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One-Attribute Sequential Assignment Match Processes in Discrete Time

Author

Listed:
  • Israel David

    (Ben Gurion University of the Negev, Beer Sheva, Israel)

  • Uri Yechiali

    (Tel Aviv University, Tel Aviv, Israel)

Abstract

We consider a sequential matching problem where M offers arrive in a random stream and are to be sequentially assigned to N waiting candidates. Each candidate, as well as each offer, is characterized by a random attribute drawn from a known discrete-valued probability distribution function. An assignment of an offer to a candidate yields a (nominal) reward R > 0 if they match, and a smaller reward r ≤ R if they do not. Future rewards are discounted at a rate 0 ≤ α ≤ 1. We study several cases with various assumptions on the problem parameters and on the assignment regime and derive optimal policies that maximize the total (discounted) reward. The model is related to the problem of donor-recipient assignment in live organ transplants, studied in an earlier work.

Suggested Citation

  • Israel David & Uri Yechiali, 1995. "One-Attribute Sequential Assignment Match Processes in Discrete Time," Operations Research, INFORMS, vol. 43(5), pages 879-884, October.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:5:p:879-884
    DOI: 10.1287/opre.43.5.879
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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. Burhaneddin Sandıkçı & Lisa M. Maillart & Andrew J. Schaefer & Mark S. Roberts, 2013. "Alleviating the Patient's Price of Privacy Through a Partially Observable Waiting List," Management Science, INFORMS, vol. 59(8), pages 1836-1854, August.
    5. Noa Zychlinski, 2023. "Applications of fluid models in service operations management," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 161-185, February.
    6. 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.
    7. 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.
    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. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Barış Ata & Anton Skaro & Sridhar Tayur, 2017. "OrganJet: Overcoming Geographical Disparities in Access to Deceased Donor Kidneys in the United States," Management Science, INFORMS, vol. 63(9), pages 2776-2794, September.
    15. 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.
    16. 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.
    17. Baris Ata & Yichuan Ding & Stefanos Zenios, 2021. "An Achievable-Region-Based Approach for Kidney Allocation Policy Design with Endogenous Patient Choice," Manufacturing & Service Operations Management, INFORMS, vol. 23(1), pages 36-54, 1-2.
    18. 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).
    19. 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.
    20. Sheldon M. Ross & Gideon Weiss & Zhengyu Zhang, 2021. "Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities," Operations Research, INFORMS, vol. 69(1), pages 266-272, January.
    21. 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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