Lagrange Multiplier Reduces Cloth Diaper Raw Material Inventory Cost

General Background The textile manufacturing industry requires efficient raw material inventory control to ensure production continuity and cost minimization. Specific Background CV ABC faces challenges in managing cloth diaper raw material inventory due to ordering policies that are not aligned with actual demand and warehouse capacity, leading to excess stock and increased costs. Knowledge Gap Previous studies often apply optimization methods separately and rarely integrate constrained optimization, reorder decision models, and demand forecasting within capacity-limited environments in small to medium textile industries. Aims This study aims to minimize total inventory costs by applying the Lagrange Multiplier method under warehouse capacity constraints and the Reorder Point (ROP) method to determine optimal reorder timing, supported by demand forecasting. Results The proposed approach yields a total inventory cost of IDR 22,194,689, lower than the company’s existing cost of IDR 23,965,625, resulting in savings of IDR 1,770,936 (7%) while achieving optimal warehouse utilization of 15.064 m³. Novelty This study demonstrates the integration of demand forecasting, Lagrange Multiplier, and ROP methods within a capacity-constrained inventory system for cloth diaper production. Implications The findings provide a practical inventory planning framework for small and medium textile manufacturers to determine optimal order quantities and reorder timing while considering storage limitations and cost efficiency. Highlights: Proposed model reduced total expenditure by 7% compared to existing practice. Storage utilization achieved full alignment with available space limits. Integrated approach determined optimal order quantity and reorder timing simultaneously. Keywords: Inventory, Lagrange Multiplier, Reorder Point