Abstract

The timetabling problem in higher education is a complex optimization challenge, shaped by multiple constraints and the need to balance institutional requirements with the well-being of the faculty. This study introduces a binary integer programming model for the equitable distribution of teaching loads within the Department of Mathematics at a public university in Paraná, Brazil. The model’s objective is to assign 49 classes to 16 professors, considering 17 daily time slots over five weekdays. Implemented using Julia/JuMP and solved with the Gurobi Optimizer, the optimal solution was reached in 30.44 seconds, with an objective value of 17,905. A 0.0000% gap between the best objective and the best bound demonstrates the optimality of the solution. The primary contribution of this work lies in incorporating constraints that are rarely explored in literature, such as limiting consecutive teaching days, enforcing contiguous blocks of classes, and penalizing evening assignments. These constraints are integrated into an objective function that balances efficiency and fairness. Unlike heuristic approaches, the model guarantees solution optimality within a competitive computational time, making it a robust alternative for medium-sized instances. The results show that the proposed model not only ensures technical feasibility but also promotes distributive equity and pedagogical coherence, contributing to both efficient academic management and faculty well-being.

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