A stochastic-programming approach for scheduling catch-up rounds in round-robin sport leagues

In most sport leagues, a schedule is announced before the start of the season. However, due to unexpected events (e.g. bad weather conditions), some games cannot be played on the announced date. To handle this, before the start of the season, empty so-called catch-up rounds are positioned in the schedule as a buffer. During the season, games can then be rescheduled to these catch-up rounds. We develop a two-stage stochastic programming approach to determine where to position the catch-up rounds in order to maintain the quality of the realized schedule. While our method is generally applicable, we demonstrate its use with soccer. Scenarios and their probabilities are deduced from historical data from 10 major European soccer leagues. We study the impact of the number of catch-up rounds and costs on the positions of catch-up rounds and compare our method with other proactive strategies from the literature. We conclude with a case study based on the English Premier League. In particular when many games cannot be played as planned and few catch-up rounds are available, our stochastic programming approach outperforms existing methods with respect to maintaining a fair ranking and avoiding cancelled games.