(287h) Simultaneous Planning and Scheduling Under Demand Uncertainty for Multi-Product Systems Using Data-Driven Bi-Level Optimization

Current industrial processes require the coordination of many interconnected pieces that involve multi-dimensional, multi-purpose, and multi-product systems. Across the different layers of supply chain management, starting from the supply chain structure to production planning and scheduling, the optimal coordination of each element and their robust response to changing market conditions is essential for increasing efficiency, resiliency, productivity, and profitability of any enterprise [1-3]. Yet, the modeling and optimization of such interdependent systems are still burdensome and requires a holistic approach to ensure feasible realizations of the individual activities of the supply chain [4]. Bi-level multi-follower programming is well-suited for the task, as scheduling problems (followers) provide constraints for the decision making in the planning problem (leader). However, there are many algorithmic challenges for this class of mathematical programs, especially when high number of integer variables are present at the scheduling problems. These challenges are further amplified in the presence of uncertainty at the tactical level where planning and scheduling decisions will have to account for unknown product demands, resource availabilities, and current market conditions [2,5].

In this work, we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming, scenario analysis, and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. The data-driven optimization of this challenging class of problems is performed using the DOMINO framework [6], and the proposed formulation and solution approach is demonstrated on a multi-product batch production plant [7]. We further analyze the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.

References

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

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

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

[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] 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, 78:1-36.

[7] Kondili, E., 1987. Optimal scheduling of batch processes. Ph.D. Thesis, Imperial College London, London, UK.