Abstract This chapter deals with a two-echelon, multicommodity, location-routing problem of relief distribution considering a covering tour for each relief item (RI) during standard relief time (initial 72-h). Due to the instability of the condition after an earthquake, the probability of disruptions in the capacity of temporary distribution centers, the number of vehicles, and the capacity of routes for delivering RIs can be tremendously high; therefore, three types of disruptions are incorporated in the model. Additionally, the conditional value at risk measure is applied to evaluate the degree of risk aversion for diverse decision in disaster circumstances, and fairness level constraint is considered to distribute fairly RIs among victims. According to the NP-hard nature of the model, a genetic algorithm is presented to solve this problem in large sizes. Finally, computational experiments are carried out to validate the model under the applied risk measure.