This paper presents a new multi-objective model for a vehicle routing problem under a stochastic uncertainty. It considers traffic point as an inflection point to deal with the arrival time of vehicles. It aims to minimize the total transportation cost, traffic pollution, customer dissatisfaction and maximizes the reliability of vehicles. Moreover, resiliency factors are included in the model to increase the flexibility of the system and decrease the possible losses that may impose on the system. Due to the NP-hardness of the presented model, a meta-heuristic algorithm, namely Simulated Annealing (SA) is developed. Furthermore, a number of sensitivity analyses are provided to validate the effectiveness of the proposed model. Lastly, the foregoing meta-heuristic is compared with GAMS, in which the computational results demonstrate an acceptable performance of the proposed SA.