Production scheduling and process control are historically separate layers of decision making within the scope of the operation of chemical processes. However, improvements in process economics provide a strong incentive for integrating control and dynamic considerations within the production scheduling framework [1, 2]. The integration of scheduling and control is a challenging task owing to the different time scales involved in making the respective decisions, and the corresponding need to balance long-term prediction with real-time execution .
In our previous work , we proposed using a (continuous-time), low-order representation of the input-output closed-loop dynamics of the process, which we referred to as a “scale-bridging model (SBM),” to incorporate dynamic information in the scheduling formulation. In this paper, we present an extension of our results to discrete-time SBMs. We focus on time-series modeling of the closed-loop process dynamics, focusing in particular on the use of autoregressive models with exogenous inputs (ARX models) to capture the relevant process components. Based on these discrete-time scale bridging models (DSBMs) , we develop a hybrid discrete- and continuous-time formulation of the integrated scheduling and control problem for continuous processes.
The DSBM is included in the scheduling calculation as a constraint, thereby providing information on the role that transitions and dynamics play in the process economics. Within this framework, we introduce a novel approach for using the DSBMs to determine transition times between product grades, using a reverse integration of the output error (RIE) of the system. The resulting integrated scheduling and control framework is computationally efficient owing to the fact that the DSBM and RIE calculation are linear. We also demonstrate that the proposed data-driven framework is widely applicable in industry, and show that DSBMs can easily be derived from operating data that are routinely collected from the operation of multi-product processes.
We present a multi-product CSTR case study to demonstrate the effectiveness of our approach. For comparison purposes, we show that the optimal schedule determined using the DSBM and RIE matches the results obtained when using a rigorous process model, while exhibiting superior computational performance.
 M. Baldea and I. Harjunkoski, “A systematic review of the integration of production scheduling and process control,” Comput. Chem. Eng., 71:377–390, 2014.
 I. Grossmann. Enterprise-wide optimization: A new frontier in process systems engineering. AIChE J., 51:1846–1857, 2005.
 C.T. Maravelias and C. Sung. Integration of production planning and scheduling: Overview, challenges and opportunities. Comput. Chem. Eng., 33(12):1919-1930, 2009.
 J. Du, J. Park, I. Harjunkoski, and M. Baldea, “A Time-Scale Bridging Approach for Integrating Production Scheduling and Process Control”, Comp. Chem. Eng http://dx.doi.org/10.1016/j.compchemeng.2015.04.026.
 C. Touretzky, I. Harjunkoski, and M. Baldea, “Autoregressive Reduced Order Models for Integrated Scheduling and Control of Process Systems”, Submitted to the 2015 Conference on Decision and Control.