Model Answer
0 min readIntroduction
Project management relies heavily on techniques to schedule, organize, and control project activities. The Critical Path Method (CPM) is a widely used technique for determining the minimum time required to complete a project. A core component of CPM is the network diagram, which visually depicts the sequence of activities and their dependencies. The Arrow-On-Node (AON) method is a common way to represent this diagram. Calculating the expected time and variance for each activity allows for probabilistic project completion time estimation and risk assessment. This answer will demonstrate the construction of an AON diagram and the subsequent calculations, assuming a hypothetical project with defined activities, durations, and dependencies.
Constructing the Network Diagram (AON Method)
The Arrow-On-Node (AON) method represents activities as arrows and nodes as events. Each arrow represents an activity, and the node signifies the start or end of an activity. Let's assume the following activities for a hypothetical project:
| Activity | Predecessor | Expected Time (weeks) | Variance (weeks2) |
|---|---|---|---|
| A | - | 5 | 1 |
| B | A | 3 | 0.25 |
| C | A | 4 | 0.64 |
| D | B | 6 | 1.44 |
| E | C | 7 | 0.81 |
| F | D, E | 4 | 0.36 |
Based on this data, the AON diagram would look like this (represented textually as creating a visual diagram is not possible in this format):
Start -> A -> B -> D -> F -> End
Start -> A -> C -> E -> F -> End
Note: In a real exam setting, you would draw this diagram with nodes representing events and arrows representing activities.
Calculating Expected Time and Variance
For each activity, the expected time (TE) and variance (σ2) are calculated as follows:
- Expected Time (TE): This is the average time an activity is expected to take. In this case, we are given the expected time directly in the table.
- Variance (σ2): This measures the spread or uncertainty in the activity's duration. We are also given the variance directly in the table.
Let's calculate the expected time and variance for each activity based on the table above:
| Activity | Expected Time (TE) | Variance (σ2) |
|---|---|---|
| A | 5 | 1 |
| B | 3 | 0.25 |
| C | 4 | 0.64 |
| D | 6 | 1.44 |
| E | 7 | 0.81 |
| F | 4 | 0.36 |
Calculating Expected Project Completion Time
To calculate the expected project completion time, we need to identify the critical path. The critical path is the longest path through the network diagram. In our example, there are two paths:
- Path 1: A -> B -> D -> F: 5 + 3 + 6 + 4 = 18 weeks
- Path 2: A -> C -> E -> F: 5 + 4 + 7 + 4 = 20 weeks
Therefore, the critical path is A -> C -> E -> F, and the expected project completion time is 20 weeks.
Calculating Project Variance
The variance of the project completion time is the sum of the variances of the activities on the critical path.
Variance (Project) = Variance(A) + Variance(C) + Variance(E) + Variance(F) = 1 + 0.64 + 0.81 + 0.36 = 2.81 weeks2
The standard deviation of the project completion time is the square root of the variance: √2.81 ≈ 1.68 weeks.
Conclusion
In conclusion, the AON method provides a clear visual representation of project activities and dependencies. Calculating the expected time and variance for each activity, and subsequently for the entire project, allows for a probabilistic assessment of project completion. Identifying the critical path is crucial for effective project management, as delays on critical path activities directly impact the overall project timeline. This analysis enables proactive risk management and informed decision-making throughout the project lifecycle.
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.