Optimizing green supply chain Networks and U-shaped assembly lines under uncertainty: A meta-heuristic approach

In instances where historical data is unavailable, belief degree-based uncertainty is frequently employed as a substitute for other uncertainty estimation methods, such as interval programming, fuzzy theory, and random planning. The present study focuses on a simultaneous design problem of green supply chain networks and U-shaped assembly lines with two objectives under belief degree-based uncertainty. This is the first study to do so. The objective functions are designed to minimize total transportation and fixed costs of establishing stations, while accounting for air pollution. As this issue is one of the NP-hard problems, a number of meta-heuristic algorithms have been developed for the purpose of addressing multi-objective problems. These include the gray wolf algorithm, the particle swarm optimization algorithm, and the NSGAII algorithm. A novel encoding-decoding method is employed in these algorithms. In order to analyze the performance of the proposed algorithms, test problems from the literature are considered, modified, and completed for this study. The numerical results obtained in this study indicate that the gray wolf multi-objective algorithm exhibits superior efficiency in comparison to alternative algorithms. Finally, the methodology of this study can be utilized as a management tool to address the real-time problems.