TEACHER TIMETABLING AND WORKLOAD ALLOCATION IN NEW SECONDARY EDUCATION SYSTEM

Abstract

The Brazilian new secundary education reform (Law No. 13,415/2017) introduced curricular and structural transformations that significantly increased the complexity of teacher workload allocation. School administrators now confront interdependent challenges, including teacher availability, balanced distribution of operational workloads, commuting constraints, and limited physical infrastructure (e.g., “classrooms,” “laboratories,” “IT infrastructure”) within a more flexible curriculum. Teacher timetabling is a classical NP-hard problem in Operations Research, and Mixed-Integer Linear Programming (MILP) provides a rigorous framework to model such interdependent constraints. This study proposes and implements an MILP optimization model for teacher workload allocation in a large public secundary educationin São José dos Pinhais, Paraná, Brazil. The real-world instance included 49 teachers and 19 classes, totaling 745 weekly hours. The formulation explicitly incorporates institutional constraints—such as daily workload limits, asynchronous class integration, and the shared-resource restriction for Physical Education—as well as teacher preferences regarding paired lessons and activity hours (HA) grouping. The model, implemented in Julia (JuMP) and solved with the Gurobi Optimizer, achieved an exact optimal solution in approximately 35 seconds. The optimization resulted in reducing one teacher’s weekly presence by a full day while maintaining the same number of working days for others. Furthermore, it eliminated the need for manual scheduling adjustments, automatically ensuring consistent allocation of asynchronous lessons and the non-overlapping use of the school’s sports court. By combining operational efficiency with adherence to teacher preferences, the proposed MILP formulation proved to be computationally tractable and applicable to real educational contexts. The model serves as a decision-support tool that enhances school organization and improves the overall management of teaching schedules.