Fair travel distances in tournament schedules: A cooperative game theory approach

The most studied problem in sports scheduling, so-called traveling tournament problem (TTP), aims at finding schedules minimizing the total distance traveled by the teams. While minimizing all the traveling between games is efficient from the overall perspective, it overlooks the distribution of the travel among the teams. Consequently, some teams may end up better than others with respect to their individual goals, an imbalance which may affect teams’ often-limited resources or preparedness for the games. This article adopts a cooperative game theory framework to obtain tournament schedules where the distances traveled by the teams are allocated according to fairness criteria. The approach consists of three steps. First, the scheduling problem is reformulated as a transferable utility game. Second, by means of well-established allocation methods, an ideal distance distribution among the teams is determined. Third, we introduce fairness measures to produce a schedule which approximately resembles the ideal distribution. We also discuss the case of not pursuing fairness, but rather a compromise between fairness and minimum total distance. We illustrate the approach by a numerical example in one of the classic TTP data instances.