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.2016551243012443), 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.