Improving the quality of the assignment of students to first-year seminars

Abstract

Many post-secondary academic institutions in the United States have a First-Year Seminar Program. These seminars are designed to support the success of new incoming first-year students by combining writing, research and active discussion among small groups of students. At Dickinson College, students are required to select six seminars they find interesting from a list of approximately 42 seminars. The college then attempts to assign each student to a seminar on their list, while maintaining course capacities. Using standard commercial optimization software, we develop an approach that not only solves this basic assignment problem, but also seeks to balance both the gender and number of international students in the seminars. In addition, we utilize Monte Carlo simulation to study how the number of seminars each student is required to select affects the likelihood that a feasible assignment exists.

Appendix

Below we provide the linear programming constraints for the max-flow model in Figure 4 (we omit the objective function).

Here, constraints (A.1)−(A.9) are flow conservation constraints that ensure the flow entering the various nodes must leave those nodes. Constraints (A.10) and (A.11) ensure that the flow originating at the source will pool at the sink, and constraints (A.12)−(A.17) enforce the capacity on the arcs.