(339f) Data-Driven Optimization of Integrated Planning and Scheduling Problems Under Demand Uncertainty

Supply chain management is an essential problem in many chemical industries, yet the optimal coordination among different layers of the supply chain network is a challenging task [1,2]. The interconnected, multi-level decision-making nature of these problems requires a holistic approach to ensure feasible realizations of the individual activities of the supply chain (i.e., the solution determined at the planning level leads to a feasible solution at the scheduling level) [3,4]. Bi-level multi-follower programming is well-suited for the task, as scheduling problems in each scheduling period (lower levels) provide constraints for the decision making in the planning problem (upper level), providing a certificate for guaranteed feasibility for the integrated problem. However, there are many algorithmic challenges for this class of mathematical programs, especially when high number of integer variables are present at the lower level problems, as in a scheduling formulation. These challenges are further amplified in the presence of uncertainty. For optimal supply chain management, one key obstacle is handling uncertainty at the tactical level, such as in production planning with uncertain demand [1,5].

In this work, a multi-stage stochastic formulation of the integrated planning and scheduling problem under demand uncertainty is proposed based on [6], where three stages are considered with an increasing level of uncertainty. To solve the resulting bi-level multi-follower problem, we build upon our previously developed DOMINO framework [7], a data-driven optimization algorithm for solving bi-level single-follower mixed-integer nonlinear programming problems. The proposed formulation and solution approach are illustrated through a planning and scheduling case study of a multi-product batch production plant [8].

References

[1] I. Grossmann. Enterprise-wide optimization: a new frontier in process systems engineering. AIChE Journal, 2005;51(7):1846-1857.

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

[3] J.-H. Ryu, V. Dua, E.N. Pistikopoulos. A bilevel programming framework for enterprise-wide process networks under uncertainty. Computers & Chemical Engineering, 2004;28:1121-1129.

[4] S. Avraamidou, E.N. Pistikopoulos. A novel algorithm for the global solution of mixed-integer bi-level multi-follower problems and its application to planning & scheduling integration. 2018 European Control Conference (ECC) June 12-15, 2018. Limassol, Cyprus, pp. 1056-1061.

[5] S. Avraamidou, E.N. Pistikopoulos. A Multiparametric Mixed-integer Bi-level Optimization Strategy for Supply Chain Planning Under Demand Uncertainty. IFAC World Congress, 2017, IFAC-PapersOnLine 50 Paper 1, pp 10178-10183.

[6] D. Wu, M.G. Ierapetritou. Hierarchical approach for production planning and scheduling under uncertainty, Chemical Engineering and Processing: Process Intensification, 2007;46(11):1129-1140.

[7] B. Beykal, S. Avraamidou, I.P.E. Pistikopoulos, M. Onel, E.N. Pistikopoulos. DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems. Journal of Global Optimization, 2020, DOI: 10.1007/s10898-020-00890-3

[8] M.G. Ierapetritou, C.A. Floudas, Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes, Industrial and Engineering Chemistry Research, 1998;37(11):4341-4359.