# Energy-Efficient Hybrid Flow-Shop Scheduling under Time-of-Use and Ladder Electricity Tariffs
## 4 Case Study
### Evaluation of the Example  
The TOU price refers to the current policy in Tianjin as shown in Table 1. As the ladder price is not apply in Tianjin, we use the high energy consumption industry ladder electricity price referring to another industry province. Considering the price of each interval, the up-step price is set 20 percent beyond the origin price and total amount in an interval is set 800 kwh per day [39]. The processing time and energy usage of each process in a stamping workshop in Tianjin are examples of real-world scheduling problems. The stamping workshop is needed to process different types of stamping parts, different types of stamping parts contain different batches, and the same process of the same type of stamping parts adopts continuous processing. Therefore, one type of stamping part could be regarded as an order containing different batches, and the production scheduling problem of the workshop could be simplified as one process. Its data demonstrates some common characteristics of the manufacturing. The data has been pre-processed in order to protect some commercial confidentiality. Considering the advantage of improvement strategies, a right-shift method is designed based on the improvement of the NSGA-II as shown at part 4.3. The population size is set to 200. The maximum evolution generation of the algorithm is the same 200 to ensure results are obtained. The mutation probability and the crossover rate are set to be 0.05 and 0.95 in original NSGA-II. From the data simulation, the Pareto optimal frontier formed in the two scheduling target dimensions of the maximum completion time and the energy consumption cost for the green scheduling considering the TOU electricity price is determined. In response to this problem, an improved non-dominated sorting genetic algorithm-II with some optimization strategies is explored. Two stages are proposed to the problem. First, an optimization solution is found according to the principles of shortest time. Then, the right-shift strategy is used to to reduce the energy consumption under the TOU and ladder electricity price. For each stage, there are two machines respectively. Table 2 shows the average processing time and power demanded of each workpiece on each machine whose data is measured from the machine. Table 3 provides an overview of the standby power of each machine tool. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Tianjin’s Commercial TOU Pricing Standard**} \\ \hline
**Type** & **High-Peak** & **Mid-Peak** & **Off-Peak** \\ \hline \multirow{2}{*}{Period} & 8:00–11:00 & 7:00–8:00 & 21:00–7:00 \\ \cline{2-4}  & 18:00–21:00 & 11:00–18:00 & \\ \hline Price (CNY/kWh) & 0.9914 & 0.6980 & 0.4186 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electricity market price for industry during the non-summertime in Tianjin, China. (Source: Tianjin Electricity Price, 2019; www.fj.sgcc.com.cn/) (accessed on 23 June 2022). The algorithm runs 10 times in order to assess the randomness, and the Pareto frontiers of the two algorithms are shown in Figure 6. It can be seen that most of the solutions obtained using the improved NSGA-II algorithm with the right-shift strategy dominate the solutions obtained by the improved algorithms. As shown in Figure 6, the X-axis represents the processing time and the Y-axis represents the TEC. It is obvious that the larger time has a lower TEC. The black points are the multi-objective solutions without adopting the right-shift method, and the red points are the multi-objective solutions when adopting the right-shift method. After adopting the right-shift method, the TEC can be reduced without changing the makespan. At the same time, it can be seen that the Pareto frontier of the improved NSGA-II algorithm with the right-shift strategy is not fluent, and the right-shift strategy does not change the overall time, but only reduces the energy consumption.