An application of the traveling tournament problem: the Argentine volleyball league

Abstract

This article describes the 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 every 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 since the teams’ home locations are scattered throughout the country and teams do not return 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: (a) how to couple the teams and (b) how to schedule the matches. We apply integer programming techniques and a tabu search heuristic to solve these issues. The resulting schedules have been successfully used in the 2007-2008, 2008-2009, 2009-2010, and 2010-2011 league seasons, reducing the total travel distance while meeting all of the teams’ requirements. This is the first reported application of the traveling tournament problem to a real-world sports league in the optimization literature.