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Optimizing rest times and differences in games played: an iterative two-phase approach

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  • David Van Bulck

    (Ghent University)

  • Dries Goossens

    (Ghent University
    FlandersMake@UGent - core lab CVAMO)

Abstract

A considerable number of sports competitions cope with limited availability of teams and sports infrastructure by organizing their timetable around a season that comprises many more time slots than games per team. However, in such timetables the rest period between teams’ consecutive games can vary considerably and the difference in the number of games played at any point in the season can become large. In this paper, we propose an iterative two-phase approach to construct relaxed round-robin timetables that are less prone to these fairness issues. In particular, the first phase determines the game-off-day pattern (GOP) set which regulates when teams play (home or away) or have an off day (also called bye). Subsequently, the second phase constructs a compatible timetable which specifies the opponents and the home advantage of the games. If no compatible timetable exists, we generate one or more logic-based Benders cuts that rule out the infeasible GOP set in future iterations. We test the two-phase approach on a problem where feasibility of the timetable and the objective value is mainly determined by when teams play games and show that our approach excels when the number of additional time slots is moderate.

Suggested Citation

  • David Van Bulck & Dries Goossens, 2022. "Optimizing rest times and differences in games played: an iterative two-phase approach," Journal of Scheduling, Springer, vol. 25(3), pages 261-271, June.
    • Handle: RePEc:spr:jsched:v:25:y:2022:i:3:d:10.1007_s10951-021-00717-3
    DOI: 10.1007/s10951-021-00717-3
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    References listed on IDEAS

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    7. Durán, Guillermo & Durán, Santiago & Marenco, Javier & Mascialino, Federico & Rey, Pablo A., 2019. "Scheduling Argentina’s professional basketball leagues: A variation on the Travelling Tournament Problem," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1126-1138.
    8. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
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    Cited by:

    1. Van Bulck, David & Goossens, Dries, 2023. "A traditional Benders’ approach to sports timetabling," European Journal of Operational Research, Elsevier, vol. 307(2), pages 813-826.
    2. Xiajie Yi & Dries Goossens, 2023. "Strategies for dealing with uncertainty in time-relaxed sports timetabling," Annals of Operations Research, Springer, vol. 320(1), pages 473-492, January.
    3. Tasbih Tuffaha & Burak Çavdaroğlu & Tankut Atan, 2023. "Round-robin scheduling with regard to rest differences," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 269-301, July.

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