(658e) Data-Driven Robust Optimization Approach for Scheduling Oil Pipeline Systems

Data uncertainty is inevitable in real-life optimization problems e.g., data related to objective function’s coefficients, demand, machine reliability, processing times (flowrate), and so forth. Assuming deterministic values for such parameters will often render the resulting schedules to be infeasible in practice, thus forcing rescheduling procedures. Deterministic MILP formulations have been extensively developed for the pipeline scheduling problem and for a variety of configurations, but research dealing with data uncertainty has been quite sparse [Zhang 2021]. Muhlbauer [Muhlbauer 2004] evaluated the probability of small fluctuations in flowrate, which may cause delays in demand fulfillment, at 17%. BeheshtiAsl et al., [BeheshtiAsl, 2019] developed a two-stage stochastic programming approach to decrease the effects of flowrate uncertainty on the schedule. Moradi et al. [Moradi 2016] applied the Γ-robustness approach to schedule a pipeline comprised of a single input and a single output to overcome demand uncertainty. It relies on conventional robust optimization and thus: (i) may not leverage the statistical information of the historical data as much as possible, and (ii) can easily become overly conservative if the uncertainty set is poorly chosen, resulting in wide perturbation ranges which increase the cost of robustness.

In this paper, we first propose a slightly small-size deterministic mixed-integer linear programming (MILP) model for the scheduling of a pipeline that coveys a variety of oil products from a single refinery to multiple distribution centers [Castro 2019a, Castro 2019b]. We then develop the robust counterpart of the deterministic MILP model to consider uncertainty in flowrate and pumping cost. To overcome the main drawbacks of conventional robust optimization, we develop a data-driven model for constructing the uncertainty set, which is based on the data-driven robust optimization approach first introduced by Shang et al., [Shang 2017]. In specific, we will rely on linear kernel-based support vector clustering (SVM), as a popular unsupervised learning approach, to construct uncertainty sets related to flowrate and pumping costs. This is primarily because linear kernel-based SVM: (i) ensures that the uncertainty set is convex, (ii) preserves the linearity of the deterministic problem, (iii) takes into account the correlation between uncertain parameters, and (iv) brings computational convenience in forming the robust counterpart. When compared with the conventional robust optimization approaches (e.g., Γ-robustness approach), it is found that at the same constraint violation, the data-driven model performs better and leads to lower pumping costs.

References

[Shang, 2017] C. Shang, X. Huang, F. You, Data-driven robust optimization based on kernel learning. Computers & Chemical Engineering, Vol. 106 (2017), 464–479.

[BeheshtiAsl, 2019] N. BeheshtiAsl, S. A.MirHassani, Benders decomposition with integer sub-problem applied to pipeline scheduling problem under flow rate uncertainty, Computers & Chemical Engineering, Vol. 123 (2019), 222-235.

[Castro 2019a] P. M. Castro, Mostafaei, H., Batch-centric scheduling formulation for treelike pipeline systems with forbidden product sequences, Computers & Chemical Engineering, Vol. 112, (2019), 2–18.

[Castro 2019b] Q. Liao, Castro, P. M., Liang, Y., Zhang, H., “Computationally efficient MILP model for scheduling a branched multiproduct pipeline system”, Industrial and Engineering Chemistry Research, Vol. 58, (2019), 5236–5251.

[Moradi 2016] S. Moradi, S.A. Mirhassani, Robust scheduling for multi-product pipelines under demand uncertainty, The International Journal of Advanced Manufacturing Technology, Vol. 87 (2016), 2541-2549.

[Muhlbauer 2004] W. Kent Muhlbauer, Pipeline risk management: Ideas, Techniques and Resources, Elsevier, USA (2004).

[Zhang 2021] Z. Li, Y. Liang, Q. Liao, B. Zhang, H. Zhang, A review of multiproduct pipeline scheduling: From bibliometric analysis to research framework and future research directions, Journal of Pipeline Science and Engineering, Vol. 1(4) (2021), 395-406.