project management. crashing a network. finding optimum duration and optimum cost of project. operations research (OR)

1. Project Management
Crashing
1

2. Activity Predecessor NT NC CT CC
A - 9 12000 6 18000
B A 14 14000 4 24000
C A 4 2000 3 2400
D C 6 44000 4 56000
E - 14 16000 13 18000
F E 6 4000 6 4000
G B, D 5 4000 3 4800
H F, G 2 12000 1 14000
Indirect cost: Rs.2000/week
2

3. 3
Activity A B C D E F G H
Predecessor - A A C - E B, D F, G
Duration 9 14 4 6 14 6 5 2
1
A
2
9
B
5
14
C
4
4
D
6
E
3
14
F
6
6
G
5
H
7
2
A – B – G – H = 9 + 14 + 5 + 2 = 30
A – C – D – G – H = 9 + 4 + 6 + 5 + 2 = 26
E – F – H = 14 + 6 + 2 = 22

4. Activity NT NC CT CC
A 9 12000 6 18000
B 14 14000 4 24000
C 4 2000 3 2400
D 6 44000 4 56000
E 14 16000 13 18000
F 6 4000 6 4000
G 5 4000 3 4800
H 2 12000 1 14000
Direct Cost 10800
Indirect cost: Rs.2000/week = 2000 x 30 = 60000
Total Cost = 168000
4

5. 5
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000

6. Activity NT NC CT CC Cost Slope
A 9 12000 6 18000 2000
B 14 14000 4 24000 1000
C 4 2000 3 2400 400
D 6 44000 4 56000 6000
E 14 16000 13 18000 2000
F 6 4000 6 4000 -
G 5 4000 3 4800 400
H 2 12000 1 14000 2000
6

7. Activity NT NC CT CC Cost Slope
A 9 12000 6 18000 2000
B 14 14000 4 24000 1000
C 4 2000 3 2400 400
D 6 44000 4 56000 6000
E 14 16000 13 18000 2000
F 6 4000 6 4000 -
G 5 4000 3 4800 400
H 2 12000 1 14000 2000
7

8. Activity NT NC CT CC Cost Slope
A 9 12000 6 18000 2000
B 14 14000 4 24000 1000
G 5 4000 3 4800 400
H 2 12000 1 14000 2000
8
A – B – G – H = 9 + 14 + 5 + 2 = 30
A – C – D – G – H = 9 + 4 + 6 + 5 + 2 = 26
E – F – H = 14 + 6 + 2 = 22

9. 9
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000
G 2 28 108800 56000 164800

10. 10
1
A
2
9
B
5
14
C
4
4
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 9 + 14 + 3 + 2 = 28
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

11. 11
1
A
2
9
B
5
14
C
4
4
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 9 + 14 + 3 + 2 = 28
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

12. Activity Crashing Available Cost Slope
A 3 2000
B 10 1000
G - -
H 1 2000
12
A – B – G – H = 9 + 14 + 3 + 2 = 28
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

13. 13
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000
G 2 28 108800 56000 164800
B 4 24 112800 48000 160800

14. 14
1
A
2
9
B
5
10
C
4
4
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 9 + 10 + 3 + 2 = 24
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

15. 15
1
A
2
9
B
5
10
C
4
4
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 9 + 10 + 3 + 2 = 24
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

16. Activity Crashing Available Cost Slope
A 3 2000
B, C 1 1400
B, D 2 7000
H 1 2000
16
A – B – G – H = 9 + 10 + 3 + 2 = 24
A – C – D – G – H = 9 + 4 + 6 + 3 + 2 = 24
E – F – H = 14 + 6 + 2 = 22

17. 17
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000
G 2 28 108800 56000 164800
B 4 24 112800 48000 160800
B, C 1 23 114200 46000 160200

18. 18
Correction required, this point forward

19. 19
1
A
2
7
B
5
10
C
4
4
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 7 + 10 + 3 + 2 = 22
A – C – D – G – H = 7 + 4 + 6 + 3 + 2 = 22
E – F – H = 14 + 6 + 2 = 22

20. 20
1
A
2
7
B
5
10
C
44
D
6
E
3
14
F
6
6
G
3
H
7
2
A – B – G – H = 7 + 10 + 3 + 2 = 22
A – C – D – G – H = 7 + 4 + 6 + 3 + 2 = 22
E – F – H = 14 + 6 + 2 = 22

21. Activity Crashing Available Cost Slope
A, E 1 4000
B, C, E 1 3400
B, D, E 1 9000
H 1 2000
21
A – B – G – H = 7 + 10 + 3 + 2 = 22
A – C – D – G – H = 7 + 4 + 6 + 3 + 2 = 22
E – F – H = 14 + 6 + 2 = 22
1
A
2
7
B
5
10
C
44
D
6
E
3
14
F
6
6
G
3
H
7
2

22. Activity NT NC CT CC Cost Slope
A 9 12000 6 18000 2000
B 14 14000 4 24000 1000
C 4 2000 3 2400 400
D 6 44000 4 56000 6000
E 14 16000 13 18000 2000
F 6 4000 6 4000 -
G 5 4000 3 4800 400
H 2 12000 1 14000 2000
22

23. 23
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000
G 2 28 108800 56000 164800
B 4 24 112800 48000 160800
A 2 22 116800 44000 160800
H 1 21 118800 42000 160800

24. 24
1
A
2
7
B
5
10
C
44
D
6
E
3
14
F
6
6
G
3
H
7
1
A – B – G – H = 7 + 10 + 3 + 1 = 21
A – C – D – G – H = 7 + 4 + 6 + 3 + 1 = 21
E – F – H = 14 + 6 + 1 = 21

25. 25
1
A
2
7
B
5
10
C
44
D
6
E
3
14
F
6
6
G
3
H
7
1
A – B – G – H = 7 + 10 + 3 + 1 = 21
A – C – D – G – H = 7 + 4 + 6 + 3 + 1 = 21
E – F – H = 14 + 6 + 1 = 21

26. Activity Crashing Available Cost Slope
A, E 1 4000
B, C, E 1 3400
B, D, E 1 9000
26
A – B – G – H = 7 + 10 + 3 + 1 = 21
A – C – D – G – H = 7 + 4 + 6 + 3 + 1 = 21
E – F – H = 14 + 6 + 1 = 21
1
A
2
7
B
5
10
C
44
D
6
E
3
14
F
6
6
G
3
H
7
1

27. 27
Activity Crashed By Duration DC IC TC
None - 30 108000 60000 168000
G 2 28 108800 56000 164800
B 4 24 112800 48000 160800
A 2 22 116800 44000 160800
H 1 21 118800 42000 160800
B, C, E 1 20 122200 40000 162200

28. 28
1
A
2
7
B
5
9
C
43
D
6
E
3
13
F
6
6
G
3
H
7
1
A – B – G – H = 7 + 9 + 3 + 1 = 20
A – C – D – G – H = 7 + 3 + 6 + 3 + 1 = 20
E – F – H = 13 + 6 + 1 = 20

29. 29
1
A
2
7
B
5
9
C
43
D
6
E
3
13
F
6
6
G
3
H
7
1
A – B – G – H = 7 + 9 + 3 + 1 = 20
A – C – D – G – H = 7 + 3 + 6 + 3 + 1 = 20
E – F – H = 13 + 6 + 1 = 20

30. Activity NT NC CT CC Cost Slope
A 9 12000 6 18000 2000
B 14 14000 4 24000 1000
C 4 2000 3 2400 400
D 6 44000 4 56000 6000
E 14 16000 13 18000 2000
F 6 4000 6 4000 -
G 5 4000 3 4800 400
H 2 12000 1 14000 2000
30

31. Activity Crashing Available Cost Slope
A, E - -
A, F - -
B, C, E - -
B, C, F - -
B, D, E - -
B, D, F - -
G, E - -
G, F - -
H - -
1
A
2
7
B
5
9
C
43
D
6
E
3
13
F
6
6
G
3
H
7
1
A – B – G – H = 7 + 9 + 3 + 1 = 20
A – C – D – G – H = 7 + 3 + 6 + 3 + 1 = 20
E – F – H = 13 + 6 + 1 = 20

32. • Minimum duration: 20 weeks
• Cost: Rs.162200
• Optimum duration: 21-24 weeks
• Optimum cost: Rs.160800
32

33. Activity NT Duration
after
crashing
CT Crashing
still
available
A 9 7 6 1
B 14 9 4 5
C 4 3 3 -
D 6 6 4 2
E 14 13 13 -
F 6 6 6 -
G 5 3 3 -
H 2 1 1 -
33
1
A
2
7
B
5
9
C
43
D
6
E
3
13
F
6
6
G
3
H
7
1