Optimización de Costos de Producción con el Uso Programación Lineal Entera en la Planeación de la Producción para el Control de Inventario de Materias Primas

This study proposes a cost reduction methodology for the manufacturing processes of sanitary faucet bodies, based on a mixed-integer linear programming (MILP) model designed to optimize production planning while maintaining inventory control within defined limits. The model integrates economic, logistical, and environmental restrictions such as import quotas, production capacity, and the reuse of brass scrap derived from machining operations. Using the R programming language and the lpSolve package, the optimal combination of raw materials—virgin brass ingots, rods, and recycled scrap—was determined for each product batch. The model minimizes production costs subject to constraints on material availability and storage levels. Results demonstrated a cumulative saving of USD 73,341 over six consecutive months and a reduction of average foundry inventory from 116 t to 62 t, confirming the model’s efficiency in ensuring sustainable production. The methodology is scalable to other manufacturing contexts where materials have multiple processing routes or restricted supply conditions.