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Optimal Control of a Paired-Kidney Exchange Program


  • Stefanos A. Zenios

    () (Graduate School of Business, Stanford University, Stanford, California 94305)


Organ exchanges are expected to increase the utilization of living donors and to alleviate the critical shortage of organs for transplantation. The typical arrangement involves a direct exchange between two blood-type incompatible donor-candidate pairs. An alternate possibility is an indirect exchange between one such pair and the highest priority candidate on the regular waiting list for cadaveric organs. This paper focuses on the mix of direct and indirect exchanges that maximizes the expected total discounted quality-adjusted life years (QALY) of the candidates in the participating pairs. Direct exchanges are preferable because the candidate receives a living-donor organ instead of the inferior cadaveric organ an indirect exchange provides. However, the latter involves a shorter wait. To capture this tradeoff, we develop a double-ended queueing model for an exchange system with two types of donorcandidate pairs, and obtain an optimal dynamic exchange policy by invoking a Brownian approximation. The policy takes the form of a two-sided regulator in which new pairs will join the exchange system to wait for a direct exchange if and only if the process modeling the exchange system is within the regulator's two barriers. In all other circumstances, new pairs will participate in an indirect exchange. Expressions for the optimal barriers are obtained under a variety of assumptions about the objective function, including one of complete candidate autonomy. The analysis identifies three design principles that will amplify the likelihood of an exchange program's success. First, exchange programs must involve the coordinated activities of multiple local transplant centers to enjoy the substantial benefits of resource pooling. Second, participant wait must be controlled through indirect exchanges. Third, the program must respect participants' autonomy and weigh that autonomy against the broader goal of maximizing their overall welfare.

Suggested Citation

  • Stefanos A. Zenios, 2002. "Optimal Control of a Paired-Kidney Exchange Program," Management Science, INFORMS, vol. 48(3), pages 328-342, March.
  • Handle: RePEc:inm:ormnsc:v:48:y:2002:i:3:p:328-342

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    References listed on IDEAS

    1. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
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    Cited by:

    1. Caulkins, Jonathan P., 2010. "Might randomization in queue discipline be useful when waiting cost is a concave function of waiting time?," Socio-Economic Planning Sciences, Elsevier, vol. 44(1), pages 19-24, March.
    2. Antonio Nicolò & Carmelo Rodríguez Álvarez, 2013. "Age based preferences in paired kidney exchange," Documentos de Trabajo del ICAE 2013-38, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    3. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Choosing Among Living-Donor and Cadaveric Livers," Management Science, INFORMS, vol. 53(11), pages 1702-1715, November.
    4. Tayfun Sönmez & M. Utku Ünver, 2009. "Matching, Allocation, and Exchange of Discrete Resources," Boston College Working Papers in Economics 717, Boston College Department of Economics.
    5. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    6. Yılmaz, Özgür, 2014. "Kidney exchange: Further utilization of donors via listed exchange," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 178-186.
    7. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    8. Murat Kurt & Mark S. Roberts & Andrew J. Schaefer & M. Utku Ünver, 2011. "Valuing Prearranged Paired Kidney Exchanges: A Stochastic Game Approach," Boston College Working Papers in Economics 785, Boston College Department of Economics, revised 14 Oct 2011.
    9. Marc Bollecker & Wilfrid Azan, 2008. "Les frontières de la recherche en contrôle de gestion : une analyse des cadres théoriques mobilisés," Post-Print halshs-00522395, HAL.
    10. Constantino, Miguel & Klimentova, Xenia & Viana, Ana & Rais, Abdur, 2013. "New insights on integer-programming models for the kidney exchange problem," European Journal of Operational Research, Elsevier, vol. 231(1), pages 57-68.


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