Optimal class assignment problem: a case study at Gunma University

TL;DR

This paper addresses the complex student-class assignment problem at Gunma University by proposing new matching algorithms that balance utility and fairness, highlighting limitations of existing mechanisms like deferred acceptance.

Contribution

It introduces minimax-rank constrained maximum-utility matchings and a fair matching concept, adapting existing methods to real-world university class assignment scenarios.

Findings

Proposed new matching algorithms balancing utility and fairness.

Identified inefficiencies in the student proposing deferred acceptance mechanism.

Applied methods to real-world data at Gunma University.

Abstract

In this study, we consider the real-world problem of assigning students to classes, where each student has a preference list, ranking a subset of classes in order of preference. Though we use existing approaches to include the daily class assignment of Gunma University, new concepts and adjustments are required to find improved results depending on real instances in the field. Thus, we propose minimax-rank constrained maximum-utility matchings and a compromise between maximum-utility matchings and fair matchings, where a matching is said to be fair if it lexicographically minimizes the number of students assigned to classes not included in their choices, the number of students assigned to their last choices, and so on. In addition, we also observe the potential inefficiency of the student proposing deferred acceptance mechanism with single tie-breaking, which a hot topic in the literature on the school choice problem.