Stability in the hospitals/residents problem with couples and ties: Mathematical models and computational studies

In the well-known Hospitals/Residents problem (HR), objective is to find a stable matching of doctors (or residents) hospitals based on their preference lists. this paper, we study HRCT, extension HR in which are allowed apply couples, and can include ties We first review three stability definitions that have been proposed literature for HRC (the restriction HRCT where not allowed) extend them HRCT. show such extensions may bring undesirable behaviour introduce new definition specifically designed then unified Integer Linear Programming (ILP) models, only minor changes required switch from one other. propose improvements decrease average solution time each ILP model preprocessing, dummy variables, valid inequalities. our models be solved more than hundred times faster when these used. addition, also chosen has impact quality (average size) obtain solution, but specific set instances, matchings significantly less likely exist particular compared other definitions. provide insights relating how certain parameters as tie density, number difference between positions available doctors, might affect size.