(520e) 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-timeMINLP 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

[1] Li J,
Misener R, Floudas CA. Continuous-time modeling and global optimization
approach for scheduling of crude oil operations. AIChE Journal, In
press, 2011.

[2] Reddy PCP,
Karimi IA, Srinivasan R. Novel solution approach for optimization crude oil operations.
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[3] Li J, Li WK,
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Elia JA, Li J, Floudas CA. Planning and scheduling under uncertainty: A review
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[5] Li Z,
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[7] Cao CW, Gu
XS, Xin Z. Chance constrained programming models for refinery short-term crude
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[8] Wang JS,
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[9] Lin X, Janak
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[10] Janak SL,
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[11] Verderame PM,
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[12] Verderame
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[13] Verderame
PM, Floudas CA. Multisite planning under demand and transportation uncertainty:
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[14] Li ZK, Ding R, Floudas CA. A
comparative theoretical and computational study on robust counterpart
optimization: I. Robust linear optimization and robust mixed-integer linear
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