## 4 Experiments  
Although the addressed tool is equipped with a dual-arm robot, it can be used as just a single-arm one in some cases due to the fact that the arms should be identified as dirty and clean ones. Thus, we have to present and analyze different scheduling strategies, and the performance of these strategies may be different for different parameter combinations. Essentially, given a parameter combination, we need to use all the four linear programs for a solution, then choose the best one. Nevertheless, it is better to test the strategies to see the differences in these strategies under different parameter combinations. In this way, we can provide a guide to the practitioners. To do so, based on the data from real production processes, for each test case, we randomly generate one of the parameters and keep others constant. In the following, we present parts of the experimental results to show the properties of these strategies. We use large amounts of data collected from a fab for experiments to test the proposed method. According to the actual production situations, the processing time of wafers in different process steps is different, and the constraints on the RTC in PM are also different. At the same time, we also consider the different rotation times in PM. With these experiments, we compare the performance of the four scheduling strategies under different parameters. The time unit is seconds and omitted in the following presentation. The algorithm is implemented using a Gurobi Python interface (gurobipy) on a personal computer equipped with Intel Core i3-10100 CPUs running at 3.60 GHz and 16.0 of RAM. To test LPs 1-4 resulting from the four scheduling strategies, a large number of experiments with different parameters are made and the results are presented as follows:  
**Example 1. ** The wafer flow pattern of this example is (1, 1, 1). Steps 1-3 are served by PM\({}_{1}\), PM\({}_{2}\), and PM\({}_{3}\), respectively. There are three cases. Case 1: The wafer processing time \(\alpha_{1}\) for Step 1 is randomly generated in [50.0, 100.0], \(\alpha_{2}=60.0\), and \(\alpha_{3}=80.0\); for RTCs, \(\delta_{1}=30.0\), \(\delta_{2}=40.0\), and \(\delta_{3}=28.0\); and the robot task time is \(\beta=1.0\), \(\beta_{0}=2.0\), and \(\mu=1.0\). The PM rotation time is \(v=2.0\). Case 1 involves variations in \(\alpha_  
Case 3: The wafer-processing times are \(\alpha_{1}=131.0\), \(\alpha_{2}=135.0\), and \(\alpha_{3}\) is randomly generated in [100.0, 160.0]; for RTCs, \(\delta_{1}=45.0\), \(\delta_{2}=32.0\), and \(\delta_{3}=46.0\); the robot task times are \(\beta=1.0\), \(\beta_{0}=2.0\), and \(\mu=2.0\); and the PM rotation time is \(v=2.0\). Case 3 involves variations in \(\alpha_{3}\) while keeping all other parameters constant. The results are shown in Figure 9.  
We test LPs 1-4 and calculate the parameter variation range within which feasible schedules can be found as shown in Figures 7-9 and Table 1. As can be seen from Figures 7-9 and Table 1, OBS can find schedules for the largest parameter variation range. As shown in Figures 7 and 9, when processing time for Steps 1 and 3 is short, OBS can find feasible schedules. Then, as the processing time increases, OHTS can also find feasible schedules. As shown in Figure 8, OHTS can find a feasible schedule when processing time for Step 2 is short. At the same time, the cycle time is the shortest. As the processing time increases, OBS achieves a shorter cycle time. In the given range of the parameter variation, the feasible ranges of TBS and THTS are smaller, and the cycle time is longer. In these cases, OBS and OHTS are obviously better. By applying LPs 1-4, when the internal chamber of the PM rotation time is shorter, from Figure 10 and Table 1, we can find that OHTS performs better. With the increase in the internal chamber rotation time of a PM, TBS presents a shorter cycle time. Within the variation range of \(\upsilon\), OBS has the widest scheduling range.