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Maximizing the expected number of transplants in kidney exchange programs with branch-and-price

Author

Listed:
  • Filipe Alvelos

    (Universidade do Minho)

  • Xenia Klimentova

    (INESC TEC, Campus da FEUP)

  • Ana Viana

    (INESC TEC, Campus da FEUP
    Polytechnic of Porto)

Abstract

In this paper, we propose a branch-and-price approach for solving the problem of maximizing the expected number of transplants in Kidney Exchange Programs (KEPs). In these programs, the decision on which transplants will be conducted is usually made with the support of optimization models with the assumption that all operations will take place. However, after a plan of transplants is defined, a pair may leave the KEP or a more accurate compatibility evaluation exam may invalidate a transplant. To model these possible events we consider probabilities of failure of vertices and of arcs and the objective of maximizing the expected number of transplants. The proposed approach is based on the so-called cycle formulation, where decision variables are associated with cycles. Built on the concept of type of cycle a branch-and-price algorithm is conceived. One subproblem is defined for each type of cycle. We present computational results of the proposed branch-and-price algorithm and compare them with solving directly the cycle formulation (with a general purpose mixed integer programming solver—CPLEX) showing that the proposed approach is the only one suitable for larger instances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:272:y:2019:i:1:d:10.1007_s10479-017-2647-4
    DOI: 10.1007/s10479-017-2647-4
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    References listed on IDEAS

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    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. 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.
    4. 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.
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