Network Techniques for Project Management
(Part-3)
Plan 401: Project Evaluation and Management
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
1
CPM Model
It is deterministic
The focus of CPM analysis is on variations in activity times as
a result of changes in resource assignments.
It seeks to determine the project schedule which minimizes
total cost.
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
2
1
Key Assumptions
1. Project Cost can be divided into two components:
i. Direct Cost : direct material, direct labor
ii. Indirect Cost : indirect supplies, rent, insurance
2. Activities of the project can be expedited by crashing which
involves employing more resources
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
3
Key Assumptions (cont.)
3. Crashing reduces time but enhances direct costs because of factors
like overtime payments, extra payments and wastages. The relationship
between time and direct activity cost can be reasonably approximated
by a downward sloping straight line.
Direct cost
of activity
Crash
Time
Normal
Time
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
Activity duration
4
2
Key Assumptions (cont.)
4. Indirect Costs associated with the project increase linearly with
project duration.
Indirect
cost of
project
Project duration
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
5
Procedure for CPM analysis
1. Obtain the critical path in the normal network. Determine the project
duration and direct cost.
2. Examine the cost-time slope of activities on the critical path obtained
and crash the activity which has the least slope.
3. Construct the new critical path after crashing as per step 2. Determine
the project duration and cost.
4. Repeat step 2 and 3 till activities on the critical path are crashed .
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
6
3
Example
(Test-1)
3
4
9
2
6
17 17
8 8
20 20
10
8
5
1
7
6
30 30
0 0
5
9
3
5
5 7
13 14
7
Indirect Cost = 2,000 tk./Week
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
7
Example (cont.) (Test-1)
Time in Weeks
Activity
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
3,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
4,000
5,500
500
3-5
7
5
2,000
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
4,000
6,800
700
6-7
10
7
6,000
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
45,200 70,400
Critical Path = 1-2-4-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
8
4
Example (cont.) (Test-2)
3
4
6
2
6
14 16
8 8
19 19
10
8
5
1
7
6
29 29
0 0
5
9
3
5
5 6
13 13
7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
9
Example (cont.) (Test-2)
Time in Weeks
Activity
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
3,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
2,000
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
4,000
6,800
700
6-7
10
7
6,000
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
46,700 70,400
Critical Path = 1-2-5-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
10
5
Example (cont.) (Test-3)
6
2
3
4
6
14 14
8 8
17 17
10
8
5
1
7
2
27 27
0 0
5
9
3
5
5 8
13 15
7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
11
Example (cont.) (Test-3)
Time in Weeks
Activity
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
3,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
2,000
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
6,800
6,800
700
6-7
10
7
6,000
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
49,500 70,400
Critical Path = 1-2-4-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
12
6
Example (cont.) (Test-4)
3
4
6
2
6
10 11
4 5
14 14
10
4
5
1
7
2
24 24
0 0
5
9
3
5
5 5
12 12
7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
Example (cont.)
(Test-4)
Time in Weeks
Activity
13
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
6,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
2,000
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
6,800
6,800
700
6-7
10
7
6,000
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
52,500 70,400
Critical Path = 1-3-5-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
14
7
Example (cont.) (Test-5)
3
4
6
2
6
10 10
4 4
13 13
10
4
5
1
7
2
23 23
0 0
5
9
3
5
5 6
10 11
5
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
Example (cont.)
(Test-5)
Time in Weeks
Activity
15
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
6,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
3,200
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
6,800
6,800
700
6-7
10
7
6,000
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
53,700 70,400
Critical Path = 1-2-4-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
16
8
Example (cont.) (Test-6)
6
2
3
4
6
10 10
4 4
13 13
7
4
5
1
7
2
20 20
0 0
5
9
3
5
5 6
10 11
5
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
Example (cont.)
(Test-6)
Cost
Time in Weeks
Activity
17
Normal
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
6,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
3,200
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
10,000
11,200
2,400
5-6
6
2
6,800
6,800
700
6-7
10
7
8,700
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
56,400 70,400
Critical Path = 1-2-4-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
18
9
Example (cont.)
(Test-7)
2.5
4
6
2
6
10 10
4 4
12.5 12.5
7
4
5
1
7
2
19.5 19.5
0 0
5
9
3
5
5 5.5
10 10.5
5
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
Example (cont.)
(Test-7)
Time in Weeks
Activity
19
Normal
Cost
Crash
Normal
Crash
Cost to
expedite
per week
1-2
8
4
6,000
6,000
750
1-3
5
3
4,000
8,000
2,000
2-4
9
6
5,500
5,500
500
3-5
7
5
3,200
3,200
600
2-5
5
1
8,000
12,000
1,000
4-6
3
2.5
11,200
11,200
2,400
5-6
6
2
6,800
6,800
700
6-7
10
7
8,700
8,700
900
5-7
9
5
4,200
9,000
1,200
Total
57,600 70,400
Critical Path = 1-2-4-6-7
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
20
10
Example (cont.)
Project Duration and Total Cost
Project
Duration
(weeks)
Total
Direct
Cost
Total
Indirect
Cost
Total Cost
Tests
Activities Crashed
Test-1
None
30
45,200
60,000
105,200
Test-2
(2-4)
29
46,700
58,000
104,700
Test-3
(2-4), (5-6)
27
49,500
54,000
103,500
Test-4
(1-2), (2-4), (5-6)
24
52,500
48,000
100,500
Test-5
(1-2), (2-4), (3-5), (5-6)
23
53,700
46,000
99,700
Test-6
(1-2), (2-4), (3-5), (5-6), (6-7)
20
56,400
40,000
96,400
Test-7
(1-2), (2-4), (3-5), (4-6), (5-6),
(6-7)
19.5
57,600
39,000
96,600
Md. Shakil Bin Kashem, Lecturer, Dept. of URP,
BUET
21
11