Recourse in Kidney Exchange Programs

We introduce the problem of selecting patient-donor pairs in a kidney exchange program to undergo crossmatch test, and we model this selection as two-stage stochastic integer programming problem. The optimal solutions new formulation yield larger expected number realized transplants than previous approaches based on internal recourse or subset recourse. settle computational complexity by showing that it remains NP-hard even for maximum cycle length equal two. Furthermore, investigate what extent different algorithmic approaches, including one Benders decomposition, are able solve instances model. empirically efficiency approach solving randomly generated study corresponding running times function length, presence nondirected donors. Summary Contribution: This paper deals with an important very complex issue linked optimization transplant matchings programs, namely, inherent uncertainty assessment compatibility between donors recipients transplants. Although has previously received some attention literature, most attempts date have focused applying selected within restricted spaces. present explicitly formulates maximization turns out be computationally difficulty, both from theoretical numerical perspective. Different proposed tested experimentally its solution. quality exchanges produced these algorithms compares favorably earlier models.