2019
DOI: 10.1016/j.ejor.2019.03.017
|View full text |Cite
|
Sign up to set email alerts
|

Mathematical models for stable matching problems with ties and incomplete lists

Abstract: 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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
24
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
5
3
2

Relationship

0
10

Authors

Journals

citations
Cited by 42 publications
(30 citation statements)
references
References 40 publications
0
24
0
Order By: Relevance
“…In particular, for Gale and Shapley's [20] college admissions model, Baïou and Balinski [5] already described the stable admissions polytope, which can be used as a basic IP formulation. Further recent papers in this line of research focused on college admissions with special features [3], stable project allocation under distributional constraints [4], the hospital-resident problem with couples [9], and ties [30,17].…”
Section: Literature Reviewmentioning
confidence: 99%
“…In particular, for Gale and Shapley's [20] college admissions model, Baïou and Balinski [5] already described the stable admissions polytope, which can be used as a basic IP formulation. Further recent papers in this line of research focused on college admissions with special features [3], stable project allocation under distributional constraints [4], the hospital-resident problem with couples [9], and ties [30,17].…”
Section: Literature Reviewmentioning
confidence: 99%
“…However, there can be some special features that can make the stable matching problem computationally hard to solve. In this case one robust approach to tackle these problems is (mixed) integer linear programming, that has been used recently for the hospital-resident problem with couples [11], ties [22,17], college admissions with lower and common quotas [4], and stable project allocation under distributional constraints [5]. In this paper we also use MILP technique for solving the underlying optimisation problem.…”
Section: Related Literaturementioning
confidence: 99%
“…Let z a,p be the score of applicant a at project p, a given constant integer in the interval [0,|A|]. For every project p, let d(p) be an integer variable in the range of [0,|A| + 1] denoting the cutoff of project p. We can link the cutoff scores with the induced matching M by the following set of constraints, as also used in Ágoston et al [2016] and Delorme et al [2019]. d(p) ≤ (1−y a,p )(|A|+1)+z a,p for each (a,p) (4) The above constraint enforces that if an applicant is assigned to a project then she reached the cutoff there.…”
Section: Milp-formulationmentioning
confidence: 99%