Lagrange Multiplier Inventory Optimization for Constrained Head Truck and Crane Tire Warehousing: Optimalisasi Persediaan Ban Head Truck dan Crane pada Gudang dengan Keterbatasan Kapasitas Menggunakan Metode Lagrange Multiplier - Syahputra, Rangga Dhika; Aryanny, Enny (Universitas Muhammadiyah Sidoarjo, 2026)
General Background: Inventory management in multi-item systems with limited warehouse capacity requires mathematical optimization to control ordering and holding costs while maintaining operational continuity. Specific Background: PT XYZ, a supplier of port heavy equipment spare parts, experienced overstock of head truck and crane tires due to fluctuating demand and a warehouse capacity limited to 25 m³, resulting in total inventory costs of Rp134,142,000 and storage requirements exceeding capacity at 29.5 m³. Knowledge Gap: Prior studies predominantly addressed manufacturing or retail settings with relatively stable demand, while applications in port heavy equipment spare parts characterized by fluctuating demand and actual capacity constraints remain limited. Aims: This study aims to determine optimal order quantities for three tire types using the Lagrange Multiplier method to minimize total inventory cost under warehouse capacity constraints, integrating time series forecasting for the January–December 2026 period. Results: The Lagrange Multiplier model produced optimal order quantities of 60, 33, and 8 units, requiring 24.6 m³ and reducing costs to Rp127,643,500 compared with the company method. Forecast-based optimization recommended 58, 32, and 9 units with ordering intervals of 16, 24, and 18 days, occupying 24.75 m³ and generating total inventory costs of Rp125,985,500. Novelty: This study integrates multi-item Lagrange Multiplier optimization with Single Exponential Smoothing forecasting and Moving Range Chart verification in a port spare parts warehousing context. Implications: The findings provide a quantitative decision framework for capacity-constrained inventory planning, supporting cost minimization and structured warehouse utilization in heavy equipment spare parts management. Highlights: Mathematical optimization generated lower total stock expenditure compared with the existing ordering approach. Forecast-integrated planning maintained storage usage within the 25 m³ limit. Defined replenishment intervals of 16, 24, and 18 days supported structured procurement scheduling. Keywords: Inventory, Lagrange Multiplier, Tire