Scheduling English Football Fixtures: Consideration of Two Conflicting Objectives

In previous work the distance travelled by UK football clubs, and their supporters, over the Christmas/New Year period was minimised. This is important as it is not only a holiday season but, often, there is bad weather at this time of the year. Whilst searching for good quality solutions for this problem, various constraints have to be respected. One of these relates to clashes, which measures how many paired teams play at home on the same day. Whilst the supporters have an interest in minimising the distance they travel, the police also have an interest in having as few pair clashes as possible. This is due to the fact that these fixtures are more expensive, and difficult, to police. However, these two objectives (minimise distance and minimise pair clashes) conflict with one another in that a decrease in one intuitively leads to an increase in the other. This paper explores this question and shows that there are compromise solutions which allow fewer pair clashes but does not statistically increase the distance travelled. This paper provides a more comprehensive study of the initial results presented at the previous PATAT conference. We present a more detailed set of computational experiments, along with a greater number of datasets. We conclude that it is sometimes possible to reduce the number of pair clashes whilst not significantly increasing the overall distance that is travelled.