# Project Robust Scheduling Based on the Scattered Buffer Technology
## 4 Unit activity Slack Algorithm (UAS)
### Metric of the Solution Robustness
#### 4.1.3 Comprehensive Effect Analysis of the Different Delay Types on the Solution Activity  
Because any solution activity may be affected by many predecessors, and the effect types of predecessors on the solution activity are various, it is necessary to comprehensively consider several different types of predecessors in the effect analysis of any solution activity, and then to establish the metric of the schedule robustness. The above analysis of the effect types and the influence factors shows that the effect force of predecessors on the solution activity (or the effect on the solution robustness) is proportional to the size of slack in front of the solution activity, and it is inversely proportional to the number of predecessors and the sum of dynamic duration of predecessors. Thus, the comprehensive influencing factors of predecessors on the solution activity can be uniformly expressed as:  
\[effect_{i}^{j}=\frac{Len_{i}^{j}-TotDu_{i}^{j}}{RanTD_{i}^{j}\times Num_{i}^{ j}} \tag{10}\]  
where \(effect_{i}^{j}\) indicates the effect force of the predecessor \(i\) on the solution activity \(j\); the higher this value, the smaller the effect on its solution activity is. However, in different types of delay, due to the different effect of predecessors on the solution activity, the quantization of this effect degree is correspondingly different. The analysis of the effect of the first type on the solution activity  
In Equation (10), \(effect_{i}^{j}\) is a positive index. To transfer this effect parameter into the standard to measure the merits and demerits of the robustness in the solution activity, and to make this standard as small as possible, it is necessary to convert \(effect_{i}^{j}\) into the reverse index; here, the authors take its reciprocal, therefore, the influence coefficient about the robustness on the solution activity in the first type can be expressed as Equation (11), which is recorded as \(fir\_effect_{i}^{j}\):  
\[fir\_effect_{i}^{j}=\frac{RanTD_{i}^{j}\times Num_{i}^{j}}{Len_{i}^{j}-TotDu_{ i}^{j}} \tag{11}\]  
The analysis of the effect of the second type on the solution activity  
According to the analysis of the above type, in the second type, as shown in Figure 2, there is no buffer time between the solution activity and its predecessors. According to Equation (11), the value of \(Len_{i}^{j}-TotDu_{i}^{j}\) should be 0, but there is no point in taking directly Equation (11) as the metric of the solution activity in the second type, so Equation (11) needs to be modified. In the first type, there are buffer times among predecessors, and \(Len_{i}^{j}\), \(TotDu_{i}^{j}\) are integers greater than zero, so there must an equation \(Len_{i}^{j}-TotDu_{i}^{j}\geq 1\). In the second type, because the effect force on the solution activity in this type is the most urgent one compared with the other two types, the value of the effect measurement standard is the maximum in this type. However, as a measuring standard,obviously, it is unnecessary to take the measure value as an infinite value in the second type. To show that the second type has the greatest influence in the three types of predecessors, \(\alpha_{i}\) can be set to replace \(Len_{i}^{j}-TotDu_{i}^{j}\), and \(\alpha_{i}\in(\,0,\,1\,)\).