Let's break down the problem into smaller steps for constructing the project network diagram, calculating the Earliest Start (ES), Earliest Finish (EF), Latest Start (LS), Latest Finish (LF) for each activity, and identifying the critical path.

Step 1: Project Network Diagram

We'll first organize the activities based on their dependencies and draw a project network diagram.

• A and B start first (no predecessors).
• C depends on A.
• D depends on A and B.
• E depends on C and D.
• F depends on D.
• G depends on F.
• H depends on G.

Project Network Diagram

plaintextCopy code
  Start
   |   
  [A] [B]
   |    |
  [C] [D]
   |     |
  [E]   [F]
   |     |
  [G]   [H]
   |
   Finish

Step 2: Calculation of ES, EF, LS, LF

To calculate the Earliest Start (ES) and Earliest Finish (EF) times, we work from left to right, based on the duration of activities. For Earliest Start (ES), each activity starts after its immediate predecessor finishes. The Earliest Finish (EF) is calculated as: $EF = ES + Duration - 1$ To calculate the Latest Start (LS) and Latest Finish (LF), we work backwards from the project’s finish date. For each activity, the Latest Finish (LF) is the latest time an activity can finish without delaying the project. The Latest Start (LS) is calculated as: $LS = LF - Duration + 1$

Step 3: Fill in the Data

Activity	Duration	Predecessors	ES	EF	LS	LF
A	2	-	0	1	0	1
B	3	-	0	2	2	4
C	4	A	2	5	2	5
D	5	A, B	2	6	4	8
E	8	C, D	6	13	6	13
F	3	D	6	8	9	11
G	2	F	8	9	11	12
H	3	G	9	11	12	14

Step 4: Critical Path

To identify the critical path, we look for the longest path from the start to finish. The critical path will have no slack, i.e., the ES and LS (and EF and LF) for the activities in this path will be the same.

• The longest path is: A → C → E → H.
• The critical path duration is: 2 + 4 + 8 + 3 = 17 days.

Final Results:

1. Critical Path: A → C → E → H
2. Project Duration (Critical Path Length): 17 days

Let me know if you would like further details or have any questions! Here are a few follow-up questions for you:

1. How do you calculate slack time for non-critical activities?
2. What happens if one of the critical path activities is delayed?
3. How do you interpret the early start and late start times for an activity?
4. What impact does shortening the duration of a non-critical path activity have on the project?
5. How can we handle resource constraints in project scheduling?

Tip: Always ensure that your network diagram clearly reflects the dependencies between activities to avoid errors in calculating the project’s schedule.