Refinery Operational Planning: A Convex Relaxation Application

CATEGORY: REFINERY PLANNING
Simpósio Brasileiro de Pesquisa Operacional, Setembro de 2013
Refinery Operational Planning: A Convex Relaxation Application
Tiago Andrade, Gabriela Ribas, Fabricio Oliveira
tiago.andrade@labnexo.com
gabriela.ribas@labnexo.com
fabricio.oliveira@puc-rio.br
Industrial Engineering Department, Pontifical Catholic University of Rio de Janeiro – PUC-Rio,
CP38097, 22453-900 Rio de Janeiro – Brazil
ABSTRACT
The oil refining activity is certainly one of the most complex activities in the chemical industry. The complexity arises mainly from the nonlinear nature of the refining processes and the several possible configurations of these processes. In addition, these nonlinear terms are responsible for ruining convexity properties of the problem, thus, removing any guarantee concerning global optimality of the solutions. In this sense, one alternative to circumvent this drawback is to use convexification techniques, which render convex approximations of the original problem. The present work proposes the use McCormick envelopes to generate a convex approximation for the refinery operational planning problem. Numerical results obtained show that the proposed approach can ensure a good solution for the problem in study, even for cases where there was no solution available employing traditional methods. render convex approximations of the original problem.
The present work proposes the use of McCormick envelopes (McCormick, 1976) to generate a convex approximation for the refinery operational planning problem. The McCormick envelopes technique can derive a convex approximation of the original nonconvex and nonlinear problem using a set of linear hyperplanes. Such a technique is especially suitable when the nonlinearities are caused by the presence of bilinear terms composed by the product of two variables with known bounds.
The main benefits of using the McCormick envelopes are that the approximation obtained is linear (and, therefore, convex) and its precision is directly related with how tight the variable bounds are. In addition, it is possible to show that, when the optimal variable values are at their bounds, then the relaxation solution and the original problem solution are exactly the same. Karuppiah and Grossmann (2006) applied a similar technique in the water treatment problem. Gounaris and Misener (2009) discuss alternative convexification relaxation schemes for the pooling problem. A broad review regarding the use of these convexification techniques is provided in Floudas and Gounaris (2009).
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