The critical path of a PERT chart is the sequence of activities that determines the minimum time required to complete a project. It is the longest path through the network diagram, and any delay in an activity on the critical path will delay the completion of the entire project.
Key Facts
- Calculation of the critical path: To calculate the critical path in PERT, you need to determine the earliest and latest start and finish times for each activity. The critical path consists of activities where the difference between their earliest and latest start or finish times is zero.
- Steps to calculate the critical path: The process of calculating the critical path in PERT involves several steps. These steps include identifying all tasks and their dependencies, creating a network diagram, calculating start and early finish dates, determining late finish dates, and finding the critical path by matching the early start/finish dates with the late start/finish dates.
- PERT formula: In PERT, the expected time (ET) for each task is calculated using the formula ET = (O + 4M + P) / 6, where O is the optimistic time, M is the most likely time, and P is the pessimistic time.
- Earliest Start and Finish Times: For each task, the earliest start time (ES) and earliest finish time (EF) are calculated. The ES for the first task is 0, and for subsequent tasks, it is the highest EF of all its immediate predecessors. The EF is calculated by adding the ET to the ES.
- Latest Start and Finish Times: The latest start time (LS) and latest finish time (LF) are calculated by moving backward through the project. The LF for the last task is equal to its EF. The LS is calculated by subtracting the ET from the LF, and for preceding tasks, the LF is the minimum LS of all its immediate successors.
- Slack or Float: Slack is the amount of time an activity can be delayed without affecting the project’s completion time. It can be calculated using the formulas S = LS – ES or S = LF – EF. Activities with zero slack are on the critical path.
Calculation of the Critical Path
To calculate the critical path in PERT, you need to determine the earliest and latest start and finish times for each activity. The critical path consists of activities where the difference between their earliest and latest start or finish times is zero.
The steps to calculate the critical path are as follows:
- Identify all tasks and their dependencies.
- Create a network diagram.
- Calculate start and early finish dates.
- Determine late finish dates.
- Find the critical path by matching the early start/finish dates with the late start/finish dates.
PERT Formula
In PERT, the expected time (ET) for each task is calculated using the formula ET = (O + 4M + P) / 6, where O is the optimistic time, M is the most likely time, and P is the pessimistic time.
Earliest Start and Finish Times
For each task, the earliest start time (ES) and earliest finish time (EF) are calculated. The ES for the first task is 0, and for subsequent tasks, it is the highest EF of all its immediate predecessors. The EF is calculated by adding the ET to the ES.
Latest Start and Finish Times
The latest start time (LS) and latest finish time (LF) are calculated by moving backward through the project. The LF for the last task is equal to its EF. The LS is calculated by subtracting the ET from the LF, and for preceding tasks, the LF is the minimum LS of all its immediate successors.
Slack or Float
Slack is the amount of time an activity can be delayed without affecting the project’s completion time. It can be calculated using the formulas S = LS – ES or S = LF – EF. Activities with zero slack are on the critical path.
Conclusion
The critical path of a PERT chart is a valuable tool for project managers. It helps them identify the tasks that are most critical to the timely completion of the project and allows them to focus their attention on those tasks.
Sources
- https://www.smartsheet.com/content/pert-critical-path
- https://www.lucidchart.com/pages/pert-chart-critical-path-method
- https://everhour.com/blog/how-to-calculate-critical-path/
FAQs
What is the critical path of a PERT chart?
The critical path of a PERT chart is the sequence of activities that determines the minimum time required to complete a project. It is the longest path through the network diagram, and any delay in an activity on the critical path will delay the completion of the entire project.
How is the critical path calculated in PERT?
The critical path in PERT is calculated by determining the earliest and latest start and finish times for each activity. The critical path consists of activities where the difference between their earliest and latest start or finish times is zero.
What is the PERT formula?
The PERT formula is used to calculate the expected time (ET) for each activity in a PERT chart. The formula is ET = (O + 4M + P) / 6, where O is the optimistic time, M is the most likely time, and P is the pessimistic time.
What is the difference between the earliest and latest start and finish times?
The earliest start time (ES) and earliest finish time (EF) are the earliest possible times that an activity can start and finish, respectively. The latest start time (LS) and latest finish time (LF) are the latest possible times that an activity can start and finish, respectively.
What is slack or float?
Slack or float is the amount of time an activity can be delayed without affecting the project’s completion time. It can be calculated using the formulas S = LS – ES or S = LF – EF. Activities with zero slack are on the critical path.
What is the purpose of a PERT chart?
A PERT chart is a project management tool that helps project managers plan, schedule, and track projects. It is used to identify the critical path of a project and to focus attention on the tasks that are most critical to the timely completion of the project.
What are the benefits of using a PERT chart?
PERT charts offer several benefits, including:
- Identifying the critical path of a project
- Helping project managers focus on the most critical tasks
- Improving project communication and coordination
- Reducing project risks
- Helping project managers make better decisions
What are some of the limitations of PERT charts?
PERT charts have some limitations, including:
- They can be complex and time-consuming to create.
- They are based on estimates, which can be inaccurate.
- They do not take into account all of the factors that can affect a project’s completion time.