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389669 Integrated Planning, Scheduling, and Dynamic Optimization of Continuous Manufacturing Processes

Planning, scheduling, and dynamic optimization of chemical processes are highly interconnected [1-5]. The aim of planning is to determine the production assignment of the manufacture processes from the enterprise level over a long time horizon. In each planning periods, scheduling is used to determine the production sequence and time, task assignment, resource allocation, etc. Dynamic optimization is to determine the optimal transition processes when different products are manufactured in a processing unit sequentially. Though the three problems are able to be solved sequentially, the integration of these problems will result in a better performance compared to sequential approaches and has gathered increasing attention recently [6-16].

However, most of the previous studies concentrate on only parts of the integrated problem. Some works focus on the integrated problem of planning and scheduling, where the transition times and the transition costs are assumed to be known parameters [12]. Some other works concentrate on the integration of scheduling and dynamic optimization considering variable transition times and transition costs, which are determined by time-dependent trajectories [7, 17-20]. The integrated problem is formulated into a mixed-integer dynamic optimization (MIDO) model, which is then reformulated into a mixed-integer nonlinear programming (MINLP) full space model by discretizing the differential equations [7, 21, 22]. The full space model characterizes all the detailed information of planning, scheduling, and dynamic optimization, however, a large amount of computational time is needed to solve the full space model due to its large-scale [23].

In this work, we propose a novel method for solving the integrated planning, scheduling, and dynamic optimization problem for a multi-product continuous process. We first reformulate the integrated MIDO problem into a large-scale MINLP full space problem. To reduce the computational complexity, we propose an efficient flexible recipe method which can approximate the full space model into an online planning and scheduling model and offline dynamic optimization models. The key is that the planning and scheduling model is linked to the dynamic models via transition times and transition costs. The relationship between a transition time and the corresponding transition cost can be approximated by a set of discrete points, which are obtained by solving the dynamic optimization problems offline. The candidate transition times and transition costs are then appended to the planning and scheduling level problem, replacing the nonlinear equations concerning the dynamic models. The flexible recipe method ends up to be a mixed-integer linear program (MILP), which is easier to solve than the original MINLP full space problem. A bi-level decomposition method is then introduced to further improve the computational efficiency of the flexible recipe method, which formulates the upper level planning problem and lower level detailed problem. The Bi-level method then solves the upper and lower level problems iteratively until a pre-determined stopping condition is met.

To demonstrate the applicability of the proposed full space modeling framework, flexible recipe method and bi-level decomposition algorithm, we investigate a methyl methacrylate (MMA) polymerization process with azobisiso-butyronitrile initiator and a toluene solvent. The dynamic model of the MMA process is described by a set of differential equations. Different products with different molecular weights are produced during the steady state production time period. Through the proper arrangement of the production manufacturing, the process industry will be able to increase their profits. An integrated model is formulated to contain decision making across production assignment, production sequence and time and transition process strategy according to specific order demand. In a small scale problem, there are 3 products and 3 24-hour-long planning periods. The result reveals that: both the flexible recipe method and the bi-level decomposition algorithm can solve the problem within 2 seconds with the MILP solver CPLEX 12, while the full space method takes 3,000 seconds computational time to solve the problem with the MINLP solver SBB. In a large scale problem, there are 5 products and 4 168-hour-long planning periods. The bi-level decomposition algorithm can solve the problem within 2 minutes and the flexible recipe method can solve the problem with about 40 min (both methods use the MILP solver CPLEX 12), while the full space method fails to obtain a feasible solution within 30 hours with the MINLP solver SBB. From the result of the case study, the computational efficiency of the proposed solution methods is demonstrated.

References

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[13] Y. Chu, F. You, J. M. Wassick, and A. Agarwal, "Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method," *Computers & Chemical Engineering, *2014.

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[15] D. J. Yue and F. Q. You, "Planning and Scheduling of Flexible Process Networks Under Uncertainty with Stochastic Inventory: MINLP Models and Algorithm," *AIChE Journal, *vol. 59, pp. 1511-1532, May 2013.

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[17] Y. F. Chu and F. Q. You, "Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation," *AIChE Journal, *vol. 59, pp. 2379-2406, Jul 2013.

[18] Y. F. Chu and F. Q. You, "Integration of production scheduling and dynamic optimization for multi-product CSTRs: Generalized Benders decomposition coupled with global mixed-integer fractional programming," *Computers & Chemical Engineering, *vol. 58, pp. 315-333, Nov 11 2013.

[19] Y. F. Chu and F. Q. You, "Integration of Scheduling and Dynamic Optimization of Batch Processes under Uncertainty: Two-Stage Stochastic Programming Approach and Enhanced Generalized Benders Decomposition Algorithm," *Industrial & Engineering Chemistry Research, *vol. 52, pp. 16851-16869, Nov 27 2013.

[20] A. Flores-Tlacuahuac and I. E. Grossmann, "Simultaneous Scheduling and Control of Multiproduct Continuous Parallel Lines," *Industrial & Engineering Chemistry Research, *vol. 49, pp. 7909-7921, Sep 1 2010.

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[23] L. T. Biegler, *Nonlinear programming: concepts, algorithms, and applications to chemical processes* vol. 10: SIAM, 2010.

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