An Integer Programming Model for the Hospitals/Residents Problem with Couples

  • Iain McBrideEmail author
  • David F. Manlove
Conference paper
Part of the Operations Research Proceedings book series (ORP)


The Hospitals/Residents problem with Couples (hrc) is a generalisation of the classical Hospitals/Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc. Further, we present an Integer Programming (IP) model for hrc and extend it the case where preference lists can include ties. Further, we describe an empirical study of an IP model for HRC and its extension to the case where preference lists can include ties. This model was applied to randomly generated instances and also real-world instances arising from previous matching runs of the Scottish Foundation Allocation Scheme, used to allocate junior doctors to hospitals in Scotland.



Iain McBride: Supported by a SICSA Prize PhD Studentship. David F. Manlove: Supported by Engineering and Physical Sciences Research Council grant GR/EP/ K010042/1.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of Computing ScienceUniversity of GlasgowGlasgowUK

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