Here's a survey that puts some emphasis on the many changes in the design of kidney exchange operations and processes that have moved it from its small beginnings to its current situation facilitating annual transplants in the thousands, and might help to scale it up further, since the supply of transplants is still far short of the need.
Kidney Exchange: an Operations Perspective
Itai Ashlagi and Alvin E. Roth
May 2020
Abstract: Many patients in need of a kidney transplant have a willing but incompatible living donor. Kidney exchange programs arrange exchanges among such incompatible patient-donor pairs, in cycles and chains of exchange, so each patient receives a compatible kidney. Kidney exchange has become a standard form of transplantation in the United States and a few other countries, in large part because of continued attention to the operational details that arose as obstacles were overcome and new obstacles became relevant. We review some of the key operational issues in the design of successful kidney exchange programs. Kidney exchange has yet to reach its full potential, and the paper further describes some open questions that we hope will continue to attract attention from researchers interested in the operational aspects of dynamic exchange.
Here's the concluding paragraph:
"Looking back, kidney exchange has accomplished a lot, but not nearly enough. The number of people waiting for a kidney transplant is growing, despite the growth of exchange. But there is room for kidney exchange to continue to grow and to increase the availability of transplants further, by designing international kidney exchanges, by starting chains with deceased donor kidneys, and by introducing other market design innovations that have yet to be explored or even conceived."
Kidney Exchange: an Operations Perspective
Itai Ashlagi and Alvin E. Roth
May 2020
Abstract: Many patients in need of a kidney transplant have a willing but incompatible living donor. Kidney exchange programs arrange exchanges among such incompatible patient-donor pairs, in cycles and chains of exchange, so each patient receives a compatible kidney. Kidney exchange has become a standard form of transplantation in the United States and a few other countries, in large part because of continued attention to the operational details that arose as obstacles were overcome and new obstacles became relevant. We review some of the key operational issues in the design of successful kidney exchange programs. Kidney exchange has yet to reach its full potential, and the paper further describes some open questions that we hope will continue to attract attention from researchers interested in the operational aspects of dynamic exchange.
Here's the concluding paragraph:
"Looking back, kidney exchange has accomplished a lot, but not nearly enough. The number of people waiting for a kidney transplant is growing, despite the growth of exchange. But there is room for kidney exchange to continue to grow and to increase the availability of transplants further, by designing international kidney exchanges, by starting chains with deceased donor kidneys, and by introducing other market design innovations that have yet to be explored or even conceived."