Assignment of swimmers to events in a multi-team meeting for team global performance optimization

Assigning swimmers to events in order to maximize global performance of the team in a multi-team meeting is not a trivial issue for coaches. In fact, often months of hard work and training is wasted if a mistake is made in the line-up decision process. Expert coaches use their long time experience in order to make correct decisions, but often without reaching an optimal assignment. Athletes preferences also affect the decision process making coaches job even harder and, furthermore, the actual goal to be achieved may vary among situations. In this paper two different integer programming models, based on an estimation of opponents performances capability, constructed following two different philosophies and addressing two different situations are proposed. The first model just maximizes the total score obtained by the team, while the second model aim to optimize the placement achieved by the team in the meeting final ranking and the advantage on the first follower in the ranking. A detailed analysis of good and bad points of the two approaches and of situations in which one approach may be preferred respect to the other is reported. A real case example, taken from an Italian Regional Master Meeting, is deeply analyzed and a discussion on the comparison among results obtained with the assignment provided by the two models and the actual lineup proposed by the coach, is provided.