## 6 Results and Discussion
### Model Validation
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Batch** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline
1 & 0.0 & 28.3 & 40.2 & 22.6 & 316.5 & 19.4 & 254.3 & 209.1 & 254.3 & 49.1 & 508.6 & 486.0 \\
2 & 71.0 & 0.0 & 89.7 & 37.2 & 316.1 & 71.4 & 247.9 & 198.3 & 247.9 & 101.0 & 526.8 & 502.0 \\
3 & 11.3 & 39.6 & 0.0 & 33.9 & 327.8 & 11.3 & 265.6 & 220.4 & 265.6 & 28.4 & 519.9 & 497.3 \\
4 & 61.1 & 6.7 & 79.8 & 0.0 & 350.7 & 61.0 & 276.5 & 222.6 & 276.5 & 90.7 & 580.1 & 553.1 \\
5 & 575.2 & 505.6 & 593.9 & 490.9 & 0.0 & 600.8 & 155.6 & 218.5 & 154.1 & 630.5 & 192.1 & 169.5 \\
6 & 21.5 & 25.5 & 40.2 & 20.4 & 285.8 & 0.0 & 229.7 & 188.9 & 229.7 & 49.1 & 459.4 & 439.0 \\
7 & 466.4 & 402.3 & 485.1 & 393.1 & 55.7 & 486.6 & 0.0 & 120.6 & 0.0 & 516.3 & 228.0 & 207.8 \\
8 & 387.4 & 327.1 & 406.1 & 321.9 & 128.2 & 403.6 & 54.0 & 0.0 & 54.0 & 433.3 & 357.5 & 330.5 \\
9 & 466.4 & 402.3 & 485.1 & 393.1 & 64.6 & 486.6 & 41.0 & 120.6 & 0.0 & 516.3 & 264.1 & 240.7 \\
10 & 15.3 & 40.8 & 5.1 & 35.7 & 301.1 & 15.3 & 245.0 & 204.2 & 245.0 & 0.0 & 474.7 & 454.3 \\
11 & 723.9 & 647.8 & 738.4 & 614.3 & 317.0 & 766.3 & 415.9 & 410.6 & 389.8 & 789.8 & 0.0 & 107.4 \\
12 & 692.7 & 618.6 & 707.2 & 587.0 & 285.8 & 733.1 & 382.6 & 383.4 & 359.4 & 756.6 & 22.6 & 0.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Energy waste matrix for mixed batches (GJ). separately, but the production constraints and corresponding energy consumption of the slabs are considered in the modeling process. Figure 5 takes minimizing completion time as the objective function. The total completion time is 3832 min, and the rolling line operation rate is the highest, reaching 97.78%. However, the scheduling process did not consider the energy consumption of the slab conversion in the reheating furnace, resulting in the CCR-type batch being arranged for production between the DHCR and HCR batches, leading to a significant waste of energy. It is calculated that this scheduling mode consumes an additional 1855.6 GJ of gas energy,  
Figure 5: Scheduling Gantt chart for minimizing completion time. Figure 6: Scheduling Gantt chart for minimizing energy waste. Figure 7: Scheduling Gantt chart for mixed model. while the total rated gas energy consumption is 32,522.6 GJ, and the wasted energy accounts for 5.71% of the total consumption. Since batch type conversion can cause energy waste, multiple conversions of different types of batches should be avoided as much as possible. Due to the energy consumption characteristics of CCR-type batches, whether a DHCR- or HCR-type batch is heated after it, the energy consumption during cold- and hot-charging slab conversion is always relatively high. So, under the objective function of minimizing energy consumption, the processing time of batch 12 of the CCR type is arranged at the end of the rolling mill, which can effectively avoid the existence of batches of the DHCR or HCR types afterwards and reduce the waste of conversion energy in the reheating furnace, as shown in Figure 6 With this scheduling sequencing, the furnaces consume 549.3 GJ more gas resources, accounting for 1.69% of the total consumption, which is 70.4% less than the minimum completion time model. However, the final completion time is 4073 min, which is 241 min more than the minimum completion time model, and the rolling line operation rate is reduced by 5.78%. The decrease in the rolling line operation rate will increase the equipment vacancy time, thereby affecting the on-time delivery level of enterprises. Figure 7 shows the Gantt chart of a mixed scheduling model considering energy consumption and completion time. Under the influence of mixed scheduling, the completion time is 3868 min, and the wasted gas is 1066.9 GJ. Compared to the minimum completion time model, 42.50% of gas resources are saved. Compared to the minimum energy consumption model, the completion time is shortened by 205 min, and the rolling line operation rate increases by 4.88%.