Advertisement

Annals of Operations Research

, Volume 272, Issue 1–2, pp 429–444 | Cite as

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

  • Filipe AlvelosEmail author
  • Xenia Klimentova
  • Ana Viana
S.I.: Advances in Theoretical and Applied Combinatorial Optimization
  • 246 Downloads

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.

Keywords

Kidney exchange problem Expected number of transplants Integer programming Branch-and-price 

Notes

Acknowledgements

We would like to thank Dr. James Trimble from the University of Glasgow, UK for his valuable comments.

References

  1. Alvelos, F., Klimentova, X., Rais, A., & Viana, A. (2015). A compact formulation for maximizing the expected number of transplants in kidney exchange programs. Journal of Physics: Conference Series, 616(1), 012011.Google Scholar
  2. Alvelos, F., Klimentova, X., Rais, A., & Viana, A. (2016). Maximizing expected number of transplants in kidney exchange programs. In Electronic notes in discrete mathematics. INOC 2015—7th international network optimization conference, vol. 52, pp. 269–276.Google Scholar
  3. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46, 316–329.CrossRefGoogle Scholar
  4. Constantino, M., Klimentova, X., Viana, A., & Rais, A. (2013). New insights on integer-programming models for the kidney exchange problem. European Journal of Operational Research, 231(1), 57–68.CrossRefGoogle Scholar
  5. Dickerson, J., Procaccia, A. D., & Sandholm, T. (2013). Failure-aware kidney exchange. In EC-13: Proc. 14th ACM conference on electronic commerce, June.Google Scholar
  6. Dickerson, J. P., Manlove, D. F., Plaut, B., Sandholm, T., & Trimble, J. (2016). Position-indexed formulations for kidney exchange. In Conference on economics and computation (EC).Google Scholar
  7. ENCKEP. (2017). European network for collaboration on kidney exchange programmes. http://www.enckep-cost.eu/.
  8. Glorie, K. M., Carvalho, M., Bouman, P., Viana, A., & Constantino, M. (2014). Clearing barter exchange markets: Kidney exchange and beyond, Chapter VI. Ph.D. thesis, Erasmus University Rotterdam.Google Scholar
  9. Glorie, K. M., de Klerk, M., Wagelmans, A. P. M., van de Klundert, J. J., Zuidema, W. C., Claas, F. H. J., et al. (2013). Coordinating unspecified living kidney donation and transplantation across the blood-type barrier in kidney exchange. Transplantation Journal, 96(6), 814–820.CrossRefGoogle Scholar
  10. Glorie, K. M., van de Klundert, J. J., & Wagelmans, A. P. M. (2014). Kidney exchange with long chains: An efficient pricing algorithm for clearing barter exchanges with branch-and-price. Manufacturing & Service Operations Management (MSOM), 16(4), 498–512.CrossRefGoogle Scholar
  11. Klimentova, X., Alvelos, F., & Ana Viana, A. (2014). A new branch-and-price approach for the kidney exchange problem. In B. M. S. Misra, A. M. A. R. C. Torre, J. G. R. M. I. Falcão, D. T. B. O. Apduhan, & O. Gervasi (Eds.), Computational science and its applications—ICCSA 2014, volume 8580 of Lecture Notes in Computer Science, pp. 237–252. Springer International Publishing.Google Scholar
  12. Klimentova, X., Pedroso, J. P., & Viana, A. (2016). Maximising expectation of the number of transplants in kidney exchange programmes. Computers & Operations Research, 73, 1–11.CrossRefGoogle Scholar
  13. Li, Y., Song, P. X., Zhou, Y., Leichtman, A., Rees, M., & Kalbfleisch, J. (2014). Optimal decisions for organ exchanges in a kidney paired donation program. Statistics in Biosciences, 6(1), 85–104.CrossRefGoogle Scholar
  14. Mak-Hau, V. (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, 33(1), 35–59.Google Scholar
  15. Manlove, D., & O’Malley, G. (2012). Paired and altruistic kidney donation in the UK: Algorithms and experimentation. Lecture Notes in Computer Science, 7276, 271–282.CrossRefGoogle Scholar
  16. Manlove, D., & O’Malley, G. (2014). Paired and altruistic kidney donation in the UK: Algorithms and experimentation. ACM Journal of Experimental Algorithmics, 19(2), 2.6:1.1–2.6:1.21.Google Scholar
  17. Pedroso, J. P. (2014). Maximizing expectation on vertex-disjoint cycle packing. In B. M. S. Misra, A. M. A. R. C. Torre, J. G. R. M. I. Falcão, D. T. B. O. Apduhan & O. Gervasi (Eds.), Computational science and its applications—ICCSA 2014, volume 8580 of Lecture Notes in Computer Science, pp. 32–46. Springer International Publishing.Google Scholar
  18. Plaut, B. Dickerson, J. P., & Sandholm, T. (2016). Fast optimal clearing of capped-chain barter exchanges. In AAAI conference on artificial intelligence (AAAI).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Centro Algoritmi / Departamento de Produção e SistemasUniversidade do MinhoBragaPortugal
  2. 2.INESC TEC, Campus da FEUPPortoPortugal
  3. 3.ISEP - School of EngineeringPolytechnic of PortoPortoPortugal

Personalised recommendations