Beyond leagues: A single incomplete round robin tournament for multi-league sports timetabling

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.