CD Chapter 16 – Pert/CPM Models for Project Management
b) Start → A → C → J → Finish Length = 85.7 weeks
Start → B → F → J → Finish Length =99.1 weeks *critical path
CD16-22
16.18 a) Let A = reduction in A due to crashing
and A ≥ 0, C ≥ 0.
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-23
b) Let B = reduction in B due to crashing
c) Let A = reduction in A due to crashing
B = reduction in B due to crashing
C = reduction in C due to crashing
D = reduction in D due to crashing
CD16-24
d)
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time Time Normal Crash Reduction per Month Start Time Finish
Activity (months) (months) Cost Cost (months) Saved Time Reduction Time
A 8 5 $25,000 $40,000 3 $5,000 0 0 8
B 9 7 $20,000 $30,000 2 $5,000 0 2 7
C 6 4 $16,000 $24,000 2 $4,000 8 2 12
D 7 4 $27,000 $45,000 3 $6,000 7 2 12
Max T ime
Project Completion Time (months) 12 <= 12
Total Cost $118,000
e) Deadline of 11 months:
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per Month Start Time Finish
Activity (months) (months) Cost Cost (months) Saved Time Reduction Time
A 8 5 $25,000 $40,000 3 $5,000 0 1 7
B 9 7 $20,000 $30,000 2 $5,000 0 2 7
C 6 4 $16,000 $24,000 2 $4,000 7 2 11
D 7 4 $27,000 $45,000 3 $6,000 7 3 11
Max Time
Project Completion Time (months) 11 <= 11
Total Cost $129,000
Deadline of 13 months:
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per Month Start T ime F inish
Activity (months) (months) Cost Cost (months) Saved Time Reduction Time
A 8 5 $25,000 $40,000 3 $5,000 0 0 8
B 9 7 $20,000 $30,000 2 $5,000 0 2 7
C 6 4 $16,000 $24,000 2 $4,000 8 1 13
D 7 4 $27,000 $45,000 3 $6,000 7 1 13
Max Time
Project Completion Time (months) 13 <= 13
Total Cost $108,000
16.19 a)
Activity
Crash
Length of Path
to Crash
Cost
B – D
50
B or D
$10,000
49
B or D
$10,000
48
B or D
$10,000
47
b)
Activity
Crash
Length of Path
to Crash
Cost
A – C – E – F
51
C
$10,000
50
C
$10,000
49
C
$10,000
48
E
$15,000
47
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-25
c)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time Time Normal Crash Reduction per Day Start Time Finish
Activity (days) (days) Cost Cost (days) Saved T ime Reduction T ime
A12 9 $210,000 $270,000 3 $20,000 0 0 12
B23 18 $410,000 $460,000 5 $10,000 0 3 20
C15 12 $290,000 $320,000 3 $10,000 12 324
D27 21 $440,000 $500,000 6 $10,000 20 047
E18 14 $350,000 $410,000 4 $15,000 24 141
F 6 4 $160,000 $210,000 2 $25,000 41 047
Max Time
Project Completion Time (days) 47 <= 47
Total Cost $1,935,000
16.20 a)
Activity
ES
EF
LS
LF
Slack
Critical Path
Start
0
0
0
0
0
Yes
A
0
3
0
3
0
Yes
B
3
7
4
8
1
No
C
3
8
3
8
0
Yes
D
7
10
9
12
2
No
E
8
12
8
12
0
Yes
Finish
12
12
12
12
0
Yes
Critical Path: Start → A → C → E → Finish
b)
Activity
Crash
Length of Path
to Crash
Cost
A – B – D
A – B – E
A – C – E
10
11
12
C
$1,333
10
11
11
E
$2,500
10
10
10
D & E
$4,000
9
9
9
B & C
$4,333
8
8
8
New Plan:
Activity
Duration
Cost
A
3 weeks
$54,000
B
3 weeks
$65,000
C
3 weeks
$68,666
D
2 weeks
$41,500
E
2 weeks
$80,000
c)
1
2
3
4
5
6
7
8
9
10
11
12
13
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per W eek Start Time Finish
Activity (weeks) (weeks) Cost Cost (weeks) Saved Time Reduction Time
A 3 2 $54,000 $60,000 1 $6,000 0 0 3
B 4 3 $62,000 $65,000 1 $3,000 4.000000002 0 8
C 5 2 $66,000 $70,000 3 $1,333 3 0 8
D 3 1 $40,000 $43,000 2 $1,500 9 0 12
E 4 2 $75,000 $80,000 2 $2,500 8 0 12
Max Time
Project Completion Time (weeks) 12 <= 12
Total Cost $297,000
13
Total Cost $298,333
1
2
3
4
5
6
7
8
9
10
11
12
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per W eek Start Time Finish
Activity (weeks) (weeks) Cost Cost (weeks) Saved Time Reduction Time
A 3 2 $54,000 $60,000 1 $6,000 0 0 3
B 4 3 $62,000 $65,000 1 $3,000 3 0 7
C 5 2 $66,000 $70,000 3 $1,333 3 1 7
D 3 1 $40,000 $43,000 2 $1,500 8 0 11
E 4 2 $75,000 $80,000 2 $2,500 7 0 11
Max Time
Project Completion Time (weeks) 11 <= 11
1
2
3
4
5
6
7
8
9
10
11
12
13
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per W eek Start Time Finish
Activity (weeks) (weeks) Cost Cost (weeks) Saved Time Reduction Time
A 3 2 $54,000 $60,000 1 $6,000 0 0 3
B 4 3 $62,000 $65,000 1 $3,000 3 0 7
C 5 2 $66,000 $70,000 3 $1,333 3 1 7
D 3 1 $40,000 $43,000 2 $1,500 7 0 10
E 4 2 $75,000 $80,000 2 $2,500 7 1 10
Max Time
Project Completion Time (weeks) 10 <= 10
Total Cost $300,833
1
2
3
4
5
6
7
8
9
10
11
12
13
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per W eek Start Time Finish
Activity (weeks) (weeks) Cost Cost (weeks) Saved Time Reduction Time
A 3 2 $54,000 $60,000 1 $6,000 0 0 3
B 4 3 $62,000 $65,000 1 $3,000 3 0 7
C 5 2 $66,000 $70,000 3 $1,333 3 1 7
D 3 1 $40,000 $43,000 2 $1,500 7 1 9
E 4 2 $75,000 $80,000 2 $2,500 7 2 9
Max Time
Project Completion Time (weeks) 9 <= 9
Total Cost $304,833
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-27
1
2
3
4
5
6
7
8
9
10
11
12
13
A B C D E F G H I J
Normal Crash Maximum Time Crash Cost
Time T ime Normal Crash Reduction per W eek Start Time Finish
Activity (weeks) (weeks) Cost Cost (weeks) Saved Time Reduction Time
A 3 2 $54,000 $60,000 1 $6,000 0 0 3
B 4 3 $62,000 $65,000 1 $3,000 3 1 6
C 5 2 $66,000 $70,000 3 $1,333 3 2 6
D 3 1 $40,000 $43,000 2 $1,500 6 1 8
E 4 2 $75,000 $80,000 2 $2,500 6 2 8
Max Time
Project Completion Time (weeks) 8 <= 8
Total Cost $309,167
16.21
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
A B C D E F G H I J
Crash Cost
Normal Crash Normal Crash Maximum Time per W eek
Time Time Cost Cost Reduction Saved Start Time Finish
Activity (weeks) (weeks) ($million) ($million) (weeks) ($million) T ime Reduction Time
A 5 3 20 30 2 5 0 2 3
B 3 2 10 20 110 0 1 2
C 4 2 16 24 2 4 3 0 7
D 6 3 25 43 3 6 3 0 9
E 5 4 22 30 1 8 2 0 7
F 7 4 30 48 3 6 2 0 9
G 9 5 25 45 4 5 7 1 15
H 8 6 30 44 2 7 9 2 15
Max Time
Project Completion T ime (weeks) 15 <= 15
Total Cost ($million) 217
16.22
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
A B C D E F G H I J
Crash Cost
Normal Crash Normal Crash Maximum Time per W eek
Time T ime Cost Cost Reduction Saved Start Time Finish
Activity (weeks) (weeks) ($million) ($million) (weeks) ($million) T ime Reduction Time
A32 28 160 180 4 5 0 0 32
B28 25 125 146 3 7 0 3 25
C36 31 170 210 5 8 32 068
D16 13 60 72 3 4 25 041
E32 27 135 160 5 5 26 058
F54 47 215 257 7 6 25 376
G17 15 90 96 2 3 41 058
H20 17 120 132 3 4 58 078
I34 30 190 226 4 9 58 092
J18 16 80 84 2 2 76 292
Max T ime
Project Completion Time (weeks) 92 <= 92
Total Cost ($million) 1,388
CD16-28
16.23 a)
Activity
ES
EF
Start
0
0
A
0
3
B
3
6
C
3
6
D
6
8
E
6
8
Finish
8
8
b)
3
4
5
6
7
8
9
10
B C D F
Estimated
Duration Estimated Cost Per Week
Activity (weeks) Cost of Its Duration
A 3 $54,000 $18,000
B 3 $65,000 $21,667
C 3 $68,667 $22,889
D 2 $41,500 $20,750
E 2 $80,000 $40,000
c)
4
5
6
7
8
9
10
11
12
13
E F G H I J K L M N
Start Cost Per Week W eek Week Week W eek Week Week Week W eek
Time of Its Duration 1 2 3 4 5 6 7 8
0 $18,000 $18,000 $18,000 $18,000 $0 $0 $0 $0 $0
3 $21,667 $0 $0 $0 $21,667 $21,667 $21,667 $0 $0
3 $22,889 $0 $0 $0 $22,889 $22,889 $22,889 $0 $0
6 $20,750 $0 $0 $0 $0 $0 $0 $20,750 $20,750
6 $40,000 $0 $0 $0 $0 $0 $0 $40,000 $40,000
W eekly Project Cost $18,000 $18,000 $18,000 $44,556 $44,556 $44,556 $60,750 $60,750
Cumulative Project Cost $18,000 $36,000 $54,000 $98,556 $143,111 $187,667 $248,417 $309,167
d)
3
4
5
6
7
8
9
10
11
12
13
B C D E F G H I J K L M N
Estimated
Duration Estimated Start Cost Per W eek Week Week W eek Week Week Week W eek W eek
Activity (weeks) Cost Time of Its Duration 1 2 3 4 5 6 7 8
A 3 $54,000 0 $18,000 $18,000 $18,000 $18,000 $0 $0 $0 $0 $0
B 3 $65,000 3 $21,667 $0 $0 $0 $21,667 $21,667 $21,667 $0 $0
C 3 $68,667 3 $22,889 $0 $0 $0 $22,889 $22,889 $22,889 $0 $0
D 2 $41,500 6 $20,750 $0 $0 $0 $0 $0 $0 $20,750 $20,750
E 2 $80,000 6 $40,000 $0 $0 $0 $0 $0 $0 $40,000 $40,000
Weekly Project Cost $18,000 $18,000 $18,000 $44,556 $44,556 $44,556 $60,750 $60,750
Cumulative Project Cost $18,000 $36,000 $54,000 $98,556 $143,111 $187,667 $248,417 $309,167
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-29
e)
Activity
Budgeted
Cost
Percent
Completed
Value
Completed
Actual Cost To
Date
Cost Overrun To
Date
A
$54,000
100%
$54,000
$65,000
$11,000
B
$65,000
100%
$65,000
$55,000
–$10,000
C
$68,666
33%
$22,660
$44,000
$21,340
Total
$187,666
$141,660
$164,000
$22,340
Michael should concentrate his efforts on activity C since it is not yet completed.
16.24 a)
Activity
ES
EF
LS
LF
Slack
Start
0
0
0
0
0
A
0
6
0
6
0
B
0
2
4
6
4
C
6
10
9
13
3
D
6
11
6
11
0
E
10
17
13
20
3
F
11
20
11
20
0
Finish
20
20
20
20
0
b)
3
4
5
6
7
8
9
10
11
12
13
14
B C D E F G H I J K L
Estimated Estimated Cost Per W eek all costs in $thousands
Duration Cost Start of Its Duration Week W eek W eek Week Week W eek
Activity (weeks) ($thousands) Time ($thousands) 1 2 3 4 5 6
A 6 420 0 70 70 70 70 70 70 70
B 2 180 0 90 90 90 0 0 0 0
C 4 540 6 135 0 0 0 0 0 0
D 5 360 6 72 0 0 0 0 0 0
E 7 590 10 84.286 0 0 0 0 0 0
F 9 630 11 70 0 0 0 0 0 0
W eekly Project Cost ($thousands) 160 160 70 70 70 70
Cumulative Project Cost ($thousands) 160 320 390 460 530 600
4
5
6
7
8
9
10
11
12
13
14
M N O P Q R S T U V W X Y Z
Week W eek Week Week W eek Week Week Week Week W eek W eek W eek W eek Week
7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
135 135 135 135 0 0 0 0 0 0 0 0 0 0
72 72 72 72 72 0 0 0 0 0 0 0 0 0
0 0 0 0 84.286 84.286 84.286 84.286 84.286 84.286 84.286 0 0 0
0 0 0 0 0 70 70 70 70 70 70 70 70 70
207 207 207 207 156.29 154.29 154.29 154.29 154.29 154.29 154.29 70 70 70
807 1014 1221 1428 1584.3 1738.6 1892.9 2047.1 2201.4 2355.7 2510 2580 2650 2720
CD16-30
c)
3
4
5
6
7
8
9
10
11
12
13
14
B C D E F G H I J K L
Estimated Estimated Cost Per W eek all costs in $thousands
Duration Cost Start of Its Duration Week W eek W eek Week Week W eek
Activity (weeks) ($thousands) Time ($thousands) 1 2 3 4 5 6
A 6 420 0 70 70 70 70 70 70 70
B 2 180 4 90 0 0 0 0 90 90
C 4 540 9 135 0 0 0 0 0 0
D 5 360 6 72 0 0 0 0 0 0
E 7 590 13 84.286 0 0 0 0 0 0
F 9 630 11 70 0 0 0 0 0 0
W eekly Project Cost ($thousands) 70 70 70 70 160 160
Cumulative Project Cost ($thousands) 70 140 210 280 440 600
4
5
6
7
8
9
10
11
12
13
14
M N O P Q R S T U V W X Y Z
Week W eek Week Week W eek Week Week Week Week W eek W eek W eek W eek Week
7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 135 135 135 135 0 0 0 0 0 0 0
72 72 72 72 72 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 84.286 84.286 84.286 84.286 84.286 84.286 84.286
0 0 0 0 0 70 70 70 70 70 70 70 70 70
72 72 72 207 207 205 205 154.29 154.29 154.29 154.29 154.29 154.29 154.29
672 744 816 1023 1230 1435 1640 1794.3 1948.6 2102.9 2257.1 2411.4 2565.7 2720
d)
••••••••••
•
•
•
••••••••
•••••••
•
•
•
•••••••••••
0
500000
1000000
1500000
2000000
2500000
3000000
0 2 4 6 8 10 12 14 16 18 20
Cumul ati ve Project Cost
W eek
Earliest start
time schedule
Latest start
time schedule
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-31
e)
Activity
Budgeted
Cost
Percent
Completed
Value
Completed
Actual Cost To
Date
Cost Overrun To
Date
A
$420,000
50%
$210,000
$200,000
-$10,000
B
$180,000
100%
$180,000
$200,000
$20,000
D
$360,000
50%
$180,000
$210,000
$30,000
Total
$960,000
$570,000
$610,000
$40,000
The project manager should focus attention on activity D since it is not yet finished and
is running over budget.
16.25 a)
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
B C D E F G H I J K L
Estimated Estimated Cost Per W eek all costs in $thousands
Duration Cost Start of Its Duration W eek Week W eek Week Week W eek
Activity (weeks) ($thousands) Time ($thousands) 1 2 3 4 5 6
A 6 180 0 30 30 30 30 30 30 30
B 3 75 025 25 25 25 000
C 4 120 0 30 30 30 30 30 0 0
D 4 140 6 35 0 0 0 0 0 0
E 7 175 3 25 0 0 0 25 25 25
F 4 80 420 0 0 0 0 20 20
G 6 210 4 35 0 0 0 0 35 35
H 3 45 10 15 0 0 0 0 0 0
I 5 125 6 25 0 0 0 0 0 0
J 4 100 10 25 0 0 0 0 0 0
K 3 60 820 0 0 0 0 0 0
L 5 50 10 10 0 0 0 0 0 0
M 6 90 14 15 0 0 0 0 0 0
N 5 150 15 30 0 0 0 0 0 0
Weekly Project Cost ($thousands) 85 85 85 85 110 110
Cumulative Project Cost ($thousands) 85 170 255 340 450 560
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
M N O P Q R S T U V W X Y Z
W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek
7 8 9 10 11 12 13 14 15 16 17 18 19 20
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
35 35 35 35 0 0 0 0 0 0 0 0 0 0
25 25 25 25 0 0 0 0 0 0 0 0 0 0
20 20 0 0 0 0 0 0 0 0 0 0 0 0
35 35 35 35 0 0 0 0 0 0 0 0 0 0
0 0 0 0 15 15 15 0 0 0 0 0 0 0
25 25 25 25 25 0 0 0 0 0 0 0 0 0
0 0 0 0 25 25 25 25 0 0 0 0 0 0
0 0 20 20 20 0 0 0 0 0 0 0 0 0
0 0 0 0 10 10 10 10 10 0 0 0 0 0
0 0 0 0 0 0 0 0 15 15 15 15 15 15
0 0 0 0 0 0 0 0 0 30 30 30 30 30
140 140 140 140 95 50 50 35 25 45 45 45 45 45
700 840 980 1120 1215 1265 1315 1350 1375 1420 1465 1510 1555 1600
CD16-32
b)
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
B C D E F G H I J K L
Estimated Estimated Cost Per W eek all costs in $thousands
Duration Cost Start of Its Duration W eek Week W eek Week Week W eek
Activity (weeks) ($thousands) Time ($thousands) 1 2 3 4 5 6
A 6 180 1 30 030 30 30 30 30
B 3 75 025 25 25 25 000
C 4 120 0 30 30 30 30 30 0 0
D 4 140 7 35 0 0 0 0 0 0
E 7 175 3 25 0 0 0 25 25 25
F 4 80 820 0 0 0 0 0 0
G 6 210 4 35 0 0 0 0 35 35
H 3 45 11 15 0 0 0 0 0 0
I 5 125 9 25 0 0 0 0 0 0
J 4 100 10 25 0 0 0 0 0 0
K 3 60 12 20 0 0 0 0 0 0
L 5 50 10 10 0 0 0 0 0 0
M 6 90 14 15 0 0 0 0 0 0
N 5 150 15 30 0 0 0 0 0 0
Weekly Project Cost ($thousands) 55 85 85 85 90 90
Cumulative Project Cost ($thousands) 55 140 225 310 400 490
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
M N O P Q R S T U V W X Y Z
W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek W eek
7 8 9 10 11 12 13 14 15 16 17 18 19 20
30 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
035 35 35 35 0 0 0 0 0 0 0 0 0
25 25 25 25 0 0 0 0 0 0 0 0 0 0
0 0 20 20 20 20 0 0 0 0 0 0 0 0
35 35 35 35 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 15 15 15 0 0 0 0 0 0
0 0 0 25 25 25 25 25 0 0 0 0 0 0
0 0 0 0 25 25 25 25 0 0 0 0 0 0
0 0 0 0 0 0 20 20 20 0 0 0 0 0
0 0 0 0 10 10 10 10 10 0 0 0 0 0
0 0 0 0 0 0 0 0 15 15 15 15 15 15
0 0 0 0 0 0 0 0 0 30 30 30 30 30
90 95 115 140 115 95 95 95 45 45 45 45 45 45
580 675 790 930 1045 1140 1235 1330 1375 1420 1465 1510 1555 1600
CD Chapter 16 – Pert/CPM Models for Project Management
CD16-33
c)
••••••••
•
•
•
•
••
•••••••
•••••
•
•
•
•
•
•••••••••••
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
0 2 4 6 8 10 12 14 16 18 20
Cumula ti ve Proj ect Co st
W eek
d)
Activity
Budgeted
Cost
Percent
Completed
Value
Completed
Actual Cost To
Date
Cost Overrun To
Date
A
$180,000
100%
$180,000
$190,000
$10,000
B
$75,000
100%
$75,000
$70,000
-$5,000
C
$120,000
100%
$120,000
$150,000
$30,000
D
$140,000
40%
$56,000
$70,000
$14,000
E
$175,000
50%
$87,500
$100,000
$12,500
F
$80,000
60%
$48,000
$45,000
-$3,000
G
$210,000
25%
$52,500
$50,000
-$2,500
I
$125,000
20%
$25,000
$35,000
$10,000
Total
$1,105,000
$644,000
$710,000
$66,000
The project manager should investigate activities D, E and I since they are not yet
finished and running over budget.
Earliest start
time schedule
Latest start
time schedule
CD16-34
Cases
16.1 a) A diagram of the project network appears below.
Sel ect a syndicate of underw rite rs
N egotiate the commitmen t o f each
memb er of the syndi cate
N ego tiate the spre ad for each
memb er of the sy ndicate
Pre pa re the reg i stra ti o n statem ent
Submi t th e r egistra tion stateme nt to the SEC
Mak e pres e ntations to
institutiona l investor s an d de velop
the inter est o f po te ntial bu yers
D istribute the
re d herr ing
C alculate the
issue pri ce
R eceive d efici ency
m emorandu m from th e
SEC
A mend statement and
r esubmit to the S EC
R eceive r egi stratio n
START
FINISH
Ev al uate the pr esti g e of ea ch p otential un de rw rite r
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CD Chapter 16 – Pert/CPM Models for Project Management
To determine the project schedule and which activities are critical, we calculate the
early start, late start, early finish, late finish, and slack below.
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Time Slack
Activity Description (weeks) ES EF LS LF (weeks) Critical?
A Evaluate prestige 3 0 3 0 3 0 Yes
B Select syndicate 1.5 3 4.5 3 4.5 0 Yes
C Negotiate commitment 2 4.5 6.5 5.5 7.5 1 No
D Negotiate spread 3 4.5 7.5 4.5 7.5 0 Yes
E Prepare registration 5 7.5 12.5 7.5 12.5 0 Yes
F Submit registration 1 12.5 13.5 12.5 13.5 0 Yes
G Present 6 13.5 19.5 16 22 2.5 No
H Distribute red herring 3 13.5 16.5 19 22 5.5 No
I Calculate price 5 13.5 18.5 17 22 3.5 No
J Receive deficiency 3 13.5 16.5 13.5 16.5 0 Yes
K Amend statement 1 16.5 17.5 16.5 17.5 0 Yes
L Receive registration 2 17.5 19.5 17.5 19.5 0 Yes
M Confirm blue sky 1 19.5 20.5 22 23 2.5 No
N Appoint registrar 3 19.5 22.5 20 23 0.5 No
O Appoint transfer 3.5 19.5 23 19.5 23 0 Yes
P Issue prospectus 4.5 23 27.5 23 27.5 0 Yes
Q Phone buyers 4 23 27 23.5 27.5 0.5 No
Project Duration 27.5
W eek
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A B C D E F G H I
Time Slack
Activity Descrip tion (weeks) ES EF LS LF (weeks) Critical?
A Evaluate prestige 3 0 = ES+ T ime = LF-Time = MIN(F4) = LF–EF = IF(Slack= 0,“Yes”,“No”)
B Select syndicate 1.5 = MAX(E3) = ES+ Time =LF-Time =MIN(F5,F6) = LF–EF = IF(Slack= 0,”Yes”,“No”)
C Negotiate commitment 2 = MAX(E4) = ES+ Time =LF–Time =MIN(F7) = LF-EF =IF(Slack= 0,“Yes”,“No”)
D Negotiate spread 3 =MAX(E4) = ES+ T ime = LF-Time = MIN(F7) = LF–EF = IF(Slack= 0,“Yes”,“No”)
E Prepare registration 5 =MAX(E5,E6) = ES+ Time =LF–Time =MIN(F8) = LF-EF =IF(Slack= 0,“Yes”,“No”)
F Submit registration 1 = MAX(E7) = ES+ Time = LF-Time = MIN(F9,F 10,F11,F12) = LF-EF =IF(Slack= 0,“Yes”,“No”)
G P resent 6 = MA X(E8) = ES+ T ime = LF-T ime = MI N(F 15) = LF–EF = IF (Slack= 0, “Yes”,“No”)
H Distribute red herring 3 = MAX(E8) = ES+ Time =LF-Time =MIN(F15) = LF-EF =IF(Slack= 0,“Yes”,“No”)
I Calculate price 5 = MAX(E8) = ES+ Time = LF-Time =MIN(F15) = LF-EF =IF(Slack= 0,“Yes”,“No”)
J Receive deficiency 3 = MAX(E8) = ES+ Time = LF-Time = MIN(F13) = LF–EF = IF(Slack= 0,“Yes”,“No”)
K Amend statement 1 = MAX(E12) = ES+ Time = LF-Time = MIN(F14) = LF–EF = IF(Slack= 0,”Yes”,“No”)
L Receive registration 2 = MAX(E13) = ES+ Time = LF-Time = MIN(F15,F 16,F17) =LF–EF = IF(Slack= 0,”Yes”,“No”)
M Confirm blue sky 1 = MAX(E9,E10,E11,E14) =ES+ Time = LF-Time =MIN(F18,F19) = LF–EF = IF(Slack= 0,”Yes”,“No”)
N Appoint registrar 3 = MAX(E14) = ES+ T ime = LF-Time = MIN(F18,F 19) =LF-EF =IF(Slack= 0,“Yes”,“No”)
O Appoint transfer 3.5 = MAX(E14) = ES+ Time =LF–Time =MIN(F18,F19) = LF–EF = IF(Slack= 0,”Yes”,“No”)
P Issue prospectus 4.5 = MAX(E15,E16,E17) = ES+ Time =LF–Time =ProjectDuration = LF–EF = IF(Slack= 0,“Yes”,“No”)
Q Phone buyers 4 = MAX(E15,E16,E17) = ES+ T ime = LF-Time = ProjectDuration = LF-EF =IF(Slack= 0,“Yes”,“No”)
W eek
Ran g e Name Cells
Activity A3:A19
Critical? I3:I19
Description B3:B19