In recent years, the hyper-competitive marketplace has led to a drastic enhancement in the importance of the supply chain problem. Hence, the attention of managers and researchers has been attracted to one of the most crucial problems in the supply chain management area called the supply chain network design problem. In this regard, this research attempts to design an integrated forward and backward logistics network by proposing a multi-objective mathematical model. The suggested model aims at minimizing the environmental impacts and the costs while maximizing the resilience and responsiveness of the supply chain. Since uncertainty is a major issue in the supply chain problem, the present paper studies the research problem under the mixed uncertainty and utilizes the robust possibilistic stochastic method to cope with the uncertainty. On the other side, since configuring a supply chain is known as an NP-Hard problem, this research develops an enhanced particle swarm optimization algorithm to obtain optimal/near-optimal solutions in a reasonable time. Based on the achieved results, the developed algorithm can obtain high-quality solutions (i.e. solutions with zero or a very small gap from the optimal solution) in a reasonable amount of time. The achieved results demonstrate the negative impact of the enhancement of the demand on environmental damages and the total cost. Also, according to the outputs, by increasing the service level, the total cost and environmental impacts have increased by 41% and 10%, respectively. On the other hand, the results show that increasing the disrupted capacity parameters has led to a 17% increase in the total costs and a 7% increase in carbon emissions. Supplementary Information The online version contains supplementary material available at 10.1007/s00521-022-07739-8.