On the assignment of students to topics: A Variable Neighborhood Search approach

Abstract

This article presents a study of a practical assignment problem found in teaching within higher education. Here, students are assigned to scientific topics for which written papers must be submitted. Often, preferences across topics exist among other side constraints that should be considered in solving the problem of interest. Characterizing attributes of real-world problems were studied for scientific departments in Economics and Business Administration at German universities by sending out 800 questionnaires, and analyzing the 203 responses. Based on earlier studies, a Variable Neighborhood Search (VNS) approach was formulated to solve the resulting assignment problem. Several neighborhood search operators were tested, and numerical results are reported for a range of problem scenarios taken from real-world cases. It was observed that VNS leads to superior results vs. single operator local search approaches. Furthermore, we were able to show that in the studied problem, the effectiveness of certain neighborhoods was, to a large extent, dependent on the structures of the underlying problem. An extension of the problem was formulated by integrating a second objective function, which simultaneously balances the workload of staff members while maximizing student utility. The VNS approach was implemented in a computer system, available free of charge, providing decision support for selected other institutions within higher education.