Lampung University

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

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    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 de?ned, 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 de?ned for each type of cycle. We present computational results of the proposed branch-and-price algorithm andcomparethemwithsolvingdirectlythecycleformulation(withageneralpurposemixe

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