Integration of Scheduling and Control for Chemical Batch Plants under Stochastic Uncertainty: A Back-Off Approach

A new back-off methodology is presented to address mixed integer dynamic optimization (MIDO) formulations that arise from modeling the integration of scheduling and control of flow-shop batch plants under stochastic parametric uncertainty. The core idea of the methodology is to generate optimal scheduling and control decisions combined with optimal unit operation times that offer dynamic feasibility in the presence of stochastic parametric uncertainty using a back-off strategy. Back-off terms are introduced in the model constraints to represent the variability of the system caused by the stochastic uncertainty. The proposed framework decomposes the MIDO problem into a parametric sensitivity analysis, a scheduling problem, a dynamic optimization problem, and a set of dynamic feasibility problems (dynamic feasibility test) that are solved in an iterative fashion until convergence. A key novelty in this work is the addition of a parametric sensitivity analysis that generates correlations included in the scheduling problem to account for process dynamics. A case study featuring a flow-shop batch plant consisting of two dynamic reaction processes and two steady-state separation processes is used to test the performance of the proposed back-off methodology. The results show that unit operation times chosen from optimization are better suited to accommodate stochastic parametric uncertainty, while the control actions enforce process operational and product quality constraints at reasonable economic costs. Hence, the method proposed in this work has the potential of addressing optimal scheduling and control problems under stochastic realizations in flow-shop batch plants.