Nowadays, the issue of supply chain network design has garnered significant attention in supply chain management. Researchers have focused on the competitiveness of markets and the pursuit of greater benefits. Therefore, this article presents a multi-objective mathematical model for the    design of a dynamic and integrated supply chain network, specifically addressing a competitive and sustainable closed-loop supply chain for a perishable commodity. The proposed model        incorporates competition between two supply chains, considering environmental, social, and resilience factors. To solve this competitive model, a two-step approach is introduced. In this two-stage approach, the first stage involves calculating equilibrium values for competitive decisions using game theory. Then, in the second stage, an innovative multi-objective algorithm based on Pareto optimization is employed to solve the network design problem, taking into account the results from the competitive stage and addressing the complexities of the proposed model. Finally, the efficiency of the proposed model and solution approach is evaluated using a numerical example analyzed graphically and statistically. The results and graphs demonstrate that the proposed model performs well and successfully achieves the intended objectives.