A Constraint Programming Approach to the Hospitals / Residents Problem

Authors:
David F. Manlove;Gregg O'Malley;Patrick Prosser;Chris Unsworth
Affiliations:
Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK;Department of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK
Venue:
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2007

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Abstract

An instance Iof the Hospitals / Residents problem (HR) involves a set of residents (graduating medical students) and a set of hospitals, where each hospital has a given capacity. The residents have preferences for the hospitals, as do hospitals for residents. A solution of Iis a stable matching, which is an assignment of residents to hospitals that respects the capacity conditions and preference lists in a precise way. In this paper we present constraint encodings for HR that give rise to important structural properties. We also present a computational study using both randomly-generated and real-world instances. We provide additional motivation for our models by indicating how side constraints can be added easily in order to solve hard variants of HR.