Regarding the five-fold increase in unexpected accidents in the past decade and the increase in its human and financial losses, the relief supply chain has always been considered by humanitarian organizations as a suitable solution to reduce the cost of disaster. One of the most important fields in this area is the routing of vehicles, which has an important role in improving service to the injured. Undoubtedly, the selection of inappropriate routes for vehicles has a negative effect on timely and suitable relief operations. Several studies have been conducted in this regard, the models presented by them are often periodic and single-product, and the demand shortage of shelters is not permitted. In this research, a multi-product relief chain network has been proposed, including three main areas: vehicle maintenance centers, distribution centers for relief supply chains and shelters. The proposed mathematical model, with a goal to maximizing the supplied demand, by a minimum of vehicle and time, addresses the dynamically routing of vehicles. In the event of excess demand, at the end of the operational periods, the amount of unsupplied demand for each type of product will also be determined in terms of each shelter. In order to validate the proposed model, information of the 4th district of Tehran province, which is published in the basic papers, is utilized and has been solved by GAMS software. The results of the numerical solution of the model showed that all relief operations are in order to maximize the supply of demand in the shortest time. Also, the amount of unsupplied demand for shelters, the amount and type of goods carried, and the route of each vehicle’ s movement in each period, are other outcomes of the model.