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Accidents and natural disasters and crises coming out of them indicate the importance of an integrated planning to reduce their effected. Therefore, disaster relief logistics is one of the main activities in disaster management. In this paper, we study the response phase of the disaster management cycle and a bi-objective model has been developed for relief chain logistic in uncertainty condition including uncertainty in traveling time an also amount of demand in damaged areas. The proposed mathematical model has two objective functions. The first one is to minimize the sum of arrival times to damaged area multiplying by amount of demand and the second objective function is to maximize the minimum ratio of satisfied demands in total period in order to fairness in the distribution of goods. In the proposed model, the problem has been considered periodically and in order to solve the mathematical model, Global Criterion method has been used and a case study has been done at South Khorasan.