Considering the phenomenon of inventory stimulating demand in real life, this article introduces an optimal control model of production inventory systems. In this model, the production rate and price level are control variables, the production rate is bounded, the inventory level is state variables, and the demand rate depends on the inventory level and price level. Three possible solutions are achieved according to different values of model parameters using the maximum principle and are analyzed in detail. By applying the model to a numerical example, a concrete transformation process of the system state is presented. In comparison with the case that demand does not depend on inventory, the impact of demand depending on inventory comes to light.
