Activity on Arrow Diagrams

08 December, 2014

When we teach students about the Critical Path Method in our PMP® exam preparation courses, we use the Activity on Node (AoN) technique exclusively to illustrate the concepts. We mention Activity on Arrow (AoA) in passing, but we have never gone into any detail with the Activity on Arrow representation.

However, that will have to change because several of our recent PMP® course students have complained that AoA questions are appearing on the PMP® exam itself and they were unprepared for them. This will not be too much of a burden for anyone giving or receiving the PMP® training because AoA is very similar to AoN – the forward and backward passes are calculated in exactly the same way, but the layout of the diagram is different and can throw unwary PMP® exam candidates if they come up against such a question in the heat of the PMP® exam.

If you understand the AoN format, then you should have no difficulty coming to grips with AoA. Remember the AoN node format from the Project Time Management knowledge area in your PMP® course notes?

Coming into the exercise, we knew the Activity Names and their durations. The names came from the Define Activities process while the durations were estimated during Estimate Activity Durations. To determine the critical path, we have to use a forward pass to determine the Early Start and the Early Finish. Then the backward pass gives us the Late Finish and Late Start, allowing us to calculate the float by subtracting the Late Finish from the Early Finish.

While the mechanics of AoN and AoA are the same, the information is presented differently.

In AoA diagrams, the Activity Name and the Activity Duration are specified on the arrow between two nodes. Then each node contains three numerical values – the Start Time, the Finish Time and the Float. This layout has consequences for the forward and the backward passes. In the forward pass, we calculate the Start Times of all the nodes.

In the example above, we take the initial Start Time of “0” and add the Duration for the first activity (“A1”) to get the Start Time for the second node. Then we proceed by adding the Duration for Activity “A2” to the Start Time in the second node to get the Start Time for the third node.

Just like in AoN representations, if we arrive at a point in the diagram where a node has several predecessors, then the largest Start Time from among the predecessors is added to the activity’s duration.

With the backward pass, the end node’s Start Time becomes its Finish Time and the backward pass proceeds by subtracting the durations of the activities leading to the end node from the end node’s Finish Time to arrive at the Finish Times for the preceding nodes. As with the AoN approach, when a node has several successors, the smallest of the successors’ Finish Times is used to base the node’s Finish Time on. The following diagram shows a completed AoA diagram.

In this example, the float has also been calculated. This is more straightforward than in the AoN equivalent because it simply involves subtracting each node’s Start Time from its Finish Time.

Being aware of the AoA layout and the meanings of the values contained on each node should equip any PMP® exam student with enough knowledge to tackle any such question on the PMP® exam itself (assuming, of course, that said PMP® exam student knows how to tackle AoN questions).

If you find the AoA method more appealing than the AoN, you might well ask why is AoN given more prominence in the scheduling world? Given that the techniques are broadly similar, why not use one or the other as you prefer? One reason is because AoA does not illustrate parallel activities as clearly as AoN. Suppose we have three activities – A1, A2 and A3 – that may be carried out in parallel. A1 is expected to take 3 days, A2 2 days and A3 5days. Using AoN, we may represent this as:

This clearly shows the critical path – activity A3 needs to be managed carefully. However, look at the equivalent AoA representation:

This is not so clear. Okay, we have highlighted the critical path, but it is not so obvious that the A1 and A2 are not on the critical path. AoA gets around this problem by introducing “dummy activities” as shown:

It is not surprising that AoN won out – it is a lot easier to use in these circumstances.

Velopi now covers both forms of Critical Path Analysis in its PMP® exam preparation courses, as well as everything else you need to obtain PMP® accreditation. Please visit our training page or contact us directly for more details.

By Velopi Seamus Collins


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