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Hybrid Scheduling with Mixed-Integer Programming at Columbia Business School

Author

Listed:
  • Ciamac C. Moallemi

    (Division of Decision, Risk and Operations, Graduate School of Business, Columbia University, New York, New York 10027)

  • Utkarsh Patange

    (Division of Decision, Risk and Operations, Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

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 in which students have unique, individualized class enrollments and one in which 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 because of 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 the week and spread out over the entire term. Our objective is to maximize interaction between different teams. Our program was used to schedule more than 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.

Suggested Citation

  • Ciamac C. Moallemi & Utkarsh Patange, 2024. "Hybrid Scheduling with Mixed-Integer Programming at Columbia Business School," Interfaces, INFORMS, vol. 54(3), pages 222-240, May.
    • Handle: RePEc:inm:orinte:v:54:y:2024:i:3:p:222-240
    DOI: 10.1287/inte.2022.0070
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