Once the schedule overlapping search algorithm is implemented to compute the overlapping durations and schedule overlapping ratios for all activities, a risk analysis is performed specifically for activities with overlaps. To assess the level of risk associated with each overlapping activity, a fuzzy analysis approach is utilized. This fuzzy methodology enables the quantification of evaluators' subjective judgments and facilitates the evaluation of schedule overlapping risks for each individual activity.
In order to evaluate the risk associated with schedule overlapping for each activity, users are required to assess the extent of schedule overlap. A comprehensive risk analysis should be performed for each risk evaluation factor, considering the level of schedule overlapping. The risk evaluation factors encompass probability (P), which spans from P1 (Very Low) to P5 (Very High), and intensity (I), which ranges from I1 (Very Low) to I5 (Very High). In this study, the risk factor will be based on the SOR value of each activity and user’s perspective.
The fuzzy degrees mentioned earlier are utilized as comprehensive evaluated fuzzy risk values, which are then transformed into trigonometric fuzzy values using the Mamdani Fuzzy Inference System in MATLAB. Fuzzy membership function range for Probability (P) and Intensity (I) is from 0 to 1. The table below shows the membership function for probability, intensity and output.
Table 3.4: Membership function and five Euclidean distance values
Membership function
Five Euclidean distance values
Very Low Low Medium High Very High
Probability (P)
[0;0.2;0.4] [0.2;0.4;0.6] [0.4;0.6;0.8] [0.6;0.8;1.0] [0.8;1.0;1.0]
Intensity (I) [0;0.1;0.3] [0.1;0.3;0.5] [0.3;0.5;0.7] [0.5;0.7;0.9] [0.7;0.9;1.0]
Output [0;0.1;0.2] [0.2;0.3;0.4] [0.4;0.5;0.6] [0.6;0.7;0.8] [0.8;0.9;1.0]
Figure 3.19: Membership function for Probability (P), Intensity (I), Output and Fuzzy Simulink
Fuzzy rules then created base on theory in part 2.1.7 of this thesis, the following table illustrated fuzzy rules in MATLAB as If-then rule:
Table 3.5: If-then rules in MATLAB
No. Probability (P) And/Or Intensity (I) Output
1 Very Low And Very Low Very Low
2 Very Low And Low Very Low
3 Very Low And Medium Very Low
4 Very Low And High Medium
5 Very Low And Very High Medium
6 Low And Very Low Low
7 Low And Low Low
8 Low And Medium Low
9 Low And High Medium
10 Low And Very High High
11 Medium And Very Low Low
12 Medium And Low Medium
13 Medium And Medium Medium
14 Medium And High Medium
15 Medium And Very High High
16 High And Very Low Medium
17 High And Low Medium
18 High And Medium High
19 High And High High
20 High And Very High High
21 Very High And Very Low Medium
22 Very High And Low High
23 Very High And Medium High
24 Very High And High Very High
25 Very High And Very High Very High
Figure 3.20: Fuzzy rule surface in MATLAB
In summary, the risk level for each risk factor is determined by considering the minimum value obtained among the five calculated Euclidean distance values. This minimum value serves as the basis for determining the overall risk priority and level associated with schedule overlapping. Each activity is assigned probability (P) and intensity (I) values, and a fuzzy analysis procedure is employed to automatically evaluate the overall risk level. The resulting risk level is categorized into five grades, ranging from VL (Very Low) to VH (Very High). The model simulation visually represents each grade with a corresponding color, enabling managers to easily assess the risk level linked to overlapping schedules. By utilizing GA analysis, the level of overlapping for activities with lower construction operation performance can be mitigated, aiding managers in developing improved schedule planning.
After risk analysis process complete, to optimize the time-cost tradeoff (the total overlapping duration and cost due to risk), the value of risk cost must be considered base on risk value. One approach to make the risk cost values more trusted and meaningful is to base them on historical data or expert opinions. Here are some methods to improve the accuracy of risk cost values:
a) Historical data: analyzing historical data from similar projects, if available, allows for the determination of the risk level for each activity. Calculating the average risk value for each activity based on past projects can serve as a starting point for the current project.
b) Expert opinions: consulting with project managers, team members, and other stakeholders experienced in similar projects can help estimate the risk level associated with each activity more accurately.
c) Risk assessment: conducting a risk assessment for each activity, taking into account factors such as resource availability, complexity, dependencies, and potential obstacles, can aid in estimating the risk level and assigning a more reliable risk cost value.
d) Sensitivity analysis: carrying out a sensitivity analysis to understand the impact of varying risk cost values on the project’s objectives can help identify which activities have the most significant effect on the project and prioritize them for further investigation and risk mitigation.
e) Risk management plan: creating a risk management plan that encompasses risk identification, assessment, mitigation, and monitoring strategies can lead to a better understanding of the project’s risks and assignment of more accurate risk cost values.
f) Regular updates: periodically revisiting the risk cost values throughout the project ensures their accuracy and relevance. Updating the values based on the new information, changes in project scope, or unforeseen risks that emerge during project execution is crucial.
The initial overlapping duration will be calculated as following:
𝑅𝑀𝑖 = 𝑂𝑖× 𝑐𝑖× 𝛼 (16) Where:
𝑅𝑀𝑖 is the risk cost of activity i;
𝑂𝑖 is the output value from Fuzzy Mamdani;
𝑐𝑖 is the cost of risk (user’s defined);
𝛼 is the penalty coefficient depending on risk degree 𝑂𝑖 and user’s perspective