Cutting Plane Approaches for the Robust Kidney Exchange Problem

Renal patients who have a willing but incompatible donor can decide to participate in a kidney exchange program (KEP). The goal of a KEP is to identify sets of incompatible pairs that can exchange donors, leading to compatible transplants for each recipient. Significant uncertainty is involved in this process, as planned transplants may be canceled for many reasons. It is therefore crucial to take into account failures while planning exchanges. In this paper, we consider a robust variant of this problem with recourse studied in the literature that takes into account failures of donors or recipients. This problem belongs to the class of defender-attacker-defender (DAD) models. We propose a cutting plane method for solving the attacker- defender subproblem based on two commonly used mixed-integer programming formulations for kidney exchange problems. Our results imply a running time improvement of one order of magnitude compared to the state-of-the-art. Moreover, our cutting plane methods can solve many previously unsolved instances. Furthermore, we propose a new practical policy for recourse in KEPs and show that the robust optimization problem concerning this policy is tractable for small to mid-size KEPs in practice.