IDEAS home Printed from https://ideas.repec.org/a/inm/ormsom/v16y2014i4p498-512.html
   My bibliography  Save this article

Kidney Exchange with Long Chains: An Efficient Pricing Algorithm for Clearing Barter Exchanges with Branch-and-Price

Author

Listed:
  • Kristiaan M. Glorie

    (Econometric Institute, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

  • J. Joris van de Klundert

    (Institute of Health Policy and Management, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

  • Albert P. M. Wagelmans

    (Econometric Institute, Erasmus University Rotterdam, 3000 DR Rotterdam, The Netherlands)

Abstract

Barter exchange markets are markets in which agents seek to directly trade their goods with each other. Exchanges occur in cycles or in chains in which each agent gives a good to the next agent. Kidney exchange is an important type of barter exchange market that allows incompatible patient–donor pairs to exchange kidneys so the involved patients can receive a transplant. The clearing problem is to find an allocation of donors to patients that is optimal with respect to multiple criteria. To achieve the best possible score on all criteria, long cycles and chains are often needed, particularly when there are many hard-to-match patients. In this paper we show why this may pose difficulties for existing approaches to the optimization of kidney exchanges. We then present a generic iterative branch-and-price algorithm that can deal effectively with multiple criteria, and we show how the pricing problem may be solved in polynomial time for a general class of criteria. Our algorithm is effective even for large, realistic patient–donor pools. Our approach and its effects are demonstrated by using simulations with kidney exchange data from the Netherlands and the United States.

Suggested Citation

  • Kristiaan M. Glorie & J. Joris van de Klundert & Albert P. M. Wagelmans, 2014. "Kidney Exchange with Long Chains: An Efficient Pricing Algorithm for Clearing Barter Exchanges with Branch-and-Price," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 498-512, October.
  • Handle: RePEc:inm:ormsom:v:16:y:2014:i:4:p:498-512
    DOI: 10.1287/msom.2014.0496
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/msom.2014.0496
    Download Restriction: no

    File URL: https://libkey.io/10.1287/msom.2014.0496?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser & Martin W. P. Savelsbergh & Pamela H. Vance, 1998. "Branch-and-Price: Column Generation for Solving Huge Integer Programs," Operations Research, INFORMS, vol. 46(3), pages 316-329, June.
    3. Tayfun Sönmez & Alvin E. Roth & M. Utku Ünver, 2007. "Efficient Kidney Exchange: Coincidence of Wants in Markets with Compatibility-Based Preferences," American Economic Review, American Economic Association, vol. 97(3), pages 828-851, June.
    4. Itai Ashlagi & Alvin E. Roth, 2012. "New Challenges in Multihospital Kidney Exchange," American Economic Review, American Economic Association, vol. 102(3), pages 354-359, May.
    5. Saidman, Susan L. & Roth, Alvin E. & Sonmez, Tayfun & Unver, M. Utku & Delmonico, Francis L., 2014. "Increasing the Opportunity of Live Kidney Donation by Matching for Two and Three Way Exchanges," MPRA Paper 58247, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    2. Vicky Mak-Hau, 2017. "On the kidney exchange problem: cardinality constrained cycle and chain problems on directed graphs: a survey of integer programming approaches," Journal of Combinatorial Optimization, Springer, vol. 33(1), pages 35-59, January.
    3. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    4. Tinglong Dai & Sridhar Tayur, 2020. "OM Forum—Healthcare Operations Management: A Snapshot of Emerging Research," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 869-887, September.
    5. Itai Ashlagi & Maximilien Burq & Patrick Jaillet & Vahideh Manshadi, 2019. "On Matching and Thickness in Heterogeneous Dynamic Markets," Operations Research, INFORMS, vol. 67(4), pages 927-949, July.
    6. Filipe Alvelos & Xenia Klimentova & Ana Viana, 2019. "Maximizing the expected number of transplants in kidney exchange programs with branch-and-price," Annals of Operations Research, Springer, vol. 272(1), pages 429-444, January.
    7. Nicolau Santos & Paolo Tubertini & Ana Viana & João Pedro Pedroso, 2017. "Kidney exchange simulation and optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1521-1532, December.
    8. Mehdi Zeynivand & Mehdi Najafi & Mohammad Modarres Yazdi, 2023. "A Recourse Policy to Improve Number of Successful Transplants in Uncertain Kidney Exchange Programs," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 476-507, May.
    9. Tuan Le & Jon M. Stauffer & Bala Shetty & Chelliah Sriskandarajah, 2023. "An optimization framework for analyzing dual‐donor organ exchange," Production and Operations Management, Production and Operations Management Society, vol. 32(3), pages 740-761, March.
    10. Klimentova, Xenia & Viana, Ana & Pedroso, João Pedro & Santos, Nicolau, 2021. "Fairness models for multi-agent kidney exchange programmes," Omega, Elsevier, vol. 102(C).
    11. R. K. Jha & B. S. Sahay & P. Charan, 2016. "Healthcare operations management: a structured literature review," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 43(3), pages 259-279, September.
    12. Biró, Péter & van de Klundert, Joris & Manlove, David & Pettersson, William & Andersson, Tommy & Burnapp, Lisa & Chromy, Pavel & Delgado, Pablo & Dworczak, Piotr & Haase, Bernadette & Hemke, Aline & J, 2021. "Modelling and optimisation in European Kidney Exchange Programmes," European Journal of Operational Research, Elsevier, vol. 291(2), pages 447-456.
    13. Avrim Blum & John P. Dickerson & Nika Haghtalab & Ariel D. Procaccia & Tuomas Sandholm & Ankit Sharma, 2020. "Ignorance Is Almost Bliss: Near-Optimal Stochastic Matching with Few Queries," Operations Research, INFORMS, vol. 68(1), pages 16-34, January.
    14. Pinar Keskinocak & Nicos Savva, 2020. "A Review of the Healthcare-Management (Modeling) Literature Published in Manufacturing & Service Operations Management," Manufacturing & Service Operations Management, INFORMS, vol. 22(1), pages 59-72, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Glorie, K.M. & Wagelmans, A.P.M. & van de Klundert, J.J., 2012. "Iterative branch-and-price for hierarchical multi-criteria kidney exchange," Econometric Institute Research Papers EI 2012-11, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Klimentova, Xenia & Viana, Ana & Pedroso, João Pedro & Santos, Nicolau, 2021. "Fairness models for multi-agent kidney exchange programmes," Omega, Elsevier, vol. 102(C).
    3. Nicolau Santos & Paolo Tubertini & Ana Viana & João Pedro Pedroso, 2017. "Kidney exchange simulation and optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(12), pages 1521-1532, December.
    4. Jorgen Kratz, 2019. "Triage in Kidney Exchange," Discussion Papers 19/04, Department of Economics, University of York.
    5. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    6. Alvin E. Roth, 2010. "Marketplace Institutions Related to the Timing of Transactions," NBER Working Papers 16556, National Bureau of Economic Research, Inc.
    7. Alvin E. Roth, 2012. "Marketplace Institutions Related to the Timing of Transactions: Reply to Priest," Journal of Labor Economics, University of Chicago Press, vol. 30(2), pages 479-494.
    8. Judd B. Kessler & Alvin E. Roth, 2014. "Don't Take 'No' For An Answer: An Experiment With Actual Organ Donor Registrations," NBER Working Papers 20378, National Bureau of Economic Research, Inc.
    9. Judd B. Kessler & Alvin E. Roth, 2012. "Organ Allocation Policy and the Decision to Donate," American Economic Review, American Economic Association, vol. 102(5), pages 2018-2047, August.
    10. Alvin E. Roth, 2009. "What Have We Learned from Market Design?," Innovation Policy and the Economy, University of Chicago Press, vol. 9(1), pages 79-112.
    11. Péter Biró & Flip Klijn & Xenia Klimentova & Ana Viana, 2021. "Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange," Working Papers 1235, Barcelona School of Economics.
    12. Andersson, Tommy & Kratz, Jörgen, 2016. "Kidney Exchange over the Blood Group Barrier," Working Papers 2016:11, Lund University, Department of Economics, revised 29 Nov 2017.
    13. Klimentova, Xenia & Biró, Péter & Viana, Ana & Costa, Virginia & Pedroso, João Pedro, 2023. "Novel integer programming models for the stable kidney exchange problem," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1391-1407.
    14. John P. Dickerson & Ariel D. Procaccia & Tuomas Sandholm, 2019. "Failure-Aware Kidney Exchange," Management Science, INFORMS, vol. 65(4), pages 1768-1791, April.
    15. Nicolò, Antonio & Rodríguez-Álvarez, Carmelo, 2017. "Age-based preferences in paired kidney exchange," Games and Economic Behavior, Elsevier, vol. 102(C), pages 508-524.
    16. Harry J. Paarsch & Alberto M. Segre & John P. Roberts & Jeffrey B. Halldorson, 2011. "Competition and Post-Transplant Outcomes in Cadaveric Liver Transplantation under the MELD Scoring System," Carlo Alberto Notebooks 213, Collegio Carlo Alberto.
    17. Tom Demeulemeester & Dries Goossens & Ben Hermans & Roel Leus, 2023. "Fair integer programming under dichotomous and cardinal preferences," Papers 2306.13383, arXiv.org, revised Apr 2024.
    18. Hyunwoo Lee & Seokhyun Chung & Taesu Cheong & Sang Hwa Song, 2018. "Accounting for Fairness in a Two-Stage Stochastic Programming Model for Kidney Exchange Programs," IJERPH, MDPI, vol. 15(7), pages 1-16, July.
    19. Eun Jeong Heo & Sunghoon Hong & Youngsub Chun, 2021. "Kidney exchange with immunosuppressants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 1-19, July.
    20. Roth, Alvin E. & Sonmez, Tayfun & Unver, Utku & Delmonico, Francis & Saidman, Susan L., 2014. "Utilizing List Exchange and Non-directed Donation through “Chain” Paired Kidney Donations," MPRA Paper 58246, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormsom:v:16:y:2014:i:4:p:498-512. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.