Taking the Critical Path (Part 2)

13 November, 2013

A schedule network diagram is an example of a directed, acyclic graph. The most common format is the Activity on Node version, where nodes (representing activities) are inter-connected to reflect their mutual dependencies.

As an example, let us look at a device that is made up of three components. Each component is built by a specialist and, when all three are ready, they are integrated to form the finished device.

Ordering the work in this fashion is logical and has plenty of parallel activities. However, despite the fact that one component only takes two days to make, the whole project is going to take eleven days, because the C2 component takes a full seven days. The journey from the Start, through the C2 build and the A assembly activity to the end is called the “critical path”. It is a vital concept, familiar to all you PMPs® out there. The critical path is the longest sequence of events in the project and dictates the project’s overall length. Project managers get sleepless nights over the critical path because, if anything goes wrong with activities on the critical path, the project will be late.

Another way to look at the critical path is that it is the one with no slack. If you have PMP® certification, you will be more familiar with the term “float”. Whoever is working on activities C2 and A will have to get the work done in eleven days. However, the people on the Start, C1, A, End path have five days’ worth of float and the Start, C3, A, End workers have four days.

A clever project manager might explore this adjustment:

If the C1 and C3 components can be integrated without the C2 component, we can get some of the integration work done before activity C2 is complete. This means that Start, C2, A2, End is now the critical path, so the C2 developers are still under pressure, but the overall schedule is reduced and the non-critical paths (Start, C1, A1, A2, End and Start, C3, A1, A2,End) have three and two days’ worth of float respectively.

This type of analysis optimizes both our resource utilization and overall schedule performance. For our small example, this is very easy and intuitive. However, in a more realistic example, where there are dozens, if not hundreds of activities, identifying the critical path and working out the floats of the other paths is not easy.

Those of you not planning to sit the PMP® exam might satisfy yourselves with the knowledge that scheduling software (such as Microsoft® Project) exists that will do all this for you. But it is good to understand the first principles. If nothing else, you will be able to do useful work if there’s a power cut of a server crash.

What we need to do is add some extra information to our nodes. We need to work out the following:

Early Start Estimated Duration Early Finish
Activity Name
Late Start Late Finish

The Early Start and Early Finish times are calculated by making a forward pass through the network diagram as follows:

Everything starts at zero, so the first activities have an Early Start of 0. Then we add the estimated durations, to get the Early Finish. The Early Finish of the preceding activity becomes the Early Start of the next activity. However, when an activity has several predecessors (such as A1 and A2 above), the biggest Early Finish of the predecessors is used for the Early Start. This makes sense: Our activity depends on all previous work (we cannot integrate two components, unless we have both to integrate), so we have to wait until all are finished before we can get to work.

At the end of the forward pass, we know how long the project will take (the Early Finish of the last activity). To calculate float, we have to conduct a backward pass and determine the Late Start and Finish times as follows:

We begin by making the Early Finish for the last activity (A2 in this example) its Late Finish. Then we subtract the estimated duration to get the Late Start. The float is calculated by subtracting the Early Start from the Late Start. In the last activity, this is zero.

Moving backwards, the Late Finish of any activity is the same as the Late Start of its successor. Although, we have no example of it here, if an activity has several successors, its Late Finish will be the lowest of the subsequent Late Starts. This is important to remember, because it is the opposite of the forward pass.

At the end of this exercise, the path where there is no float (Start, C2, A2, End) is the critical path. Both the other paths have float, so they are deemed non-critical paths. In other words, the C1 and C3 specialists have the luxury of having extra time to recover from problems.

Those of you interested in the PMP® exam (or anyone who wants to be buzzword compliant), will need to understand the term “Free Float” and “Total Float”. These are straightforward concepts, but not obviously named.

If you look at activities C1 and A1 in our example, C1 has three days of float. However, if it is delayed by two or three days, activity A1 will not be able to make its Early Start date. In other words, the float that activity C1 is using up is having consequences downstream. It is effectively reducing the float available to subsequent activities. However, if activity C1 is delayed by one day, activity A1 will meet its Early Start date. Therefore, activity C1 has one day of “Free Float” available.

The three days float that we calculated for activity C1 in the backward pass represents C1’s Total Float. It has that much slack but, if it uses it up, it will prevent activity A1 from having any float. As another example, suppose both activities C1 and C3 (activity A1’s predecessors) finish on time, then activity A1 will meet its Early Start time. Now both activity A1’s Free and Total Floats are two days. If it finishes on time, there is no benefit to the schedule, because activity A2 must wait for activity C2 to complete. So activity A1 can be delayed by two days without having any downstream consequences. But after two days, it will affect activity A2 and this is a problem, because A2 does not have any sort of float (its Early and Late Starts are the same).

Or putting it another way: Free Float is the amount of slack an individual activity has without having any effect on the downstream processes – i.e. they will all start on their Early Start times. However, Total Float is when using up an activity’s float pushes its successors out so that they start after their Early Start times. The consequences of using up Total Float (as opposed to Free Float), is to eat up float from the successor activities to cope with a delay.

Another concept you might encounter in your PMP® exam is that of Negative Float. Negative Float can occur when a hard deadline is inserted into the schedule. A typical example is when the project manager presents a schedule and the response is: “That’s great, but it needs to be ready for the Hanover Fair”. Putting that constraint into the schedule can squeeze the schedule enough to push the Late Start times in front of the Early Starts. This is clearly absurd, so the schedule needs to be compressed to meet the constraint. In other words, a schedule containing negative float cannot, realistically, be met.

For more information on network diagrams or scheduling in general, please check out our project management training courses or contact us directly. We offer both PMP® and PMI-SP® (Project Management Institute’s Scheduling Professional) courses, the latter being entirely focused on scope and schedule management.

By Velopi Seamus Collins


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