Organ tralantation is one of the fundamental and effective treatment techniques for the patients who have critical health problems. There exists a huge gap between the numbers of donors and patients waiting for an organ. This is a worldwide problem. In the USA Each day, an average of 79 people receive organ tralants. However, an average of 22 people die each day waiting for tralants that can't take place because of the shortage of donated organs. This research presents a mixed-integer linear programming (MILP) model to cope with the supply chain network design (SCND) of the organ tralant. The model consists of a bi-objective mathematical programming model that minimizes total cost and time. . Because of the imprecise nature of the studied network, the model has been considered under uncertainty. For this reason, a novel robust possibilistic approach has been applied and compared to the deterministic model. For larger problems, proposed a meta-heuristics based algorithm. Besides, several sensitivity analyses were conducted to validate the effectiveness and efficiency of the proposed model, and managerial insights were provided.