Welcome to KnowledgeHut. In today's video, we are going to learn some basics of Project
Scheduling, including the determination of Slack Values and finding the Critical Path.
We will be dealing with the activities, the expected activity duration, earliest start
time, earliest finish time, latest start time and latest finish time in the whole operation.
Now suppose activity A and B are without any predecessors, therefore these activities can
begin at the start of the project. Activity C needs
A to be completed before it can start. D requires both A&B to be completed, E needs D to be
completed, F needs both C&E to be completed and G requires E to finish first. Since there
are no activities after F&G, therefore, both of them can go to the finish.
Now, this is how the network will look with activity nodes. The numbers below the activity
name represent the time required by the respective activities.
Let us do the Forward Pass, A is the first activity so it can start right away, therefore
its earliest start time will be 0. It will take 7 days to be completed so its earliest
finish time will be 0+7=7 days. Similarly, B will have the earliest start time of 0 and
earliest finish time of 9.
C needs A to finish first, and we have already seen that A has the earliest finish time of
7, therefore, earliest start time for C will be 7. After these 7 days, C will take 12 days
to complete and therefore earliest finish time of C will be 12+7=19.
D needs both A&B to finish first, A has earliest finish time of 7 days and B has 9 days, so
we can say that on day 9 both these activities will be finished, therefore earliest start
time for D will be 9. Now D will finish in 8+9=17 days.
E has only D as its predecessor, so it can start as soon as D ends. After going on for
9 days, it'll end on 26th day of the project.
F needs E&C to finish first, both of them will not finish before 26 as E has earliest
finish at 26. Therefore F can start at the earliest at around 26 and finish at 32 after
consuming its 6 days.
G only has one predecessor, E. And E will finish on 26, therefore, G can start at the
earliest at 26. And it can finish at the earliest at 26+5= 31.
As we can see that the last activity to finish is F which will finish on day 32, therefore
we can say that the project will take 32 days.
Now let's do the Backward Pass. Since the project completion time is 32 days,
F&G cannot take more time than 32 days. Therefore the latest finish time for both these activities
has to be 32 days.
Now let us start calculating the latest start times of activities by subtracting the activity
time from the latest finish time.
For G it will be 32-5=27, for F it will be 32-6=26.
Now E has F&G as its successors and their latest start time is 26 and 27 respectively.
So E has to finish at 26 in order for F to start on the same day. By now you must have
observed that while doing Backward Pass the latest finish time of an activity must be
the minimum of the latest start time of its successor.
Thus, for E the latest start time will be 26-9=17.
Since D has only E as its successor, the latest start time for E becomes D's latest finish
time. And the latest start time will be 17-8=9.
Similarly, C has only F as its successor, therefore, the latest finish time for C is
26 and the latest start time would be 26-12=14.
Now A has C&D as its successors and the minimum of their latest start is 9, therefore, A's
latest finish will also be 9. And its latest start will be 9-7=2
Similarly, B has D as its successor with the latest start of 9 which becomes B's latest
finish and therefore B's latest start becomes 0. Here finishes our Backward Pass.
Now let us calculate the Slack for each activity. Slack is the delay which we can allow in an
activity in such a way that it does not cause any delay in the deadline of the project.
The formula for calculating slack is "LS-ES" or "LF-EF"
So for A it can be "2-0" or "9-7", which is 2. For B it will be 0, 7 for
C, for D, E and F it will be 0 again, and for G it will be 1.
Now the slack of 7 days in C shows that it can be delayed for 7 days without causing
any delay in the project. C can begin any time between day 7 and day 14. Also, it can
end any time between day 19 and 26.
All the activities with zero slack cannot be delayed without extending the project completion
time. All such activities are called Critical Activities. The path they form is known as
"Critical Path" which is the longest path in the network. Here B D E and F form the Critical
Path.
So this was all about "Project Scheduling" and "Critical Path". Make sure to subscribe
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