2026 Volume 69 Issue 1 Pages 23-38
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. We use existing successful approaches to contribute the work of Gunma University; however, in practice, one method does not always yield the best results, and 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, that assigned to their last choices, that assigned to their penultimate choices, and so on. In addition, we compare our methods with the Boston mechanism and the deferred acceptance mechanism. We also observe the potential inefficiency of the student proposing deferred acceptance mechanism with single tie-breaking, which is a hot topic in the literature on the school choice problem.
