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The location-routing problem is a relatively new branch of logistics system. Its objective is to determine a suitable location for constructing distribution warehouses and proper transportation routing from warehouse to the customer. In this study, the location-routing problem is investigated with considering fuzzy servicing time window for each customer. Another important issue in this regard is the existence of congested times during the service time and distributing goods to the customer. This caused a delay in providing service for customer and imposed additional costs to distribution system. Thus we have provided a mathematical model for designing optimal distributing system. Since the vehicle location-routing problem is Np-hard, thus a solution method using genetic meta-heuristic algorithm was developed and the optimal sequence of servicing for the vehicle and optimal location for the warehouses were determined through an example.