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A Time-dependent Stopping Problem with Application to Live Organ Transplants

Author

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  • Israel David

    (Tel Aviv University, Tel Aviv, Israel)

  • Uri Yechiali

    (Tel Aviv University, Tel Aviv, Israel)

Abstract

We consider a time-dependent stopping problem and its application to the decision-making process associated with transplanting a live organ. “Offers” (e.g., kidneys for transplant) become available from time to time. The values of the offers constitute a sequence of independent identically distributed positive random variables. When an offer arrives, a decision is made whether to accept it. If it is accepted, the process terminates. Otherwise, the offer is lost and the process continues until the next arrival, or until a moment when the process terminates by itself. Self-termination depends on an underlying lifetime distribution (which in the application corresponds to that of the candidate for a transplant). When the underlying process has an increasing failure rate, and the arrivals form a renewal process, we show that the control-limit type policy that maximizes the expected reward is a nonincreasing function of time. For non-homogeneous Poisson arrivals, we derive a first-order differential equation for the control-limit function. This equation is explicitly solved for the case of discrete-valued offers, homogeneous Poisson arrivals, and Gamma distributed lifetime. We use the solution to analyze a detailed numerical example based on actual kidney transplant data.

Suggested Citation

  • Israel David & Uri Yechiali, 1985. "A Time-dependent Stopping Problem with Application to Live Organ Transplants," Operations Research, INFORMS, vol. 33(3), pages 491-504, June.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:3:p:491-504
    DOI: 10.1287/opre.33.3.491
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    Citations

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    Cited by:

    1. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2004. "The Optimal Timing of Living-Donor Liver Transplantation," Management Science, INFORMS, vol. 50(10), pages 1420-1430, October.
    2. Theophilus Dhyankumar Chellappa & Ramasubramaniam Muthurathinasapathy & V. G. Venkatesh & Yangyan Shi & Samsul Islam, 2023. "Location of organ procurement and distribution organisation decisions and their impact on kidney allocations: a developing country perspective," Annals of Operations Research, Springer, vol. 321(1), pages 755-781, February.
    3. Oguzhan Alagoz & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2007. "Determining the Acceptance of Cadaveric Livers Using an Implicit Model of the Waiting List," Operations Research, INFORMS, vol. 55(1), pages 24-36, February.
    4. Amir Elalouf & Ariel Rosenfeld & Ofir Rockach, 2023. "The Extended David-Yechiali Rule for Kidney Allocation," Mathematics, MDPI, vol. 11(2), pages 1-16, January.
    5. 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.
    6. Stefanos A. Zenios & Glenn M. Chertow & Lawrence M. Wein, 2000. "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," Operations Research, INFORMS, vol. 48(4), pages 549-569, August.
    7. Sang-Phil Kim & Diwakar Gupta & Ajay Israni & Bertram Kasiske, 2015. "Accept/decline decision module for the liver simulated allocation model," Health Care Management Science, Springer, vol. 18(1), pages 35-57, March.
    8. Yael Deutsch & Israel David, 2020. "Benchmark policies for utility-carrying queues with impatience," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 97-120, June.
    9. Sheldon Ross & David Wu, 2013. "A generalized coupon collecting model as a parsimonious optimal stochastic assignment model," Annals of Operations Research, Springer, vol. 208(1), pages 133-146, September.
    10. Anna Krasnosielska-Kobos & Elżbieta Ferenstein, 2013. "Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem," Dynamic Games and Applications, Springer, vol. 3(2), pages 220-235, June.
    11. Levy, Amnon, 2005. "A decision-rule for transplanting non-cadaveric organs," European Journal of Operational Research, Elsevier, vol. 164(2), pages 548-554, July.
    12. Mustafa Akan & Oguzhan Alagoz & Baris Ata & Fatih Safa Erenay & Adnan Said, 2012. "A Broader View of Designing the Liver Allocation System," Operations Research, INFORMS, vol. 60(4), pages 757-770, August.
    13. Burhaneddin Sandıkçı & Lisa M. Maillart & Andrew J. Schaefer & Oguzhan Alagoz & Mark S. Roberts, 2008. "Estimating the Patient's Price of Privacy in Liver Transplantation," Operations Research, INFORMS, vol. 56(6), pages 1393-1410, December.
    14. Xuanming Su & Stefanos A. Zenios, 2006. "Recipient Choice Can Address the Efficiency-Equity Trade-off in Kidney Transplantation: A Mechanism Design Model," Management Science, INFORMS, vol. 52(11), pages 1647-1660, November.
    15. Sakine Batun & Andrew J. Schaefer & Atul Bhandari & Mark S. Roberts, 2018. "Optimal Liver Acceptance for Risk-Sensitive Patients," Service Science, INFORMS, vol. 10(3), pages 320-333, September.
    16. Dimitris Bertsimas & Vivek F. Farias & Nikolaos Trichakis, 2013. "Fairness, Efficiency, and Flexibility in Organ Allocation for Kidney Transplantation," Operations Research, INFORMS, vol. 61(1), pages 73-87, February.
    17. 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.
    18. Uri Yechiali, 2022. "Transplant queueing," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 489-491, April.
    19. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    20. Bradley Sturt, 2021. "A nonparametric algorithm for optimal stopping based on robust optimization," Papers 2103.03300, arXiv.org, revised Mar 2023.
    21. Kargar, Bahareh & Pishvaee, Mir Saman & Jahani, Hamed & Sheu, Jiuh-Biing, 2020. "Organ transportation and allocation problem under medical uncertainty: A real case study of liver transplantation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    22. Howard, David H., 2002. "Why do transplant surgeons turn down organs?: A model of the accept/reject decision," Journal of Health Economics, Elsevier, vol. 21(6), pages 957-969, November.
    23. Perlman, Yael & Elalouf, Amir & Yechiali, Uri, 2018. "Dynamic allocation of stochastically-arriving flexible resources to random streams of objects with application to kidney cross-transplantation," European Journal of Operational Research, Elsevier, vol. 265(1), pages 169-177.
    24. Sahar Ahmadvand & Mir Saman Pishvaee, 2018. "An efficient method for kidney allocation problem: a credibility-based fuzzy common weights data envelopment analysis approach," Health Care Management Science, Springer, vol. 21(4), pages 587-603, December.

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