Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies.

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques like MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is a manual and time-consuming process. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies.