The challenges faced by classical supply chain management affect efficiency with regard to business. Classical supply chain management is associated with high risks due to a lack of accountability and transparency. The use of optimization algorithms is considered decision-making support to improve the operations and processes in green manufacturing. This paper suggests a solution to the green lot size optimization problem using bio-inspired algorithms, specifically, the butterfly algorithm. For this, our methodology consisted of first collecting the real data, then the data were expressed with a simple function with several constraints to optimize the total costs while reducing the CO₂ emission, serving as input for the butterfly algorithm BA model. The BA model was then used to find the optimal lot size that balances cost-effectiveness and sustainability. Through extensive experiments, we compared the results of BA with those of other bio-inspired algorithms, showing that BA consistently outperformed the alternatives. The contribution of this work is to provide an efficient solution to the sustainable lot-size optimization problem, thereby reducing the environmental impact and optimizing the supply chain well. Conclusions: BA has shown that it can achieve the best results compared to other existing optimization methods. It is also a valuable chainsaw tool.

The firefly algorithm is one of the best latest bio-inspired algorithms, which proved its performance in solving continuous and discrete optimization problems. This paper presents a more detailed...