Selecting a balanced team – formation of netball teams for a series of trial matches

Each year, in order to choose the best netball team to represent the State of Victoria at primary school level, a series of trial matches was organised during which players' performances could be evaluated. In forming the teams for these trials, it was not possible to place every player in their preferred position and so each was required to nominate three positions, in order of preference, in which they would like to play. Each player was also given a rank by the organisers, based on previous ability, so that the better players could be placed in their preferred positions first. The whole process of team formation was carried out manually and took considerable time. As a result of this work the organisers now have at their disposal a user-friendly computer program whose core is a linear programming assignment algorithm that achieves their objectives in a fraction of the previous time and also enables them to cater for last-minute changes that often occur to the database. In addition, the program contains a smoothing algorithm which ensures that the teams produced are of roughly equal ability. This requirement, although not originally verbalised by the organisers, became evident as the work progressed.