(373ae) Data-Driven Approaches for the Optimization of Complex Planning and Scheduling Problems in Multi-Product Industries

Increased competitiveness in the chemical industry has led to multi-product factories; therefore, achieving enterprise-wide optimization (EWO) is paramount for process industries [1]. This involves integrating and coordinating planning and scheduling activities, which are essential components of EWO execution. One significant challenge for achieving EWO is the effective integration and coordination of optimal decisions across individual, yet interlinked, problems that occur at different timescales. Scheduling problems coordinate the assignment and duration of tasks for production within shorter decision timescales (e.g., hours), whereas planning problems analyze product demand to determine the optimal production targets across a longer timescale (e.g., weeks or months) [2,3]. These two different layers of the EWO problems can simultaneously be addressed using bi-level optimization [4] with scheduling problems imposed as a constraint on the planning level. However, such hierarchical decision-making problems suffer from certain practical obstacles because of the computational complexities. While many solution strategies rely on transforming bi-level optimization into one-level problems using Karush-Kuhn-Tucker optimality conditions [3], the presence of integer decisions and the highly nonlinear nonconvex nature of the scheduling problems preclude the use of such reformulation strategies. Heuristics [5], branch-and-bound, cutting plane, and parametric techniques [3] were previously developed to overcome algorithmic challenges surrounding bi-level optimization. However, addressing problems with mixed-integer nonlinear formulations remains relatively limited, with existing solutions [6] struggling to handle a high number of variables.

In this work, we utilize data-driven optimization with the DOMINO framework [7] to overcome the aforementioned challenges in EWO problems with planning levels subject to mixed-integer nonlinear (MINLP) scheduling levels with high number of variables. We previously showed the successful application of the DOMINO framework in achieving near-optimal solutions for general constrained bilevel optimization problems encompassing continuous linear, continuous nonlinear, mixed-integer linear, or integer nonlinear lower levels [7]. Now, we demonstrate the successful application of DOMINO in solving bilevel optimization problems with MINLP lower levels through case studies that explore different levels of complexity, ranging from scheduling crude oil operations using a continuous-time formulation to scheduling continuous manufacturing processes using a traveling salesman problem formulation [8,9]. We test the computational efficiency of a range of data-driven optimizers, including NOMAD, PSO, and ARGONAUT. Our results show that we can find the near-optimal solution for high dimensional integrated planning and scheduling problems using our data-driven approach. We also present Gantt charts to provide useful insights into the efficiency, and viability of different data-driven optimization approaches when comparing the scheduling solutions.

Acknowledgement:

JS & VC gratefully acknowledge the financial support under the EPSRC grants EP/V051008/1 & EP/W003317/1.

References:

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[3] Dempe, Stephan, et al. "Bilevel programming problems." Energy Systems. Springer, Berlin 10 (2015): 978-3.

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[5] Biswas, Arpan, and Christopher Hoyle. "A literature review: solving constrained non-linear bi-level optimization problems with classical methods." International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Vol. 59193. American Society of Mechanical Engineers, 2019.

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[7] Beykal, S. Avraamidou, I.P. Pistikopoulos, M. Onel, and E.N. Pistikopoulos, “Domino: Data-driven optimization of bi-level mixed-integer nonlinear problems,” Journal of Global Optimization, 78, pp. 1-36, 2020.

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[9] Z. Jia, M. Ierapetritou, and J.D. Kelly, “Refinery short-term scheduling using continuous time formulation: Crude-oil operations,” Industrial & Engineering Chemistry Research, 42(13), pp. 3085-3097. 2003