A mathematical programming approach to paired kidney exchange: the case of Turkey

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Background: Kidney exchange has become a very common and important treatment alternative for patients suffering from serious kidney diseases with incompatible donors. Factors such as blood type, HLA matches and PRA existence are considered to determine compatibility. In a paired exchange, two incompatible patient-donor pairs switch their donors who are compatible with the other recipient. Currently, each hospital in Turkey operates individually in a decentralized manner using its own list. This list may contain patients having more than one incompatible donor, which differentiates the current work from those existing in literature. Methods: In this study, mathematical models are developed to propose an easy and practical approach for the paired kidney exchange problem in Turkey. Data are generated by employing a real data set provided by a hospital specialized in kidney transplantation. Results: The optimal solutions are obtained by using GAMS/CPLEX, and different scenario analyses are performed to measure the impact of "gender differences" and "age" on the solution. Furthermore, the original patient-donor list provided by the hospital is used to compare the model's solution with the planned transplantations. The study also evaluates a centralized approach which integrates all hospitals performing paired kidney exchange in Istanbul. Conclusions: As the optimal solution of the model is obtained in a basis of seconds, the developed approach offers an easy and applicable procedure for paired kidney exchange. Comparison of decentralized and centralized approaches reveals that the centralized approach is more favorable in terms of HLA compatibility and number of transplantations.



OR in health services, paired kidney exchange, living donor, mathematical modelling