Question

Consider the following work breakdown structure: Given a due date of 210 days, what is the earliest you can start activity D without delaying the project?

		Time Estimates (days)
Activity	Precedes	Optimistic			Most Likely			Pessimistic
Start	A,B		-			-			-
A	C,D		44			50			56
B	D		45			60			75
C	E		42			45			48
D	F		31			40			49
E	F		27			36			39
F	End		58			70			82

		50
		60
		70
		100
		140

Answer 1

We find the expected duration for each activity as shown below:

Based on the expected durations and predecessor relationships, we prepare a project network diagram as shown below:

The above network diagram in the form of formulas is shown below for better understanding and reference:

The above project diagram is prepared as per the legend shown in the top-left corner.

EST = Early start time

LST = Late start time

EFT = Early finish time

LFT = Late finish time

SLK = Slack = LST - EST or Slack = LFT - EFT

The EST of an activity = EFT of previous activity

EFT of an activity = EST + Duration

Similarly, LFT & LST are calculated during the backward pass.

Project duration = 200 as seen from the network diagram.

Required duration = 210.

As seen from above, the Earliest start for Activity D = EST in the box for D = 60.

Hence,

The Earliest we can start activity D without delaying the project = Earliest start for D = 60

Answer: 60

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