A Two-Phase Multicommodity Flow Approach for Classroom Assignment

A common problem faced by universities is the assignment of courses to campus-hosted spaces. An optimal solution is difficult to reach, given the number of constraints present. Increasing student enrollment across campus leads to a need for a model that optimally assigns courses to spaces that maximizes the total number of courses taught in person. This paper poses a solution to this problem by generating a two-phase model to allocate courses to campus-hosted spaces. The two-phase approach to classroom assignment consists of a minimum-weighted bipartite matching for priority assignment and a multicommodity flow model to assign remaining courses. The optimal solution minimizes the walking distance between classrooms for professors teaching back-to-back courses and the walking distance between classrooms and professors’ offices. The proposed model also minimizes the excess capacity of used campus-hosted classrooms and considers priority assignment. The model was tested on Spring 2022 course data from The University of Tennessee. The results of this model show a decrease in professor walking distance between courses and offices, as well as a decrease in percent excess capacity across used campus-hosted classrooms. With an optimal assignment of courses to campus-hosted classrooms, university resources can be used in a more optimal way that can increase student and professor retention rates.