(368e) Integrated Scheduling and Control for Multiproduct Continuous and Batch Processes

Simultaneous scheduling and control involves process scheduling and control problems with an integrated framework in which production time and task transitions are considered simultaneously. Using the simultaneous approach a Mixed Integer Dynamic Optimization (MIDO) problem is formed and then is discretized into Mixed Integer Nonlinear Programming (MINLP) through collocation point method [1]. Solving the resulting MINLP generates the optimal production time, product sequence and transition profiles between different products. However, the resulting MINLP is generally computational very expensive. In the literature in order to achieve better computational performance, Lagrangean decomposition was applied to the integrated model, resulting in a master scheduling problem and a primal control problem [2]. Other works that decoupled MIDO problem into dynamic optimization  problem and MILP problem can be found in [3] where the solution was obtained using an iterative approach.

In our study, we explore the structure of the integrated optimization problem for continuous and batch processes and establish an efficient decomposition scheme based on the mathematical structure of the corresponding model. In continuous processes, we decompose the scheduling problem into an optimization model for the production time and a separate one for product sequence, and integrate the sequence consideration with the control problem. In this way, two sub-problems are formed. One is an MINLP dealing with the production sequence and control profile during transitions, and the other is an NLP dealing with the production time for each product considering the market demands. For batch processes, we decompose the integrated problem into an MINLP problem generating the optimal production sequence and operating conditions during process and an NLP yielding the optimal batch sizes to satisfy demands.

We prove the separability of the resulting two sub-problems analytically after decomposition.  Unlike the Lagrangean decomposition approach, no iteration is needed in our approach. Moreover, the computational complexity is significantly reduced compared to the simultaneous scheduling and control problem under varying demand. The main contribution of this work is that there is no need to solve the entire integrated problem for different demand specifications because the only decision variables that need to be updated are the production times, and the batch sizes for continuous, and batch processes, respectively. Based on this finding we are investigating the integration of the planning level decisions moving towards enterprise wide optimization.

References:

(1) Flores-Tlacuahuac, A.; Grossmann, I. E., Simultaneous Cyclic Scheduling and Control of a Multiproduct CSTR. Industrial & Engineering Chemistry Research 2006, 45, (20), 6698-6712.

(2) Terrazas-Moreno, S.; Flores-Tlacuahuac, A.; Grossmann, I. E., Lagrangean heuristic for the scheduling and control of polymerization reactors. AIChE Journal 2008, 54, (1), 163-182.

(3) Nystrom, R. H.; Franke, R.; Harjunkoski, I.; Kroll, A., Production campaign planning including grade transition sequencing and dynamic optimization. Computers & Chemical Engineering 2005, 29, (10), 2163-2179.