University Course Timetabling Optimization Using Binary Integer Linear Programming:A Case Study of the College of Technical Sciences in Bani Walid

الملخص

University course timetabling remains a classic combinatorial optimization problem, and it sits at the heart of how academic institutions manage their resources. The task becomes considerably harder when operational constraints are tight: teaching facilities are few, lecture durations are fixed, and scheduling periods are limited. A wide range of optimization approaches has been proposed in the literature, yet comparatively few studies examine timetabling environments in which temporal structures are tightly constrained and institutional resources are scarce.

This study presents a Binary Integer Linear Programming (BILP) model that generates conflict-free university course timetables while minimizing theoretical overflow into the laboratory. Binary decision variables are used to assign courses to specific classrooms and time slots. A thorough set of hard constraints governs these assignments: they guarantee timetable feasibility, prevent scheduling conflicts, enforce the exclusive use of classrooms and instructors, and reserve the computer laboratory for practical courses alone.

The approach was evaluated through a real-world case study at the Department of Engineering Management and Administrative Leadership, College of Technical Sciences in Bani Walid, Libya. The department offers 48 undergraduate courses across eight academic semesters, taught by 13 faculty members. Its scheduling environment is notably restrictive: only ten weekly time slots are available, a consequence of a five-day academic week with two three-hour teaching periods per day, together with four theoretical classrooms and one computer laboratory. Under these conditions, the BILP model produced a completely conflict-free timetable with 96.0% overall resource utilization, zero hard-constraint violations (one controlled theoretical overflow into the laboratory was permitted to preserve overall feasibility), and proven mathematical optimality