Maximising expectation of the number of transplants in kidney exchange programmes

•Maximisation of the expected number of transplants in kidney exchange programmes.•New schemes for the rearrangement of matchings in case of dropout or other failure.•New tree search algorithm for computing optimum expectation exchanges.•Effectiveness of the approach supported by comprehensive computational experiments

This paper addresses the problem of maximising the expected number of transplants in kidney exchange programmes. New schemes for matching rearrangement in case of failure are presented, along with a new tree search algorithm used for the computation of optimal expected values. Extensive computational experiments demonstrate the effectiveness of the algorithm and reveal a clear superiority of a newly proposed scheme, subset-recourse, as compared to previously known approaches.