Examples of Network Diagram Questions (1) Question No. 1
You have to manage a project with activities and their respective durations as listed in Table 1 below:
Table 1: Project Data for Construction of Precedence Diagram Activity
Immediate Predecessor
Duration (months)
A
None
2
B
A
4
C
A
2
D
B
2
E
B, C
4
F
A, E
6
G
D
4
H
D, E, F
2
I
G, H
6
J
H, F
6
K
H, I, J
4
1) Construct a precedence diagram to analyze your project. 2) What is the project duration? 3) What are the critical activities? 4) Show the critical path on your precedence diagram. 5) When is the latest time that activity G must be completed in order that the project is not delayed? 6) When is the earliest time that activity D can possibly be completed? 7) What is the free float for activity E with respect to activity H?
CEPB 323 Project Management & Construction: Examples of network diagram questions
Answers
1) Refer to Figure A2. 14 G 1 8 8 4 12
0 0
A 2
2 2
2 2
B 4
6 6
12 6
D 14 2 8
4 2
C 2
6 4
6 6
E 10 4 10
10 10
F 16 6 16
18 18
16 16
I 24 6 24
H 18 2 18
24 24
18 18
K 28 4 28
J 24 6 24
Figure A2: Precedence diagram for question no. 4 Answers: Critical activities: Critical Path: Project duration:
A, B, E, F, H, I, J and K. 28 months
2) Project duration = 28 months. 3) Critical activities: A, B, E, F, H, I, J & K. 4) The critical path is indicated by the bold arrows in the precedence diagram. 5) The latest time that activity G must be completed in order that the project is th not delayed is by end of the 18 month. 6) The earliest time that activity D can possibly be completed is by end of the 8 month.
th
7) The free float for activity E with respect to activity H: 16 – 10 = 6 months.
Question No. 2
You have to manage a project with activities and their respective durations as listed in Table 2 below: 1) Construct an arrow diagram to analyze your project. 2) What is the project duration? 3) What are the critical activities? 4) Show the critical path on your arrow diagram.
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CEPB 323 Project Management & Construction: Examples of network diagram questions
Table 2: Project Data for Construction of Arrow Diagram Activity
Immediate Predecessor
Duration (months)
A
None
2
B
A
8
C
A
2
D
A
4
E
B
2
F
D
2
G
E
4
H
B, C
4
I
A, F
6
J
A, F, G, H
2
K
I
2
L
A, F, J, K
4
5) When is the earliest time that activity H can start? 6) When is the latest time that activity F must start? 7) What is the total float for activity I?
Answers
1) Refer to Figure A3. 2) Project duration = 22 months. 3) Critical activities: A, B, E, G, J and L. 4) The critical path is indicated by the bold arrows in the precedence diagram. th
5) The earliest time that activity H must start is at the beginning of the 11 month. th
6) The latest time that activity F must start is at the beginning of the 9 month.
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CEPB 323 Project Management & Construction: Examples of network diagram questions
7) The total float for activity I is 10 – 8 = 2 months.
1
0
A
2
0
2
2
2
B 10
2
8 10
3
10
2
D
8
2
4
6
E 12 2 12
5
C 12
2
4
10 10
2
6
4
4
8
F 10
6
2
8
12
G 16
12
4 16
12
H 16
10
4 14
7
16
8
10 8
16
I
16
6 14
J 18
10
2 18
16
K 18
14
2 16
18
L 22
18
4 22
11
9
Figure A3: Arrow diagram for question no. 5 Critical activities: Critical Path: Project duration:
A, B, E, G, J and L 22 months
Question No. 3
You have to manage a project with activities and their respective durations as listed in Table 3 below. The critical path is along activities A, C, F, I, K and L. 1) What is the expected project duration? nd
2) What is the probability of completing the project by the end of the 32 month? 3) What is the project duration if it is based on a 99% probability to complete the project?
Answers
1) The expected project duration is the sum of critical activities durations (refer to Table A1), T E = 29 months.
2) Calculations for the relevant activities are as shown in Table A1 below: t e = (a + 4m + b) / 6 2
υ
= [(b – a) / 6]
σ TE
= √ (υ1-2 + υ2-3 + ...+ υi-j ) = √ (0.11 + 0.11 + 0.44 + 0.44 + 0.11 + 1.00) = 1.49
z
= ( T S - T E ) / σ TE = ( 32 – 29 ) / 1.49 = 2.01 Page 4 of 7
CEPB 323 Project Management & Construction: Examples of network diagram questions
Therefore from Table 1, the probability of completing the project by the end of nd the 32 month is 0.98 or 98%.
3) A 99% probability to complete the project refers to a value of deviation from Table 1, Z = 2.5
Therefore the project duration based on a 99% probability to complete the project: z = ( T S - T E ) / σ TE T S = z σ TE + T E
= (2.5)(1.49) + 29 = 30.68 months.
Table 3: Project Data for PERT Analysis
Immediate Predecessor
Activity
Duration (months) Optimistic
Most likely
Pessimistic
A
None
1
2
3
B
A
1
2
3
C
A
7
8
9
D
B
1
2
3
E
D
1
2
3
F
C, E
1
3
5
G
D
2
4
6
H
C, E
4
5
6
I
F
2
4
6
J
F, G, H
1
2
3
K
I
5
6
7
L
J, K
3
6
9
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CEPB 323 Project Management & Construction: Examples of network diagram questions
Table A1: Project Data for PERT Analysis. Calculations for the relevant activities Duration (months) Activity
Immediate Predecessor
Optimistic (a)
Most likely (m)
Pessimistic (b)
Expected time (te)
Standard deviation (υ)
A
None
1
2
3
2
0.11
C
A
7
8
9
8
0.11
F
C, E
1
3
5
3
0.44
I
F
2
4
6
4
0.44
K
I
5
6
7
6
0.11
L
J, K
3
6
9
6
1.00
Project duration =
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29
CEPB 323 Project Management & Construction: Examples of network diagram questions
Formula and Tables
Table 1: PERT Probability Table
te = a + 4m + b 6
υ = σ2 = {(b – a)/6}2 σTE = √(υ1-2 + υ2-3 + υ3-4 + υ4-5 + …… + υi-j ) z
=
(T S – T E ) / σTE
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