(347d) Data-Driven Optimization of Mixed-Integer Nonlinear Integrated Planning and Scheduling Problems for Multiproduct Manufacturing Processes

Industries in today's highly competitive and interconnected markets can only survive on thin profit margins. Maintaining competitiveness, sustainability, and development in this environment necessitates careful attention to enterprise planning, and effective coordination across production plants and distribution centers [1]. However, optimizing such interdependent systems is very challenging and requires a systematic approach to ensure each activity in the supply chain is feasible and can realistically be implemented. The case of simultaneous optimization of the planning and scheduling activities in the process industries has been a focal point of research within the process systems engineering = literature with their monolithic integration being predominantly explored [2,3].

Bi-level multi-follower programming offers a holistic approach to enterprise-wide optimization because the lower-level scheduling problems act as a constraint on the planning (upper) level decisions [4]. Yet, bi-level programs are NP-hard and algorithmic difficulties are even more pronounced in the presence of large number of integer variables and nonlinearities involved at the scheduling level which prevents the use of Karush-Kuhn-Tucker optimality conditions for reducing the bi-level formulation to a single-level problem.

In this work, we address such mathematical challenges associated with planning problems subject to mixed-integer nonlinear (MINLP) scheduling levels using data-driven optimization algorithms. We formulate the problem as a bi-level program and address its optimization using the DOMINO framework [5]. DOMINO samples the production targets of the planning level using Design of Experiments and solves the scheduling level to global optimality at those production targets over the entire planning period. The input samples and the output optimality information are then used to perform data-driven optimization with existing subroutines. We have previously shown that DOMINO can retrieve the near-optimal guaranteed feasible solutions to various kinds of benchmark bi-level formulations (e.g., LP-LP, LP-MILP, NLP-NLP, NLP-MIQP, etc.) [5] as well as LP-MILP formulations of integrated planning and scheduling problems with and without demand uncertainty [6,7]. Here, we further extend this algorithm to solve lower-level problems with MINLP scheduling components and provide guaranteed feasible solutions to one of the most challenging bi-level formulations using local and global data-driven optimization algorithms. We demonstrate the applicability of our approach on a multiproduct continuous manufacturing process formulated as a traveling salesman problem [8] and examine how thousands of constraints and hundreds of continuous and binary variables at both levels affect the solution quality.

References

[1] Papageorgiou, L.G., 2009. Supply chain optimisation for the process industries: Advances and opportunities. Computers & Chemical Engineering, 33(12), pp.1931-1938.

[2] Grossmann, I., 2005. Enterprise‐wide optimization: A new frontier in process systems engineering. AIChE Journal, 51(7), pp.1846-1857.

[3] Maravelias, C.T. and Sung, C., 2009. Integration of production planning and scheduling: Overview, challenges and opportunities. Computers & Chemical Engineering, 33(12), pp.1919-1930.

[4] Avraamidou, S. and Pistikopoulos, E.N., 2018. A novel algorithm for the global solution of mixed-integer bi-level multi-follower problems and its application to Planning & Scheduling integration. In 2018 European Control Conference (ECC), pp. 1056-1061. IEEE.

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

[6] Beykal, B., Avraamidou, S. and Pistikopoulos, E.N., 2022. Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty. Computers & Chemical Engineering, 156, p.107551.

[7] Beykal, B., Avraamidou, S. and Pistikopoulos, E.N., 2021. Bi-level mixed-integer data-driven optimization of integrated planning and scheduling problems. In Computer Aided Chemical Engineering (Vol. 50, pp. 1707-1713). Elsevier.

[8] Charitopoulos, V.M., Papageorgiou, L.G. and Dua, V., 2019. Closed-loop integration of planning, scheduling and multi-parametric nonlinear control. Computers & Chemical Engineering, 122, pp.172-192.