Robust dynamic optimization with application to kidney exchange

Kidney exchange provides a life-saving alternative to long waiting lists for patients in need of a new kidney. We derive a variety of mathematical models for the kidney exchange optimization problem, where the general goal is to maximize some form of social welfare vis-à-vis transplanting kidneys. We explore the implications of making the optimization problem dynamic (considering the future evolution of the exchange pool when optimizing now), failure-aware (where possible post-algorithmic match failures are accounted for), and fairness-aware (losing overall efficiency at the cost of a more balanced matching). Our goal is to provide an empirically grounded framework that combines each of these dimensions in a theoretically sound way. We support our models with real results from one of the largest fielded kidney exchanges in the world.