The university coursework timetabling problem: An optimization approach to synchronizing course calendars

In university settings, scheduling coursework over an academic term and across several courses is an extremely difficult task, owing to numerous complexities and constraints, such as the uniqueness of each student and instructor’s schedules, workload limits, syllabus considerations, university policies, and the length of the academic term. In addition to the inherent difficulty, the activity is usually performed arbitrarily and with little to no coordination among the relevant decision-makers, including department chairs and faculty members. Although mathematical models have been developed to address similar educational timetabling problems, models that tackle the scheduling of coursework, in particular, are lacking. In this regard, the present study introduces the university coursework timetabling problem (UCWTP), and proposes an optimization tool as a solution approach. The UCWTP involves scheduling a set of coursework covering different courses and several course sections over an academic term such that the quality of the resulting timetable is optimized. To model the case, a multi-objective mixed integer linear programming model was formulated with constraints divided into two types, hard and soft, with the latter defining the quality of the timetable based on three dimensions: (1) compliance with curriculum requirements, (2) adherence to student workload limits, and (3) adherence to instructor workload limits. The hypothetical case considered yielded promising results as a 100% weighted satisfaction was attained, equivalent to an average improvement of 9.45% relative to multiple heuristically constructed timetables. The exact algorithm proves to be sufficiently effective as a solution approach, yielding reasonable computational times of less than 2 min for real-world university scenarios.