最优班级分配问题：群马大学的案例研究
Optimal class assignment problem: a case study at Gunma University
摘要：
在这项研究中，我们考虑现实世界中的问题，分配学生的类，其中每个学生都有一个偏好列表，排序的一个子集的类的偏好顺序。虽然我们使用现有的方法来包括群马大学的日常课堂作业，但需要根据现场的实际情况进行新的概念和调整，以找到更好的结果。因此，我们提出了最小最大秩约束的最大效用匹配和最大效用匹配与公平匹配之间的折衷，其中如果匹配在词典上最小化分配到未包括在其选择中的班级的学生数量，分配到其最后选择中的学生数量等，则称匹配是公平的。我们也观察到，学生提出的延迟接受机制与单一的平局打破，这是一个热门的文献中的择校问题的潜在效率。
英文摘要：
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.
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