Next-Generation Inventory Optimization: Advanced Inventory Management Harnessing Demand Variability Integrating Fuzzy Logic and Granular Differentiability

\n Using fuzzy logic, the paper proposes a special inventory control method, considering the complexity and uncertainty of real supply chain management in a single time frame. The fundamental novelty is the acceptance of a non-linear demand function considering several important variables, including product quality, price, and supply levels. Combining these elements helps the model better explain the complex demand dynamics resulting from initial demand patterns, logistical operations, unpredictability in advertising rates, stock levels, selling prices, and product quality. By using its approaches to maximize inventory levels and price decisions in the face of uncertainty, this model could help to improve inventory management activities by offering a more complete knowledge of demand patterns. Given the complexity of current supply chains, it emphasizes the need to consider inventory management issues outside of traditional linear demand models.\nDefuzzing will ensure that the model is successful and stable. Our research shows that granular differentiability should be integrated with defuzzification. Granular differentiability generates fuzzy derivatives based on horizontal membership functions, thereby adding a new dimension. Our study is noteworthy for being the first to apply the granular differentiation approach to production inventory systems. Our work addresses both analytical methods and numerical simulations to maximize loosely defined controls using granular differentiation. Using this special technique, we want to increase our knowledge of production inventory systems that operate in fuzzy environments as well as our optimization strategies. This work clarifies how uncertainty affects decision-making procedures in such systems, therefore providing useful information for the field.\n