I would like to start the topics which can bring more fruits with little scope of doubts. If a little attention is paid on these topics, there are very less chances of ambiguity. Yes, you have guessed it right, I will concentrate on the topics with numerical problems.
Today I will talk about the above topics in the subject of the post. Numerical problems are not lengthy and the calculations involved are very simple.
Critical Path - This is the longest duration path in the network diagram but the shortest possible time to complete the project. I am assuming here that you have already prepared the network diagrams and know its basic concepts. Once you have the network diagram ready, look at the each possible path from start to finish, calculate the duration of each path, the path with the longest duration is the critical path. It is possible to have more than one critical paths in a project. More the critical paths riskier the project.
Let's look at an example. Click on the below image to enlarge.
There are three paths -
1. Start-A-C-D-F-H-End = 11 days
2. Start-A-C-E-H-End = 8 days
3. Start-B-G-I-End = 12 days
Path 3 (Start-B-G-I-End) shown in Red is the critical path as this has the longest duration.
Path 1 (Start-A-C-D-F-H-End) is near critical path. A project manager not only should watch out for the critical path but also should concentrate upon the near critical path as this has the potential to become a critical path if not managed well.
Free Float - This is the time by which an activity can be delayed without delaying the early start of its successor activity.
Free float of an activity = (ES of the next activity - EF of that activity) - 1
(Note: -1 is there if you are considering the 1st day of the project as 1 but if you consider the 1st day of the project as 0th day, -1 will be omitted)
Total Float - This is the total time by which an activity can be delayed without delaying the scheduled end date of the project.
Total float of an activity = (LF - EF) of that activity OR (LS-ES) of that activity
Unless specifically asked for free float in questions consider float=total float.
Activities on the critical path have ZERO float.
In the above diagram,
Free Float for activity F = ES of H - EF of F - 1 = 11-10-1 = 0
Total Float for activity F = (LS - ES) of F OR (LF - EF) of F= 11-10 = 1
Free Float for activity E = ES of H - EF of E - 1 = 11-7-1 = 3
Total Float for activity E = (LS - ES) of E OR (LF - EF) of E = 11-7 = 4