###### Abstract  
As the main energy-consuming equipment, the reheating furnace plays an important role in the scheduling of continuous casting and hot rolling for a steel mill. This paper studies the energy consumption of cold and hot slab conversion mode in a reheating furnace, forming four conversion relationships, with the goal of minimizing the coupling function between the maximum completion time of the hot rolling and the energy waste of the reheating furnace, and modelling the scheduling of a continuous casting-hot rolling process. An improved ordered pair bat algorithm is used to solve for special process conditions of the proposed scheduling model. The effectiveness of the proposed model and algorithm is verified by solving the different slab charging sequence and conversion mode. Moreover, a comparative study of different types of batches is also conducted, and it is found that the model can save more than 5000 GJ per month for the steel mill, which can achieve the goal of effective energy saving and increasing enterprise profit. steel mill scheduling; continuous casting-hot rolling process; cold- and hot-charging slabs conversion; reheating furnace; ordered pair bat algorithm; energy saving +
Footnote †: journal: Applied sciences  
small batches makes it impossible to have continuous hot charge production, and there must be a conversion between hot charging and cold charging mode in production. In fact, when both hot- and cold-charging slabs are mixed in the reheating furnace, there will be temperature differences between adjacent processed slabs. It not only has a significant impact on the reheating quality of the slab but also affects the production rhythm of the slab, leading to energy waste in the reheating furnace. In today's increasingly tense energy situation, if effective production scheduling can be carried out on the reheating furnace, the energy conversion consumption during the mixing of cold-charging and hot-charging slabs will be minimized, and the effective utilization of energy will increase. This can not only alleviate the current national and international energy shortage but also greatly increase the profits of the enterprise itself. Therefore, when modelling the scheduling of the continuous casting-hot rolling process, it is not only necessary to consider the scheduling of the continuous casting process and hot-rolling line, but also the impact of the reheating furnace, forming a multi-process, collaborative integrated model of continuous casting, reheating furnace, and hot rolling. This integrated scheduling can significantly affect production efficiency, product delivery time, and customer satisfaction, while reducing enterprise energy consumption and improving its scheduling enforceability. In the existing research, most of them focus on the production-matching problem of continuous casting, hot rolling, and energy considerations are focused on minimizing residence time or maximizing the hot-charging rate. This paper mainly focuses on the continuous casting and hot rolling problem of steel enterprises that takes into account the energy conversion mode of reheating furnaces. And an improved ordered pair bat algorithm is adopted to achieve the weighted coupling optimization goal of minimizing completion time and energy waste. Ultimately, it achieves energy-saving and profit maximization for steel mills. Overall, the comparison between this study and the existing research is shown in the Table 1.  
The contributions made by the research in this paper are mainly:  
1. Previous research on the energy savings of reheating furnaces mostly focused on thermal energy, and scheduling often aimed to minimize the residence times for each slab without exploring the cold and hot conversion of slabs in the furnace. This study considered the cold-charging and hot-charging slabs conversion mode of the reheating furnace and formed corresponding energy-consumption expressions;
2.