In the refining industry, the profit made is mainly dependent on the crude oil procurements and plant operations. In order to enhance the profitability of a refinery, an optimization formulation subject to the refinery model is employed to plan the optimal crude purchases and decide the operations according to that procurement. However, two major challenges in optimizing this system are that the crude qualities are not known accurately at the time of purchase and the LP- based refinery model is relatively too simple to reflect the true behavior of the refining process. Hence, the objective of this research is to provide a systematic and efficient approach to maximize refining profitability in the presence of uncertainties using more realistic refinery model.
Towards this end, a nonlinear model using Geddes fractional index (FI) [1,2] is applied to describe the behavior of the crude distillation unit (CDU) for yield prediction, and integrated with the entire plant-wide model  with pooling processes. To incorporate uncertainties in the crude oil properties, the optimization scheme is modeled as a scenario-based two-stage stochastic program. In stage I, the best crude oil combination is selected among a set of candidates and their purchase amounts are determined to maximize the expected profit across all scenarios. In stage II, the uncertainties are realized and the optimal operations, such as the cut point temperatures for the CDU and flow rates in the pooling processes are determined according to the real qualities of the crudes, associated with each scenario, such that all important quality specifications are satisfied.
The proposed scheme takes into account uncertainties in the crude quality, nonlinearity from the pooling and units, and logical decisions, resulting in a large-scale mixed-integer non-linear programming (MINLP) formulation. The global optimization of such problems is extremely difficult because of the existence of many nonlinear, non-convex terms. We first show that our well-developed feasibility and optimality-based domain reduction techniques can substantially reduce the solution time of the state-of-the-art software, such as ANTIGONE , to obtain an ε-optimal solution for the nominal scenario. Then the non-convex generalized Benders decomposition (NGBD) methodology [5, 6] is further enhanced by the new adaptive piecewise convex relaxation [7, 8] to solve the stochastic program more efficiently. The results of the stochastic scheme are compared with the deterministic approach to demonstrate the benefits of expected profit maximization and variance reduction. Even though the complexity of the new optimization model is substantially increased due to the multi-scenario and non-convex formulation, the proposed enhanced NGBD approach is still able to find and verify a high quality solution with a small relative gap, whereas the traditional NGBD and other commercial software cannot find a comparable solution in several days.
 R. L. A. Geddes, A general index of fractional distillation power for hydrocarbon mixtures. AIChE Journal, vol. 4, 1958, 389-392.
 A.M. Alattas, I. E. Grossmann and I. Palou-Rivera, Integration of nonlinear crude distillation unit model in refinery planning optimization, Industrial and Engineering Chemistry Research, vol. 50, 2011, 6860-6870.
 J. P. Favennec, Refinery operation and management, Editions TECHNIP, Paris, 2001.
 R. Misener and C. A. Floudas. ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, Journal of Global Optimization, vol. 59, 2014, pp. 503-526.
 X. Li, A. Tomasgard and P. I. Barton, Decomposition strategy for the stochastic pooling problem, Journal of Global Optimization, vol. 54, 2012, pp. 765-790.
 X. Li, A. Tomasgard and P. I. Barton, Nonconvex generalized Benders decomposition for stochastic separable mixed-integer nonlinear programs, Journal of Optimization Theory and Applications, vol. 151, 2011, pp. 425-454.
 X. Li, Y. Chen, P. I. Barton, Nonconvex generalized Benders decomposition with piecewise convex relaxations for global optimization of integrated process design and operation problems, Industrial and Engineering Chemistry Research, vol. 51, 2012, 7287-7299.
 Y. Chen, Optimal design and operation of energy polygeneration systems, Ph.D. Thesis, 2013.