Bi-level Optimization of Inventory and Production

A quantitative approach to inventory integration and production management is applied. Quantifying the relationships between inventory and production allows for minimizing inventory costs and maximizing production. A general optimization problem is derived that integrates inventory and production decisions. The optimization is formalized as a bi-level problem. The inventory and production objective functions are hierarchically integrated. The solution to the bi-level problem provides both optimal arguments for inventory size and production volumes. The problem is applied to the inventory of agricultural products that meet the required nutritional content for animal feed. The inventory delivery costs are minimized and nutritional content is maximized to meet the given nutritional level of the animal feed. Empirical results provide advantages for the bi-level solutions obtained. A sensitive analysis of the inventory is performed and the corresponding changes in the feed content are evaluated.