# Energy-Efficient Hybrid Flow-Shop Scheduling under Time-of-Use and Ladder Electricity Tariffs
## 4 Case Study
### Evaluation of the Example
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Jobs**} & \multicolumn{8}{c}{**Average Processing Time (h)/Average Power Demanded (kW)**} \\ \  
A non-dominated solution of improved NSGA-II algorithm (f1 = 23.6 h, f2 = 6173.6 yuan) corresponding to the processing sequence 8-2-10-7-5-3-12-13-14-6-4-9-11-15-1 is chosen as an example. Figure 7 is a Gantt graph with right shift operation under TOU and ladder electricity price, and Figure 8 is a Gantt graph without right shift operation at the TOU and ladder electricity price (f1 = 23.6 h, f2 = 6453.08 yuan). The are 16 machines (one stage has parallel machines) and 12 jobs in the HFSP. While there is an optimization solution, Job 8 will work first in the machine 1 (M1), and Job 2 work on the machine 2 (M1), Job 7 and Job 10 will start after the previous jobs finishing the process. As shown in Figure 7, X axial represents the processing time (hour in a day), while the Y axial represents the Machine index. While M1 and M2 are the parallel machines in the same stage, each line belonging to the machine represents the jobs processed above the machine, The legend on the right represents job Index, while each color represents the different job. The comparison shows that there are many processes that have shifted the processing time. For example, workpiece 12 on machine 7 and workpieces 11 on machine 16 had been transferred from high electricity price to low price. By maintaining the production efficiency  
Figure 8: Gantt after the Right-Shift. Figure 7: Gantt before Right-Shift. and reducing the energy consumption cost by 4.33%, a total of 279.48 yuan is saved. In the trend chart of the processing cycle, the total electricity consumption trend chart of all machines is shown in Figure 7, where TEC represents the total electricity consumption of all machines. The periods of high electricity prices are close to 10 h and 20 h, and the total electricity load of all machines decreases after the machine is moved to the right. Therefore, the electricity load has shifted significantly under the TOU electricity price, achieving the goal of \"shaving peaks and filling valleys\", effectively reducing energy consumption costs and carbon emissions. The above conclusions shows that the right shift operation is effective for processing workpiece allocation without changing the maximum complete time. Moving high-energy-consuming workpieces into the low-electricity price range can greatly reduce costs and energy consumption. To some extent, carbon emissions would also be reduced with the emission factor of electricity. It could be said that this optimization method is also effective for green production. In this paper, we develop a model that combines time-of-use and ladder electricity tariffs for scheduling production. The traditional research about HFSP considers a single economic indicator and has performed good work to search the optimal jobs' sequence. For instance, the NEH technique, which is based on calculating processing time, can solve in a short amount of time. According to the research results of adjusting the tradeoff between makespan and energy consumption in literature, it is suggested to apply the existing multi-objective algorithm or set innovation for the existing algorithms in this issue. The choice of plans after scheduling is also worth studying. Since the solution obtained is a set of pareto optimal solution sets, the corresponding choices will be different for different processing purposes. Based on the right shift procedure to reduce energy consumption, manufacturers considered that the difference in processing efficiency and energy consumption will also lead to differences in program selection. As shown in Table 4, the shortest completion time is 23.1 h, while the energy consumption cost is 7498.6 yuan. Although different scheduling schemes had different emphasis, they can consider the coordination of the two scheduling objectives of time, cost, and carbon emissions to some extent.