A decomposition-based two-stage online scheduling approach and its integrated system in the hybrid flow shop of steel industry

Steelmaking-continuous casting (SCC) is one of the most critical building blocks in the modern steel industry. Many random events occur in the real-world SCC production system. In this paper, we propose a two-stage online scheduling policy that protects the baseline schedule by the slacks provided by intra-flow times and casting speeds. The main task of the two-stage online scheduling model is: (1) to make "here-and-now" decisions for minimizing economic costs and penalties caused by constraint violations; (2) make "wait-and-see" decisions for online scheduling. Afterward, we propose a decomposition-based optimization algorithm that divides the online scheduling problem into a master problem (MP) to seek partial solutions at the last processing stage and a slave problem (SP) to check optimal solutions for upstream processing stages. Then, we employ the IBM ILOG CPLEX to solve MP and use the constraint programming (CP) optimizer to solve SP. Sensitivity analyses and algorithm comparisons are conducted on a set of well-synthetic and realistic instances to validate the proposed model and algorithm. The results show that the proposed online scheduling model and algorithm can solve realistic in-dustrial case studies. Finally, we also develop a scheduling system integrating the proposed model and algorithm.