Integer programming methods for special college admissions problems

Ágoston, Kolos Csaba; Bíró, Péter; McBride, Iain

doi:10.1007/s10878-016-0085-x

Cited by 22 publications

(16 citation statements)

References 28 publications

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“…The applicant knows that (s)he has no chance to be admitted to the state-financed programme of faculty , but (s)he wants to avoid paying the tuition, therefore her list contains the state-financed programme of faculty in the first place, the student-financed programme of faculty in the second, and the student-financed programme of faculty in the third position. Then our technique concludes that facultý Agoston et al, 2016). Consequently, it remains strategy-proof only essentially, for example, when the applicants believe they have no chance to influence the score limits.…”

Section: Recovering Preferences From the List Of Applicationsmentioning

confidence: 95%

University rankings from the revealed preferences of the applicants

Csató

Tóth

2020

European Journal of Operational Research

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A methodology is presented to rank universities on the basis of the lists of programmes the students applied for. We exploit a crucial feature of the centralised assignment system to higher education in Hungary: a student is admitted to the first programme where the score limit is achieved. This makes it possible to derive a partial preference order of each applicant. Our approach integrates the information from all students participating in the system, is free of multicollinearity among the indicators, and contains few ad hoc parameters. The procedure is implemented to rank faculties in the Hungarian higher education between 2001 and 2016. We demonstrate that the ranking given by the least squares method has favourable theoretical properties, is robust with respect to the aggregation of preferences, and performs well in practice. The suggested ranking is worth considering as a reasonable alternative to the standard composite indices.

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Section: Recovering Preferences From the List Of Applicationsmentioning

confidence: 95%

University rankings from the revealed preferences of the applicants

Csató

Tóth

2020

European Journal of Operational Research

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“…Variables y c ik and y f jk can be seen as a replacement of the summations of x iq and x pj over the sets F ≤ j (i) and C ≤ i (j). These variables have certain similarities with the cut-off scores for the college admission problem [2] and the radius formulation for the p-median problem [13].…”

Section: Reducing the Number Of Non-zero Elementsmentioning

confidence: 99%

“…Similar to the case for kidney exchange programmes [39], this allows for a more efficient pairing of children and families, at the cost of a slightly increased delay between entering the system and being paired. In such a system Coram has decided that the goal should be to find a stable matching that pairs as many children as possible and/or has maximum overall weight 2 . Moreover, Coram would like to ensure that the computed matching is viable in the long term.…”

Section: Introduction 1backgroundmentioning

confidence: 99%

Mathematical models for stable matching problems with ties and incomplete lists

Delorme

García

Gondzio

et al. 2019

European Journal of Operational Research

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We present new integer linear programming (ILP) models for N P-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from real-world applications, and (ii) larger instances that are randomlygenerated. In the case of SMTI, we consider instances arising from the pairing of children with adoptive families, where preferences are obtained from a quality measure of each possible pairing of child to family. In this case we seek a maximum weight stable matching. We present new algorithms for preprocessing instances of SMTI with ties on both sides, as well as new ILP models. Algorithms based on existing state-of-the-art models only solve 6 of our 22 real-world instances within an hour per instance, and our new models incorporating dummy variables and constraint merging, together with preprocessing and a warm start, solve all 22 instances within a mean runtime of a minute. For HRT, we consider instances derived from the problem of assigning junior doctors to foundation posts in Scottish hospitals. Here we seek a maximum size stable matching. We show how to extend our models for SMTI to HRT and reduce the average running time for real-world HRT instances by two orders of magnitude. We also show that our models outperform by a wide margin all known state-of-the-art models on larger randomly-generated instances of SMTI and HRT.

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“…Similarly encouraging results have been obtained for some special college admission problems, which are present in the Hungarian higher education system. These special features also makes the problem NP-hard in general, but at least one of these challenging features, turned out to be solvable even in a real data involving more than 150,000 applicants [6]. Finally, the last paper that we highlight with regard to this topic deals with the problem of finding stable solutions in the presence of ties [31].…”

Section: Introductionmentioning

confidence: 98%

Stable project allocation under distributional constraints

Ágoston

Bíró

Szántó

2018

Operations Research Perspectives

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In a two-sided matching market when agents on both sides have preferences the stability of the solution is typically the most important requirement. However, we may also face some distributional constraints with regard to the minimum number of assignees or the distribution of the assignees according to their types. These two requirements can be challenging to reconcile in practice. In this paper we describe two real applications, a project allocation problem and a workshop assignment problem, both involving some distributional constraints. We used integer programming techniques to find reasonably good solutions with regard to the stability and the distributional constraints. Our approach can be useful in a variety of different applications, such as resident allocation with lower quotas, controlled school choice or college admissions with affirmative action.

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Integer programming methods for special college admissions problems

Cited by 22 publications

References 28 publications

University rankings from the revealed preferences of the applicants

University rankings from the revealed preferences of the applicants

Mathematical models for stable matching problems with ties and incomplete lists

Stable project allocation under distributional constraints

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