Class Timetable Allocation in Higher Education Using Binary Integer Programming: A Case Study in the Academic Department of Mathematics at a Public University in Paraná, Brazil
Bibliographic record
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".