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Dynamic allocation of stochastically-arriving flexible resources to random streams of objects with application to kidney cross-transplantation

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  • Perlman, Yael
  • Elalouf, Amir
  • Yechiali, Uri

Abstract

Two distinct random streams of discrete objects flow into a system and queue in two separate lines. Concurrently, two distinct types of resources arrive stochastically over time. Upon arrival, each resource unit is matched with a waiting object. One resource type is ʻflexible’ and can be allocated to either one of the object types. However, units of the other, non-flexible, resource type can be allocated only to units of one specific object type. The allocation probabilities are not fixed and may depend on both queue sizes of the two objects. If a resource unit is not allocated immediately, it is lost. The goal is to find an optimal state-dependent probabilistic dynamic allocation policy. We formulate the system as a two-dimensional Markov process, analyze its probabilistic behavior, and derive its performance measures. We then apply the model to the problem of kidney cross-transplantation and propose a new measure of system effectiveness, called Expected Value of Transplantation (EVT), based on the histocompatibility between kidneys and candidates. We further show that it is possible to balance the objectives of achieving equity in candidates’ expected waiting times (EW) and maximizing EVT by equating the value of EW/EVT between the two groups.

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  • 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.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:169-177
    DOI: 10.1016/j.ejor.2017.07.068
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    References listed on IDEAS

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    1. Israel David & Uri Yechiali, 1995. "One-Attribute Sequential Assignment Match Processes in Discrete Time," Operations Research, INFORMS, vol. 43(5), pages 879-884, October.
    2. 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.
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    6. Bendersky, Michael & David, Israel, 2016. "Deciding kidney-offer admissibility dependent on patients’ lifetime failure rate," European Journal of Operational Research, Elsevier, vol. 251(2), pages 686-693.
    7. Mahvareh Ahghari & Bariş Balcioĝlu, 2009. "Benefits of cross-training in a skill-based routing contact center with priority queues and impatient customers," IISE Transactions, Taylor & Francis Journals, vol. 41(6), pages 524-536.
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    Cited by:

    1. Heng-Li Liu & Quan-Lin Li, 2023. "Matched Queues with Flexible and Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.
    2. Hanukov, Gabi & Avinadav, Tal & Chernonog, Tatyana & Yechiali, Uri, 2019. "Performance improvement of a service system via stocking perishable preliminary services," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1000-1011.
    3. Li, Mengling & Riyanto, Yohanes E. & Xu, Menghan, 2023. "Prioritized organ allocation rules under compatibility constraints," Games and Economic Behavior, Elsevier, vol. 141(C), pages 403-427.
    4. Katarína Cechlárová & Martina Hančová & Diana Plačková & Tatiana Baltesová, 2021. "Stochastic modelling and simulation of a kidney transplant waiting list," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 909-931, September.
    5. Uri Yechiali, 2022. "Transplant queueing," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 489-491, April.
    6. Chai, Xudong & Jiang, Tao & Chang, Baoxian & Liu, Liwei, 2021. "On a multiple priorities matching system with heterogeneous delay sensitive individuals," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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