A new robust possibilistic mathematical model for organ transplantation network design by organ characteristics, waiting time and multi-mode transportation with a case study

The organ transplantation network has an important role in saving people with disabilities. The proposed network in this paper considers various components, including donor hospitals, isolation hospitals, additional isolation hospitals, and transplant centers. The donor hospitals transfer the brain-dead individuals to isolation hospitals or additional isolation hospitals. These hospitals start to remove the organs from bodies and, after testing, send them to transplant centers. However, this process can lead to queuing issues, thereby increasing wait times for recipients. Once healthy organs are transferred to transplant centers, the transplant operation can commence. The organ's characteristics are pivotal in ensuring successful matching with the recipient. Coordination within the network is facilitated through the organ procurement unit. For this purpose, a novel mixedinteger non-linear problem (MINLP) model is presented with three objective functions: minimizing network costs, reducing network times, and minimizing outdated units. A new integrated robust possibilistic solution approach is suggested to deal with uncertain parameters and to manage the multi-objective nature of the problem. To analyze the performance of the presented model, a real case study in Iran is applied with four scenarios. The main results indicate that these scenarios have varying impacts on the primary decision-making process. Consequently, the utilization of air mode vehicles is prioritized over ground vehicles in the second and third scenarios. The expiration time of the shelf life of organs and the duration of ischemia are crucial factors that significantly impact the transfer of organs among different echelons within the transplantation network. Also, the effectiveness of the proposed solution method is examined through two compromise solution approaches from the related literature and compared against a basic model to assess the efficiency. Finally, sensitivity analyses are conducted to assess the performance of the proposed model and solution approach in relation to the introduced network.