Integration of scheduling and control with online closed-loop implementation: Fast computational strategy and large-scale global optimization algorithm

In this paper, we propose a novel integration method to solve the scheduling problem and the control problem simultaneously. The integrated problem is formulated as a mixed-integer dynamic optimization (MIDO) problem which contains discrete variables in the scheduling problem and constraints of differential equations from the control problem. Because online implementation is crucial to deal with uncertainties and disturbances in operation and control of the production system, we develop a fast computational strategy to solve the integration problem efficiently and allow its online applications. In the proposed integration framework, we first generate a set of controller candidates offline for each possible transition, and then reformulate the integration problem as a simultaneous scheduling and controller selection problem. This is a mixed-integer nonlinear fractional programming problem with a non-convex nonlinear objective function and linear constraints. To solve the resulting large-scale problem within sufficiently short computational time for online implementation, we propose a global optimization method based on the model properties and the Dinkelbach's algorithm. The advantage of the proposed method is demonstrated through four case studies on an MMA polymer manufacturing process. The results show that the proposed integration framework achieves a lower cost rate than the conventional sequential method, because the proposed framework provides a better tradeoff between the conflicting factors in scheduling and control problems. Compared with the simultaneous approach based on the full discretization and reformulation of the MIDO problem, the proposed integration framework is computationally much more efficient, especially for large-scale cases. The proposed method addresses the challenges in the online implementation of the integrated scheduling and control decisions by globally optimizing the integrated problem in an efficient way. The results also show that the online solution is crucial to deal with the various uncertainties and disturbances in the production system.