An optimization framework for analyzing dual‐donor organ exchange

We study an optimal matching problem in the context of dual‐donor organ exchange, where a portion of two living donors' organs are transplanted to a single patient. This dual‐donor transplant technique is becoming more widespread for lung and liver transplants. However, multiple medical compatibility criteria pose a serious challenge for matching a patient with two compatible donors. In the United States and many other countries, laws prohibit commercial (for‐profit) deals for human organs, so donor exchanges are run by nonprofit organizations connecting donors with people in need of organs, with the goal of increasing transplant matches. We propose a simple chain mechanism in dual‐donor organ exchange to increase the number of patient–dual‐donor matches, which would maximize the number of patients receiving transplants. Based on this objective, we propose a general simple chain optimization framework for finding the maximum patient matching, taking into account multiple compatibility criteria (e.g., blood type and weight), and determine the complexity status of the problem. We provide theoretical results on the structures of simple chains, as well as a polynomial time algorithm to obtain the maximum patient matching simple chain with blood type compatibility. Through a numerical study for multiple compatibility criteria, we show that in many scenarios, a simple chain substantially increases the number of patients matched with dual donors for transplants, as opposed to exchange cycles. We also address the problem of maximizing the number of patients matched for dual‐donor organ transplants via two‐way and three‐way exchange cycles, subject to donors' and recipients' medical compatibility criteria, along with a discussion of their computational complexity. Finally, we characterize the general configurations of large n‐way exchange cycles and provide theoretical insights for their structural properties. Our findings provide general optimization models for dual‐donor organ exchange operators to increase the number of patients matched for transplant, given multiple compatibility criteria. In addition, we show how exchange operators, using simple chains, can increase patient matches and reduce simultaneous surgical resource requirements over exchange cycles.