Question:
1.Draw an activity-on-arrow (AON) diagram for these 15 project tasks (A to O). Calculate, display and clearly label on the diagram, the earliest and latest start and finish times and float of each task? Clearly show Workings
2. What effect will each of the following changes (when considered separately) have on the critical path(s) and the completion time of the overall project? Give reasons for your answer.
- Activity D is delayed by 2 weeks.
- Activity G is completed in 8 weeks.
3. Clearly show how the project network you have drawn in (b) above needs to be amended to represent the logical constraint that activity O cannot start until at least 4 days after activity M has finished. How are the overall project completion time and critical path(s) affected if this condition is imposed?
Answer:
1.Project Plan
|
Task Name
|
Completion time
|
Start
|
Finish
|
Early Start
|
Early Finish
|
Late Start
|
Late Finish
|
Free Slack
|
Predecessors
|
|
Activity
|
19 wks
|
Thu 3/8/18
|
Wed 7/18/18
|
Thu 3/8/18
|
Wed 7/18/18
|
Thu 3/8/18
|
Wed 7/18/18
|
0 wks
|
|
|
A
|
3 wks
|
Thu 3/8/18
|
Wed 3/28/18
|
Thu 3/8/18
|
Wed 3/28/18
|
Thu 3/8/18
|
Wed 3/28/18
|
0 wks
|
|
|
B
|
4 wks
|
Thu 3/8/18
|
Wed 4/4/18
|
Thu 3/8/18
|
Wed 4/4/18
|
Thu 3/15/18
|
Wed 4/11/18
|
0 wks
|
|
|
C
|
4 wks
|
Thu 3/8/18
|
Wed 4/4/18
|
Thu 3/8/18
|
Wed 4/4/18
|
Thu 3/15/18
|
Wed 4/11/18
|
0 wks
|
|
|
D
|
4 wks
|
Thu 3/29/18
|
Wed 4/25/18
|
Thu 3/29/18
|
Wed 4/25/18
|
Thu 3/29/18
|
Wed 4/25/18
|
0 wks
|
1
|
|
E
|
4 wks
|
Thu 3/29/18
|
Wed 4/25/18
|
Thu 3/29/18
|
Wed 4/25/18
|
Thu 5/31/18
|
Wed 6/27/18
|
9 wks
|
1
|
|
F
|
2 wks
|
Thu 4/5/18
|
Wed 4/18/18
|
Thu 4/5/18
|
Wed 4/18/18
|
Thu 4/12/18
|
Wed 4/25/18
|
1 wk
|
2
|
|
G
|
3 wks
|
Thu 4/5/18
|
Wed 4/25/18
|
Thu 4/5/18
|
Wed 4/25/18
|
Thu 5/3/18
|
Wed 5/23/18
|
4 wks
|
2
|
|
H
|
4 wks
|
Thu 4/5/18
|
Wed 5/2/18
|
Thu 4/5/18
|
Wed 5/2/18
|
Thu 4/26/18
|
Wed 5/23/18
|
2 wks
|
2
|
|
I
|
6 wks
|
Thu 4/5/18
|
Wed 5/16/18
|
Thu 4/5/18
|
Wed 5/16/18
|
Thu 4/12/18
|
Wed 5/23/18
|
0 wks
|
3
|
|
J
|
4 wks
|
Thu 4/5/18
|
Wed 5/2/18
|
Thu 4/5/18
|
Wed 5/2/18
|
Thu 5/3/18
|
Wed 5/30/18
|
0 wks
|
3
|
|
K
|
4 wks
|
Thu 4/26/18
|
Wed 5/23/18
|
Thu 4/26/18
|
Wed 5/23/18
|
Thu 4/26/18
|
Wed 5/23/18
|
0 wks
|
4,6
|
|
L
|
5 wks
|
Thu 5/24/18
|
Wed 6/27/18
|
Thu 5/24/18
|
Wed 6/27/18
|
Thu 5/24/18
|
Wed 6/27/18
|
0 wks
|
7,11
|
|
M
|
5 wks
|
Thu 5/17/18
|
Wed 6/20/18
|
Thu 5/17/18
|
Wed 6/20/18
|
Thu 5/24/18
|
Wed 6/27/18
|
1 wk
|
8,9
|
|
N
|
4 wks
|
Thu 5/3/18
|
Wed 5/30/18
|
Thu 5/3/18
|
Wed 5/30/18
|
Thu 5/31/18
|
Wed 6/27/18
|
4 wks
|
10
|
|
O
|
3 wks
|
Thu 6/28/18
|
Wed 7/18/18
|
Thu 6/28/18
|
Wed 7/18/18
|
Thu 6/28/18
|
Wed 7/18/18
|
0 wks
|
5,12,13,14
|
Arrow On Network Diagram illustrating forward pass and backward pass calculation
Critical Path initially ![]()
![]()
2.
Project Plan
2.1 Task D gets delayed to 2 weeks. So, overall project completion time changes from 19 weeks to 21 weeks.
|
Task Name
|
Completion time
|
Start
|
Finish
|
Early Start
|
Early Finish
|
Late Start
|
Late Finish
|
Free Slack
|
Predecessors
|
|
Activity
|
21 wks
|
Thu 08-03-18
|
Wed 01-08-18
|
Thu 08-03-18
|
Wed 01-08-18
|
Thu 08-03-18
|
Wed 01-08-18
|
0 wks
|
|
|
A
|
3 wks
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 08-03-18
|
Wed 28-03-18
|
0 wks
|
|
|
B
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
0 wks
|
|
|
C
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
0 wks
|
|
|
D
|
6 wks
|
Thu 29-03-18
|
Wed 09-05-18
|
Thu 29-03-18
|
Wed 09-05-18
|
Thu 29-03-18
|
Wed 09-05-18
|
0 wks
|
1
|
|
E
|
4 wks
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 14-06-18
|
Wed 11-07-18
|
11 wks
|
1
|
|
F
|
2 wks
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 26-04-18
|
Wed 09-05-18
|
3 wks
|
2
|
|
G
|
3 wks
|
Thu 05-04-18
|
Wed 25-04-18
|
Thu 05-04-18
|
Wed 25-04-18
|
Thu 17-05-18
|
Wed 06-06-18
|
6 wks
|
2
|
|
H
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 10-05-18
|
Wed 06-06-18
|
2 wks
|
2
|
|
I
|
6 wks
|
Thu 05-04-18
|
Wed 16-05-18
|
Thu 05-04-18
|
Wed 16-05-18
|
Thu 26-04-18
|
Wed 06-06-18
|
0 wks
|
3
|
|
J
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 17-05-18
|
Wed 13-06-18
|
0 wks
|
3
|
|
K
|
4 wks
|
Thu 10-05-18
|
Wed 06-06-18
|
Thu 10-05-18
|
Wed 06-06-18
|
Thu 10-05-18
|
Wed 06-06-18
|
0 wks
|
4,6
|
|
L
|
5 wks
|
Thu 07-06-18
|
Wed 11-07-18
|
Thu 07-06-18
|
Wed 11-07-18
|
Thu 07-06-18
|
Wed 11-07-18
|
0 wks
|
7,11
|
|
M
|
5 wks
|
Thu 17-05-18
|
Wed 20-06-18
|
Thu 17-05-18
|
Wed 20-06-18
|
Thu 07-06-18
|
Wed 11-07-18
|
3 wks
|
8,9
|
|
N
|
4 wks
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 14-06-18
|
Wed 11-07-18
|
6 wks
|
10
|
|
O
|
3 wks
|
Thu 12-07-18
|
Wed 01-08-18
|
Thu 12-07-18
|
Wed 01-08-18
|
Thu 12-07-18
|
Wed 01-08-18
|
0 wks
|
5,12,13,14
|
2.1 Change in Critical Path
2. Project Plan
2.2 Task G gets completed in 8 weeks. So, overall project completion time changes from 19 weeks to 20 weeks.
|
Task Name
|
Completion time
|
Start
|
Finish
|
Early Start
|
Early Finish
|
Late Start
|
Late Finish
|
Free Slack
|
Predecessors
|
|
Activity
|
20 wks
|
Thu 08-03-18
|
Wed 25-07-18
|
Thu 08-03-18
|
Wed 25-07-18
|
Thu 08-03-18
|
Wed 25-07-18
|
0 wks
|
|
|
A
|
3 wks
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 15-03-18
|
Wed 04-04-18
|
0 wks
|
|
|
B
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
0 wks
|
|
|
C
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 22-03-18
|
Wed 18-04-18
|
0 wks
|
|
|
D
|
4 wks
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 05-04-18
|
Wed 02-05-18
|
0 wks
|
1
|
|
E
|
4 wks
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 07-06-18
|
Wed 04-07-18
|
10 wks
|
1
|
|
F
|
2 wks
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 19-04-18
|
Wed 02-05-18
|
1 wk
|
2
|
|
G
|
8 wks
|
Thu 05-04-18
|
Wed 30-05-18
|
Thu 05-04-18
|
Wed 30-05-18
|
Thu 05-04-18
|
Wed 30-05-18
|
0 wks
|
2
|
|
H
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
2 wks
|
2
|
|
I
|
6 wks
|
Thu 05-04-18
|
Wed 16-05-18
|
Thu 05-04-18
|
Wed 16-05-18
|
Thu 19-04-18
|
Wed 30-05-18
|
0 wks
|
3
|
|
J
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 10-05-18
|
Wed 06-06-18
|
0 wks
|
3
|
|
K
|
4 wks
|
Thu 26-04-18
|
Wed 23-05-18
|
Thu 26-04-18
|
Wed 23-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
1 wk
|
4,6
|
|
L
|
5 wks
|
Thu 31-05-18
|
Wed 04-07-18
|
Thu 31-05-18
|
Wed 04-07-18
|
Thu 31-05-18
|
Wed 04-07-18
|
0 wks
|
7,11
|
|
M
|
5 wks
|
Thu 17-05-18
|
Wed 20-06-18
|
Thu 17-05-18
|
Wed 20-06-18
|
Thu 31-05-18
|
Wed 04-07-18
|
2 wks
|
8,9
|
|
N
|
4 wks
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 07-06-18
|
Wed 04-07-18
|
5 wks
|
10
|
|
O
|
3 wks
|
Thu 05-07-18
|
Wed 25-07-18
|
Thu 05-07-18
|
Wed 25-07-18
|
Thu 05-07-18
|
Wed 25-07-18
|
0 wks
|
5,12,13,14
|
2.2 Change in Critical Path
![]()
3.
Project Plan
The activity O cannot get started until at least 4 days after the activity M has finished. Therefore, the completion time for activity O is 5.4 weeks. The overall completion time of the project does not get affected.
|
Task Name
|
Duration
|
Start
|
Finish
|
Early Start
|
Early Finish
|
Late Start
|
Late Finish
|
Free Slack
|
Predecessors
|
|
Activity
|
19 wks
|
Thu 08-03-18
|
Wed 18-07-18
|
Thu 08-03-18
|
Wed 18-07-18
|
Thu 08-03-18
|
Wed 18-07-18
|
0 wks
|
|
|
A
|
3 wks
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 08-03-18
|
Wed 28-03-18
|
Thu 08-03-18
|
Wed 28-03-18
|
0 wks
|
|
|
B
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 15-03-18
|
Wed 11-04-18
|
0 wks
|
|
|
C
|
4 wks
|
Thu 08-03-18
|
Wed 04-04-18
|
Thu 08-03-18
|
Wed 04-04-18
|
Tue 13-03-18
|
Mon 09-04-18
|
0 wks
|
|
|
D
|
4 wks
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
0 wks
|
1
|
|
E
|
4 wks
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 29-03-18
|
Wed 25-04-18
|
Thu 31-05-18
|
Wed 27-06-18
|
9 wks
|
1
|
|
F
|
2 wks
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 05-04-18
|
Wed 18-04-18
|
Thu 12-04-18
|
Wed 25-04-18
|
1 wk
|
2
|
|
G
|
3 wks
|
Thu 05-04-18
|
Wed 25-04-18
|
Thu 05-04-18
|
Wed 25-04-18
|
Thu 03-05-18
|
Wed 23-05-18
|
4 wks
|
2
|
|
H
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Tue 24-04-18
|
Mon 21-05-18
|
2 wks
|
2
|
|
I
|
6 wks
|
Thu 05-04-18
|
Wed 16-05-18
|
Thu 05-04-18
|
Wed 16-05-18
|
Tue 10-04-18
|
Mon 21-05-18
|
0 wks
|
3
|
|
J
|
4 wks
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 05-04-18
|
Wed 02-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
0 wks
|
3
|
|
K
|
4 wks
|
Thu 26-04-18
|
Wed 23-05-18
|
Thu 26-04-18
|
Wed 23-05-18
|
Thu 26-04-18
|
Wed 23-05-18
|
0 wks
|
4,6
|
|
L
|
5 wks
|
Thu 24-05-18
|
Wed 27-06-18
|
Thu 24-05-18
|
Wed 27-06-18
|
Thu 24-05-18
|
Wed 27-06-18
|
0 wks
|
7,11
|
|
M
|
5.4 wks
|
Thu 17-05-18
|
Fri 22-06-18
|
Thu 17-05-18
|
Fri 22-06-18
|
Tue 22-05-18
|
Wed 27-06-18
|
0.6 wks
|
8,9
|
|
N
|
4 wks
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 03-05-18
|
Wed 30-05-18
|
Thu 31-05-18
|
Wed 27-06-18
|
4 wks
|
10
|
|
O
|
3 wks
|
Thu 28-06-18
|
Wed 18-07-18
|
Thu 28-06-18
|
Wed 18-07-18
|
Thu 28-06-18
|
Wed 18-07-18
|
0 wks
|
5,12,13,14
|
Change in Critical Path
References:
Kerzner, H. and Kerzner, H.R., 2017. Project management: a systems approach to planning, scheduling, and controlling. John Wiley & Sons.
Pinto, J.K., 2015. Project management: achieving competitive advantage. Prentice Hall.
