AN INTEGER LINEAR PROGRAMMING MODEL FOR MAXIMIZING PREFERENCE SATISFACTION IN UNIVERSITY TIMETABLING

Abstract

Manual university course timetabling is a time-consuming, complex, and conflict-prone combinatorial optimization problem, widely recognized as NP-hard due to its intricate constraints. This research automates and optimizes this task for the Department of Statistics at our university using a novel Integer Linear Programming (ILP) model. Implemented in Python with the Gurobi solver, the model maximizes weighted instructor preferences while strictly adhering to hard constraints, including student cohorts, faculty availability, and room capacity, alongside specific pedagogical constraints necessitating consecutive periods for intensive subjects and non-consecutive days to optimize student study intervals. The model successfully scheduled all 27 courses to global optimality within 285.15 seconds, achieving a 0% MIP gap and an average preference satisfaction rate of 89.6%. The resulting system generates complete, conflict-free timetables that respect constraints such as lunch breaks and workload limits, demonstrating a significant improvement in efficiency and solution quality over traditional manual methods, offering a scalable solution applicable to broader academic contexts.