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.

数学编程公式被开发用于确定兼容性图中的器官捐赠交换对链，其中成对交换可能会失败。目标是最大化预期值，其中已知对以给定的概率失败。在以前的工作中，即 Dickerson 等人的工作。(Manag Sci 65(4):323–340, 2019) 这个 NP-hard 问题是启发式解决的，或者仅针对有限的路径长度。尽管问题看起来高度非线性，但我们将其表述为混合整数线性程序。还提出了一种近似求解较大实例的计算上易于处理的分层公式，并提出了一项计算研究来评估所提出的公式。