A A Hybrid Approach to Student Class Sectioning Timothy S. Vaughan
University of Wisconsin – Eau Claire Journal of Higher Education Management, 35(4), 67-76 (ISSN 2640-7515). © Copyright 2020 by American Association of University Administrators. Permission to reprint for academic/scholarly purposes is unrestricted provided this statement appears on all duplicated copies. All other rights reserved.
This article demonstrates the effectiveness of reserving a percentage of seats in each section of a multi-section course for mathematically optimized student assignment. The performance of this approach is compared to that of a fully optimized solution, as well as to the case of opening all seats to normal registration in which students self-select their course section. Results suggest that most of the benefit of a fully optimized assignment can be realized by holding a portion of seats in reserve for optimization. The hybrid approach involves a “Phase I” registration period, in which a subset of total planned seating capacity is made available for students to self-select their class section using normal campus registration procedures. This is followed by “Phase II” in which reserve seats are allocated using a student preference-based assignment model. This hybrid approach achieves much of the benefit of a fully optimized solution, while retaining many of the (often overlooked) benefits associated with the simpler self-selection system. The hybrid approach also provides a smaller scale, easily accessible optimization problem for Phase II, not requiring specialized heuristic solution methods. As such, the system provides a practical balance between operational simplicity and optimized efficiency. In our application, approximately 75% to 80% of available seating is made available to the “Phase I” registration, with 20% to 25% of seats held in reserve for “Phase II”. In Phase II, unregistered students (as well as a small number who are not entirely satisfied with the section they registered for in Phase I) submit their ranked section preferences. These students are then assigned to sections using a straight-forward assignment problem that is easily solved using a commercially available LP solver. The course in question is a required senior level capstone course, typically taken in the last semester prior to graduation. As failure to provide a feasible seating alternative could delay a student’s graduation, it is critical that some portion of seats are withheld for effective allocation. In Phase I, students gain access to registration according to number of credits completed, presumably giving higher priority to those students who are closer to graduation. Academic records for students requesting a section during “Phase II” are screened, to ensure those seats are first allocated to students needing the course in order to graduate at the end of the semester. Note that the capstone course provides lesser ability to “smooth” course enrollments, as compared to lower level courses where overflow demand can be pushed into a subsequent term, or in the case of elective courses for which other alternatives exist. We thus have a well-defined set of students who need to be assigned to a section of the course in question, as opposed to having a broader set of alternatives that would require a more expansive analysis in order to optimize. The remainder of this paper is organized as follows: Section 2 presents a review of literature and examination of the “state of the art” in schedule optimization. Section 3 presents additional discussion and motivation for the hybrid approach. The assignment model is presented in Section 4, with sample results from actual implementation presented in Section 5. Section 6 presents experimental results, characterizing the relationship between overall solution quality vs. the percentage of total seating capacity allocated to Phase I vs. Phase II. 67
