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.

翻译：在这项研究中,我们考虑了将学生分配到每个学生都有偏好名单的班级、按偏好顺序排列一组班级的现实问题。虽然我们使用现有办法将贡马大学的每日班级分配包括在内,但需要根据实地实际情况,提出新的概念和调整,以找到更好的结果。 因此,我们建议小型级别限制的最大功用匹配,并在最大功用匹配和公平匹配之间达成妥协,如果在词汇学上尽量减少被分配到未列入其选择的班级的学生人数,分配到最后选择的学生人数,等等,那么,这种匹配据说是公平的。 此外,我们还注意到学生提出推迟接受机制、单一断绝关系(这是关于学校选择问题的文献中的一个热题)的潜在效率低下。