Optimal kidney exchange (OKE) is an optimization problem faced by programs for kidney paired donations (also called Kidney Exchange Programs). Such programs have large databases of patient-donor pairs, where the donor is willing to donate a kidney in order to help the patient, but cannot do so due to medical incompatibility. The centers try to arrange exchanges between such pairs. For example, the donor in pair A donates to the patient in pair B, the donor in pair B donates to the patient in pair C, and the donor in pair C donates to the patient in pair A.
The objective of the OKE problem is to find an optimal arrangement of such exchanges. "Optimal" usually means that the number of transplants is as large as possible, but there may be other objectives. A crucial constraint in this optimization problem is that a donor gives a kidney only if his patient receives a compatible kidney, so that no pair loses a kidney from participating. This requirement is sometimes called individual rationality.
The OKE problem has many variants, which differ in the allowed size of each exchange, the objective function, and other factors.[1]
^Ashlagi, Itai; Roth, Alvin E. (2021-09-01). "Kidney Exchange: An Operations Perspective". Management Science. 67 (9): 5455–5478. doi:10.1287/mnsc.2020.3954. ISSN 0025-1909.
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