Multicriteria Seminar Assignments in a University Considering Preference Quotas

There is a long tradition of assigning students to courses taking into account various objective functions, e.g., maximizing lecturer and student preferences and/or balanced workload within departments, as well as constraints, e.g., such as capacity, minimum workload, and/or degree progress. Theoretical approaches here often provide efficient algorithms that can be useful in academic decision making. In this paper, we discuss the main findings on seminar assignment problems at the FernUniversität in Hagen, Germany, considering lower bounds related to ratios. The incorporation of such bounds is important when, for example, chairs try to meet preference quotas with respect to certain categories of students. However, the inclusion of such bounds undermines the total unimodularity of the multicriteria seminar assignment problem. In this paper, we show that the property of total unimodularity can be preserved without affecting the structure of the generic problem. We then use this structure to quickly find an optimal solution. Our findings are complemented by preliminary numerical results.