Integer Linear Programming for the Tutor Allocation Problem: A Practical Case in a British University

TL;DR

This paper presents an integer linear programming approach to optimize tutor assignments in a university setting, significantly improving manual allocations and providing insights into factors affecting model performance.

Contribution

The study develops a practical ILP model for tutor allocation, demonstrating its effectiveness on real and synthetic data, and analyzing key input parameters influencing outcomes.

Findings

Significant improvement over manual assignment in a real case

Model performs well on randomly generated instances

Input parameters impact preferences satisfaction and model efficiency

Abstract

In the Tutor Allocation Problem, the objective is to assign a set of tutors to a set of workshops in order to maximize tutors' preferences. The problem is solved every year by many universities, each having its own specific set of constraints. In this work, we study the tutor allocation in the School of Mathematics at the University of Edinburgh, and solve it with an integer linear programming model. We tested the model on the 2019/2020 case, obtaining a significant improvement with respect to the manual assignment in use. Further tests on randomly created instances show that the model can be used to address cases of broad interest. We also provide meaningful insights on how input parameters, such as the number of workshop locations and the length of the tutors' preference list, might affect the performance of the model and the average number of preferences satisfied.