Issue: 2023/Vol.33/No.3, Pages 1-27
THE SEKO ASSIGNMENT. EFFICIENT AND FAIR ASSIGNMENT OF STUDENTS TO MULTIPLE SEMINARS
Tobias Hoßfeld
Cite as: T. Hoßfeld. The SEKO assignment. Efficient and fair assignment of students to multiple seminars. Operations Research and Decisions 2023: 33(3), 1-27. DOI 10.37190/ord230301
Abstract
Seminars are offered to students for education in various disciplines. The seminars may be limited in terms of the maximum number of participants, e.g., to have lively interactions. Due to capacity limitations, those seminars are often offered several times to serve the students’ demands. Still, some seminars are more popular than others and it may not be possible to grant access to all interested students due to capacity limitations. In this paper, a simple, but efficient random selection using key objectives (SEKO) assignment strategy is proposed which achieves the following goals: (i) efficiency by utilizing all available seminar places, (ii) satisfying all students by trying to assign at least one seminar to each student, and (iii) fairness by considering the number of assigned seminars per student. We formulate various theoretical optimization models using integer linear programming (ILP) and compare their solutions to the SEKO assignment based on a real-world data set. The real-world data set is also used as the basis for generating large data sets to investigate the scalability in terms of demand and number of seminars. Furthermore, the first-in first-out (FIFO) assignment, as a typical implementation of fair assignments in practice, is compared to SEKO in terms of utilization and fairness. The results show that the FIFO assignment suffers in real world situations regarding fairness, while the SEKO assignment is close to the optimum and scales regarding computational time in contrast to the ILP.
Keywords: assignment problem, limited capacity, utilization, at least on seminar (ALOS) ratio, fairness, integer linear programming (ILP), first-in first-out (FIFO) assignment, random selection using key objectives (SEKO)
Received: 1 June 2022 Accepted: 1 June 2023
Published online: 21 September 2023