Integrated Scheduling and Dynamic Optimization by Stackelberg Game: Bilevel Model Formulation and Efficient Solution Algorithm

We propose a novel method to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The scheduling problem and the dynamic optimization problems are collaborated by a Stackelberg game (leader–followers game). Mathematically, the integrated problem is formulated into a bilevel program. The scheduling problem in the upper level acts as the leader, while the dynamic optimization problems in the lower level are the followers. The follower problems have their own objectives, but the leader problem can coordinate the follower problems to pursue its objective. To efficiently solve the bilevel program, we develop a decomposition algorithm. It first solves the lower-level problems to determine the response functions. The response functions are then represented by piecewise linear functions to solve the upper-level problem. The integrated method is consistent with the ISA 95 standard and can be easily implemented in an IT infrastructure following the standard. The performance of the proposed method is demonstrated in a complicated batch plant in comparison with the traditional sequential method which solves the scheduling problem and the dynamic optimization problems separately, and the simultaneous method which formulates the integrated problem into a monolithic model.