Reports from Emergency organizations indicate an increase in the number of natural disasters and the financial and human losses caused by them. With this in mind, designing a relief network that can meet all the demand at the lowest cost and in the shortest possible time in the event of a disaster is of particular importance to communities and high-level government decision-makers. In this research, a relief facility location model has been considered, with the aim of fully covering the demand at the appropriate time, followed by minimizing social costs. Also, another issue that highlights the value of an effective relief network is the attention to social justice in it, which in the proposed model is also achieved through a new constraint.