Sports Scheduling: Minimizing Travel for English Football Supporters

Abstract

The football authorities in England are responsible for generating the fixtures for the entire football season but the fixtures that are played over the Christmas period are given special consideration as they represent the minimum distances that are traveled by supporters when compared with fixtures played at other times of the year. The distances are minimized at this time of the year to save supporters having to travel long distances during the holiday period, which often coincides with periods of bad weather. In addition, the public transport system has limited services on some of the days in question. At this time of the year every team is required to play, which is not always the case for the rest of the season.When every team is required to play, we refer to this as a complete fixture. Additionally, each team has to to play a home game and an away game. Therefore, over the Christmas period we are required to produce two complete fixtures, where each team has to have a Home/Away pattern of HA or AH. In some seasons four complete fixtures are generated where each team is required to have a Home/Away pattern of HAHA (or AHAH).Whether two or four fixtures are generated there are various other constraints that have to be respected. For example, the same teams cannot play each other and we have to avoid (as far as possible) having some teams play at home on the same day. This chapter has three main elements. i) An analysis of seven seasons to classify them as two or four fixture seasons. ii) The presentation of a single mathematical model that is able to generate both two and four fixture schedules which adheres to all the required constraints. Additionally, the model is parameterized so that we can conduct a series of experiments. iii) Demonstrating that the model is able to produce solutions which are superior to the solutions that were used in practise (the published fixtures) and which are also superior to our previous work. The solutions we generate are near optimal for the two fixture case. The four fixture case is more challenging and the solutions are about 16% of the lower bound. However, they are still a significant improvement on the fixtures that were actually used. We also show, through three experimental setups, that the problem owner might actually not want to accept the best solution with respect to the overall minimized distance but might want to take a slightly worse solution but which offers a guarantee as to the maximum distance that has to be traveled by the supporters within each division.