Student assignments with preferences and maximum diversity

Abstract

The paper considers the assignment of students to seminars regarding three hierarchical objectives: maximizing the students’ preferences, maximizing the within seminar diversity, minimizing the between seminar diversity variation. While the first objective pictures the students, preferences, the second and third picture the school’s preference of having comparable seminar groups. To reach this aim the paper extends the well-known Maximally Diverse Grouping Problem and its balanced version by the first objective, the students’ interests. The students’ interests are pictured by a preference sequence the students have for the offered seminars, e.g. because of the scheduled time, the topic or the lecturer. We present solution approaches that include properties from game theory in the assignment and result in an assignment of students to seminars including the students’ as well as the school’s preferences. Our results show that the presented solution approaches are able to solve instances of practical relevant size within half an hour (close to) optimality. Furthermore, in our artificial test instances, including student preferences in the assignment only led to a small reduction of the maximal diversity for instances of realistic size (2–3% difference for seminars with 20 students).