1. Types of float

• Total Float: Total float is the amount of time an activity can be delayed without delaying the project end date or an intermediary milestone, while still adhering to any imposed schedule constraints. When people refer to “float”, they typically mean total float.
• Free Float: Free float is the amount of time an activity can be delayed without delaying the early start date of its successor(s) while still adhering to any imposed schedule constraints. Only non-critical activities have free float.
• Project Float: Project float (also referred to as positive total float) is the amount of time a project can be delayed without delaying the externally imposed project completion date required by the customer or management, or the date previously committed to by the Project Manager.

2. Relationship between the Critical Path and Float

As we know, the Critical Path Method (CPM) is a vital tool for keeping projects on schedule. When analyzing a project’s Network Diagram, there is always at least one critical path - this is the sequence of activities whose total duration is longer than that of any other path. One important point to remember about the critical path is that every individual activity on this path must be completed on time for the entire project to finish as scheduled. A delay in any one of the critical path activities will cause the entire project to be delayed. That’s precisely why it is called the Critical Path.

Therefore, activities on the Critical Path generally have a Float value of zero. If these activities are delayed or a strict deadline is imposed on the project (e.g., the total duration of the Critical Path is 100 days, but the completion deadline is set at 90 days), the Float may become negative. This issue must be identified and resolved before project execution begins, and the Project Manager is responsible for ensuring a realistic and achievable project schedule.

3. Calculating Float using Forward Pass and Backward Pass

Float helps identify how much scheduling flexibility each activity has. In some PMP exam questions, Float can be easily estimated, but in most cases, manual calculations are required. Float can be calculated using one of the following formulas:

Float = Late start (LS) - Early start (ES)

Float = Late finish (LF) - Early finish (EF)

Free Float = ES of next Activity - EF of current Activity - 1

In there:

• Early start: The earliest time an activity can begin. An activity near the end of the path will only start early if all of the previous activities in the path also started early. If one of the previous activities in the path slips, that will push it out.
• Early finish: The earliest time an activity can finish. It’s the date that an activity will finish if all of the previous activities started early and none of them slipped.
• Late start: The latest time that an activity can start. If an activity is on a path that’s much shorter than the critical path, then it can start very late without delaying the project - but those delays will add up quickly if other activities on its path also slip.
• Late finish: The latest time that an activity can finish. If an activity is on a short path and all of the other activities on that path start and finish early, then it can finish very late without causing the project to be late.

For example, as shown in the diagram above:

• The critical path (Start - A - B - C - Finish) has a duration of (6 + 5 + 7) = 18.
• The other path (Start - D - C - Finish) has a duration of (2 + 7) = 9. It’s a lot shorter than the critical path, so there should be a lot of play in those activities (except C, because C is on the Critical Path).
• That means the early start and early finish for D are really early - they can end a lot sooner than A, B, and C, which will free up their resources for you to use.
• Even if Activity D starts really late, since the path it’s on is so much shorter than the critical path, the project will still be on time.
   

a. How to calculate Early start, Early finish, Late start, Late finish?

You can use a method called Forward pass to add the early start and finish to each path in your network diagram. Once you’ve done that, you can use Backward pass to add the late start and finish. It makes your network diagrams look a little more complicated, but it gives you a lot of valuable information. An activity can be noted with the following ES, EF, LS, LF indicators:

• Take a forward pass through the network diagram: Start at the beginning of the critical path and move forward through each activity. Follow these three steps to figure out the early start and early finish:
  • 1. The ES (early start) of the first activity in the path is 1. The EF (early finish) of any task is its ES plus its duration minus 1. So start with Activity A. It’s the first in the path, so ES = 1, and EF = 1 + 6 – 1 = 6. This means Activity A starts at the beginning of day 1 and finishes at the end of day 6. The reason we subtract 1 in the EF formula is that early start is measured at the beginning of the day, while early finish is marked at the end of the day. For example, if an activity has a duration of 1 day, its early start would be at the beginning of day 1, and its early finish would be at the end of day 1 - thus both ES and EF would be 1.
  • 2. Now move forward to the next activity in the path (Start - A - B - C - Finish), which is Activity B in this diagram. To figure out ES, take the EF of the previous task and add 1. So for Activity B, you can calculate ES = 6 + 1 = 7, and EF = 7 + 5 – 1 = 11.
  • 3. Activity C has two predecessors (activity B and D). Which one do you use to calculate EF? Since C can’t start until both B and D are done, use the one with the latest EF. That means you need to figure out the EF of Activity D (its ES is 1, so its EF is 1 + 2 – 1 = 2). Now you can move forward to Activity C and calculate its EF. The EF of Activity D is 2, which is smaller than B’s EF of 11, so for Activity C, the ES = 11 + 1 = 12, and EF = 12 + 7 – 1 = 18. 
  • Note: When an activity has more than one predecessor, its early start (ES) should be based on the predecessor with the latest early finish (EF).

• Take a backward pass to find late start and finish: You can use a backward pass through the same network diagram to figure out the late finish and start for each activity.
  • You’re calculating the latest any activity can start and finish, so it makes sense that you need to start at the end of the project and work backward - and the last activity on the critical path is always the last one in the project. Then do these three steps, working backward to the next longest path, then the next longest, and so on, until you’ve filled in the LS and LF for all of the activities. Fill in the LF and LS for the activities on each path, but don’t replace any LF or LS; you’ve already calculated.
  • 1. Start at the end of the path, with Activity C. The LF (late finish) of the last activity is the same as the EF. Calculate its LS (late start) by subtracting its duration from the LF and adding 1. So, LS = 18 – 7 + 1 = 12.
  • 2. Now move backward to the previous activity in the path - in this case, Activity B. Its LF is the LS of Activity C minus 1, so LF = 12 – 1 = 11. Calculate its LS in the same way as step 1: LS = 11 – 5 + 1 = 7.
  • 3. Now do the same for Activity A. LF is the LS for Activity B minus 1, so LF = 7 – 1 = 6. And LS is LF minus duration plus 1, so LF = 6 – 6 + 1 = 1.
  • 4. Now you can move onto the next longest path, Start-D-C-Finish. If there were more paths, you’d then move on to the next longest one, and so on, filling in LF and LS for any nodes that haven’t already been filled in.
    Note: When a task is a predecessor to two later tasks, use the one with the lower LS to calculate its LF.

The diagram below illustrates a case where Activity D has multiple successors, while Activity H has multiple predecessors.

b. Calculating Free Float for an Activity

For the given network diagram below:

Free Float for Activity G

= Early Start of Activity E – Early Finish of Activity G – 1

= 6 – 3 – 1

= 2

Total float for Activity G 

= Late Finish of Activity G – Early Finish of Activity G

= 18 – 3

= 15

From these results: Free Float for Activity G is 2 days, meaning G can be delayed by 2 days without impacting the early start of Activity E. Total Float for Activity G is 15 days, meaning G can be delayed by up to 15 days before it causes the entire project to be delayed.

c. Calculation Formulas:

• Forward pass:
  • EF = ES + duration – 1
  • ES (successor) = max predecessors’ (EFs+Lags) + 1
• Backward pass:
  • LF (last activities before finish) = max these EFs
  • LS = LF – duration + 1 = LF – (duration – 1)
  • LF (predecessor) = min successors’ (LSs-Lags) – 1
• Free Float = Min successors’ (ESs – Lags) – EF – 1

4. Calculating Float using the Critical Path Method

Once we’ve identified the critical path, we can do many useful things with it. One of the most valuable applications is calculating the Flloat of individual activities. Luckily, it’s not hard to figure out the float for any activity in a network diagram. Using this method can be quicker than the traditional Forward Pass and Backward Pass approach.

First, you write down the list of all of the paths in the diagram, and you identify the critical path. The float for every activity in the critical path is zero. For example, in the network diagram below:

1. There are three paths in this network:

• Start → A → B → C → Finish = 11 (The path with the longest duration is the critical path)
• Start → D → E → Finish = 7
• Start → D → F→ G → Finish = 8

2. The float for each of the activities on the critical path is zero.

3. Find the next longest path. Subtract its duration from the duration of the critical path, and that’s the float for each activity on it. That’s how you figure out how long any of its activities can slip before it delays the project.

4. Do the same for the next longest path, and so on through the rest of the network diagram. Pretty soon, you’ll fill in the float for every activity!

5.  Note: When filling in the float to each activity, make sure not to fill it in again if the float has already been calculated.

5. Quick Float calculation method with "tips"

The general formula to QUICKLY calculate the float of an activity:

Float (A) = Critical path duration – longest path (A)

                = LS – ES = LF – EF (also Total Float)

Explanation: Float of an activity A equals the total duration of the Critical Path minus the duration of the longest path that contains activity A. With this formula, calculating Float for an activity becomes very quick, helping us save a lot of time when taking the PMP exam.

Example with a network diagram:

There are 3 paths in this network diagram:

• Start → A → B → C → Finish = 11 (This is the Critical Path as it has the longest duration)
• Start → D → E → Finish = 7
• Start → D → F→ G → Finish = 8

1. Applying the formula to calculate Float for A, the longest path containing A is Start → A → B → C → Finish: 

                        Float (A) = Critical path duration - longest path (A) = 11 - 11 = 0

2. Applying the formula to calculate Float for B, the longest path containing B is Start → A → B → C → Finish:

                        Float (B) = Critical path duration - longest path (B) = 11 - 11 = 0

3. Applying the formula to calculate Float for C, the longest path containing C is Start → A → B → C → Finish:

                        Float (C) = Critical path duration - longest path (C) = 11 - 11 = 0

4. Applying the formula to calculate Float for D, the longest path containing D is Start → D → F→ G → Finish = 8:

                        Float (D) = Critical path duration - longest path (D) = 11 - 8 = 3

5. Applying the formula to calculate Float for E, the longest path containing E is Start → D → E → Finish = 7:

                        Float (E) = Critical path duration - longest path (E) = 11 - 7 = 4

6. Applying the formula to calculate Float for F, the longest path containing F is Start → D → F→ G → Finish = 8:

                        Float (F) = Critical path duration - longest path (F) = 11 - 8 = 3

7. Applying the formula to calculate Float for G, the longest path containing G is Start → D → F→ G → Finish = 8:

                        Float (G) = Critical path duration - longest path (G) = 11 - 8 = 3

6. Summary

Total float, free float, and project float are important concepts in project schedule management. A project manager needs to carefully calculate these values to build a reasonable and achievable project schedule. For the PMP exam, float can be calculated in various ways, and we hope the small “tips” presented above can help you save a significant amount of time during the test.

 Content compiled by: Trainer Nguyễn Hải Hà, Trainer Nguyễn Sĩ Triều Châu

References: Head First PMP 4, Rita PMP 9, PMStudycircle

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