A Mathematical Model for Class Scheduling: A Case Study with the Federal University of Maranhão

Source abstract

Assigning university courses to classrooms is a recurring operational task that balances scarce space, laboratory requirements, and institutional inclusion policies. This chapter presents a mathematical programming approach to that task at the Federal University of Maranhão (UFMA), Brazil. After the weekly timetable is fixed, each meeting must receive a feasible room. We model the decision as an integer linear programme with two ordered goals: use as few rooms as possible, and, among such compact plans, reduce the placement of mobility-impaired student groups on upper floors. The chapter updates the educational timetabling and classroom-assignment literatures (including recent artificial intelligence [AI]-assisted scheduling), positions the contribution against prior CAP and fairness models, states a notated formulation with a justified lexicographic rule, and details a reproducible workflow with open artefacts. A case study at the Department of Informatics for the term 2023.1 shows that lexicographic optimization cuts room usage relative to both the historical hand-made plan and a constructive heuristic while improving the mobility criterion. Equally compact plans differ widely in accessibility, so an explicit second-stage optimization is necessary in practice. Additional experiments (weighted sums, disability and laboratory sensitivities, concurrent load, and five synthetic department profiles with 20 replicas each) confirm that the accessibility spread is structural. Open data and solver scripts accompany the chapter.