Sustainable Inventory Optimization: A Multi-Item EOQ Model with All-Unit Discount, Capacity Constraint, and Carbon Emission - Roland Y.H. Silitonga; Heavie Zipora Setiawan (Engineering Science Letter, 2026)
Inventory is one of the operational components that contributes to carbon emissions through warehouse electricity consumption; however, this aspect has not yet been integrated into conventional inventory models, despite growing attention to green supply chain management. This study develops a multi-item Economic Order Quantity model that considers all-unit discounts, warehouse capacity constraints, and carbon emissions as cost components and examines the effect of carbon emission variables on the mathematical model structure. The development was carried out by adding a carbon cost variable, calculated as the product of average warehouse energy consumption, the carbon emission factor, and the carbon tax, to the storage cost equation and the formula for the optimal reorder interval. Solutions were obtained through an iterative approach to determine a valid discount price interval. Proportional adjustments were then applied to satisfy the warehouse capacity constraint. A numerical example involving three product items yielded an optimal cycle time t* = 0.144 periods, a reorder interval after capacity adjustment G = 0.108 periods, and total inventory costs of IDR 2,086,099,971 per planning period. The addition of carbon emission variables increases the holding cost component and reduces the optimal reorder interval compared to the reference model, resulting in a total inventory cost IDR 1,488,996 higher than the reference model. Sensitivity analysis results indicate that warehouse capacity has the greatest influence on total costs compared to carbon emission parameters. This study contributes to the integration of environmental aspects into a deterministic multi-item inventory model, thereby providing a more comprehensive decision-making framework for retail managers.