Example On Cost Budgeting In Cpm.docx
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Ex: The relevant data about a project is shown below. Sl. No.
Activity
1 2 3 4 5 6 7 8 9 10 11 12 13
A B C D E F G H I J K L M
Precedence Relationship
Normal Duration in days
Normal Cost in Rs.
Crashed Duration in days
Crashed Cost in Rs.
4 3 8 2 3 2 1 6 3 2 2 4 3
6,000 2,000 8,000 5,000 4,500 2,000 3,000 9,000 4,500 5,000 1,500 3,500 6,000
2 3 4 1 1 2 1 4 2 1 2 1 2
8,000 2,000 10,000 6,000 7,500 2,000 3,000 10,000 6,000 8,000 1,500 5,000 8,500
NIL A B B B D C C E F and I G H and J K and L
Ans: First we solve taking only the normal duration and cost of the activities.
Tail Event Early, iE Late, iL
Head Event Early, jE Late, jL
Activity
Duration
ij
0
0
4
Total [jL – iE – D].
Float Free [jE – iE –D]
Indep. [jE – iL –D]
4
0
0
0
A
1-2
D 4
B
2-3
3
4
4
7
7
0
0
0
C
3-4
8
7
7
15
15
0
0
0
D
3-5
2
7
7
9
17
8
0
0
E
3-6
3
7
7
10
16
6
0
0
F
5-7
2
9
17
13
19
8
2
0
G
4-8
1
15
15
16
23
7
0
0
H
4-9
6
15
15
21
21
0
0
0
I
6-7
3
10
16
13
19
6
0
0
J
7-9
2
13
19
21
21
6
6
0
K
8-10
2
16
23
25
25
7
5
0
L
9-10
4
21
21
25
25
0
0
0
M
10-11
3
25
25
28
28
0
0
0
1
Considering the normal durations the critical path is ABCHLM; duration = 28 days and total cost = Rs. 60,000. Budget vrs time
Next we solve taking the crash duration and cost of the activities: Crashing program with cost
Marginal Cost Analysis on the project: Length of Path in weeks
Activity to crash
Crash cost in Rs.
Total Cost in Rs.
ABCGKM
ABCHLM
ABDFJLM
ABEIJLM
Nil
0
60,000
21
28
20
22
H
500
60,500
21
27
20
22
H
500
61,000
21
26
20
22
C
500
61,500
20
25
20
22
C
500
62,000
19
24
20
22
C
500
62,500
18
23
20
22
2
C
500
63,000
17
22
20
22
L
500
63,500
17
21
19
21
L
500
64,000
17
20
18
20
L
500
64,500
17
19
17
19
A
1,000
65,500
16
18
16
18
A
1,000
66,500
15
17
15
17
M
2,500
69,000
14
16
14
16
Fully crashed project duration is 16 days and project cost is Rs. 69,000. When the activities are fully crashed, there are two critical paths - ABCHLM and ABEIJLM.
3
Activity
1 2 3 4 5 6 7 8 9 10 11 12 13
A B C D E F G H I J K L M
Precedence Relationship
Normal Duration in days
Normal Cost in Rs.
Crashed Duration in days
Crashed Cost in Rs.
4 3 8 2 3 2 1 6 3 2 2 4 3
6,000 2,000 8,000 5,000 4,500 2,000 3,000 9,000 4,500 5,000 1,500 3,500 6,000
2 3 4 1 1 2 1 4 2 1 2 1 2
8,000 2,000 10,000 6,000 7,500 2,000 3,000 10,000 6,000 8,000 1,500 5,000 8,500
NIL A B B B D C C E F and I G H and J K and L
Ans: First we solve taking only the normal duration and cost of the activities.
Tail Event Early, iE Late, iL
Head Event Early, jE Late, jL
Activity
Duration
ij
0
0
4
Total [jL – iE – D].
Float Free [jE – iE –D]
Indep. [jE – iL –D]
4
0
0
0
A
1-2
D 4
B
2-3
3
4
4
7
7
0
0
0
C
3-4
8
7
7
15
15
0
0
0
D
3-5
2
7
7
9
17
8
0
0
E
3-6
3
7
7
10
16
6
0
0
F
5-7
2
9
17
13
19
8
2
0
G
4-8
1
15
15
16
23
7
0
0
H
4-9
6
15
15
21
21
0
0
0
I
6-7
3
10
16
13
19
6
0
0
J
7-9
2
13
19
21
21
6
6
0
K
8-10
2
16
23
25
25
7
5
0
L
9-10
4
21
21
25
25
0
0
0
M
10-11
3
25
25
28
28
0
0
0
1
Considering the normal durations the critical path is ABCHLM; duration = 28 days and total cost = Rs. 60,000. Budget vrs time
Next we solve taking the crash duration and cost of the activities: Crashing program with cost
Marginal Cost Analysis on the project: Length of Path in weeks
Activity to crash
Crash cost in Rs.
Total Cost in Rs.
ABCGKM
ABCHLM
ABDFJLM
ABEIJLM
Nil
0
60,000
21
28
20
22
H
500
60,500
21
27
20
22
H
500
61,000
21
26
20
22
C
500
61,500
20
25
20
22
C
500
62,000
19
24
20
22
C
500
62,500
18
23
20
22
2
C
500
63,000
17
22
20
22
L
500
63,500
17
21
19
21
L
500
64,000
17
20
18
20
L
500
64,500
17
19
17
19
A
1,000
65,500
16
18
16
18
A
1,000
66,500
15
17
15
17
M
2,500
69,000
14
16
14
16
Fully crashed project duration is 16 days and project cost is Rs. 69,000. When the activities are fully crashed, there are two critical paths - ABCHLM and ABEIJLM.
3
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