# Project Robust Scheduling Based on the Scattered Buffer Technology
## 4 Unit activity Slack Algorithm (UAS)
### Metric of the Solution Robustness
#### Three Types of Delay in the Solution Activity
The characteristic of this type of delay is that, on the longest path between the predecessors and its solution activity, the time interval between the solution activity and its immediate predecessor is 0 (no buffer time), while there are time buffers among the predecessors. As the location of the buffer time is far away from the solution activity, the sensitivity of the solution activity to the delay is greater. The buffer area is taken as a dividing line, so the schedule is divided into two parts. In this type, although there are buffer times among the predecessors that can alleviate the effect of predecessors on the solution activity, this buffer can only absorb the delay impact of the predecessors on the left buffer area; it is ineffective to the predecessors on the right. When the number of predecessors on the right is greater, the delay impact on the solution activity is more obvious. In this type of delay, due to the difference of the buffer location and the buffer size on the path, the influence of the predecessors in two sides on the solution activity is also different, so the influence degree of the predecessors on the solution activity is also related to the buffer location on the whole. For example, take the resource flow network and scheduling shown in Figure 3a,b, the solution Activity 11 is the research object. To study the delay impact of the predecessor Activity 3 on the solution Activity 11 (all the predecessors between the predecessor Activity 3 and the solution Activity 11 are shown in the red area in Figure 3a), the longest path is \(3-7-5-9-10-11\), as shown in Figure 3b. On the longest path, because there is no buffer time between the solution Activity 11 and its immediate predecessor Activity 10, the delay of predecessor Activities 7, 5, 9, and 10 will have a direct impact to the solution Activity 11. There is one day (6 - 5 = 1) of buffer time between the predecessor Activity 3 and the predecessor Activity 7; this buffer time will absorb the delay effect on the predecessor Activity 3. Figure 3: The impact analysis of the delay of predecessor Activity 3 on the solution activity: (**a**) resource flow network and (**b**) minimal makespan schedule. Figure 2: The impact analysis of the delay of predecessor Activity 4 on the solution activity: (**a**) resource flow network and (**b**) minimal makespan schedule. In conclusion, in the delay effect of each predecessor on the solution activity, there are three types of effect. However, the number of the predecessors of the solution activity and the effect types of the predecessors are different, so the degree of impact on the delay of the solution activity may be different. In fact, the buffer time in front of the solution activity plays a security role in its execution so that it can be executed according to the schedule. Through the above analysis, the first type has the weakest effect on the solution activity; the second type has the most direct and urgent effect on the solution activity; and the third one is the combination of the first type and the second one, and its influence power on the solution activity is somewhere in between of the first two. In fact, in the third type, when the buffer of predecessors is located on the right of it, the influence of the predecessors on the solution activity will tend to the first type, and when the buffer is on the left, the influence will tend to the second type.