Raw material inventory solution in iron and steel industry using Lagrangian relaxation

Because raw material inventories can compensate for the unexpected demand fluctuations as well as variability in the replenishment process, large inventories are maintained to ensure the continuity of production. But storing them increases the inventory cost. Therefore, how to best balance raw material inventory and production demands under capacity constraints has become the serious subject faced by most large steel companies. This paper studies the raw material inventory problem abstracted from the production of Shanghai Baoshan Iron and Steel Complex (Baosteel) in a theoretical light, which provides the scientific foundation for practical applications. Safety stock and safety lead time are first introduced to absorb the random fluctuations. Then, a constrained optimization model is formulated to minimize the total cost attributed to raw material inventories. By using a synergistic combination of Lagrangian relaxation, ordinal introduction of constraints algorithm and heuristic algorithms, high-quality plans are obtained in a timely manner.