Interpreting PERT Charts

Video coming soon3 worked examples

Theory

Once a PERT chart has been constructed and the forward and backward scans are complete, we can analyse the data to find out where a project has flexibility and where it does not.

1. Float Time (Slack Time)

Some activities have more time available to be completed than they actually require, while others only have exactly enough time. This extra, flexible time is called the Float Time (or Slack Time).

\text{Float} = \text{Latest End Time} - \text{Earliest Start Time} - \text{Duration}

The float time must always be greater than or equal to zero.

2. Essential vs. Critical Activities

You must be able to clearly explain the difference between these two types of activities to a non-mathematician:

Essential Activity: An activity that is needed for the project to be finished, but it has some flexibility in its time constraints ( $\text{Float} > 0$ ). A delay to an essential activity will not necessarily delay the overall project, provided the delay is shorter than the float time.
Critical Activity: An activity that has absolutely no flexibility ( $\text{Float} = 0$ ). It must be completed exactly on schedule. Any delay to a critical activity will automatically delay the completion date of the entire project.

3. The Critical Path

The Critical Path is the sequence of connected critical activities that runs from the start of the project right through to the end.

Every activity network will have at least one critical path, but it is possible for a project to have multiple.
The length of the critical path determines the absolute minimum time required to complete the whole project.

Worked examples

Example 1

Example 1: Calculating Float and Identifying Activities

A local council is planning a summer festival. After completing a PERT chart, the project manager looks closely at two specific tasks:

Task C (Book catering vans): Earliest Start Time = 14 days, Latest End Time = 26 days, Duration = 5 days.
Task F (Erect main stage): Earliest Start Time = 22 days, Latest End Time = 28 days, Duration = 6 days.

(a) Calculate the float time for Task C and Task F.

(b) State, with a valid reason, which of these tasks is a critical activity and which is an essential activity.

(a)

Task C Float = $26 - 14 - 5 = 7$ days.
Task F Float = $28 - 22 - 6 = 0$ days.

(b)

Task F is a critical activity because its float time is exactly zero.

Task C is an essential activity because its float time is greater than zero.

Example 2

Example 2: Interpreting the Critical Path

A software development team generates a PERT chart for a new app update. The table below shows the final node values calculated for each task.

Task	Duration (weeks)	Earliest Start Time	Latest End Time
A	2	0	2
B	4	2	6
C	3	2	7
D	5	6	11
E	4	7	11

(a) Identify the critical path for this project.

(b) State the minimum completion time for the entire project.

(a) First, find the tasks with a float of zero ( $\text{LET} - \text{EST} - \text{Dur} = 0$ ).

A: $2 - 0 - 2 = 0$ (Critical)
B: $6 - 2 - 4 = 0$ (Critical)
C: $7 - 2 - 3 = 2$ (Essential)
D: $11 - 6 - 5 = 0$ (Critical)
E: $11 - 7 - 4 = 0$ (Critical)

Because B precedes D (end of week 6), and C precedes E (end of week 7), the continuous path is A → B → D.

(Note: Even though E has 0 float within its own branch boundaries based on these specific numbers, a true critical path must connect end-to-end governing the maximum duration).

(b) The minimum completion time is 11 weeks (the final LET of the project).

Example 3

Example 3: The Impact of Delays

A construction firm is building a new office block. The critical path for the project is exactly 45 weeks long.

Task G (Install Windows) is an essential activity with a float time of 4 weeks.
Task H (Plaster Walls) is a critical activity on the critical path.

(a) Due to a supply chain issue, Task G is delayed by 3 weeks. State the impact this will have on the minimum completion time of the project, justifying your answer.

(b) Due to staff illness, Task H is delayed by 2 weeks. Determine the new minimum completion time for the overall project.

(a)

This will have no impact on the final completion time. Because Task G has a float of 4 weeks, a delay of 3 weeks can be entirely absorbed without affecting the overall schedule.

(b)

Because Task H is a critical activity, it has a float of 0. Therefore, a 2-week delay will instantly delay the whole project by 2 weeks.

The new minimum completion time is 45 + 2 = 47 weeks.

Ready to practise?

9 Interpreting PERT Charts questions with answers and video solutions