Accounting for fairness in a two-stage stochastic programming model for kidney exchange programs

Kidney exchange programs, which allow a potential living donor whose kidney is incompatible with his or her intended recipient to donate a kidney to another patient in return for a kidney that is compatible for their intended recipient, usually aims to maximize the number of possible kidney exchanges or the total utility of the program. However, the fairness of these exchanges is an issue that has often been ignored. In this paper, as a way to overcome the problems arising in previous studies, we take fairness to be the degree to which individual patient-donor pairs feel satisfied, rather than the extent to which the exchange increases social benefits. A kidney exchange has to occur on the basis of the value of the kidneys themselves because the process is similar to bartering. If the matched kidneys are not of the level expected by the patient-donor pairs involved, the match may break and the kidney exchange transplantation may fail. This study attempts to classify possible scenarios for such failures and incorporate these into a stochastic programming framework. We apply a two-stage stochastic programming method using total utility in the first stage and the sum of the penalties for failure in the second stage when an exceptional event occurs. Computational results are provided to demonstrate the improvement of the proposed model compared to that of previous deterministic models.