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Integer programming methods for special college admissions problems

Author

Listed:
  • Kolos Csaba Ágoston

    (Corvinus University of Budapest)

  • Péter Biró

    (Corvinus University of Budapest
    Hungarian Academy of Sciences)

  • Iain McBride

    (University of Glasgow Sir Alwyn Williams Building)

Abstract

We develop integer programming (IP) solutions for some special college admission problems arising from the Hungarian higher education admission scheme. We focus on four special features, namely the solution concept of stable score-limits, the presence of lower and common quotas, and paired applications. We note that each of the latter three special feature makes the college admissions problem NP-hard to solve. Currently, a heuristic based on the Gale–Shapley algorithm is being used in the Hungarian application. The IP methods that we propose are not only interesting theoretically, but may also serve as an alternative solution concept for this practical application, and other similar applications. We finish the paper by presenting a simulation using the 2008 data of the Hungarian higher education admission scheme.

Suggested Citation

  • Kolos Csaba Ágoston & Péter Biró & Iain McBride, 2016. "Integer programming methods for special college admissions problems," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1371-1399, November.
    • Handle: RePEc:spr:jcomop:v:32:y:2016:i:4:d:10.1007_s10878-016-0085-x
    DOI: 10.1007/s10878-016-0085-x
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    References listed on IDEAS

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    8. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
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    Citations

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    3. Péter Biró & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Working Papers 1235, Barcelona School of Economics.
    4. Haris Aziz & Anton Baychkov & Peter Biro, 2021. "Cutoff stability under distributional constraints with an application to summer internship matching," Papers 2102.02931, arXiv.org, revised Oct 2023.
    5. Klimentova, Xenia & Biró, Péter & Viana, Ana & Costa, Virginia & Pedroso, João Pedro, 2023. "Novel integer programming models for the stable kidney exchange problem," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1391-1407.
    6. Biró, Péter & Gyetvai, Márton, 2023. "Online voluntary mentoring: Optimising the assignment of students and mentors," European Journal of Operational Research, Elsevier, vol. 307(1), pages 392-405.
    7. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    8. Csató, László & Tóth, Csaba, 2020. "University rankings from the revealed preferences of the applicants," European Journal of Operational Research, Elsevier, vol. 286(1), pages 309-320.
    9. Pitchaya Wiratchotisatian & Hoda Atef Yekta & Andrew C. Trapp, 2022. "Stability Representations of Many-to-One Matching Problems: An Integer Optimization Approach," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3325-3343, November.

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