Journal of Combinatorial Optimization

, Volume 32, Issue 4, pp 1371–1399 | Cite as

Integer programming methods for special college admissions problems

  • Kolos Csaba Ágoston
  • Péter Biró
  • Iain McBride


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.


College admissions problem Integer programming Stable score-limits Lower quotas Common quotas Paired applications Simulations 

Mathematics Subject Classification

C61 C63 C78 



Péter Biró: Supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2016), by OTKA grant no. K108673, and also by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. Iain McBride: Supported by a SICSA Prize Ph.D. Studentship.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Operations Research and Actuarial SciencesCorvinus University of BudapestBudapestHungary
  2. 2.Institute of Economics, Research Centre for Economic and Regional StudiesHungarian Academy of SciencesBudapestHungary
  3. 3.School of Computing ScienceUniversity of Glasgow Sir Alwyn Williams BuildingGlasgowUK

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