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Living donors are a significant and increasing source of livers for transplantation, mainly due to the insufficient supply of cadaveric organs. We consider the problem of optimally timing a living-donor liver transplant in order to maximize the patient's total reward such as quality-adjusted life expectancy. We formulate a Markov decision process (MDP) model in which the state of the process is described by patient health. We derive structural properties of the MDP model, including a set ofdoi:10.1287/mnsc.1040.0287 fatcat:htjtor5yrndwjosgcfjdm2ingq