Model Answer
0 min readIntroduction
Project management is a critical aspect of modern organizational success, demanding efficient planning, execution, and control. Estimating project duration accurately is paramount, and techniques like PERT are employed to account for uncertainty in activity times. PERT utilizes a weighted average of optimistic, pessimistic, and most likely time estimates to determine the expected duration. Furthermore, it calculates the standard deviation to quantify the variability in the project completion time, providing a range of possible outcomes. This answer will detail the methodology for calculating both the expected duration and standard deviation of a project, assuming the necessary activity time estimates are available.
Understanding the Concepts
Before calculating the expected duration and standard deviation, it’s essential to understand the underlying concepts. PERT uses three time estimates for each activity:
- Optimistic Time (a): The shortest possible time to complete the activity.
- Most Likely Time (m): The most realistic time to complete the activity.
- Pessimistic Time (b): The longest possible time to complete the activity.
Calculating Expected Duration (TE)
The expected duration (TE) for each activity is calculated using the following formula:
TE = (a + 4m + b) / 6
This formula gives more weight to the most likely time (m) while considering the optimistic (a) and pessimistic (b) estimates. To find the expected duration of the *entire project*, you must first calculate the TE for each activity, then perform a critical path analysis to identify the longest path through the project network. The sum of the TEs along the critical path represents the expected project duration.
Calculating Standard Deviation (σ)
The standard deviation (σ) for each activity’s duration is calculated using the following formula:
σ = (b - a) / 6
This formula measures the variability or uncertainty associated with the activity’s duration. A larger standard deviation indicates greater uncertainty. To calculate the standard deviation of the *entire project*, you sum the variances (σ2) of the activities along the critical path. The square root of this sum gives the project’s standard deviation.
Project Standard Deviation = √(Σ σi2), where σi is the standard deviation of each activity on the critical path.
Illustrative Example
Let's consider a simplified project with three activities on the critical path:
| Activity | Optimistic (a) | Most Likely (m) | Pessimistic (b) | TE (a+4m+b)/6 | σ (b-a)/6 |
|---|---|---|---|---|---|
| Activity A | 2 | 4 | 8 | 4.67 | 1.00 |
| Activity B | 3 | 5 | 7 | 5.17 | 0.67 |
| Activity C | 1 | 3 | 5 | 3.00 | 0.67 |
Expected Project Duration: 4.67 + 5.17 + 3.00 = 12.84 units of time.
Project Standard Deviation: √(1.002 + 0.672 + 0.672) = √(1 + 0.45 + 0.45) = √1.9 = 1.38 units of time.
Interpreting the Results
The expected duration of 12.84 units of time represents the most likely completion time. The standard deviation of 1.38 units of time indicates the degree of uncertainty. Using statistical principles, we can estimate the probability of completing the project within a certain timeframe. For example, approximately 68% of the time, the project will be completed within one standard deviation of the expected duration (12.84 ± 1.38), i.e., between 11.46 and 14.22 units of time. Similarly, approximately 95% of the time, the project will be completed within two standard deviations of the expected duration.
Limitations
PERT assumes a beta distribution for activity times, which may not always be accurate. It also relies on accurate estimates of optimistic, pessimistic, and most likely times, which can be subjective. Furthermore, it doesn't account for resource constraints or other external factors that can impact project duration.
Conclusion
In conclusion, calculating the expected duration and standard deviation of a project using PERT provides valuable insights into the potential completion time and associated uncertainty. By utilizing the weighted average formula for expected duration and the standard deviation formula, project managers can make informed decisions regarding scheduling, resource allocation, and risk management. While PERT has limitations, it remains a powerful tool for project planning and control, especially in situations where activity times are uncertain.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.