  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.
