Scheduling the South American Qualifiers to the 2018 FIFA World Cup by integer programming

Every four years, the 10 national teams members of the South American Football Confederation (CONMEBOL) compete for one of the slots available to South America in the final phase of the FIFA World Cup. The qualifying phase consists of a double round robin tournament, played in 9 match-days, with every team playing twice on each match-day. The overall tournament is spread throughout 2 years, so match-days are months apart from each other. After using a same mirrored schedule for about twenty years, and persistent complaints from its members, CONMEBOL decided to change the schedule for the 2018 World Cup. Supported by one of CONMEBOL’s members, we used integer programming to construct schedules that overcome the main drawbacks of the previous approach. After exploring many design criteria, we proposed a candidate schedule based on a French scheme. The main feature of the proposed schedule is that every team plays once at home and once away on each match-day, stepping away from traditional symmetric (mirrored) schemes. This proposal was unanimously approved by CONMEBOL members and its currently being implemented.