Optimization of Economic Order Quantity Inventory Model for Backorders through Trapezoidal Fuzzy Number and Regression Sensitivity Analysis

Abstract

In the presence of fuzzy conditions, this research proposes an approach to optimization for an EOQ (Economic Order Quantity) inventory model that incorporates trapezoidal fuzzy numbers. Fuzzy sets are used to express input parameters and decision variables in EOQ models, that are then developed using Lagrangian optimization techniques. After the total cost function is defuzzified, Lagrangian conditions are used to determine the optimal policy. The method seeks to find the optimal lot size and backorder level while accounting for linear \& fixed backorder prices. Numerical examples are presented to contrast crisp and fuzzy scenarios, demonstrating the viability of the proposed approach. Furthermore, the paper explores the use of linear regression models to obtain coefficients and intercepts, which reflect the sensitivity of total inventory cost to changes in each variable. Positive coefficients indicate an increase in total inventory cost with an increase in the corresponding variable, while negative coefficients suggest the opposite. The magnitude of these coefficients quantifies the strength of the relationship between the variable and total inventory cost. Sensitivity analysis based on these coefficients allows for insights into the most influential variables affecting total inventory cost, thereby guiding decision-making processes in inventory management and facilitating cost-reduction efforts.