| Sumario: | The application of Operations Research in the medical field has been the key to save more lives in a variety of decision-making problems. With the aid of mathematical models and algorithms developed for specific problems, we can now develop plans and polices, and take decisions that can lead to optimal or near optimal solutions. This is the case of the Kidney Exchange Problem addressed in this thesis. Recently, a new idea has arisen for those patients with renal disease in need of a transplant and have a willing but incompatible donor. Let us suppose we have two incompatible patient-donor pairs (PDPs), that is, in each pair, the donor is not compatible (blood type or crossmatch) with the recipient; however, the donor of pair A is compatible with the recipient of pair B, and the donor of pair B is compatible with the recipient of pair A. Then they can swap kidneys and both pairs would benefit from this exchange. This exchange is called a cycle and has cardinality.
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