Maximizing student opportunities for in-person classes under pandemic capacity reductions
Introduction
In 2020, almost every aspect of everyday life was disrupted by the coronavirus (COVID-19), and strict physical-distancing rules to mitigate its propagation introduced a host of operational challenges. By October 2020, the University of Connecticut (UConn) was praised by White House coronavirus response coordinator Dr. Deborah Birx as having one of the highest in-person classroom participation rates.1 This notable overall success of UConn resulted from unprecedented efforts by hundreds of faculty and staff to plan for and maintain safety. While much of the credit belongs to our colleagues in public health for innovations in waste-water testing, for example, here we highlight the innovative use of optimization to make the best use of scarce classroom capacity, which had been drastically reduced to meet distancing protocols. Our work provided the opportunity for as many students and faculty to return to campus as possible, setting the stage for subsequent public health victories in keeping them healthy and safe once on campus. These efforts represent one important early step that resulted in UConn's recognition as a leading university in their COVID-19 response.2 Despite the challenges introduced by social distancing, after all optimizations, subsequent scheduling adjustments, and student add/drops, approximately 34% of all UConn courses (19% of all seats) took place with some level of in-person instruction.
The number of cases and deaths in the State of Connecticut was relatively large at the beginning of the pandemic, so the local and state governments took several actions to reduce infection rates, such as the prohibition of large gatherings. As a consequence, UConn closed its six campuses in April. At that time, the timetabling activities and student registration for the Fall 2020 semester had already been mostly completed. However, physical-distancing constraints led to significant reductions in room capacity. Consequently, traditional in-person instruction for larger sections became physically impossible.
As many students and faculty communicated their desire to have in-person instruction, the university elaborated a safe reopening plan, which included creating new teaching modalities to maximize the number of student seats assigned to in-person classes. Particularly relevant for this work is a Split-Delivery modality, in which 50% of students attend a teaching session on-campus while the other 50% learn online, reversing on alternating course days. Instructors were given the opportunity to indicate their preferred teaching modality for each course, but due to space restrictions, requests for in-person instruction could be denied, and these classes could be relegated to online instruction instead. This aspect incorporated a new dimension to the problem, involving decisions about the teaching modalities of each course. Additionally, this led to a weighted assignment problem, where the weights are the number of seats assigned to physical rooms. In particular, the weight of a class assigned to Split-Delivery Learning is only 50% of the weight of the same class when assigned to in-person instruction, whereas online classes had a weight of zero. These modifications resulted in a challenging problem, mainly because teaching modalities had to be assigned at the planning level and virtually every room assignment made in the past was infeasible, so decision makers had no warm start solution. Additionally, the weight component transformed a previous feasibility problem into an optimization problem, for which the manual identification of high-quality solutions was challenging and laborious given the dimensions of the problem. In particular, the assignment problem for Storrs, the flagship campus of UConn, involved almost 1,500 classes, 45,000 seats, and approximately 200 rooms.
With these changes, the timetabling decision support system (DSS) used by the university became unsatisfactory. Namely, significant modifications to the software were necessary, and as the vendor's response times were expected to increase in the period, UConn initially decided to do all the timetabling activities manually for Fall 2020. The collaboration with the authors allowed the university not only to revisit this initial decision but also to incorporate some additional flexibility in the assignment of teaching modalities to courses, with direct impact in the assignment of rooms to classes.
In this article, we present the DSS that we developed to solve the assignment problem for UConn. Our solution consists of a two-stage framework, which maximizes student opportunities for in-person instruction in the first stage and minimizes assignment discrepancies in the second. We discuss how our DSS was conceived and adopted by UConn for the Fall semester of 2020 as an interactive system and present several insights extracted from this work.
The manuscript is structured as follows. Section 2 we present a literature overview. The timetabling problem solved by UConn is discussed in detail in Section 3. We introduce the notation and the formal definition of the problem in Section 4. A greedy approach is described in Section 5, and our theoretical and algorithmic contributions are introduced in Section 6. In Section 7 and Section 8 we present our results and insights, respectively. We conclude with directions for future work in Section 9.
Section snippets
Literature review
The timetabling problem has attracted considerable attention from the scientific community due to its numerous real-world applications [1], [2], [3]. Traditional timetabling problems address the assignment of courses to rooms and meeting times. In curriculum-based timetabling problems, the assignments should avoid conflicts between courses scheduled for the same term in the standard curriculum [4]. Conversely, post enrollment-based course timetabling problems assume that student enrollment is
Timetabling at the university of connecticut
The timetabling problem solved by UConn each semester consists of the following decisions: 1) Number of sections offered for each course in each campus; 2) Assignment of instructors to classes; 3) Scheduling of each individual class; and 4) Assignment of classes to rooms. Once these steps are finalized, students work with faculty and staff advisors to find a feasible schedule that meets their educational goals and then register for classes in successive waves based on seniority. The vast
Formal description and notation
Let be a set of classes (or courses), be a set of rooms, and be a set of weeks. Within each week, the planning horizon is represented by the discrete set ; each element of represents the number of minutes elapsed since the beginning of the week, i.e., 0 represents Monday at 00:00, 1 is Monday at 00:01, …, and 10080 is Sunday at 24:00.
A pair s ≡ (b, e) in with b < e defines a slot; b(s) and e(s) are the start time and the end time of slot s, respectively, and e(s) − b(s)
Greedy heuristic algorithm
Before establishing a collaboration with the authors, the administrative staff at UConn decided not to use Astra Schedule (or any other decision-support system) to design a new assignment plan for Fall 2020 but to use a “manual” approach. This decision was made because the administrative staff was not confident that they would be able to configure and extract satisfactory results from the software within such a short period of time. Their approach of choice at the time is best approximated as a
Exact two-stage framework
Our solution approach is an exact two-stage algorithm. In the first stage, we identify an optimal solution using the objective function described in Section 4; two mixed-integer linear programming formulations are proposed to solve this problem. The second stage uses a different objective function and additional constraints to find a solution that is optimal for the first stage and minimizes the discrepancy between room capacities and class sizes.
Development, deployment, and results
In this section we discuss how the project was conducted and present our results. The models and algorithms are implemented in Gurobi version 9.0.0 through the Python 3.6 API.4 All executions are conducted on an Intel(R) Core(TM) i7-8565U CPU at 1.80GHz, 1992Mhz, 1 core and 8GB of memory, with the optimization software using the standard parameters of Gurobi; in particular, all presolve functionalities were active in the experiments.
Insights about the adoption of SP learning
We analyze below alternative scenarios and show how a better “appreciation” of the SP modality, both in terms of adoption and on the weight it has in the objective function, could lead to (numerically) better results.
Conclusion
In this paper, we presented an optimization approach to the assignment of classes to rooms for Fall 2020 at the University of Connecticut, confronted with drastic reductions in room capacities due to COVID, alternating-use teaching modalities, and hundreds of unique course meeting patterns. The resulting NP-hard problem was solved several times as decision support for UConn schedulers and Department Heads, who used our results as an optimized master schedule that could later be adjusted for
CRediT authorship contribution statement
David Bergman: Conceptualization, Methodology, Software, Resources, Data Curation, Visualization. Carlos Cardonha: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data Curation, Writing, Visualization, Supervision, Writing - original draft, Writing - review & editing. Robert Day: Conceptualization, Resources, Formal analysis, Data Curation, Writing - original draft, Writing - review & editing.
Acknowledgements
The authors would like to thank all the people from UConn involved in this initiative, including approximately 175 Associate Deans and Department Heads, and the program directors and administrative staff that support them. We also thank the upper administration for their support, with special thanks to the “Classroom Committee” with whom we implemented the results described here: Peter Diplock (CETL), Brian Rockwood & Marc Hatfield (Registrar), Maria Groza (UPDC), Aris Ristau (Facilities),
Carlos Cardonha is an assistant professor at the Department of Operations and Information Management at the University of Connecticut. His primary research interests are optimization, mathematical programming, and theoretical computer science, with focus on the application of techniques in mixed integer linear programming, combinatorial optimization, and algorithms design to operations research problems.
References (28)
Using information on unconstrained student demand to improve university course schedules
J. Oper. Manag.
(2005)- et al.
Recent research directions in automated timetabling
Eur. J. Oper. Res.
(2002) - et al.
A survey of approaches for university course timetabling problem
Comput. Ind. Eng.
(2015) - et al.
A graph-based hyper-heuristic for educational timetabling problems
Eur. J. Oper. Res.
(2007) A two-stage multiobjective scheduling model for [faculty-course-time] assignments
Eur. J. Oper. Res.
(1996)- et al.
A multi-objective course scheduling model: combining faculty preferences for courses and times
Comput. Oper. Res.
(1998) - et al.
On the k-coloring of intervals
Disc. Appl. Math.
(1995) - et al.
Slotmanager: a microcomputer-based decision support system for university timetabling
Decis. Supp. Sys.
(2000) - et al.
An optimization-based dss for student-to-teacher assignment: classroom heterogeneity and teacher performance measures
Decis. Supp. Sys.
(2019) - et al.
Udpskeduler: a web architecture based decision support system for course and classroom scheduling
Decis. Supp. Sys.
(2012)
A web-based group decision support system for academic term preparation
Decis. Supp. Sys.
An interactive system for constructing timetables on a pc
Eur. J. Operat. Res.
Visopt: a visual interactive optimization tool for p-median problems
Decis. Supp. Sys.
Wastewater treatment: new insight provided by interactive multiobjective optimization
Decis. Supp. Sys.
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Carlos Cardonha is an assistant professor at the Department of Operations and Information Management at the University of Connecticut. His primary research interests are optimization, mathematical programming, and theoretical computer science, with focus on the application of techniques in mixed integer linear programming, combinatorial optimization, and algorithms design to operations research problems.
David Bergman is an associate professor of operations and information management at the University of Connecticut. His research focus is on developing novel solution methodology for large-scale automated decision making.
Robert Day has a PhD in Applied Mathematics and Operations Research from the University of Maryland. Robert W. Day is a world-leader in auction design research, with several billions of dollars in revenue generated for government consulting clients in telecommunications regulation. His work emphasizes the synthesis of cutting-edge ideas from Computer Science, Economics, and Operations Research. With additional research in Hospital Management, Scheduling, Expected Utility Theory, and Grid Computing, his work has been recognized with the Dantzig Dissertation Award and the INFORMS Computing Society Prize.