  Algorithms for exchange of kidneys is one of the key successful applications
in market design, artificial intelligence, and operations research. Potent
immunosuppressant drugs suppress the body's ability to reject a transplanted
organ up to the point that a transplant across blood- or tissue-type
incompatibility becomes possible. In contrast to the standard kidney exchange
problem, we consider a setting that also involves the decision about which
recipients receive from the limited supply of immunosuppressants that make them
compatible with originally incompatible kidneys. We firstly present a general
computational framework to model this problem. Our main contribution is a range
of efficient algorithms that provide flexibility in terms of meeting meaningful
objectives. Motivated by the current reality of kidney exchanges using
sophisticated mathematical-programming-based clearing algorithms, we then
present a general but scalable approach to optimal clearing with
immunosuppression; we validate our approach on realistic data from a large
fielded exchange.
