Organ transplantation network design is a critical issue for continuing human life. This paper presents a new triobjective robust optimization model for the design of transplantation networks that are adaptable to disruption scenarios. This paper presents a new mixed-integer non-linear programming (MINLP) model to construct a scenario-based transplantation supply chain. In this regard, objective functions of the proposed scenario-based model are developed to minimize the delivery time of the organs after disruption and maximize the quality of organs and the compatibility of blood types. Afterward, the queue of people in health facilities with limiting capacity may reduce the surgeries and lead to death risk. Therefore, it is necessary to examine a queue system that reflects the situation and changes over time. The risk of climate change over the network can be created from the queue and affects the quality of organs. When the risk of climate change makes delay receiving the organs by transplant centers, the compatibility of blood types is a helpful method to handle surgery rates and decrease the mortality rate. Moreover, one of the other issues that have an impact on the decisions of the managers in the transplant process is related to making an appropriate decision by respecting uncertain conditions. For this reason, this paper has proposed a new hybrid solution approach based on the scenario-based robust optimization approach and the compromise solution method to tackle different uncertainties in an optimization model. In addition, the proposed model is NP-hard, and this paper utilizes two metaheuristic optimization algorithms to solve the problem, including genetic algorithm (GA) and black widow optimization (BWO). The empirical examples are provided to validate the performance of the proposed model, and these represent the advantage of BWO over GA. After introducing essential analyses, the comparative analysis and managerial insights are explained.