Piecewise Linear Approximation Based MILP Method for PVC Plant Planning Optimization.

This paper presents a new piecewise linear modeling method for the planning of polyvinyl chloride (PVC) plants. In our previous study ( Ind. Eng. Chem. Res., 2016, 55, 12430-12443, DOI: 10.1021/acs.iecr.6b02825), 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 really difficult to solve due to the process intrinsic nonlinearities, i.e., the operating cost or energy-consuming characteristics of calcium carbide furnaces, electrolytic cells, and CHP units. The present paper intends to address this challenge by using the piecewise linear modeling 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 a kind of continuous piecewise linear (CPWL) model, which is proven to be effective for any continuous linear functions with arbitrary dimensions on compact sets in any given precision, and is the basis for 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. [ABSTRACT FROM AUTHOR]