An Optimization Model for a Network of Organ Transplants with Uncertain Availability

Thanks to advances in modern medicine and the presence of an increasingly efficient organizational network, nowadays transplantation can save thousands of lives every year. In our paper we present a supply chain model with transplant centers and donor hospitals, where we assume that the medical teams move to the hospitals, take the organs, and go back to the transplant centers, using the most suitable transport mode. Since the availability of organs in each donor hospital is unknown a priori, we introduce a random variable which gives us an expected value of such an availability. The aim of the model is to obtain a social optimum in which we intend to minimize the total costs, given by transport costs of both teams and organs, as well as those of transplant patients, the costs of removal, of transplantation and of post-transplantation, the costs of disposal of diseased or non-functioning organs and of the damaged ones, and the penalties. We deduce the associated variational inequality formulation and an existing result for the solution. Finally, we present some numerical examples.