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.
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Acknowledgements
David Van Bulck is a postdoctoral research fellow funded by the Research Foundation—Flanders (FWO) [1258021N].
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A preliminary version of this article appeared in the Proceedings of the 13th International Conference on the Practice and the Theory of Automated Timetabling. PATAT 2021: Volume 1, pp. 172-187.
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Van Bulck, D., Goossens, D. Optimizing rest times and differences in games played: an iterative two-phase approach. J Sched 25, 261–271 (2022). https://doi.org/10.1007/s10951-021-00717-3
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DOI: https://doi.org/10.1007/s10951-021-00717-3