A compact formulation for maximizing the expected number of transplants in kidney exchange programs

Kidney exchange programs (KEPs) allow the exchange of kidneys between incompatible donor-recipient pairs. Optimization approaches can help KEPs in defining which transplants should be made among all incompatible pairs according to some objective. The most common objective is to maximize the number of transplants. In this paper, we propose an integer programming model which addresses the objective of maximizing the expected number of transplants, given that there are equal probabilities of failure associated with vertices and arcs. The model is compact, i.e. has a polynomial number of decision variables and constraints, and therefore can be solved directly by a general purpose integer programming solver (e.g. Cplex).This work is financed by the ERDF — European Regional Development Fund through the COMPETE Programme (operational programm for competitiveness), by National Funds through the FCT — Funda¸c˜ao para a Ciˆencia e a Tecnologia (Portuguese Foundation for Science and Technology) within project “KEP - New models for enhancing the kidney transplantation process. FCT ref: PTDC/EGE-GES/110940/2009”, by the North Portugal Regional Operational Programme (ON.2 O Novo Norte), under the National Strategic Reference Framework (NSRF), through the European Regional Development Fund (ERDF), and by national funds through FCT within project ”NORTE-07-0124-FEDER-000057”. This work has also been supported by FCT — Funda¸c˜ao para a Ciˆencia e a Tecnologia (Portuguese Foundation for Science and Technology) within project scope: PEst-OE/EEI/UI0319/2014.info:eu-repo/semantics/publishedVersio