Cutting Plane Approaches for the Robust Kidney Exchange Problem

TL;DR

This paper introduces a cutting plane approach to solve a robust kidney exchange problem accounting for donor and recipient failures, significantly improving solution times and handling larger instances.

Contribution

It proposes a novel cutting plane method for the attacker-defender subproblem in robust kidney exchange, enhancing computational efficiency and scalability.

Findings

One order of magnitude faster than previous methods

Can solve many previously unsolvable instances

Proposes a practical recourse policy for KEPs

Abstract

Renal patients which 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 such incompatible pairs that can exchange donors, leading to compatible transplants for each recipient. There is significant uncertainty involved in this process, as planned transplants may be canceled for a plethora of 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 vertex failures, i.e., withdrawing donors and/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. 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 a large number of 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.