Kidney exchange now has a broad literature across multiple disciplines

 One pleasure of following an area of research for a long time is getting to see how its academic literature becomes both deeper and broader.  That's certainly been the case with kidney exchange, which now has (of course) a big medical literature, but has also spurred research in the economics and operations research communities.  Here's a recent survey of the OR literature:

Barkel, M., Colley, R., Delorme, M., Manlove, D., & Pettersson, W. (2025). Operational research approaches and mathematical models for kidney exchange: A literature survey and empirical evaluation. European Journal of Operational Research. 

Abstract: "Kidney exchange is a transplant modality that has provided new opportunities for living kidney donation in many countries around the world since 1991. It has been extensively studied from an Operational Research (OR) perspective since 2004. This article provides a comprehensive literature survey on OR approaches to fundamental computational problems associated with kidney exchange over the last two decades. We also summarise the key integer linear programming (ILP) models for kidney exchange, showing how to model optimisation problems involving only cycles and chains separately. This allows new combined ILP models, not previously presented, to be obtained by amalgamating cycle and chain models. We present a comprehensive empirical evaluation involving all combined models from this paper in addition to bespoke software packages from the literature involving advanced techniques. This focuses primarily on computation times for 49 methods applied to 4320 problem instances of varying sizes that reflect the characteristics of real kidney exchange datasets, corresponding to over 200,000 algorithm executions. We have made our implementations of all cycle and chain models described in this paper, together with all instances used for the experiments, and a web application to visualise our experimental results, publicly available. "

 

"The first papers to study algorithms or mechanisms for KE-Opt were the landmark papers of Roth et al., 2004, Roth et al., 2005. When the objective is to maximise the number of transplants, KE-Opt is 
-hard in general (Abraham et al., 2007).

... 

 

"The main contributions of this survey paper are as follows:
 

•A detailed literature survey (with over 210 references) of OR approaches to KE-Opt, covering the following topics: algorithms and complexity for KE-Opt; hierarchical optimisation in KE-Opt; enabling equal access to transplantation; dynamic KEPs; uncertainty and robustness in KEPs; multi-hospital and international KEPs; recipients’ preferences; dataset generators and software tools; emerging topics; and other related surveys.
•A systematic exposition of all the key existing ILP approaches for KE-Opt, describing separately models for representing optimal solutions comprising only cycles from those comprising only chains. As a consequence, combined ILP models for KE-Opt can be obtained by mixing a cycle model with a chain model. We also use a running example (appearing in the Supplementary Material) to illustrate all models for the benefit of the reader. 

•A comprehensive empirical evaluation of all combined ILP models for KE-Opt that are described in this paper, together with “off-the-shelf” approaches involving advanced techniques such as column generation and branch-and-price, where we have been able to obtain and execute the third-party software. The main aim is to compare execution times of the different approaches considered on randomly generated datasets that reflect the characteristics of real data from the UK’s KEP. In particular, we tested 49 methods on 4320 instances, corresponding to over 200,000 algorithm executions, and amounting to over 10 years of computational processing time in total, across multiple cores running in parallel.
•An interactive tool to allow the reader to analyse the data resulting from our experiments that is publicly available at https://optimalmatching.com/kep-survey-2025, allowing custom heatmaps to be created by varying instance sets, models to be considered and measures of performance.
•All of the implementations of the combined cycle and chain ILP models presented in this paper are available for the reader to access at https://doi.org/10.5281/zenodo.14905243, and the benchmark instances used for the experiments are available for download at https://doi.org/10.5525/gla.researchdata.1878."