Optimization models and methods for kidney transplantation programs

Kidney transplantation can occur in two different settings: the organ to be transplanted can be removed either from a deceased donor or from a living donor. When a patient has the opportunity to receive a transplant from a living donor, it is the preferred treatment since it offers the highest chance of success. However, for a donor and a patient to be medically compatible, several conditions must be met, and in some cases, patients are unable to receive a kidney from their associated healthy donor, but they can possibly receive a kidney from another compatible donor. Programs have been set up in many countries, or associations of countries, for the benefit of patients who lost both of their kidneys’ function and require a transplant. In the case of living donor transplantations, kidney exchange programs aim to identify exchanges between incompatible patient-donor pairs, while in the case of deceased donor transplantations, the programs aim to allocate the deceased donor kidneys to a waiting list of patients under some allocation rules.
This dissertation addresses problems related to both cases. In particular, we explore combinatorial optimization problems and mathematical models related to living donor kidney transplantation by considering two variants of the basic problem encountered by kidney exchange programs. The problems discussed are handled from a mathematical perspective through the provision of integer linear programming formulations and the discussion of the computational complexity of the problems, among other results. Furthermore, numerical experiments are presented to assess and to test the theoretical results and to compare our work to recent literature. Finally, we also discuss modeling questions related to the operations of a deceased donor transplantation program.