Acquisition and Production Management with Two Inventories under Fluctuating Prices and Demand

We propose a continuously deterministic procurementproduction-inventory model to optimize the raw material procurement and production problem with raw material inventory and finished products inventory when the raw material purchasing price,the production cost,the raw material inventory holding cost,the finished products holding cost,and the demand rate fluctuate over time.We use Hamilton-Lagrange function and Pontryagin's maximum principle in optimal control theory to analyze the model,and we obtain the necessary and sufficiency conditions of the optimal solution to the model.We find some optimal policies regarding the procurement and production under some special circumstances.