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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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    1. 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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    3. Péter Biró & Sofya Kiselgof, 2015. "College admissions with stable score-limits," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(4), pages 727-741, December.
    4. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
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    7. Yuichiro Kamada & Fuhito Kojima, 2012. "Stability and Strategy-Proofness for Matching with Constraints: A Problem in the Japanese Medical Match and Its Solution," American Economic Review, American Economic Association, vol. 102(3), pages 366-370, May.
    8. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, vol. 81(3), pages 415-440, June.
    9. Fleiner, Tamas, 2003. "On the stable b-matching polytope," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 149-158, October.
    10. Péter Biró & Flip Klijn, 2013. "Matching With Couples: A Multidisciplinary Survey," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 1-18.
    11. Alvin E. Roth & Uriel G. Rothblum & John H. Vande Vate, 1993. "Stable Matchings, Optimal Assignments, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 803-828, November.
    12. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    13. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
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    Cited by:

    1. P'eter Bir'o & M'arton Gyetvai, 2021. "Online voluntary mentoring: Optimising the assignment of students and mentors," Papers 2102.06671, arXiv.org.
    2. Delorme, Maxence & García, Sergio & Gondzio, Jacek & Kalcsics, Jörg & Manlove, David & Pettersson, William, 2019. "Mathematical models for stable matching problems with ties and incomplete lists," European Journal of Operational Research, Elsevier, vol. 277(2), pages 426-441.
    3. 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.
    4. 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.
    5. 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.
    6. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
    7. 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.
    8. 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.
    9. L'aszl'o Csat'o & Csaba T'oth, 2018. "University rankings from the revealed preferences of the applicants," Papers 1810.04087, arXiv.org, revised Feb 2020.
    10. P'eter Bir'o & Avinatan Hassidim & Assaf Romm & Ran I. Shorrer & S'andor S'ov'ag'o, 2020. "The Large Core of College Admission Markets: Theory and Evidence," Papers 2010.08631, arXiv.org, revised Aug 2022.
    11. 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.
    12. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.
    13. 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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    More about this item

    Keywords

    College admissions problem; Integer programming; Stable score-limits; Lower quotas; Common quotas; Paired applications; Simulations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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