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

Abstract

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).