Planning Optimization Of Polyvinyl Chloride Production Based On Piecewise Linear Approximation

Production planning and scheduling of large and complex industrial processes has become the frontiers and difficulties in the field of the industry control.Polyvinyl chloride(PVC)is a kind of important chemical products,which has been widely used in our daily life.According to the real PVC production process,considering the material production system and the utility systems,this paper presents a multiperiod planning optimization model to reduce the total cost.We use the HH model to approximate all the nonlinear items in the previously proposed MINLP model.This method can avoid the nonlinear problems in modeling stage.Moreover,a hierarchical decomposition algorithm is proposed in this paper to accelerate the computation progress.In the end,considering the uncertainties of real process,a stochastics planning model is formulated by stochastic programming techniques and chance constrained programming.The main researches in this paper are as follows:According to our previous study,a multiperiod mixed-integer nonlinear programming(MINLP)model was developed to demonstrate the importance of integrating both the material processing and the utility systems.However,the optimization problem is very difficult to solve due to the process intrinsic nonlinearities.This paper intends to address this challenge by using the piecewise linear modelling approach that provides good approximation of the global nonlinearity with locally linear models.Specifically,a hinging hyperplanes(HH)model is introduced to approximate the nonlinear items in the original MINLP model.HH model is the basis of the linearization MINLP model.As a result,with the help of auxiliary variables,the original MINLP can be transformed into a mixed-integer linear program(MILP)model,which then can be solved by many established efficient and mature algorithms.Computational results show that the proposed model can reduce the solving time by up to 97% or more and the planning results are close to or even better than those obtained by the MINLP approach.Due to the piecewise linear modelling approach,a lot of auxiliary variables have been introduced to represent the different partition points,and the scale of the model become larger.However,it is difficult to solve due to the large scale and the complex nonconvexity.Thus,a hierarchical decomposition algorithm is proposed in this paper to accelerate the computation progress.The problem is divided into two levels,in the first level,the operating states(i.e.,start/stop operations)of equipment are optimized,which would be the hard-to-solve binary variables in the plantwide planning model;in the second level,the determined binary variables are embedded into the plantwide planning model,and thus a reduced scale scheduling optimization is executed.Finally,using the same case analysis verify the validity of the algorithm.The deterministic optimization problem of PVC production has been solved in our previous studies.However,in the real production process,there are many uncertainties,such as the market demand of products,raw material price and others.In this paper,time-varying uncertainties from both the raw material price and the market demand of products are considered.Specifically,from the practical view,the uncertainty level exhibits an increasing tendency along with the time.Using the stochastic programming techniques,a stochastic model is formulated,and then,the stochastic model is transformed into a multi-period mixed-integer linear programming(MILP)model by chance constrained programming and piecewise linear approximation method.