Efficiency is a key success factor in complex supply chain networks. It is imperative to ensure proper flow of goods and services in humanitarian supply chains in response to a disaster. In this work, a mathematical model for designing a humanitarian supply chain network and vehicle routing problem considering cross-dock is proposed where a Non-dominated sorting genetic algorithm (III) has been used for implementing the proposed model in a large-scale problem. Since the model has been implemented in a large-scale case, various sensitivity analyses are performed to extract more interesting results. Accordingly, the results have shown that the costs have more effect on the first objective function (patients compared to total injuries) and the second one (shortage), respectively. Compared to the other two objective functions, the impact on the cost function is negligible. The effect of transportation cost of relief goods/ supplies from the supplier to the warehouse on the first objective function is higher than the others; however, the effect of this cost is further than that of the cost from the supplier to the distributor, accordingly, in comparison to the previous cost, the output has been more reacted to this cost. The transportation cost from the distributor to the warehouse (cross-docking) has less effect on the cost function unlike the transportation cost from the supplier to the warehouse. Nevertheless, as the result shows an increase in the cost can lead to a considerable increase in the ratio of patients to total injuries as well as shortage. In other words, the objective functions would deteriorate when this parameter tends to be increased.