Some models of graphs for scheduling sports competitions
Discrete Applied Mathematics
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Sports tournaments, home-away assignments, and the break minimization problem
Discrete Optimization
A polynomial-time algorithm to find an equitable home-away assignment
Operations Research Letters
The traveling tournament problem with predefined venues
Journal of Scheduling
Soccer schedules in Europe: an overview
Journal of Scheduling
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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.