  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.
