A constrained optimization for a multi-factor lead-time supply chain model under a type-2 fuzzy environment

This study addresses key challenges in modern two-echelon supply chains, including quality management, lead time, and environmental factors. A nonlinear multi-factor lead-time reduction function is developed to better reflect real-world conditions, which is unexplored in existing literature. In addition, the impact of inspection errors on inventory decisions remains unaddressed in fuzzy environments with multiple constraints, leading to inefficiencies in handling defective products. To bridge this gap, this study incorporates two types of errors in quality inspection and models all associated supply chain costs using type-2 trapezoidal fuzzy numbers, providing a comprehensive framework for managing uncertainty. The model also considers renewable energy sources and external carbon emission factors, addressing sustainability concerns in supply chain operations. The fmincon optimization technique evaluates the model under multi-factor and traditional lead-time reduction strategies to achieve best optimal solutions. Numerical results show improved cost efficiency under the best-of-two strategy for supply chain decision-makers.