Constrained Inventory Optimization Using Lagrange Multiplier in Animal Feed Production - Putri , Sri Defiana; Aryanny, Enny (Academia Open, 2026)
General Background: Raw material inventory control is critical in manufacturing because excessive stock can create warehouse overcapacity, higher holding costs, and inefficient procurement decisions. Specific Background: Animal feed production requires animal-based raw materials with limited warehouse capacity, making optimal multi-item ordering essential for cost efficiency and storage utilization. Knowledge Gap: Previous inventory studies have rarely applied the Lagrange Multiplier method to animal-based raw material control in the animal feed industry while explicitly considering warehouse capacity constraints. Aims: This study aimed to optimize raw material inventory control by determining order quantities that minimize total inventory cost under limited storage capacity. Results: Using quantitative inventory calculations, the conventional method produced a total inventory cost of IDR 1,166,757,379. The EOQ approach still exceeded the available warehouse capacity, indicating that unconstrained optimization was not feasible. The Lagrange Multiplier method produced optimal order quantities of 173.99 tons for material A, 225.16 tons for material B, and 111.45 tons for material C. The resulting storage requirement was 2,393.03 m³, within the available 2,393.46 m³ capacity. Total inventory cost decreased to IDR 894,288,924, producing 26.8% cost savings. Novelty: This study applies constrained Lagrange Multiplier optimization to multi-item animal-based raw material inventory. Implications: The findings support more efficient purchasing, capacity-based ordering, warehouse utilization, and inventory cost control. Highlights: EOQ exceeded the available storage limit. Proposed ordering quantities fit within warehouse capacity. Total spending declined by 26.8%. Keywords: Inventory, EOQ, Lagrange Multiplier, Raw Material Control.