Sustainability in the lean supply chain is the consideration of all economic, social and environmental aspects in an integrated system. This study aims to design a novel multi-objective sustainable lean supply chain (LSC) network under uncertainty which all economic, social and environmental aspects are considered. The designed LSC network model incorporates multiple echelons, including retailers, distribution centers, production centers, suppliers, and final customers. The purpose of this paper is to demonstrate how a robust-fuzzy optimization technique can be used to control uncertainty parameters such as transportation costs, facility capacity, and demand. The deployment of this technique in the design of the LSC network leads to increased reliability in supplying the customer demand. The model’s objective functions are to minimize the total cost of designing LSC networks (economic aspect), to minimize waste in production units (environmental aspect), and to maximize the overall sustainability performance indicator (SPI) (social aspect). To achieve these objectives and to identify the Pareto front, we investigated both exact and meta-heuristic methods. The results indicated that when lean management tools are used in supply chain network conditions, the SPI increases and waste in the production units decreases. Additionally, it increases the cost of network design. Moreover, increasing the effect of uncertainty results in increased demand and decreased capacity in the supply chain network, resulting in an increase in network-related costs. However, the increase in the rate of uncertainty has resulted in an increase in waste in manufacturing units and a decline in the SPI. Finally, it was determined through numerous experiments and statistical tests that meta-heuristics algorithms are more efficient at solving the designed model in less time. As a result, the most efficient solution method was determined to be the MOGWO algorithm.
