A Full-fuzzy Economic Order Quantity Model with Deterioration, Inflation, and Shortage using ϵ-spread Method

Abstract

This paper develops a comprehensive fuzzy economic order quantity (EOQ) model that incorporates deterioration, inflation, and shortage under a full-fuzzy decision-making environment. Unlike classical EOQ formulations that rely on precise parameter values, the proposed approach represents all major cost and system parameters—including demand, ordering cost, holding cost, shortage cost, deterioration rate, and inflation rate—as triangular fuzzy numbers. The fuzzified model is constructed using fuzzy arithmetic operations, and the resulting fuzzy total cost is converted into a crisp objective function through the signed-distance defuzzification method. The defuzzified cost function remains analytically tractable, strictly convex, and guarantees a unique optimal order quantity. A detailed numerical example is provided to illustrate the development of the fuzzy total cost structure, the derivation of the optimality conditions, and the computation of the optimal solution. Sensitivity analysis is conducted by varying each input parameter within a $\pm 20\%$ range, demonstrating the robustness of the model and highlighting the relative influence of system parameters on the optimal inventory decision. The results reveal that deterioration and inflation significantly affect replenishment policies, and the fuzzy modelling framework offers improved flexibility and realism for inventory systems operating under uncertain and fluctuating economic conditions.