Kidney exchange programs (KEP's) represent an additional possibility of transplant for patients suffering from end stage kidney disease. If a patient has a willing living donor with whom the patient is not compatible, the pair patient-donor can join a pool of incompatible pairs and, if compatibility between patient and donor in two our more pairs exists, organs can be exchanged between them. The problem can be modeled as an integer program that, in general, aims * This work is financed by the ERDF -European Regional Development Fund through the Operational Programme for Competitiveness and Internationalization -COMPETE 2020 Programme, and by National Funds through the Portuguese funding agency, FCT -Fundação para a Ciência e a Tecnologia, within project "mKEP -Models and optimization algorithms for multicountry kidney exchange programs" (POCI-01-0145-FEDER-016677), by COST Action CA15210 ENCKEP, supported by COST (European Cooperation in Science and Technology) -http://www.cost.eu/. Biró is supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3), and by the Hungarian Scientific Research Fund -OTKA (no. K129086).