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Scheduling double round-robin tournaments with divisional play using constraint programming

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  • Carlsson, Mats
  • Johansson, Mikael
  • Larson, Jeffrey

Abstract

We study a tournament format that extends a traditional double round-robin format with divisional single round-robin tournaments. Elitserien, the top Swedish handball league, uses such a format for its league schedule. We present a constraint programming model that characterizes the general double round-robin plus divisional single round-robin format. This integrated model allows scheduling to be performed in a single step, as opposed to common multistep approaches that decompose scheduling into smaller problems and possibly miss optimal solutions. In addition to general constraints, we introduce Elitserien-specific requirements for its tournament. These general and league-specific constraints allow us to identify implicit and symmetry-breaking properties that reduce the time to solution from hours to seconds. A scalability study of the number of teams shows that our approach is reasonably fast for even larger league sizes. The experimental evaluation of the integrated approach takes considerably less computational effort to schedule Elitserien than does the previous decomposed approach.

Suggested Citation

  • Carlsson, Mats & Johansson, Mikael & Larson, Jeffrey, 2017. "Scheduling double round-robin tournaments with divisional play using constraint programming," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1180-1190.
    • Handle: RePEc:eee:ejores:v:259:y:2017:i:3:p:1180-1190
    DOI: 10.1016/j.ejor.2016.11.033
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    References listed on IDEAS

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    1. Rasmussen, Rasmus V., 2008. "Scheduling a triple round robin tournament for the best Danish soccer league," European Journal of Operational Research, Elsevier, vol. 185(2), pages 795-810, March.
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    3. Henz, Martin & Muller, Tobias & Thiel, Sven, 2004. "Global constraints for round robin tournament scheduling," European Journal of Operational Research, Elsevier, vol. 153(1), pages 92-101, February.
    4. Martin Henz, 2001. "Scheduling a Major College Basketball Conference---Revisited," Operations Research, INFORMS, vol. 49(1), pages 163-168, February.
    5. Rasmussen, Rasmus V. & Trick, Michael A., 2008. "Round robin scheduling - a survey," European Journal of Operational Research, Elsevier, vol. 188(3), pages 617-636, August.
    6. Larson Jeffrey & Johansson Mikael, 2014. "Constructing schedules for sports leagues with divisional and round-robin tournaments," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 10(2), pages 119-129, June.
    7. Rasmussen, Rasmus V. & Trick, Michael A., 2007. "A Benders approach for the constrained minimum break problem," European Journal of Operational Research, Elsevier, vol. 177(1), pages 198-213, February.
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    Cited by:

    1. Li, Miao & Davari, Morteza & Goossens, Dries, 2023. "Multi-league sports scheduling with different leagues sizes," European Journal of Operational Research, Elsevier, vol. 307(1), pages 313-327.
    2. David Van Bulck & Dries Goossens & Jo¨rn Scho¨nberger & Mario Guajardo, 2020. "An Instance Data Repository for the Round-robin Sports Timetabling Problem," Management and Labour Studies, XLRI Jamshedpur, School of Business Management & Human Resources, vol. 45(2), pages 184-200, May.

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