A bi-level programming model for kidney exchange program

Kidney exchange, also called kidney paired donation (KPD), provides a context in which incompatible patient–donor pairs (PDPs) are allowed to exchange donors through cycles or chains initiated by altruistic donors (NDDs) to receive a compatible donor. Graph theory provides a frame work to illustrate the problem, which will be modeled and optimized by mathematical optimization. In this paper, we propose a bi-level model to maximize not only the number of transplantations, but also the overall efficiency of transplants.