An Integer Linear Programming Model for the Examination Timetabling Problem: A Case Study of a University in Thailand

This paper considers the examination timetabling problem (ETTP) at the College of Industrial Technology (CIT) of the King Mongkut’s University of Technology North Bangkok in Thailand. A new integer linear programming (ILP) formulation for the ETTP at the CIT is presented. The objectives were to minimize both the number of examination days (the main objective) and the number of rooms used throughout the entire examination period (the secondary objective). In this paper, a course can have multiple sections, and an examination room can accommodate exams for more than one course section. To illustrate the proposed ILP model, real data on courses acquired from the CIT were used to generate two test problems: a small problem and a large problem. The small problem included 32 courses with 69 sections. The large problem included 73 courses with 341 sections, which was the real data required for generating the midterm examination timetable for all first-year courses in the first semester of 2021. Both problems were solved using the CPLEX solver software. The results show that the proposed model could find an optimal examination timetable for the small problem with a computational time of 2 min and 46 s. It also could find a good feasible midterm examination timetable that satisfied the requirements of the CIT for the large problem within the 2-h time limit, much less time than that compared to manual scheduling by the CIT’s administrative staff. The obtained midterm examination timetable required five examination days and could reduce 104 examination rooms compared to assigning each course section to a separate examination room. The proposed ILP model can be used in a real-life situation and can be a good option to generate an optimal schedule or a good feasible schedule for examinations at the CIT or other institutions that have similar requirements.