Scheduling of Crude Oil Operations Under Uncertainty: A Robust Optimization Framework Coupled with Global Optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Optimal crude oil scheduling can increase profits by exploiting cheaper but poor quality crudes, minimizing crude changeovers, avoiding ship demurrage, and managing crude inventory optimally. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed integer nonlinear programming (MINLP) optimization model.

The crude oil scheduling problem has received considerable attention with researchers developing different models based on discrete- and continuous-time representations [1]. In our previous work [1], we have developed a novel unit-specific event-based continuous-time MINLP formulation, and have proposed a branch and bound global optimization algorithm with piecewise-linear underestimation of the bilinear terms for this problem. The proposed model incorporated many realistic operational features such as single buoy mooring (SBM), multiple jetties, multi-parcel vessels, crude blending, brine settling, crude segregation, and fifteen important volume-based or weight-based crude property indices, and significantly reduced the number of bilinear terms and problem size compared to the discrete-time formulation of Reddy et al. [2] and Li et al. [3]. The proposed branch and bound global optimization algorithm resulted in better integer feasible solutions, which were guaranteed to be within 2% of global optimality.

All of the aforementioned models assume that the parameters used in the models are deterministic in nature. However, frequent uncertainties in practice are unavoidable such as demand fluctuations, ship arrival delays, crude quality specification variations, uncertainty on crude profit margin, demurrage cost, inventory cost, changeover cost and safety stock penalty, and equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal crude schedule obtained using nominal parameter values may often be suboptimal or even become infeasible. In general, two approaches can be used to address those uncertainties: reactive scheduling and preventative scheduling [4]. For detailed reviews on planning and scheduling under uncertainty, the reader is directed to Li and Ierapetritou [5], and Verderame et al. [4]

Robust optimization focuses on developing preventive models to minimize the effects of uncertainties on the performance measure such as profit, and operating cost. Its main objective is to ensure that the generated solutions are robust, while maintaining a high level of solution quality. Li et al. [6] developed scenario-based models for demand and ship arrival uncertainties separately. However, the number of scenarios exponentially increases with the number of uncertain parameters, and hence makes their model intractable for practical problems with large number of uncertain parameters. Cao et al. [7] proposed an optimization model based on chance constrained programming to generate robust schedules under demand uncertainty during scheduling of crude oil operations. However, their approach cannot be used to deal with uncertain parameters following a discrete probability distribution [8]. More importantly, their approach results in composition discrepancy. Recently, Wang and Rong [8] developed a two-stage robust optimization model for crude oil scheduling problem to address demand and ship arrival uncertainty separately. Although their model can cope with a wide variety of uncertainties, the generated schedule from their model also results in composition discrepancy. Most importantly, these approaches cannot ensure the generated solution to be feasible for the nominal parameters.

In this paper, we extend the robust optimization framework proposed by Lin et al. [9], Janak et al. [10], Verderame and Floudas [11-13] and Li et al. [14] to develop a deterministic robust counterpart optimization model for demand and ship arrival uncertainty during crude oil scheduling operations. The robust solution from the robust optimization framework is guaranteed to be feasible for the nominal parameters. The recently proposed branch and bound global optimization algorithm with piecewise-linear underestimation of bilinear terms by Li et al. [1] is also extended to solve the non-convex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach and the extended branch and bound global optimization algorithm. The computational results demonstrate that the obtained schedules are robust in the presence of demand and ship arrival uncertainty.

References

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