Quick response to the relief needs right after disasters through efficient emergency logistics distribution is vital to the alleviation of disaster impact in the affected areas. In this paper, by focusing on the distribution of relief commodities after disaster, the best possible allocation for the affected areas is specified and shortest path to vehicle transporting is determined. The objective of the proposed model is the minimization of the maximum distance traveled by each vehicle in order to achieve fairness in response to the wounded. In our proposed model, the location of demand is uncertain and determined by the simulation approach. The proposed approach solves the proposed model and determines appropriate allocation and best route for vehicles according to the allocation, simultaneously. Consequently, using genetic algorithm with two-part chromosome structure in routing and allocation problems. Computational results show the efficiency and effectiveness of the proposed model and algorithm for solving real decision-making problems.