“…These allow for a larger number of kidney transplants (compared to those one could perform based on deceased donors only) and thus more lives saved. Centralised clearinghouses for kidney exchange are in operation on a nationwide scale in a number of countries including the US (Roth et al, 2004(Roth et al, , 2005Ashlagi and Roth, 2012), The Netherlands (Keizer et al, 2005) and the UK (Johnson et al, 2008). The problem of maximising the number of kidney transplants performed through cycles and chains is NP-hard (Abraham et al, 2007a), though algorithms based on Mixed Integer Programming have been developed and are used to solve this problem at scale in the countries mentioned (Abraham et al, 2007a;Dickerson et al, 2013;Manlove and O'Malley, 2012;Glorie et al, 2014).…”