Paired and altruistic kidney donation in the UK: Algorithms and experimentation

We study the computational problem of identifying optimal sets of kidney exchanges in the UK. We show how to expand an integer programming-based formulation due to Roth et al. [2007] in order to model the criteria that constitute the UK definition of optimality. The software arising from this work has been used by the National Health Service Blood and Transplant to find optimal sets of kidney exchanges for their National Living Donor Kidney Sharing Schemes since July 2008. We report on the characteristics of the solutions that have been obtained in matching runs of the scheme since this time. We then present empirical results arising from experiments on the real datasets that stem from these matching runs, with the aim of establishing the extent to which the particular optimality criteria that are present in the UK influence the structure of the solutions that are ultimately computed. A key observation is that allowing four-way exchanges would be likely to lead to a moderate number of additional transplants

Modelling and optimisation in European Kidney Exchange Programmes

The complex multi-criteria optimisation problems arising in Kidney Exchange Programmes have received considerable attention both in practice and in the scientific literature. Whereas theoretical advancements are well reviewed and synthesised, this is not the case for practice. We present a synthesis of models and methods applied in present European Kidney Exchange Programmes, which is based on detailed descriptions we created for this purpose. Most descriptions address national programmes, yet we also present findings on emerging cross-national programmes. The synthesis provides a systematic and detailed description of the mo

Modelling and optimisation in European Kidney Exchange Programmes

The complex multi-criteria optimisation problems arising in Kidney Exchange Programmes have received considerable attention both in practice and in the scientific literature. Whereas theoretical advancements are well reviewed and synthesised, this is not the case for practice. We present a synthesis of models and methods applied in present European Kidney Exchange Programmes, which is based on detailed descriptions we created for this purpose. Most descriptions address national programmes, yet we also present findings on emerging cross-national programmes. The synthesis provides a systematic and detailed description of the models and methods the programmes use, revealing important commonalities as well as considerable variation among them. Rather than distilling a single best practice from these results, we find that the variation in models and methods arises because of variation in country characteristics, policies, and ethics. The synthesised state of the art may benefit future national and cross-national initiatives and direct future theoretical contributions within and across the boundaries of the Operations Research discipline

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Existing exact solution methods for KEP either are designed for the case where only cyclic exchanges are considered, or can handle long chains but are scalable as long as cycles are short. We develop the first decomposition method that is able to deal with long cycles and long chains for large realistic instances. More specifically, we propose a branch-and-price framework, in which the pricing problems are solved (for the first time in packing problems in a digraph) through multi-valued decision diagrams. Also, we present a new upper bound on the optimal value of KEP, stronger than the one proposed in the literature, which is obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths