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.

相当数量的体育比赛通过围绕赛季安排时间表来应对球队和体育基础设施的有限可用性，该赛季包含的时间段比每支球队的比赛多得多。然而，在这样的时间表中，球队连续比赛之间的休息时间可能会有很大差异，并且赛季中任何时候的比赛场数差异可能会很大。在本文中，我们提出了一种迭代的两阶段方法来构建不太容易出现这些公平问题的宽松循环时间表。特别是，第一阶段确定了比赛休息日模式 (GOP) 集，该模式规定了球队何时比赛（主场或客场）或休息日（也称为再见）。随后，第二阶段构建了一个兼容的时间表，其中指定了比赛的对手和主场优势。如果不存在兼容的时间表，我们会生成一个或多个基于逻辑的 Benders 削减，以排除未来迭代中不可行的 GOP 集。我们在一个问题上测试了两阶段方法，其中时间表和目标价值的可行性主要取决于团队何时玩游戏，并表明我们的方法在额外时隙数量适中时表现出色。