A green EOQ model with dynamic demand forecasting and carbon tax optimization using fuzzy differential equations

Traditional Economic Order Quantity (EOQ) models assume static demand and cost parameters, limiting their applicability in volatile and environmentally regulated supply chains. This paper presents an advanced EOQ model that incorporates dynamic, AI-forecasted demand, carbon emission considerations, and fuzzy uncertainty modeling. Demand is modeled as a time-varying fuzzy exponential function derived from machine learning techniques such as Long Short-Term Memory (LSTM) networks and Gradient Boosted Regression Trees (GBRT). The model accounts for carbon emissions per unit and associated tax costs, integrating environmental impact into the total inventory cost structure. A fuzzy differential equation framework is employed to model uncertain demand and cost parameters. The total cost function—comprising ordering, holding, purchasing, and carbon emission costs—is minimized over the replenishment cycle using a hybrid numerical optimization approach, combining Euler's method with fuzzy Taylor series expansion. Numerical simulations and sensitivity analyses reveal that the proposed model adapts effectively to fluctuations in demand and environmental policies, outperforming classical EOQ formulations. The results demonstrate the model’s potential to support sustainable inventory decisions in modern supply chain systems.