Scheduling a Double Round Robin Tournament with Triples

In amateur or youth sports leagues, the teams play all matches during their leisure time. Thus, a schedule with a smaller number of rounds is preferred. To reduce the number of rounds and required referees, teams are willing to play multiple matches within the same round. We organize these matches in triples, where three teams meet at the venue of one of them and play against each other, at the cost of potentially unevenly distributed home-field advantages. The travel distances of all teams now depend on their assignment to the respective triple and the choice of the home team, ruling out the constraint of alternating home-field advantages between the matches of the same team pair. Therefore, we introduce a new tournament format, the double round robin tournament with triples (2RR-T). By deriving a binary linear optimization model for this new format, we can compute tournament schedules that minimize the total travel distance. After adjusting orbital shrinking to break the resulting symmetries in the possible assignments, we perform an extensive computational study to examine the efficiency of the proposed solution approaches on a new publicly available set of benchmark instances. Furthermore, we apply our approach to the “Basketball Senioren Landesliga Brandenburg”, a German amateur basketball league using this format, compare the resulting schedule with the existing one, and evaluate the triple format against the traveling tournament problem and a format with coupled team pairs.