Scheduling the Brazilian Soccer Tournament: Solution Approach and Practice

Sports, with their massive investments in players and structures, have become a big business. Professional and amateur leagues face challenging problems, including logistics, revenue maximization, broadcast rights, fairness issues, game attractiveness, and security. The annual Brazilian soccer tournament is a compact, mirrored double round-robin tournament played by 20 teams in each of its two main divisions; it is possibly the world's most attractive soccer tournament because of the quality of the teams and players in the competition. With substantial revenue and community pride on the line, devising optimal schedules is crucial to players, teams, fans, sponsors, cities, and for security issues. Fair and balanced schedules for all teams are a major issue for ensuring attractiveness and confidence in the tournament outcome. The organizers seek schedules that satisfy a number of constraints. As often as possible, the most important games should be played in weekend rounds so that the open TV channels can broadcast many attractive games. We describe the integer programming formulation of the scheduling problem and the three-phase decomposition approach we proposed for solving it. We also report on the practical experience we observed after two years of running the system and the main results achieved during its successful history.