Integer programming methods for special college admissions problems

TL;DR

This paper develops Integer Programming solutions for complex college admission problems with special features, offering a potential alternative to existing heuristics and advancing the theoretical understanding of such NP-hard problems.

Contribution

It introduces IP methods tailored for special college admission problems, addressing features that make them NP-hard, and proposes an alternative to heuristic solutions.

Findings

IP methods effectively solve certain special admission problems

The approach offers a theoretical and practical alternative to heuristics

Potential applicability to other NP-hard matching problems

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 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 also for other ones.