A Course Timetabling Formulation under Circumstances of Online Education

This study addresses the adaptation of the course timetabling problem to the online education system forced by the Covid-19 pandemic. The seating capacity constraint that shapes the timetabling decision in online education conditions loses its validity. It is replaced by a bandwidth constraint that restricts the number of instantaneous connections. Overlapping courses in the same time slot increase the number of instant connections and excessive connections cause technical problems. Bandwidth constraint requires the distribution of total connection in a day over all time slots. However, while this is achieved, the time slots should be allocated fairly to the departments. In this study, a multi-objective mathematical model is proposed that distributes the courses fairly on the day and time slot axis and distributes the total number of connections to time slots in each day as equally as possible. The model adopts the maximum difference minimizing approach and requires solving the objectives sequentially according to the order of them.The model was tested with the real data of the 2020-2021 fall semester of a 7 department faculty. The model has 12084 decision variables and 15567 constraints and an optimal solution gets in approximately 28 minutes. Results were compared with a decentralized and manually prepared timetable. The comparison shows that the model is superior to the manual timetable in the distribution of courses across the day and time slot. Also, the model can reduce the number of students in the peak time slot by 22% compared to manual scheduling.