The school class allocation problem—maximising friendship requests subject to diversity requirements

Abstract

Friendship groups are an important element in both the social and academic well-being of school students, particularly in their younger years. Each year, school management has to assign students to a particular class in their new grade in junior school, and in doing so make and break friendship preferences as other criteria need to be satisfied in order to ensure diversity. This ongoing administrative task is time consuming and does not always result in the most equitable allocation. Coupled with the lack of transparency of the process, this can lead to teacher and parent frustration. This paper formulates and solves a mathematical programming model for this problem and shows that better solutions can likely be found in a fraction of the time using software that is freely available.

Keywords:

• quadratic programming
• education
• decision support systems
• integer programming

Acknowledgements

I thank the Trinity College Gawler South School for its interest and participation in this project, the Defence Science and Technology Organisation for allowing me to develop and apply my skills in mathematical programming and the referees for their constructive comments.