(158f) Travelling Salesman Problem (TSP) Based Integration of Planning, Scheduling and Control for Continuous Processes

Advanced decision making in the process industries requires efficient use of information available at the different hierarchical decision levels ^[1]. Traditionally, planning, scheduling and control problems are solved in a decoupled way, neglecting the strong interdependence among them. Integrated Planning, Scheduling and Control (iPSC) aims to address this issue ^[2,3]. In the last few years, a considerable amount of research work has focused on the integration of scheduling and control in order to enhance feasibility, robustness and profitability of the operations in the chemical industries while planning was until recently dealt hierarchically. Formulating the iPSC problem results in a complex optimisation problem involving continuous (algebraic and differential) and integer variables. Since planning, scheduling and control problems consider different time scales (varying from seconds for control to weeks or months for scheduling and planning), the final optimisation problem can be computationally intensive ^[4,5]. Until now, most of the research done in the context of integrating the control with operations has used as basis for the planning and scheduling, time-slot based formulations and little to none attention has been given to immediate precedence formulations such as the one presented in Liu et al. (2008) ^[6]where the authors proposed a Travelling Salesman Problem (TSP) formulation.

In the present work, we propose a new approach for the iPSC problem of continuous processes aiming to reduce model and computational complexity. The original nonlinear dynamics, which arise in the control of the process, are approximated with piece wise affine (PWA) dynamics within specific regions of validity. For the planning and scheduling we use a TSP based formulation ^[6] where the planning periods are modelled in discrete time while the scheduling within each week is in continuous time. Another key feature of the proposed iPSC framework is that backlog and multiple orders from different customers are allowed. The resulting iPSC problem is a Mixed Integer Programming (MIP) problem and different solution strategies are employed and analysed. Model Predictive Control (MPC) is employed to account for the stability and recursive feasibility of the underlying control problem. Finally, the proposed iPSC approach is tested on a number of case studies and compared with existing approaches.

References

1. Grossmann, I. E. (2012). Advances in mathematical programming models for enterprise-wide optimization. Computers & Chemical Engineering, 47, 2-18.
2. Chu, Y., & You, F. (2015). Model-based integration of control and operations: Overview, challenges, advances, and opportunities. Computers & Chemical Engineering, 83, 2-20.
3. Baldea, M., & Harjunkoski, I. (2014). Integrated production scheduling and process control: A systematic review. Computers & Chemical Engineering, 71, 377-390.
4. Chu, Y., & You, F. (2014). Integrated planning, scheduling, and dynamic optimization for batch processes: MINLP model formulation and efficient solution methods via surrogate modeling. Industrial & Engineering Chemistry Research, 53(34), 13391-13411.
5. Gutiérrez-Limón, M. A., Flores-Tlacuahuac, A., & Grossmann, I. E. (2014). MINLP formulation for simultaneous planning, scheduling, and control of short-period single-unit processing systems. Industrial & Engineering Chemistry Research, 53(38), 14679-14694.
6. Liu, S., Pinto, J. M., & Papageorgiou, L. G. (2008). A TSP-based MILP model for medium-term planning of single-stage continuous multiproduct plants. Industrial & Engineering Chemistry Research, 47(20), 7733-7743.