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Linearized formulations for failure aware barter exchange

Optimization Letters volume 16, pages 1301–1313 (2022)Cite this article

Abstract

Mathematical programming formulations are developed for determining chains of organ-donation exchange pairs in a compatibility graph where pairwise exchanges may fail. The objective is to maximize the expected value where pairs are known to fail with given probabilities. In previous work, namely that of Dickerson et al. (Manag Sci 65(4):323–340, 2019) this NP-hard problem was solved heuristically or exactly only for limited path lengths. Although the problem appears highly nonlinear, we formulate it as a mixed-integer linear program. A computationally tractable layered formulation that approximately solves larger instances is also proposed and a computational study is presented for evaluating the proposed formulations.

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Availability of data and material

The datasets generated during and/or analysed during the current study are available in the PSPP repository, https://github.com/noamgold/PSPP-Data/.

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Authors and Affiliations

  1. Department of Management, Bar-Ilan University, Ramat Gan, 5290002, Israel

    Noam Goldberg

  2. LIRMM, CNRS, University of Montpellier, Montpellier, France

    Michael Poss

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  1. Noam Goldberg
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  2. Michael Poss
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Correspondence to Noam Goldberg.

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Goldberg, N., Poss, M. Linearized formulations for failure aware barter exchange. Optim Lett 16, 1301–1313 (2022). https://doi.org/10.1007/s11590-021-01778-1

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  • DOI: https://doi.org/10.1007/s11590-021-01778-1

Keywords

  • Longest path
  • MILP
  • Layered formulation
  • Clearing algorithms
  • Kidney exchange
  • Failure aware barter exchange