Study On Control And Optimization For The Inventory Problem

Iron and steel production process includes multiple stages, while each production stage involves multiple parallel production lines. Before each line, there is a raw material warehouse used to store its raw materials, and after each line, there is a product warehouse used to store products. Since the steel production has the features of high set-up costs and continuous production, controlling and optimizing of the inventory involved in the production process has great significance for keeping sufficient material supply for the production line, reducing production costs and storage costs and improving the profits.This paper mainly studies the control and optimization problems of the actual production inventory model in the cold rolling production process. Based on the control theory, Lyapunov stability theory and convex set theory, practical inventory problem is solved by LMI approach. The main contents can be listed as follows:(1) For the production-inventory control problem in the cold rolling production process, the demand is characterized by a limited energy and uncertainty disturbances, by deriving the characteristics of the production process, the production-inventory problem which consists of inventory level> production rate and demand rate is formulated as a model. Then the stability of the inventory level is analyzed, and it can keep the inventory level get the balance point even there is an external disturbances.(2) Since the practical production process involves the uncertain parameters and delay, a model is formulated to describe a time-delay and uncertain production-inventory system, then the robust stability is analyzed. Finally, a memoryless state feedback control law is established in order to make the system having certain robust property and H∞property.(3) For the uncertain continuous system, a production-inventory optimal control model with uncertain parameters has been formulated with the objective of minimizing the difference between the production rate and ideal production rate and the difference between the inventory level and the ideal inventory level. The problem has been transformed to the matrix approximation problem with matrix inequalities constraints, and it has been proven that the problem has unique solution. Furthermore, the problem has been converted to the generalized eigenvalue problem of LMI.