Optimized Inventory Control Model Using Integrated Fuzzy Parameters and Graded Mean Integration for Production Cost Efficiency

This paper presents a mathematical model designed to optimize inventory management by minimizing total inventory costs in a production setting. Traditional inventory models often fall short in addressing uncertainties that arise in real-world production environments. To overcome this, we propose an integrated inventory model that incorporates fuzzy numbers, specifically trapezoidal fuzzy numbers, to represent uncertain parameters. This approach captures the variability in production quantities, lead times, and demand rates. By applying the Graded Mean Integration (GMI) method for defuzzification, the model translates fuzzy data into actionable insights for inventory control. Using partial derivatives and optimization techniques, we derive optimal cycle time and cost parameters for managing production and inventory under uncertainty. Our results provide a robust framework for cost-efficient inventory management that adapts to the complexities of real-life production scenarios.