An Integer Linear Programming Approach to a Large-Scale University Course Scheduling Problem

Scheduling educational institution courses for multiple departments presents a significant challenge due to the complexity of constraints and requirements. This paper addresses the University Course Scheduling Problem (UCSP) using a binary Integer Linear Programming (ILP) approach to generate semester schedules for winter or summer semesters. The approach incorporates both hard constraints - such as avoiding simultaneous sessions for the same semester, adhering to room capacities, and ensuring lecturers are not doublebooked - and soft constraints, including preferences for lecture times. While the whole methodology integrates tools for data management, optimization modeling, and a structured workflow to create detailed schedules for lecturers, students, and room allocations, this paper focuses on the ILP-formulation of these constraints. The construction of these matrices is systematically explained through practical examples, illustrating how the relationships between courses, lecturers, rooms, and time slots are encoded. To validate the proposed approach, a case study was conducted at the Niederrhein University of Applied Sciences. This study addresses the scheduling requirements of three engineering departments with more than 50 degree programs and 260 modules, demonstrating the applicability of the matrixdriven ILP method.