Integer Linear Programming for the Tutor Allocation Problem: A practical case in a British University. (January 2022) - Caselli, Giulia
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 and we showed that such improvement could be maintained while optimizing other key metrics such as load balance among groups of tutors and total number of courses assigned. 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. Highlights: The assignment of tutors to workshops is a practical problem faced by universities. We propose a mathematical model for a real case of the problem. The implemented algorithm finds an optimal solution for the real case. We introduce a set of additional constraints to make the allocation fairer. Further computational experiments demonstrate the model scalability.