The Optimal Control Problems Of Production-Inventory Management System With Contraints

For a company which is both production type and sales type, its operational effectiveness has been directly affected by the productivity and inventory. So the production-inventory management is an important and realistic problem of business management. The optimal control theory is an important theoretical support for the productivity and inventory being adjusted rationally, and the most profits of the enterprises being guaranteed. At present, the study has been paid more attention by overseas scholars.According to different considerations when the models are created, the production-inventory model may be classified as the general production-inventory model where the perishable items in warehouses are not considered and the production-inventory model for perishable items. Every optimal control problem refers to various circumstances, because the optimal control problem is always subjected to all kinds of constraint conditions, such as boundary constraint, terminal inequality constraint, terminal equality constraint and differential equation constraint and so on. Based on previous research, the research of this thesis is carried out from two aspects.Firstly, for the general production-inventory model which is generally considered by many scholars, its solution methods of the rate of the optimal control when the control variable takes boundary constraint, differential equation constraint, and state variable which is provided with terminal inequality constraint, terminal equality constraint are discussed, respectively. The possibility and rationality of the solution methods is verified by means of numerical examples.Secondly, while the volume of stock is kept at a certain level, at the same time, considering the effects of productivity on sales rate, and deterioration on the rate of optimal control of the production-inventory system, the new production-inventory model for perishable items is created. The solution methods of the optimal control problem when the model's control variable takes boundary constraint and its state variable is provided with terminal inequality constraint are discussed, respectively. It is not considered in the previous literature, and the production-inventory model is proved to apply more widely than the general production-inventory model by numerical examples.