Most sports associations regularly face the problem of determining and scheduling games for dozens if not hundreds of non-professional (youth) teams. For practical reasons and player convenience, it is key that the schedule respects venue capacities and minimizes travel distance. A classic approach is to split up teams over leagues, and then have each league play a round robin tournament. In a round robin tournament, each team competes against every other team in the tournament an equal number of times. This paper proposes an alternative approach, organizing a single yet incomplete round robin tournament involving all teams. In this format, which can be seen as a static Swiss system tournament, each team plays the same number of games, but teams are not required to face the same opponents. We exploit this flexibility to reduce the total travel distance and venue capacity conflicts. We provide theoretical results on the computational complexity of finding an incomplete round robin tournament, as well as sufficient conditions on its existence. Besides a Benders’ decomposition for the classic round robin approach, we develop a relax-and-fix and an iterative two-phase decomposition metaheuristic for the incomplete round robin approach. The metaheuristic first determines the home-away status of teams based on their club’s venue capacity, and thereafter selects suitable opponents while minimizing travel distances. Extensive experiments using real-life benchmark instances from the literature confirm the advantage of an incomplete round robin tournament compared to the classic multi-league round robin approach and validate the effectiveness of the proposed heuristics.

中文翻译：

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超越联赛：用于多联赛体育时间表的单个不完整循环赛


大多数体育协会经常面临为数十支甚至数百支非职业（青年）球队确定和安排比赛的问题。出于实际原因和玩家的方便，时间表尊重场馆容量并尽量减少旅行距离是关键。一种经典的方法是将球队划分为多个联赛，然后让每个联赛进行循环赛。在循环赛中，每支球队与锦标赛中的其他每支球队竞争的次数相同。本文提出了一种替代方法，组织一个涉及所有团队的单一但不完整的循环赛。在这种可以看作是静态瑞士制锦标赛的形式中，每支球队打相同数量的比赛，但不需要球队面对相同的对手。我们利用这种灵活性来减少总行驶距离和场馆容量冲突。我们提供了关于寻找不完整循环锦标赛的计算复杂性的理论结果，以及其存在的充分条件。除了经典循环方法的 Benders 分解外，我们还为不完整的循环方法开发了一个 relax-and-fix 和一个迭代的两阶段分解元启发式方法。元启发式方法首先根据俱乐部的场地容量确定球队的主客场状态，然后选择合适的对手，同时最大限度地减少旅行距离。使用文献中真实基准实例进行的广泛实验证实了与经典的多联赛循环方法相比，不完整的循环锦标赛的优势，并验证了所提出的启发式方法的有效性。