(577e) Continuous Production Scheduling: Representation, Modeling and Computational Advances

Research in the field of chemical production scheduling (CPS) has addressed numerous processing characteristics such as batch mixing/splitting, changeovers, utilities, and material transfer restrictions in order to accurately model features of real-world applications; however, continuous processes have received less attention in the literature. Modeling continuous processes, particularly with transient operations (such as startups, shutdowns, and transitions), has been a challenge because the approaches that involve integrated scheduling–dynamic optimization usually lead to accurate models, but they can only be applied to systems with few units and tasks due to computational limitations. Inversely, the standalone scheduling approaches generally rely on coarse approximations of the transient operations that lead to solutions which may not be feasible in practice. Furthermore, the majority of the solution methods for scheduling models have been developed for batch processes.

In this talk, we will review advances that have been made over the next five years to address continuous production scheduling. First, we propose a general mixed-integer linear programming (MILP) model that retains computational efficiency while, at the same time, effectively accounts for system dynamics during transient operations¹. With the proposed modeling formulation in mind, we then develop a comprehensive chemical production scheduling representation, denoted as the General Material Task System (GMTS), that allows one to express problems in multiple production environments, with various characteristics (e.g., transient operations) and under different constraints (e.g., storage policies)². The GMTS also provides a way to represent process-relevant information such as utility usage, processing rate ranges, and associated costs. This novel representation, in conjunction with the previously proposed model for the scheduling of continuous processes, provides a general optimization framework that can be implemented in a variety of applications to improve manufacturing operations.

Though problem generality is one critical goal, and our efforts to address it have been specified above, another ubiquitous challenge is the need to computationally enhance scheduling models. We propose a demand propagation algorithm (DPA), implemented as a preprocessing step, that utilizes demand information, network connectivity, and other known system parameters to calculate minimum bounds on production³. These parameters are used in a series of tightening constraints to tighten the feasible space of the linear programming (LP) relaxation of the MILP problem, which consequently reduce computational times significantly. All models incorporating tightening constraints outperformed the original model, and for approximately 80% of the instances we tested, our best-performing formulations improved solution times by an order of magnitude. This technique is not restricted to continuous production scheduling models or even CPS models; it can be applied to any time-based scheduling models with known demand information.

Other methods to reduce computational resources of continuous production scheduling models are discussed. One such approach involves the use of multiple and nonuniform time grids because, when strategically employed, multi-grid models have been shown to be computationally more effective than single grid models⁴. Utility-specific grids can be applied to general resources such as cooling and heating utilities. In addition to multiple heterogeneous time grids, utility information can be used to further reduce solution times of continuous CPS models through the use of tightening constraints because the utility requirements of tasks are known a priori. This information combined with the knowledge of utility availability enables us to exploit the structure of problem instances and enforce bounds on task execution. This procedure draws parallels to the preprocessing bound calculations of the DPA, where bounds on task execution are generated based on restrictions due to utility availability.

Keywords

Computing and systems engineering, production scheduling, continuous processes, solution methods

References

1. Wu Y, Maravelias CT. A general framework and optimization models for the scheduling of continuous chemical processes. AIChE J. 2021;67(10). doi:10.1002/aic.17344
2. Samadi A, Maravelias CT. A Comprehensive Chemical Production Scheduling Representation. Comput Chem Eng. Published online February 1, 2024:108552. doi:10.1016/J.COMPCHEMENG.2023.108552
3. Samadi A, Maravelias CT. Computational enhancements of continuous production scheduling MILPs using tightening constraints. Comput Chem Eng. 2024;184:108609. doi:10.1016/J.COMPCHEMENG.2024.108609
4. Velez S, Maravelias CT. Multiple and nonuniform time grids in discrete-time MIP models for chemical production scheduling. Comput Chem Eng. 2013;53:70-85. doi:10.1016/j.compchemeng.2013.01.014