Linearized formulations for failure aware barter exchange

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 known fail with given probabilities. In previous work, namely that Dickerson et al. (Manag Sci 65(4):323–340, 2019) this NP-hard problem was solved heuristically or exactly only limited path lengths. Although appears highly nonlinear, we formulate it as mixed-integer linear program. A computationally tractable layered formulation approximately solves larger instances also proposed and computational study presented evaluating formulations.