  In Kidney Exchange Programs (KEPs), each participating patient is registered
together with an incompatible donor. Donors without an incompatible patient can
also register. Then, KEPs typically maximize overall patient benefit through
donor exchanges. This aggregation of benefits calls into question potential
individual patient disparities in terms of access to transplantation in KEPs.
Considering solely this utilitarian objective may become an issue in the case
where multiple exchange plans are optimal or near-optimal. In fact, current KEP
policies are all-or-nothing, meaning that only one exchange plan is determined.
Each patient is either selected or not as part of that unique solution. In this
work, we seek instead to find a policy that contemplates the probability of
patients of being in a solution. To guide the determination of our policy, we
adapt popular fairness schemes to KEPs to balance the usual approach of
maximizing the utilitarian objective. Different combinations of fairness and
utilitarian objectives are modelled as conic programs with an exponential
number of variables. We propose a column generation approach to solve them
effectively in practice. Finally, we make an extensive comparison of the
different schemes in terms of the balance of utility and fairness score, and
validate the scalability of our methodology for benchmark instances from the
literature.
