The multi-league sports scheduling problem, or how to schedule thousands of matches

We consider the simultaneous scheduling of multiple sport leagues, with interdependencies arising from teams in different leagues belonging to the same club. Teams from the same club share the same venue with limited capacity. We minimize the total capacity violation in polynomial time when each league has the same, even number of teams. We introduce two generalizations: one where teams from a club have to play according to the same pattern, and one where club capacities differ throughout the season.