Two-stage chance-constrained programming based on Gaussian mixture model and piecewise linear decision rule for refinery optimization

Abstract

The two-stage chance-constrained program (CCP) is studied for a refinery optimization problem. In stage-I, the refinery decision-makers determine the type and quantity of crude oil procurement under operational uncertainties to maximize the expected profit under all possibilities. In stage-II, process unit flowrates are adjusted based on the realized uncertainties and available crude oil, while introducing probabilistic constraints to manage the off-spec risk. To solve such a two-stage optimization problem, we propose a novel approach using Gaussian mixture model (GMM) to characterize uncertainties, and piecewise linear decision rule for stage-II operations. Comparing to the conventional scenario-based mixed-integer linear program (MILP), our new approach offers three advantages. First, it leverages a well-developed global optimization scheme for joint CCP to avoid scenario generation and potential bias. Second, the data-driven GMM enables CCP to handle uncertainties with general distributions. Third, the stage-II variables are parameterized via Gaussian component induced piecewise linear decision rule to strike an excellent trade-off between optimality and computational time. A simplified refinery plant, consisting of distillation, cracker, reformer, isomerization, and desulfurization units, is used as a test bed to demonstrate the superiority of the proposed optimization method in solution time, probabilistic feasibility, and optimality over the large-scale scenario-based MILP.