In natural disasters, having a capable network of collecting and distributing crucial items such as blood is one of the major concerns. However, due to damage to the infrastructure after disasters, mobile blood collecting facilities (blood mobiles) are usually required. This paper aims to decide the locations of mobile facilities in each period for collecting donated blood, plan the blood distribution from the fixed and mobile facilities to the main blood centers, as well as from blood centers to the hospitals and field-hospitals, under uncertain conditions. To do so, a multi-period, bi-objective mixed-integer mathematical model is developed under a multiple-scenario, aiming to minimize the unsatisfied blood demand as well as the total cost of the network. In the proposed model, the blood group compatibility matrix, failure rate of the facilities, and patients' urgency levels are considered. An augmented epsilon-constraint method is applied to solve this bi-objective model. Due to the complex nature of the proposed blood supply chain model, the Lagrangian relaxation approach is used to solve the proposed model. An expected Istanbul earthquake is considered, and the blood supply planning through the Red Crescent's European branch is performed utilizing the proposed model to examine its validity. According to the numerical results, the mobile facilities' locations in each period under each scenario are determined, the unsatisfied demand in each hospital and field-hospital for each blood type are reported, and the tradeoff between the supply chain costs and unsatisfied demand are discussed in detail. Finally, to illustrate the robustness of the proposed model, a detailed sensitivity analysis is performed. According to the study results, opening new blood centers near the high-demand sub-districts for faster testing and supply, increasing the hospitals' capacities, and usage of drones and helicopters for blood distribution are suggested can be considered as managerial insights.