In the aftermath of a disaster, acquiring and fulfilling blood demand is essential to prevent further loss of lives. Consequently, in recent years, the concept of blood supply chain design for disaster relief has gained immense importance. This article addresses this issue by developing a novel bi-objective scenario-based mathematical model to minimize the system's costs while enhancing the blood supply rate. The proposed framework encompasses three echelons of blood centers, hospitals, and backup blood centers. The model is developed using a set of techniques, including backup coverage, lateral transshipment, gift card, buffer storage, and blood transfusion. This specific combination aims to reduce blood shortages in the system by improving the coordination among different echelons of the network and encouraging more eligible individuals to donate blood. Next, the model is evaluated by applying it to a case study concerning a probable dangerous earthquake in Tehran capital of Iran. Furthermore, a Lagrangian relaxation method is implemented on the model to improve its capability in dealing with larger-scale problems with higher efficiency. Finally, the results and analysis demonstrate our approach's validity and advantages in satisfying the blood demand in a disaster time.