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Abstract
As universities begin the return to in-person course work, uncertainty remains about the future of SARS-CoV-2 virus and its variants. In the years to come, other novel pathogens may emerge. Pandemic-driven social distancing requirements reduce the number of students in classrooms, and when these requirements are instituted mid-semester, universities must make quick changes to classroom assignments and course delivery mode. In this work, we introduce two integer programs to optimize mid-semester changes: (i) a conflict-matrix-based model that determines new classroom capacities and designs the corresponding seat map, and (ii) a hierarchical model that optimizes room assignment and course delivery mode according to prioritized objectives. We test our methods with University of Michigan's engineering course schedule for Fall 2021, under a hypothetical 3-foot social distancing requirement. We compare the performance of the models under different hierarchical objectives and room assignment assumptions and discuss the managerial implications of our results.
Keywords:
course scheduling, integer programming, multiobjective optimization, hierarchical optimization, pandemic response
(ProQuest: ... denotes formulae omitted.)
1. Introduction
With the outbreak of the novel SARS-CoV-2 pathogen in March 2020, many universities experienced a disruptive, unanticipated shift to remote learning to ensure student safety. The return to in-person classes in Fall 2021, amidst the continuing threat of the Delta variant [1], gave an opportunity for universities to plan for these disturbances. In this paper, we introduce models to prepare for mid-semester changes due to an epidemiological outbreak that requires social distancing. These models can be useful in the face of newly emerging pathogens that are transmitted by aerosols.
Our first integer program maximizes usable seats in a fixed layout classroom under a social distancing requirement, identifying new classroom capacities. Our second model considers course schedule updates under new capacities. Because this is a mid-semester change, we assume class times must stay the same, but room assignments and mode of delivery can change. We introduce an integer program to assign delivery mode and room location to each course, while maximizing a reward function defined by university administration. We apply our methods to University of Michigan's Fall 2021 engineering course schedule and find that under a 3-foot social distancing requirement, our approach allows us to increase the percentage of general classes that can remain fully in person from...