Hybrid Scheduling with Mixed-Integer Programming at Columbia Business School

We describe the hybrid scheduling system that we implemented at Columbia Business School during the Covid-19 pandemic. The system allows some students to attend in-person classes with social distancing, while their peers attend online, and schedules vary by day. We consider two variations of this problem: one where students have unique, individualized class enrollments, and one where they are grouped in teams that are enrolled in identical classes. We formulate both problems as mixed-integer programs. In the first setting, students who are scheduled to attend all classes in person on a given day may, at times, be required to attend a particular class on that day online due to social distancing constraints. We count these instances as “excess.” We minimize excess and related objectives, and analyze and solve the relaxed linear program. In the second setting, we schedule the teams so that each team’s in-person attendance is balanced over days of week and spread out over the entire term. Our objective is to maximize interaction between different teams. Our program was used to schedule over 2,500 students in student- level scheduling and about 790 students in team-level scheduling from the Fall 2020 through Summer 2021 terms at Columbia Business School.