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Optimal class assignment problem: a case study at Gunma University

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  • Akifumi Kira
  • Kiyohito Nagano
  • Manabu Sugiyama
  • Naoyuki Kamiyama

Abstract

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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  • Akifumi Kira & Kiyohito Nagano & Manabu Sugiyama & Naoyuki Kamiyama, 2021. "Optimal class assignment problem: a case study at Gunma University," Papers 2103.16879, arXiv.org.
    • Handle: RePEc:arx:papers:2103.16879
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    References listed on IDEAS

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    1. Tamás Fleiner & Naoyuki Kamiyama, 2016. "A Matroid Approach to Stable Matchings with Lower Quotas," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 734-744, May.
    2. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    3. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    4. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    5. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    6. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    7. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    8. Yu Yokoi, 2017. "A Generalized Polymatroid Approach to Stable Matchings with Lower Quotas," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 238-255, January.
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