Supply chain design in today 's world requires a balance between conflicting economic goals and sustainability requirements. The aim of this study is to present a mathematical model for sustainable supply chain design which covers three dimensions of profitability, environmental and social. The innovation of this paper lies in the simultaneous consideration of the Human Development Index (HDI) and the value creation index within a closed-loop supply chain in the Iranian tire industry. In the baseline paper from which this problem was modeled, only the forward supply chain was taken into account. A bi-objective mixed integer linear programming (MILP) model was developed which follows the first objective function to maximize the profitability and the second objective function to minimize the co2 emissions in the transportation facilities and routes. The human development index was added to the model to account for the social dimension of sustainability. The proposed model was validated with small dimensions and using exact solution methods. Then, due to the complexity of the problem, two metaheuristic algorithms have been developed to solve it in real dimensions and their performance is compared with the exact solutions. The results indicate that metaheuristic algorithms have good performance in achieving the optimal solutions with short computational time. The sensitivity analysis also shows that considering sustainability considerations, it has a significant effect on the feasibility and final configuration of the supply chain network. The proposed model can be used as an analytical tool to managers to better understand complex relationships between profitability and sustainability and make informed decisions in the design of supply chain network.