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A General Formulation for the Teaching Assignment Problem: Computational Analysis Over a Real-World Dataset

Moa Johannesson, Lina Brink, Alvin Combrink, Sabino Francesco Roselli, Martin Fabian

TL;DR

The paper tackles the Teacher Assignment Problem (TAP) by formulating a rigorous mathematical model that captures the structure of Teaching Assistants, courses, and tasks, while incorporating workload, continuity, and preference considerations. It evaluates three solver paradigms—SMT, MILP, and CP-SAT—on five real-world yearly instances (2022–2026) drawn from a Chalmers dataset, benchmarking against manual scheduling. Results show substantial improvements in workload alignment and stability, with CP-SAT often delivering the best trade-off between solution quality and runtime. The work demonstrates practical utility for decision-support in TA assignment and outlines concrete avenues for scalability, data augmentation, and enhanced constraint handling in future work.

Abstract

The Teacher Assignment Problem is a combinatorial optimization problem that involves assigning teachers to courses while guaranteeing that all courses are covered, teachers do not teach too few or too many hours, teachers do not switch assigned courses too often and possibly teach the courses they favor. Typically the problem is solved manually, a task that requires several hours every year. In this work we present a mathematical formulation for the problem and an experimental evaluation of the model implemented using state-of-the-art SMT, CP, and MILP solvers. The implementations are tested over a real-world dataset provided by the Division of Systems and Control at Chalmers University of Technology, and produce teacher assignments with smaller workload deviation, a more even workload distribution among the teachers, and a lower number of switched courses.

A General Formulation for the Teaching Assignment Problem: Computational Analysis Over a Real-World Dataset

TL;DR

The paper tackles the Teacher Assignment Problem (TAP) by formulating a rigorous mathematical model that captures the structure of Teaching Assistants, courses, and tasks, while incorporating workload, continuity, and preference considerations. It evaluates three solver paradigms—SMT, MILP, and CP-SAT—on five real-world yearly instances (2022–2026) drawn from a Chalmers dataset, benchmarking against manual scheduling. Results show substantial improvements in workload alignment and stability, with CP-SAT often delivering the best trade-off between solution quality and runtime. The work demonstrates practical utility for decision-support in TA assignment and outlines concrete avenues for scalability, data augmentation, and enhanced constraint handling in future work.

Abstract

The Teacher Assignment Problem is a combinatorial optimization problem that involves assigning teachers to courses while guaranteeing that all courses are covered, teachers do not teach too few or too many hours, teachers do not switch assigned courses too often and possibly teach the courses they favor. Typically the problem is solved manually, a task that requires several hours every year. In this work we present a mathematical formulation for the problem and an experimental evaluation of the model implemented using state-of-the-art SMT, CP, and MILP solvers. The implementations are tested over a real-world dataset provided by the Division of Systems and Control at Chalmers University of Technology, and produce teacher assignments with smaller workload deviation, a more even workload distribution among the teachers, and a lower number of switched courses.
Paper Structure (10 sections, 2 equations, 5 figures, 2 tables)

This paper contains 10 sections, 2 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Teacher Assignment Problem Model
  3. Teaching Assistant Set
  4. Course and Task Sets
  5. Additional Parameters
  6. Decision Variables
  7. SMT Formulation of the Teacher Assignment Problem
  8. Experiments
  9. Conclusion
  10. Appendix

Figures (5)

  • Figure 1: Comparison of assigned versus target hours for each TA in year 2022 among solvers Gurobi, SCIP, CP-SAT, and Z3, as well as the manual teacher assignment.
  • Figure 2: Comparison of the number of assigned courses (upper) and number of new courses (lower) between solvers output and manual teacher assignment for year 2022.
  • Figure 3: Comparison of the TAs' assigned versus target hours between solvers and manual assignment for 2023--2026.
  • Figure 4: Comparison of the number of assigned courses between solvers and manual assignment for 2023--2026.
  • Figure 5: Comparison of the number of assigned new courses between solvers and manual assignment for 2023--2026.