<![CDATA[General Background: Managing spare parts inventory is crucial for maintaining operational efficiency in manufacturing industries. Specific Background: PT ABC experienced overstocking of steel plate materials, causing increased storage costs and exceeding warehouse capacity. Knowledge Gap: Current company methods lack optimization under space constraints, leading to inefficiencies. Aims: This study aims to determine the optimal order quantity that minimizes total inventory costs while considering warehouse space limitations. Method: The Lagrange Multiplier approach was applied to optimize inventory levels under capacity constraints, using data on demand, ordering and holding costs, and storage volume. Results: The proposed method reduced total inventory costs to Rp46,259,547, compared to Rp185,458,780 using the company’s approach, achieving a 75.05% reduction. Novelty: Unlike standard EOQ-based systems, this study integrates Lagrange Multipliers to handle physical constraints, producing feasible and cost-effective solutions. Implications: Implementing this approach in similar manufacturing contexts can significantly reduce storage costs and prevent inefficiencies caused by overstocking.Highlights: Lagrange Multiplier reduced inventory costs by over 75%. Optimal inventory levels aligned with warehouse limits. Forecasting enhanced ordering precision for future cycles. Keywords: Inventory Management, Lagrange Multiplier, Spare Parts, Warehouse Capacity, Cost Reduction]]>
