A Greedy Heuristic for Scheduling Hybrid Medical School Courses with Metaverse Integration

University course scheduling is a complex NP-hard optimization problem that becomes even more challenging when incorporating modern instructional formats such as metaverse-based education. This study proposes a tailored greedy algorithm to address hybrid course scheduling, involving both traditional and metaverse courses. The model incorporates a comprehensive set of constraints reflecting real-world scheduling challenges, such as room capacities, time availability, and the eligibility of professors and rooms—particularly for metaverse settings, where specialized hardware, digital platforms, and instructional preparedness must be considered. A binary integer programming formulation defines decision variables, constraints, and an objective function that maximizes the weighted alignment of professors with metaverse courses. Synthetic datasets of varying sizes were generated to test the algorithm's performance. The results demonstrate the algorithm’s efficiency in producing feasible timetables that align with institutional constraints and instructional goals. The greedy algorithm provides a robust and scalable initial solution for use in metaheuristic optimization frameworks. Its design promotes adaptive scheduling strategies that can accommodate technological advances in higher education while preserving feasibility and instructional quality.