Abstract
A fair schedule helps in improving the competitiveness and attractiveness of sports tournaments and in turn contributes positively to the sports economy. Break minimization and carryover effects minimization are considered to be two important criteria of fairness in scheduling of compact round-robin tournaments, and most related research looks at these problems separately. Various studies have sought to minimize the carryover effects in tournaments so that the number of breaks per team does not exceed a specific level. This study, however, is the first effort to define an integrated problem that aims to minimize the carryover effects and the number of breaks simultaneously for round-robin tournaments. We first introduce the mathematical formulation for the problem, whose objective measures how well a schedule simultaneously performs with respect to the number of breaks and the carryover effects. We then develop a heuristic method for this computationally hard problem. Comparing our results with the previous literature and the current practices of some European leagues, we show that our method provides schedules with better objective function values.
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Appendices
Appendix
A schedule template for 16 teams
Table 14 provides a schedule template for the single round-robin tournament with 16 teams. The first team is the one who plays at home. The coe value is 330 and the number of breaks is 26 (1 team with no breaks, 6 teams with one break, 7 teams with two breaks, 2 team with three breaks). The occurrence of a break for a team is highlighted in bold.
B Schedule template for 18 teams
Table 15 provides a schedule template for the single round-robin tournament with 18 teams. The coe value is 418 and the number of breaks is 36 (4 teams with one break, 10 teams with two breaks, 4 teams with three breaks).
C Schedule template for 20 teams
Table 16 provides a schedule template for the single round-robin tournament with 20 teams. The coe value is 506 and the number of breaks is 44 (1 team with no breaks, 3 teams with one break, 8 teams with two breaks, 7 teams with three breaks, 1 team with four breaks).
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Çavdaroğlu, B., Atan, T. Integrated break and carryover effect minimization. J Sched 25, 705–719 (2022). https://doi.org/10.1007/s10951-022-00744-8
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DOI: https://doi.org/10.1007/s10951-022-00744-8