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Manual methods – part 3c – task flow charts

Activity-on-Node networks

We can use a simple example to show how we calculate the following:

Earliest Start Time
Earliest Finish Time
Latest Start Time
Latest Finish Time

We can also see how the concept of ‘float’ is developed together with the ‘critical path’.

AON network bubble diagramAON network bubble diagram large

The diagram above shows a simple Activity-on-Node network for a project containing 6 tasks.

For ease of explanation we are using arrows to better show the flow of events but the actual Activity-on-Node flow chart would not have arrows only lines.

These tasks have the following durations:

Task #1, 2 days
Task #2, 4 days
Task #3, 6 days
Task #4, 3 days
Task #5, 2 days
Task #6, 2 days

The sequence shows that tasks #1 to #4 follow on from each other in a Finish to Start relationship or dependency.
Whereas, task #5 cannot start until task #1 has completed and task #6 cannot start until task #5 is complete.

For this simple project let us construct the data in the circle (bubble) segments.

Earliest Start Time (EST)

This is probably the easiest part to work out.
The Earliest Start Time (EST) is shown in the diagram by the yellow boxes.
For task #1 this will be day 0. Task #2 can only begin once task #1 has finished so the Earliest Start Time (EST) for task #2 will be the Earliest Finish Time (EFT) for task #1 as shown by the pale pink boxes.

The Earliest Finish Time (EFT) for task #1 will be it’s Earliest Start Time (EST), day 0 plus its ‘duration’, 2 days (the green boxes) giving a value of project day 2 for the Earliest Finish Time (EFT).
This process can be repeated for all of the tasks to the project end.

So the Earliest Start Time (EST) for task #4 becomes project day 12 and the Earliest Start Time (EST) for task #6 becomes project day 4.

Earliest Finish Time (EFT)

We have seen from the explanation above that the Earliest Finish Time (EFT) is the Earliest Start Time (EST) plus the duration.
This is indicated for all of the tasks by the pale yellow boxes. Hence, the Earliest Finish Time (EFT) for task #4 is project day 15 and the Earliest Finish Time (EFT) for task #6 is project day 6.

Thus, we can see that the overall duration of the project, if all goes to estimations, will be 15 days based upon the Earliest Finish Time (EFT) of task #4.

Latest Start Time (LST)

The Latest Start Time (LST), the blue boxes, cannot be worked out by going forward in the Activity-on-Node network.
We have to work backwards from the ‘END’ point by first considering the Latest Finish Time (LFT), the orange boxes, see below.
This is often known as the ‘backward pass’ with previous calculations being the ‘forward pass’.

Latest Finish Time (LFT)

Task #6 has no further dependencies so provided it completes on project day 15 there will be no delay in the completion of the project.
Hence, Latest Finish Time (LFT) for task #6 is project day 15. From this its Latest Start Time (LST) will be the Latest Finish Time (LFT) minus its ‘duration’ of 2 days giving a value for the Latest Start Time (LST) of project day 13.

This in turn becomes the Latest Finish Time (LFT) for task #5. As task #5 has a duration of 2 days it will have a Latest Start Time (LST) of project day 11. From this information we can ascertain other factors known as ‘float’ and ‘critical path’.


Let us look at task #6. It has an Earliest Finish Time (EFT) of project day 6 and a Latest Finish Time (LFT) of project day 15.
The difference between these values is 9 project days. So, provided task #6 completes anytime within these 9 days it will not delay the completion of the project. We say that task #6 has 9 days FLOAT.

It is very common for people to also use the word ‘slack’ instead of float. Although this is very similar it is subtly different.
Slack really only applies to Activity-on-Arrow networks and the events that are created. This is discussed later.

Let us now have a look at task #5. This comes before task #6. using the logic above it would appear that it also possesses 9 days float. However, this is not the case if you wish task #6 to start at its original designated time. There is in fact ZERO float as the Latest Finish Time (LFT) of task #5 is project day 4 which governs the Earliest Start Time (EST) of task #6.

However, MS (Microsoft) project defines the above slack (float) as ‘free slack’.
This is the slack (float) that a task possesses before it will affect the start time of the dependent task in front of it.
The ‘free slack’ for task #5 is ZERO and the ‘free slack’ for task #6 is 9 days.

Notice that if task #5 were delayed by 9 days task #6 would still be able to start on time and finish on time on project day 15.
Any further delays would affect the project completion date.
This slack (float) is known as ‘total’ slack’ that is the amount of days you can delay a task before it affects the end date.

So, examining tasks #5 and #6 we have.

Task #5
Free slack = 0 days
Total slack = 9 days

Task #6
Free slack = 9 days
Total slack = 9 days
These are the same for this case.

Critical path

When the ‘total slack’ for a task is ZERO any delay will affect the project end date.
It is thus critical for this task that there are no delays.
Hence, any task with ‘total slack’ of ZERO will be on the ‘CRITICAL PATH’.
This is the position for the tasks #1, #2, #3 and #4.

The critical path is shown by the red arrows.

The arrow-on-node technique is described under PRINCE2® 2009.

An activity-on-node diagram (sometimes called an arrow diagram) can be used to schedule dependent activities within a plan.
It helps a Project Manager to work out the most efficient sequence of events needed to complete any plan and enables the creation of a realistic schedule.
[see Plans - The PRINCE2 approach - Prepare the schedule - Define activity sequence]

Under PRINCE2 2009 [see ‘The Complete Project Management plus PRINCE2’] planning is covered by the Plans theme.
The purpose of the Plans theme is to facilitate communication and control by defining the means of delivering the products (the where and how, by whom, and estimating the when and how much).
[see Plans - Purpose]

Identifying the plan activities and dependencies for a schedule are also covered within this theme.
[see Plans - The PRINCE2 approach - Identify activities and dependencies]

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