In this study a scenario-based multi-objective fuzzy model was provided in the SCLSC , which in addition to three aspects of sustainability including, social impact such as the creation of job opportunities, customer satisfaction, and so on, environmental impact such as reducing air pollution, and so on, economic impact such as reducing cost, increasing the reliability of the SC and product routing have been modeled. Two algorithms, including MOPSO and NSGA-II Algorithms, were applied to solve the proposed model. After tuning their parameters by the Taguchi method, their performance in problems with different dimensions were tested followed by evaluating them by powerful criteria. The proposed model was implemented on Chipboard Pooya Company in Iran in two scenarios of economic recession and prosperity aimed at evaluating its accuracy. A sensitivity analysis was eventually performed on the proposed model followed by making some suggestions to develop the model.