Impact Of Additional Donors in Lung Exchange

In this thesis, we mainly focus on lung exchange. There are significant differences between lung and kidney exchanges. While in kidney exchange patients come with a single donor, lung exchange often requires two donors. Incompatible patient-donor-donor triples can exchange donor lungs with other triples.We consider a model in which some patients bring three donors; one is compatible and two are incompatible with themselves. We design a two stage mechanism to show that bringing additional donor to the exchange pool will improve effi- ciency of the matching system through increasing number of patients that can be matched. Additionally, we provide a necessary condition that shows when allowing additional donors can also reduce the number of necessary transplant teams to run the exchange sequence, and therefore increase,what we call, implementational efficiency.