A Review of Integrated Optimization Method of Batch Planning and Scheduling for Steelmaking-Continuous Casting-Hot Rolling Production Under Uncertain Environment Based on Lagrangian Relaxation Framework

The integrated process of steelmaking, continuous casting, and hot rolling (SM-CC-HR) covers the entire process from refining liquid steel to manufacturing semi-finished steel products. Its batch planning and scheduling are connected to the production contract plan at the upper level and the production process control at the lower level, which is the key to achieving efficient and full process steel manufacturing. Batch planning determines the location of the slabs to be produced in the converter, ladle, continuous casting machine, and hot rolling mill by combining production orders, process standards, and production conditions. Production scheduling, guided by batch planning, combines production performance indicators, process constraints, etc., to determine the equipment selection and start-stop times of specific production units at each process. The synergy of the two aims to optimize production profitability, energy consumption, efficiency, etc., through rational decisions, ensuring the efficiency and flexibility of the steel production process. However, due to the traditional “divide and conquer” management mode and the influence of many uncertain factors, it is difficult to ensure the flexible balance between the demand and capacity, as well as a reasonable matching of logistics and resources among the production processes that operate independently. Considering the uncertain environment and the integration of SM-CC-HR, this paper summarizes the research status of previous scholars from three aspects: mathematical modeling, model optimization, and algorithm optimization based on the Lagrangian framework. It discusses the research status of batch planning and scheduling methods for SM-CC-HR production based on the Lagrangian relaxation framework, analyzes the problems existing in current research, and points out the main research directions and important research contents in the future, in order to promote the research and application of batch planning and scheduling problems for SM-CC-HR under uncertain environments.