THE STUDENTS/DEPARTMENTS ALLOCATION PROBLEM WITH GROUP CONSTRAINTS — AN APPLICATION OF DISCRETE CONVEX ANALYSIS

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  • 学生にグループ分けのある学科配属問題― 離散凸解析の適用例
  • ガクセイ ニ グループ ワケ ノ アル ガッカ ハイゾク モンダイ : リサン トツカイセキ ノ テキヨウレイ

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Abstract

<p>The first-year students of the Faculty of Science and Technology of Keio University belong to one of the five groups and are allocated to eleven departments just before proceeding to the second grade. Each student must be allocated to one of the three or four departments pre-assigned to her/his group. By constraints on quotas between the groups and the departments, the standard students/departments stable allocation problem is not applicable to this allocation problem. Since eight departments accept students from two groups, a decision-maker, who allocates the first-year students to the departments, repeatedly decided the quotas between the groups and the pre-assigned departments, and solved the standard students/departments stable allocation problem, by trial and error.</p><p>In this paper, we propose a variant of the students/departments stable allocation problem in which the students are partitioned into several non-empty sets, and develop two algorithms for the variant or its relaxation problem. We also report results of two algorithms applied to real students/departments allocation problems of the Faculty of Science and Technology of Keio University in academic years 2015 and 2016. Our algorithm applying discrete convex analysis gave nice results for the real allocation problems.</p>

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