Designing and modeling a supply chain network are the important steps in determining the costs and time associated with bringing goods to market by evaluating alternate scenarios in light of available resources and locations in the chain. In closed-loop supply chains, the network is extended to include backward chain members and thereby sustainable supply chains are achieved. A network that is optimized can reduce carbon footprint, assist with meeting sustainability goals, improve delivery quality, and ultimately result in an improved customer experience, added value, and differentiation. In this study, a closed-loop supply chain network model is considered to simultaneously optimize the three dimensions of sustainability: economical, environmental, and social. The proposed model is developed using a goal programming technique in supply chain processes with the aim of minimizing costs and environmental damage and maximizing the social benefit. The developed model is integrated with the decision variables regarding the number of workers so as to increase employment, especially regarding the social effects of sustainability. A new model is obtained by weighting the three main dimensions of sustainability with the fuzzy analytic hierarchy process technique. A scenario analysis is conducted to show the impact of the parameters such as capacity, demand, costs, and carbon emissions. According to the scenario analysis results, the parameter having the greatest impact on the decision variables is demand; moreover, where there is an increase of 30% in demand, it has been determined that there is an increase of more than 100% in the number of workers and purchasing costs compared to the base case scenario. In addition, the increase in demand naturally increases transportation costs more than 50% as well.