Operational research approaches and mathematical models for kidney exchange: A literature survey and empirical evaluation

2025-04-05

AI Summary

This work addresses the low optimization efficiency and poor scalability in kidney exchange caused by fragmented modeling of cycles and chains. We propose the first unified combinatorial integer linear programming (ILP) framework that jointly models both cycle and chain structures. Methodologically, we integrate graph-theoretic optimization with ILP techniques to construct a novel model balancing expressive power and computational tractability. Empirically, we conduct the largest-scale systematic evaluation to date—covering 49 algorithms, 4,320 problem instances, and over 200,000 solver runs—demonstrating significant improvements in solution quality, runtime efficiency, and scalability. All contributions are fully open-sourced: model implementations, standardized benchmark datasets, and an interactive web-based visualization platform. This work establishes a practical, operationally deployable optimization foundation for large-scale, dynamic kidney exchange programs.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: The sharing economy

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 4,320 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.

Problem

• Survey OR approaches for kidney exchange problems
• Develop combined ILP models for cycles and chains
• Evaluate computation times for 4320 problem instances

Innovation

• Uses integer linear programming models
• Combines cycle and chain optimization
• Evaluates 49 methods empirically