Modeling And Convex Optimization Methods For Production And Inventory Planning For Steel Manufacturing System

Production and inventory planning is to decide production quantity and make in-ventory policy according to customer demands,manufacturing and management require-ments.The purpose is to reduce production and inventory costs,and guarantee produc-tion stability.The steel manufacturing system consists of multiple production stages and multi-echelon inventories,the production process is complex,and there are multiple va-rieties of products involved.These characteristics bring great difficulties to solve the focused problems in this dissertation by directly utilizing the conventional modeling and optimization methods.Thus,the research on modeling and optimization for production and inventory planning in steel manufacturing system becomes the critical scientific top-ics.At the same time,reasonable production and inventory planning would keep the iron and steel production process continuously,and reduce the inventory.This dissertation focuses on a series of production and inventory planning problems derived from steel manufacturing systems and proposing the modeling methods combin-ing operations research,control theory and data analytics,and the corresponding convex optimization methods are designed to solve these models.For multi-stage production and inventory planning problem with concern of production changeover,a data and mech-anism fusion modeling method is proposed.For multi-stage production and inventory planning problem concerning parallel production lines,a dynamic model with feedback is established based on data analytics.For production and inventory control problem with stochastic demand,the probability is introduced into control theory,and the distri-butionnally robust control modeling method is proposed.For production and inventory coordinated planning problem based on convex optimization,a marginal distribution ro-bust model is proposed.To solve these models,a series of convex optimization methods are designed to transform or relax the above models into polynomial time-solvable convex optimization problems,respectively.The main works of this dissertation are summarized as follows:(1)Multi-stage production and inventory planning problem with concern of changeover derived from cold rolling production is studied.Since the mechanism models of the relationship between input and output in the actual production process are difficult to achieve,robust support vector regression is developed to predict units' output;con-sidering the unknown exact distribution of uncertain demand,the robust model is built based on data analytics;the robust model is transformed to a mixed-integer linear pro-gramming by using convex optimization method and dual theory,then the new model can be efficiently solved.Finally,the feasibility and effectiveness of the proposed method are verified by numerical experiments based on actual data.(2)Multi-stage production and inventory planning problem concerning parallel pro-duction lines derived from steelmaking-hot rolling-cold rolling production process is studied.Due to the complex production process and various operation conditions,the mechanism of production and inventory dynamic system is difficult to describe.Thus a hybrid modeling method based on data analytics and dynamic feedback is proposed.Combining the mechanism model and the data driven approach,the linear decision rules are introduced to feedback,and the dynamic closed-loop model is built.Through mathe-matical transformation,matrix analysis and the convex optimization method,the dynamic closed-loop model can be transformed to a linear programming model which can be ef-ficiently solved.Finally,the feasibility and effectiveness of the proposed method are verified by numerical experiments based on actual data.(3)The production and inventory control problem with stochastic demand derived from cold rolling production process is studied.Since the practical production and inven-tory system is random and dynamics,a distributionnally robust control modeling method is proposed.Based on probability and robust control theory,the distributionnally robust inventory control is built,which is robust and less conservative compared to traditional robust control.By mathematical transformations including convex optimization method-s,matrix analysis and dual theory,a semidefinite programming model is built and then simplified with lower dimensions,which can be further reduced to a second-order cone problem.The second-order cone problem is tractable even for large scale problems,which is suitable for practical applications.The proposed method is extended to discrete control systems and continuous control systems,respectively.Finally,the feasibility and effec-tiveness of the proposed method are verified by numerical experiments based on actual data.(4)Production and inventory coordinated scheduling problem based on convex op-timization derived from hot rolling production process is studied.To overcome the dif-ficulties caused by the randomness and high coupling of production process,a marginal distribution robust model is proposed.In contrast to traditional methods based on prob-ability distribution hypothesis,the marginal distribution robust model is established by constructing network flows and a two-stage model.A completely positive decomposi-tion together with the dual theory of convex optimization is proposed,and in order to transform the model to a copositive programming,which has semidefinite programming relaxation that can be solved in polynomial time.Finally,the feasibility and effectiveness of the proposed method are verified by numerical experiments based on actual data.