Scheduling the professional Ecuadorian football league by integer programming

A sports schedule sets the dates and venues of games among teams in a sports league. Constructing a sports schedule is a highly restrictive problem. The schedule must meet constraints due to regulations of a particular sports league federation and it must guarantee the participation of all teams on equal terms. Moreover, economic benefits of the teams and other agents involved in this activity are expected. Until 2011, the Ecuadorian football federation (FEF) had developed schedules for their professional football championship manually. In early 2011, the authors presented to the FEF authorities evidence that the use of mathematical programming to create feasible sports schedules could easily exceed the benefits obtained by the empirical method. Under this premise, this work presents an integer programming formulation, solved to optimality, for scheduling the professional football league in Ecuador, and also a heuristic approach based on three-phases for its solution. The schedules obtained met the expectations of the FEF and one of them was adopted as the official schedule for the 2012 edition of the Ecuadorian professional football championship.