An Integer Linear Program for Periodic Scheduling in Universities

Abstract: Efficient scheduling of periodic meetings is a critical challenge in various service-oriented domains, including academic settings, healthcare, and legal consultancy. This study presents a robust Integer Linear Programming (ILP) model to optimize the scheduling of faculty-student meetings. The proposed model incorporates practical constraints such as minimum intervals between consecutive meetings, differing time requirements for undergraduate, masters, and PhD students, and dedicated emergency time slots for unplanned visits. The objective function aims to achieve an equitable distribution of meetings throughout the planning period while prioritizing earlier time slots and seamlessly integrating emergency appointments. To validate the effectiveness of the model, both numerical examples and a case study are examined. The results highlight the ability of the model ability to generate optimal schedules within a computationally efficient framework, leveraging the power of Gurobi optimization software. The model demonstrates significant versatility, extending its applicability beyond academic settings to any scenario requiring periodic scheduling of services, such as patient visits in healthcare or client consultations in legal practices. Future extensions of the model may include dynamic scheduling to adapt to real-time changes in availability and the coordination of schedules across multiple service providers.