Green fuzzy scheduling approach of hydraulic cylinder manufacturing workshop based on nonlinear grey wolf optimizer incorporating simulated annealing

As manufacturing transitions towards the Industry 5.0 paradigm, simultaneously enhancing production efficiency while ensuring environmental sustainability and system resilience presents a critical managerial decision-making challenge in discrete manufacturing. This paper addresses the trade-off between production makespan and resource-environmental impact in hydraulic cylinder manufacturing systems, particularly where uncertain processing times significantly undermine the resilience of production operations. To align with the Industry 5.0 objectives of sustainable and robust manufacturing, we propose a novel green fuzzy scheduling framework grounded in a real-world enterprise context. First, processing time uncertainty is modeled using interval type-2 fuzzy sets to enhance the robustness of production planning. A multi-objective optimization model is then developed to simultaneously minimize the makespan and the integrated resource environmental impact factor, thereby harmonizing economic viability with ecological sustainability. To solve this NP-hard problem, a Nonlinear Grey Wolf Optimizer incorporating Simulated Annealing is constructed. This approach integrates global search capabilities with local refinement strategies to effectively navigate the complex decision space. Empirical validation is conducted through a case study at a hydraulic cylinder enterprise. The results demonstrate that the proposed method outperforms existing practical scheduling solutions, reducing the makespan by 4.74% and the integrated resource environmental impact factor by 10.60%. These findings provide actionable managerial insights for fostering resilient, green, and efficient manufacturing systems in the Industry 5.0 era.