(425a) Global Optimization of Crude Oil Scheduling with Discrete and Continuous-Time Formulations

Optimization of scheduling operations in refineries has been recognized as a relatively inexpensive and fast way to improve key performance indices [1]. A distinctive feature of refinery scheduling problems is the blending of different types of crudes or liquid fuels for meeting quality specifications on process streams or customer orders. These are challenging problems since they involve modeling tanks of varying composition with non-convex bilinear terms, as well as complicating logistic constraints.

In this work, we focus on crude oil scheduling [2-8], which can be classified as a non-convex, mixed-integer nonlinear programming (MINLP) problem, belonging to one of the most complex fields in optimization [9]. Recent developments have occurred at the level of the: (i) mathematical formulation, with tighter source-based formulations for the closely related multi-period pooling problem of refined petroleum products [10,11]; (ii) global optimization algorithm, with efficient piecewise relaxation techniques [12,13]. The latter also include major performance improvements in the most recent versions of commercial solvers BARON [14] and GloMIQO [15].

In our previous work [8], a source-based continuous-time formulation was used underneath a rather complex Resource-Task Network (RTN) process model. The main novelty of this work is to present a simpler formulation by modelling logistic constraints through Generalized Disjunctive Programming (GDP) [9,16-17]. Furthermore, we also present its discrete-time counterpart. It should be highlighted that the discrete-time representation concept was part of the seminal paper [2] but has lost relevance in the last decade or so (when applied to this particular problem). The main motivation for revisiting discrete-time is that the inventory cost term in one of the two alternative objective functions considered becomes linear compared to continuous-time.

Results over a set of test problems from the literature show indeed that the discrete-time formulation is better when minimizing total cost, despite requiring an order of magnitude larger number of time slots. It was particularly surprising to find out that nonlinear scheduling problems with roughly 100 time points can be tackled to global optimality. On the other hand, the continuous-time approach is preferable when maximizing the gross margin.

The research study also involved the comparison of different global optimization algorithms. A two-stage MILP-NLP strategy relying on the standard McCormick relaxation [18] on the first iteration and on normalized multiparametric disaggregation [13] to close the gap, was shown competitive to commercial solvers BARON 16.3.4 and GloMIQO 2.3 for the objective of cost minimization. More specifically, the McCormick relaxation unexpectedly resulted in zero MILP relaxation gap when using a discrete-time formulation; (ii) normalized multiparametric disaggregation was slightly better when relying on continuous-time.

Acknowledgments: Financial support from Fundação para a Ciência e Tecnologia (FCT) through the Investigador FCT 2013 program and project UID/MAT/04561/2013.

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