学生の選好に同順位を含む研究室配属問題

抄録

We consider the laboratory assignment problem in which laboratories have minimum and maximum quotas. MSDA proposed by Fragiadakis, et al., is an efficient algorithm to solve the laboratory assignment problem, but it is incomplete to find a fair assignment. In this paper, we show three extensions of the laboratory assignment problem and translations from the extensions to constraint optimization problems. The first extension enables a completeness to find a fair assignment if it exists, but loses strategy-proofness. The original and first extended laboratory assignment problem may have no fair assignment. This is caused by redundant claims of an empty seat. The second extension based on the first one ensures that the laboratory assignment problem has at least one fair assignment by making a claim of an empty seat stricter. The third extension introduces tied ranks to students' preferences over laboratories, for example, students can specify multiple laboratories as their first choice. This extension gives the Žexibility to specify students' preferences and makes it possible to find more desirable assignments. The experimental results show that our approaches requires more computational time compared with MSDA, but can always find a fair assignment and a more desirable one.