Integration of Scheduling and Dynamic Optimization of Batch Processes under Uncertainty: Two-Stage Stochastic Programming Approach and Enhanced Generalized Benders Decomposition Algorithm

Integration of scheduling and dynamic optimization significantly improves the overall performance of a production process compared to the traditional sequential method. However, most integrated methods focus on solving deterministic problems without explicitly taking process uncertainty into account. We propose a novel integrated method for sequential batch processes under uncertainty. The integrated problem is formulated into a two-stage stochastic program. The first-stage decisions are modeled with binary variables for assignment and sequencing while the second-stage decisions are the remaining ones. To solve the resulting complicated integrated problem, we develop two efficient algorithms based on the framework of generalized Benders decomposition. The first algorithm decomposes the integrated problem according to the scenarios so that the subproblems can be optimized independently over each scenario. Besides the scenario decomposition, the second algorithm further decomposes dynamic models from the scheduling model, resulting in a nested decomposition structure. For a complicated case study with more than 3 million variables/equations under 100 scenarios, the direct solution approach does not find a feasible solution while the two decomposition algorithms return the optimal solution. The computational time for the first algorithm is 23.9 h, and that for the second algorithm is only 3.3 h. Furthermore, the integrated method returns a higher average profit than the sequential method by 17.6%.