An integer programming approach to the Hospitals/Residents problem with ties

Kwanashie, A. and Manlove, D. F. (2014) An integer programming approach to the Hospitals/Residents problem with ties. In: Operations Research Proceedings 2013: Selected Papers of the International Conference on Operations Research, OR2013. Series: Operations Research Proceedings. Springer International Publishing, pp. 263-269. ISBN 9783319070001 (doi: 10.1007/978-3-319-07001-8_36)

Abstract

The classical Hospitals/Residents problem (HR) models the assignment of junior doctors to hospitals based on their preferences over one another. In an instance of this problem, a stable matching M is sought which ensures that no blocking pair can exist in which a resident r and hospital h can improve relative to M by becoming assigned to each other. Such a situation is undesirable as it could naturally lead to r and h forming a private arrangement outside of the matching. The original HR model assumes that preference lists are strictly ordered. However in practice, this may be an unreasonable assumption: an agent may find two or more agents equally acceptable, giving rise to ties in its preference list. We thus obtain the Hospitals/Residents problem with Ties (HRT). In such an instance, stable matchings may have different sizes and MAX HRT, the problem of finding a maximum cardinality stable matching, is NP-hard. In this paper we describe an Integer Programming (IP) model for MAX HRT. We also provide some details on the implementation of the model. Finally we present results obtained from an empirical evaluation of the IP model based on real-world and randomly generated problem instances.

• Item Type: Book Sections
• Additional Information: International Conference on Operations Research (OR2013), Rotterdam, 3-6 Sept. 2013.<p></p> The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-319-07001-8_36 <p></p>
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Manlove, Professor David and Kwanashie, Mr Augustine
• Authors: Kwanashie, A., and Manlove, D. F.
• College/School: College of Science and Engineering > School of Computing Science
• Publisher: Springer International Publishing
• ISSN: 0721-5924
• ISBN: 9783319070001
• Copyright Holders: Copyright © 2014 Springer International Publishing
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher.
• Data DOI: 10.5525/gla.researchdata.244