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

TL;DR

This paper introduces a comprehensive mathematical model for the Teacher Assignment Problem, optimizing teacher-course assignments to improve workload balance and reduce course switching, validated on real-world data.

Contribution

It presents a new general formulation for the problem and evaluates it using advanced solvers on real data, demonstrating improved assignment quality.

Findings

Smaller workload deviation in assignments

More even workload distribution among teachers

Fewer course switches in the assignments

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.