A Formulation of a Mixed Integer Schedule for the Problem of Schedules in a Federal Institute with Restrictions on Teaching Hours

This work proposes a formulation of mixed integer programming for the problem of timetables of the IFMG – Congonhas Campus, seeking to expand the adherence of the model to the institutional rules and improve the operational quality of the solutions. The proposed approach is based on Mixed Integer Programming (MIP) and uses a multistage hierarchical strategy. The formulation incorporates restrictions related to teaching hours, synchronization between disciplines, grouping of curricular components and pedagogical continuity of offers. The optimization process is structured in three integrated models, solved hierarchically, so that the optimal values obtained in each step are preserved in the subsequent steps. The first model focuses on minimizing the occurrence of windows in the disciplines; the second minimizes the penalties for allocating teaching hours, respecting daily limits and interstices between shifts; and the third minimizes the windows in teachers' schedules. The resolution was carried out through the CPLEX solver, with Python implementation. Computational experiments conducted with real campus data, covering 71 professors and 357 disciplines, demonstrated the effectiveness of the approach. Compared to the manual schedule, the model reduced the penalties for teaching hours by 53.2\%, in addition to eliminating allocations at prohibited times and cases of teachers not being included in valid schedules, maintaining the inexistence of windows in the class schedules.