Relief operations and planning to implement them are essential due to the unpredictability of natural disaster occurrences and their concomitant damages. The Crisis and Disaster Management Organization’s responsibility is to execute plans, coordinate, control relief, and rescue operations to reduce the impacts and consequences of these disasters. Thus, this organization should attend to the struck regions’ needs with their maximum power as soon as possible. This study has initially reviewed the latest available literature regarding the humanitarian supply chain to determine the research gap. Accordingly, in this research, a mathematical model with a leader-follower approach for relief delivery in the crisis response phase was designed, which took into account the policies of the country of Iran for the distribution of relief items. The amount of inventory of suppliers was also considered as uncertain. Then, to validate it, a numerical example was solved by the metaheuristic algorithm MOEA/D. The results indicated that the designed model is valid and the selected algorithm to solve it has an acceptable performance. Finally, some effective parameters were selected in the model and the sensitivity of the model was evaluated based on their changes.