Fuzzy Lagrangian optimization for uncertain inventory systems with regression-based validation

Abstract

This study introduces a fuzzy modeling framework aimed at optimizing inventory management systems with the dual objectives of minimizing total cost and maximizing profit. A comprehensive mathematical model has been developed to assess total cost by incorporating fuzzy parameters, effectively addressing uncertainty and imprecision in production quantities. The Graded Mean Integration Method was utilized for defuzzification, facilitating the precise interpretation of fuzzy values. By extending the Lagrangian optimization technique, the model identifies the optimal production quantities subject to specified constraints. The proposed methodology demonstrates significant potential for enhancing decision-making processes in inventory systems operating under conditions of uncertainty.