
    DOI: 10.1007/s10479-017-2595-z
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    References listed on IDEAS

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    1. Toffolo, Túlio A.M. & Wauters, Tony & Van Malderen, Sam & Vanden Berghe, Greet, 2016. "Branch-and-bound with decomposition-based lower bounds for the Traveling Umpire Problem," European Journal of Operational Research, Elsevier, vol. 250(3), pages 737-744.
    2. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    3. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    4. Knust, Sigrid, 2010. "Scheduling non-professional table-tennis leagues," European Journal of Operational Research, Elsevier, vol. 200(2), pages 358-367, January.
    5. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    6. VANDERBECK, François & WOLSEY, Laurence A., 2010. "Reformulation and decomposition of integer programs," LIDAM Reprints CORE 2188, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Dries Goossens & Frits Spieksma, 2009. "Scheduling the Belgian Soccer League," Interfaces, INFORMS, vol. 39(2), pages 109-118, April.
    8. Michael A. Trick & Hakan Yildiz & Tallys Yunes, 2012. "Scheduling Major League Baseball Umpires and the Traveling Umpire Problem," Interfaces, INFORMS, vol. 42(3), pages 232-244, June.
    9. Michael A. Trick & Hakan Yildiz, 2011. "Benders' cuts guided large neighborhood search for the traveling umpire problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(8), pages 771-781, December.
    10. Schonberger, J. & Mattfeld, D. C. & Kopfer, H., 2004. "Memetic Algorithm timetabling for non-commercial sport leagues," European Journal of Operational Research, Elsevier, vol. 153(1), pages 102-116, February.
    11. Barry McCollum & Edmund Burke, 2014. "The practice and theory of automated timetabling," Annals of Operations Research, Springer, vol. 218(1), pages 1-2, July.
    12. Januario, Tiago & Urrutia, Sebastián & Ribeiro, Celso C. & de Werra, Dominique, 2016. "Edge coloring: A natural model for sports scheduling," European Journal of Operational Research, Elsevier, vol. 254(1), pages 1-8.
    13. Xue, Li & Luo, Zhixing & Lim, Andrew, 2015. "Two exact algorithms for the traveling umpire problem," European Journal of Operational Research, Elsevier, vol. 243(3), pages 932-943.
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