The Critical Path Method (CPM) is a project management technique used to determine the longest sequence of activities that must be completed on time for the project to be completed by its deadline. In other words, it helps identify which tasks are critical to the project’s success and must not be delayed, as any delay in these tasks will delay the entire project.

CPM was developed around 1957 by DuPont and Remington Rand for scheduling chemical plant projects.

Key Concepts of CPM:

1. Activities: The individual tasks or work packages that need to be completed as part of the project.
2. Dependencies: The relationships between activities. Some tasks can’t start until others are finished (these are called dependent activities).
3. Duration: The amount of time each activity will take to complete.
4. Earliest Start (ES) and Latest Finish (LF): These help identify the time frames within which each task must be completed to avoid delays.
5. Slack (or Float): The amount of time that a task can be delayed without affecting the overall project duration. Tasks on the critical path have zero slack.

6. Crashing an Activity

   • Definition: Crashing is a schedule compression technique used to reduce the duration of a project by adding more resources (e.g., workers, overtime, equipment).

   • The shortest possible duration of an activity after maximum crashing is called Crash Point

   • Purpose: To meet deadlines or shorten project duration without changing the project scope.

   • Trade-off: Increases cost due to extra resources.

   • Example: Hiring additional workers to complete a construction task faster.

Term	Meaning	Significance	Allowed in Network?
Dangling	Not connected to end or next task	Design flaw	❌ No
Looping	Circular path (A → B → A)	Logical error	❌ No
Dummy	Zero-duration task to show dependency	Maintains logic	✅ Yes
Slack	Delay time allowed without project delay	Used in scheduling	✅ Yes

Steps to Apply the Critical Path Method:

1. List all activities required to complete the project.
2. Determine dependencies between activities (which tasks need to precede others).
3. Estimate the duration of each activity.
4. Create a project network diagram that visually represents the activities and their dependencies.
5. Calculate the earliest start and finish times (forward pass) and the latest start and finish times (backward pass) for each activity.
6. Identify the critical path, which is the longest path through the network. This path determines the minimum project duration. Tasks on the critical path have zero slack.

Example:

Imagine a project with the following activities and durations:

• A: 5 days
• B: 3 days (depends on A)
• C: 2 days (depends on A)
• D: 4 days (depends on B and C)

The critical path is the longest path through the network of activities, which in this case is A → B → D (with a total duration of 5 + 3 + 4 = 12 days).

Importance of CPM:

• Project Scheduling: Helps in determining the minimum project time and in scheduling tasks efficiently.
• Resource Allocation: By identifying the critical tasks, project managers can allocate resources more effectively to prevent delays.
• Risk Management: Critical tasks are at higher risk of causing delays, so focusing on them can help avoid project overruns.

In summary, the Critical Path Method is a valuable tool in project management for ensuring that projects are completed on time by identifying essential tasks and their dependencies.