Control of Wood Raw Material Inventory with Lagrange Multiplier Method in PT. XYZ

• XYZ is a company engaged in the manufacturing industry that uses wood as the main raw material located in the city of Surabaya. PT. XYZ has a problem of less-than-optimal control of raw material inventory which has an impact on the swelling of inventory costs and over capacity of storage space. This study aims to determine the control of wood raw material inventory according to the capacity of the storage space so as to provide a minimum total inventory cost at PT. XYZ. The method used is the Lagrange Multiplier method. Based on the results of the study, the total new storage space was 287.99 m³. The total annual inventory cost of Rp 130.753.379 is smaller than the company's method of Rp 152.898.329, the Lagrange Multiplier method provides savings of 14.48%. The size of the spruce wood order is 58.69 m³ with each order being 9 days, basswood wood is 34.42 m³ with each order being 13 days, and pine wood is 50.89 m³ with each order being 18 days. This study proves that the Lagrange Multiplier method is an effective approach to overcome storage capacity constraints, optimize order quantities, and minimize inventory costs.