An Application of the Traveling Tournament Problem: The Argentine Volleyball League

This article describes an optimization process used to schedule the First Division of Argentina’s professional volleyball league. The teams in the league are grouped into couples, and matches are held on Thursdays and Saturdays. In each pair of consecutive Thursday–Saturday matches, the two teams in each couple play against two teams from another couple. Minimization of travel distances is critical because the teams’ home locations are scattered throughout the country and teams do not return to their home sites between consecutive away matches, making this problem a variation of the well-known traveling tournament problem. The coupled format gives rise to two key decisions: (1) how to couple the teams, and (2) how to schedule the matches. We apply integer programming techniques and a tabu search heuristic to solve these questions. The league successfully used the resulting schedules in its 2007–2008, 2008–2009, 2009–2010, and 2010–2011 seasons, reducing the total travel distance while meeting all of the teams’ requirements. This is the first application of the traveling tournament problem to a real-world sports league reported in the optimization literature.