Balanced home–away assignments

In recent years several approaches for generating sports league schedules have been proposed. In this paper we consider foundations for a two-stage approach to construct schedules for a single round robin tournament (or the first half series of a double round robin tournament). In the first stage for each game a mode (home or away) has to be determined and in the second stage the games have to be scheduled in their assigned modes. We study a problem of the first stage where balanced home–away assignments have to be constructed such that for each team the numbers of home and away games differ by at most one. After showing that it is easy to construct balanced home–away assignments we propose repairing mechanisms for unbalanced home–away assignments. Then, neighborhoods on the set of balanced home–away assignments are defined which are shown to be connected. Finally, situations with preassignments are studied.