Carbon Augmented EOQ Model for Deteriorating Items, Integrating Emission Costs and Sustainability into Inventory Optimization

This paper develops a sustainable Economic Order Quantity (EOQ) model for deteriorating items by explicitly integrating higher-order deterioration effects and carbon taxation. Unlike traditional models that approximate spoilage linearly, the proposed approach solves the exact nonlinear inventory differential equations to obtain closed-form solutions for inventory level and total cost. Carbon emission costs arising from production, storage, transportation, and disposal are incorporated through a carbon price (λ), transforming traditional cost components into carbon-adjusted equivalents. The resulting cost function remains strictly convex with respect to the replenishment cycle, and optimality conditions are obtained analytically and via the Newton–Raphson algorithm. Numerical results identify an optimal cycle of T * = 8 days with a total cost of | 980.17 per day. Incorporating carbon pricing increases total cost by about 28% but reduces optimal cycle time, promoting smaller lot sizes and lower emissions. Sensitivity analyses exhibit that higher carbon prices and deterioration rates result in frequent replenishment 1 and lower inventory levels. The model delivers an effective framework for balancing cost efficiency and environmental accountability under carbon-regulated supply chains.