Abstract
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.
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References
Aldershof, B., & Carducci, O. M. (1996). Stable matching with couples. Discrete Applied Mathematics, 68, 203–207.
Biró, P., Irving, R. W., & Schlotter, I. (2011). Stable matching with couples: An empirical study. ACM Journal of Experimental Algorithmics, 16, Section 1, article 2, 27 p.
Gusfield, D., & Irving, R. W. (1989). The stable marriage problem: Structure and algorithms. Cambridge: MIT Press.
McBride, I., & Manlove, D. F. (2013). The hospitals/residents problem with couples: Complexity and integer programming models. Technical Report, Computing Research Repository, Cornell University Library.
McDermid, E. J., & Manlove, D. F. (2010). Keeping partners together: Algorithmic results for the hospitals/residents problem with couples. Journal of Combinatorial Optimization, 19(3), 279–303.
Ng, C., & Hirschberg, D. S. (1991). Three-dimensional stable matching problems. SIAM Journal on Discrete Mathematics, 4, 245–252.
Ronn, E. (1990). NP-complete stable matching problems. Journal of Algorithms, 11, 285–304.
Roth, A. E. (1984). The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy, 92(6), 991–1016.
Roth, A. E. (1990). New physicians: A natural experiment in market organization. Science, 250, 1524–1528.
Acknowledgments
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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McBride, I., Manlove, D.F. (2014). An Integer Programming Model for the Hospitals/Residents Problem with Couples. In: Huisman, D., Louwerse, I., Wagelmans, A. (eds) Operations Research Proceedings 2013. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-07001-8_40
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DOI: https://doi.org/10.1007/978-3-319-07001-8_40
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