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Optimisation: Mathematics and Brazilian football

At the conference Celso C. Ribeiro held a talk on scheduling the Brazilian football league.
This week SINTEF ICT organised an international conference about  timetabling – and football.

For those that don't know, football is the most important sport in Brazil. The optimisation system that produces the schedule each year has been used since 2009. The schedule should satisfy constraints ranging from fairness to safety issues, and from technical issues to broadcasting criteria.

Around the world, only a few professional leagues have adopted optimisation software. In Norway, for many years SINTEF has optimised several sport schedules.

Several constraints
In his talk on the the 9th International Series of Conferences on the Practice and Theory of Automated Timetabling (PATAT 2012), Celso Ribeira discussed constraints to consider when finding a football schedule. Many constraints are vital, but some constraints only satisfy some teams' concerns regarding impartiality.

Also, teams are frightened to lose two classics in a row. They believe losing both would have strong negative impact on their team's motivation.

Request good schedules

Maximum gate attendance and TV audience are major concerns since most revenues come from broadcast and merchandising rights; sponsors request good schedules to draw large audiences.

For example, when the Rio de Janeiro "classic" is played between rival teams Fluminense and Flamengo, the Brazilian football association does not want any other "classic" to be played at the same time in order to have the public's sole focus on that game.

Experience tells us that the optimisation system contributes a great deal to the attractiveness of the Brazilian football league. Before the optimisation system was in place, the winners were known up to four rounds before the end of the season – now it is only known at the very end.

Fair and balanced schedules for all teams are key issues for attractiveness and confidence in the outcome of a competition.