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**The critical path method, and calculating float using the forward and backward pass.**

This is something that can really trip people up, and it is something that’s also good to know for your general project management activities and for the PMP exam. First of all, we’re assuming that you understand what Float is, which is basically any leeway that you have, or any any wiggle room that you have in the project schedule.

This is an example project schedule here. We’ve got Activity 1, 2, 3 and 4 and this is our schedule Network diagram where we’re describing the different times for our schedule. For example, the early start of this activity, the early finish, the activity name, the duration of that activity, the late start, the late finish and finally the float or leeway that we have in that particular activity, that gives us any leeway that we have in the overall project schedule.

**So what is the forward and backward pass how we go to use it?**

Well, when finding our critical path which is the path that has zero leeway, we first need the early start and early finish times. And we do that via the forward pass. So that’s our first step.

Second step is a backward pass. That’s how we get the late start and late finish times.

And then finally to calculate float we look at the difference between the late start and the early start, and the critical path ultimately is the path that has zero float on all of those activities.

Now that is quite a bit to take in. So the best way is to go through an example and this will really help.

**Step 1 – Enter the Durations**

First of all, we want to enter the durations of each activity. How long is it going to take? Even if it’s an estimate – this one we’ve got five days, five days, 15 days – that’s their durations.

**Step 2 – Perform the Forward Pass**

- Early Start and Early Finish times
- EF = ES + Duration – 1
- ES = (highest) previous EF + 1

Now that we have activity durations, we can perform the forward pass, which is all about Early Start and Early Finish times. We’ve got our early start on the left, and early finish on the right, and the way we figure this out is once we’ve got our first early finish we add one, and that’s our next early start. In our first activity’s case we’ve got 5 plus 1 is 6 is our next early start. The highest previous early finish of 15 plus one equals 16 on our schedule Network diagram.

**Step 3 – Perform the Backward Pass**

- We calculate our Late Start and Late finish times
- Enter highest EF in last box
- LS = LF – Duration + 1
- LF = (lower) LS – 1

Once we have the early start and finish times we can get the late start and late finish times via the backward pass. The way we do that is we enter the highest early finish in the last box. So obviously this one only had one – we had 30 and 30 is where we’re sitting for our for our late finish times.

Now, we minus the duration and add 1, so 30 minus 15 plus 1 equals 16. So that’s how we get the late start for this particular one when we’re doing the backward pass. We’re working backwards. Now we take the late start and we minus one again. So we’ve got 15 – our duration of ten, plus one equals 6. And again, the lowest one here is what we want to use – minusing one to give us five for our late finish, and minusing 5 which would give us 0 plus 1 which will give us one for our late start there as well.

**Step 4 – Calculate Float**

- Float = Late start – Early Start

Now finally with all of that information, we can calculate our float. This will help us get the critical path on our Schedule Network Diagram. Float is the late start minus the early start. So 1 minus 1 equals 0, 6 minus 6 equals 0, but 11 minus 6 gives us 5 – so we have a little bit of project float or leeway, or a bit of wiggle room for that particular activity, but we don’t have any for the others because they are still zero.

So if we know that the critical path is the one with no wiggle room on it, then we can say that the critical path in this case is Activity 1, Activity 3, and Activity 4. And we can also say that this activity up here might be able to be delayed by five days.

That is the idea of Of the critical path method on your schedule Network diagram using the forward and backward pass to calculate float and any wiggle room in your project schedule.

*– David McLachlan*