Networking
Analysis
Assignment I
Q1. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
-
|
A
|
A
|
B
|
B
|
D&G
|
|
Duration (Days)
|
10
|
9
|
9
|
8
|
7
|
11
|
5
|
Q2. Draw the network from the following
activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
|
Immediate Predecessor
|
-
|
A
|
A
|
B
|
A
|
B
|
C&D
|
F
|
G
|
G
|
G
|
H&I
|
E&J
|
Q3. Draw the network from the following
activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
|
Immediate Predecessor
|
-
|
A
|
A
|
A
|
B
|
C
|
C
|
D
|
F
|
H
|
I
|
EKG
|
LJ
|
Q4. Draw the network from the following
activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
|
Immediate Predecessor
|
-
|
-
|
B
|
A
|
C
|
C
|
F
|
F
|
H
|
I
|
DEGJ
|
I
|
KL
|
Q5. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
|
Immediate Predecessor
|
-
|
-
|
A
|
A
|
BC
|
D
|
|
Duration (Days)
|
12
|
10
|
5
|
6
|
16
|
16
|
Q6. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
|
Immediate Predecessor
|
-
|
A
|
B
|
C
|
B
|
E
|
D&F
|
E
|
H
|
G&I
|
J
|
|
Duration (Days)
|
13
|
8
|
10
|
9
|
11
|
10
|
8
|
6
|
7
|
14
|
18
|
Q7. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
Immediate Predecessor
|
-
|
A
|
A
|
B
|
B
|
C
|
C
|
D
|
EF
|
G
|
|
Duration (Days)
|
3
|
5
|
8
|
4
|
2
|
9
|
3
|
12
|
10
|
6
|
Q8. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
|
Immediate Predecessor
|
-
|
-
|
A
|
A
|
C
|
D
|
B
|
E&F
|
G
|
|
Duration (Days)
|
8
|
6
|
14
|
5
|
11
|
7
|
11
|
4
|
18
|
Q9. Draw the network from the following activities
and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Immediate Predecessor
|
-
|
-
|
-
|
A
|
B
|
C
|
DE
|
FG
|
|
Duration (Days)
|
2
|
4
|
3
|
1
|
6
|
5
|
7
|
2
|
Q10. Draw the network from the following
activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
A
|
A
|
A
|
B
|
E
|
C
|
D
|
G
|
D
|
J
|
FHI
|
Q11. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Immediate Predecessor
|
-
|
-
|
A
|
A
|
B
|
B
|
D&E
|
F&G
|
|
Duration (Days)
|
4
|
7
|
3
|
3
|
2
|
2
|
2
|
3
|
Q12. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
A
|
A
|
B
|
C
|
C
|
E
|
F
|
GH
|
GH
|
I
|
J
|
|
Duration
|
2
|
4
|
6
|
8
|
6
|
10
|
10
|
14
|
8
|
12
|
4
|
10
|
Q13. Draw the network from the following activities
and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
N
|
|
Immediate Predecessor
|
-
|
-
|
A
|
C
|
D
|
E
|
E
|
D
|
BD
|
FGHI
|
J
|
J
|
KL
|
M
|
|
Duration
|
10
|
24
|
14
|
21
|
14
|
25
|
10
|
20
|
8
|
13
|
4
|
12
|
4
|
4
|
Q14. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
|
Immediate Predecessor
|
-
|
-
|
-
|
AB
|
BC
|
C
|
D
|
GEF
|
|
Duration
|
1
|
2
|
2
|
2
|
4
|
1
|
4
|
8
|
Q15. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
M
|
|
Immediate Predecessor
|
E
|
A
|
B
|
K
|
-
|
E
|
F
|
F
|
F
|
IL
|
CGH
|
D
|
IL
|
|
Duration
|
5
|
1
|
2
|
14
|
16
|
1
|
2
|
3
|
2
|
3
|
4
|
2
|
2
|
Q16. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
-
|
-
|
AB
|
AB
|
CDE
|
CDE
|
|
Duration
|
4
|
7
|
6
|
5
|
7
|
6
|
5
|
Q17. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
-
|
-
|
AB
|
B
|
B
|
FC
|
B
|
EH
|
EH
|
CDFJ
|
K
|
|
Duration
|
3
|
4
|
2
|
5
|
1
|
3
|
6
|
4
|
4
|
2
|
1
|
5
|
Q18. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
-
|
-
|
C
|
ABD
|
ABD
|
EF
|
ABD
|
H
|
G
|
G
|
IJK
|
|
Duration
|
4
|
3
|
3
|
2
|
1
|
2
|
3
|
3
|
5
|
2
|
4
|
2
|
Q19. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
Immediate Predecessor
|
-
|
-
|
AB
|
B
|
A
|
C
|
EF
|
DF
|
GH
|
I
|
|
Duration
|
3
|
8
|
4
|
2
|
1
|
7
|
5
|
6
|
8
|
9
|
Q20. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
-
|
-
|
BC
|
A
|
C
|
E
|
E
|
DFH
|
E
|
IJ
|
G
|
|
Duration
|
9
|
4
|
7
|
8
|
7
|
5
|
10
|
8
|
6
|
9
|
10
|
2
|
Q21. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
-
|
A
|
BC
|
D
|
E
|
BC
|
F
|
FG
|
HI
|
B
|
FGK
|
|
Duration
|
30
|
7
|
10
|
14
|
10
|
7
|
21
|
7
|
12
|
15
|
30
|
15
|
Q22. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
A
|
A
|
BC
|
B
|
DE
|
D
|
|
Duration
|
3.3
|
6.7
|
3.0
|
11.0
|
7.7
|
6.0
|
4.0
|
Q23. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
|
Immediate Predecessor
|
-
|
-
|
A
|
B
|
C
|
C
|
CD
|
FG
|
E
|
I
|
H
|
|
Duration
|
3
|
8
|
9
|
6
|
10
|
14
|
11
|
10
|
5
|
4
|
1
|
Q24. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
-
|
B
|
B
|
B
|
E
|
ADC
|
|
Duration
|
10
|
8
|
5
|
6
|
8
|
5
|
12
|
Q25. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
|
Immediate Predecessor
|
-
|
A
|
A
|
A
|
CD
|
BE
|
|
Duration
|
3
|
5
|
5
|
4
|
2
|
3
|
Q26. Draw the network from the following
activities and Find Critical Path & Total Project Duration
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
A
|
A
|
A
|
BC
|
CD
|
EF
|
|
Duration
|
7
|
4
|
5
|
6
|
7
|
5
|
6
|
Networking
Analysis
Assignment II
Q1. A project has the following activities
|
Activity
|
1-2
|
1-3
|
1-4
|
2-5
|
3-5
|
4-6
|
5-6
|
|
Duration
|
3
|
8
|
9
|
6
|
10
|
14
|
11
|
Required: 1. Draw the
project network
2.
Find the critical path and total project duration
3.
Find earliest start time, latest start time earliest
finish time and latest finish time
4.
Find out total float, Head event slack, Free Float,
Tail Event slack and independent Float.
Q2. A project has the following activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
|
Immediate Predecessor
|
-
|
-
|
-
|
A
|
A
|
B
|
C
|
D
|
EF
|
|
Duration
|
7.8
|
20
|
33
|
18
|
20
|
9
|
9.8
|
8
|
4
|
Required: 1. Draw the
project network
2 Find the critical path and total
project duration
3 Find earliest start
time, latest start time earliest finish time and latest finish time
4. Find out total float,
Head event slack, Free Float, Tail Event slack and independent Float.
Q3. A project has the following activities
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
|
Immediate Predecessor
|
-
|
-
|
-
|
A
|
B
|
B
|
C
|
D
|
E
|
FG
|
HI
|
|
Duration
|
3
|
2
|
2
|
4
|
4
|
7
|
4
|
2
|
5
|
6
|
3
|
Required: 1. Draw the
project network
2 Find the critical path and total
project duration
3 Find earliest start
time, latest start time earliest finish time and latest finish time
4. Find out total float,
Head event slack, Free Float, Tail Event slack and independent Float.
Q4. For the following data; draw a network,
fine the critical path and the slack time after calculating the earliest
expected time and the latest allowable
|
Activity
|
1-2
|
1-3
|
2-4
|
2-5
|
2-6
|
3-7
|
3-8
|
4-9
|
5-9
|
6-10
|
7-10
|
8-11
|
9-12
|
10-12
|
11-13
|
12-13
|
|
Duration
|
5
|
8
|
6
|
4
|
4
|
5
|
3
|
1
|
3
|
5
|
4
|
9
|
2
|
4
|
1
|
7
|
Q5. A small maintenance project consist of the
following twelve jobs whose precedence relations are indented with their node
numbers.
|
Job (i-j)
|
1-2
|
1-3
|
1-4
|
2-3
|
2-5
|
2-6
|
3-7
|
4-5
|
5-6
|
6-7
|
6-8
|
7-8
|
|
Duration
|
10
|
4
|
6
|
5
|
12
|
9
|
12
|
15
|
6
|
5
|
4
|
7
|
Required: 1. Draw an arrow
diagram representing the project
2 Find the critical path and total
project duration
3 Find earliest start
time, latest start time earliest finish time and latest finish time
4. Find out total float,
Head event slack, Free Float, Tail Event slack and independent Float.
Q6. The monthly maintenance work in a machine
shop consist of 10 steps A to J. The interrelationship between them are identified
by event number
|
Step
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
Event number
|
1-2
|
2-3
|
2-4
|
3-5
|
3-6
|
4-6
|
4-7
|
5-8
|
6-8
|
7-8
|
|
Duration
|
3
|
5
|
8
|
4
|
2
|
9
|
3
|
12
|
10
|
6
|
Required: 1. Draw a
network
2 Compute early and latest start and
finish time for each activity
3 How much slack does
activity (3-5), Activity (4-6) and Activity (7-8) have?
4. Identify the critical
path and critical activity
5. If activity 2-3 takes 8
days instead of 5 days what will be the project completion time?
Q7. Draw a network diagram from the following
activities and find critical path activities
|
Job
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
|
Immediate Predecessor
|
-
|
A
|
B
|
C
|
B
|
E
|
DF
|
E
|
H
|
GI
|
J
|
|
Duration
|
13
|
8
|
10
|
9
|
11
|
10
|
8
|
6
|
7
|
14
|
18
|
Q8. The NRB Company is planning to design,
develop and market a new racing cycle. The project is composed of the following
activities.
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
L
|
|
Immediate Predecessor
|
-
|
-
|
-
|
C
|
ABD
|
ABD
|
EF
|
ABD
|
H
|
G
|
G
|
IJK
|
|
Duration
|
4
|
3
|
3
|
2
|
1
|
2
|
3
|
3
|
5
|
2
|
4
|
2
|
Construct the network, determine the
critical path and the duration of the above project.
Q9 A small project consist of seven
activities for which the relevant data are given below
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
|
Immediate Predecessor
|
-
|
-
|
-
|
AB
|
AB
|
CDE
|
CDE
|
|
Duration
|
4
|
7
|
6
|
5
|
7
|
6
|
5
|
Required 1. Draw
the network and find the project completion time
2.
Calculable total float for each of the activities
3.
Draw the time scaled diagram.
Q10.
|
Activity
|
1-2
|
1-3
|
1-4
|
2-4
|
2-5
|
3-6
|
4-6
|
5-7
|
6-7
|
6-8
|
7-8
|
8-9
|
|
Duration
|
4
|
12
|
10
|
8
|
6
|
8
|
10
|
10
|
0
|
8
|
10
|
6
|
With the help of the activities
given above draw a network. Determine a critical path, earliest start time, earliest finish
time, latest start time, latest finish time, total float and free float.
Networking
Analysis
Assignment III
Q1. A Project has the followings activities and characteristics
|
Activity
|
1-2
|
1-3
|
1-4
|
2-5
|
3-5
|
4-6
|
5-6
|
|
|
|
|
Optimistic
|
2
|
4
|
1
|
5
|
2
|
6
|
4
|
|
|
|
|
Most Likely
|
5
|
10
|
7
|
8
|
8
|
9
|
7
|
|
|
|
|
Pessimistic
|
8
|
16
|
13
|
11
|
14
|
12
|
10
|
|
|
|
A)
Find expected duration of each activity.
B)
Draw the project network and expected duration of the
project.
C)
Find variance of activities on critical path and its
standard Deviation
Ans:- a) Critical Path
1-3-5-6 & Duration 25
b)
Variance (3)
Q2. A Project has the followings activities and characteristics
|
Activity
|
1-2
|
1-3
|
1-4
|
2-5
|
3-5
|
4-6
|
5-6
|
|
|
|
|
Optimistic
|
2
|
6
|
1
|
3
|
2
|
6
|
4
|
|
|
|
|
Most Likely
|
5
|
6
|
7
|
9
|
8
|
9
|
7
|
|
|
|
|
Pessimistic
|
8
|
6
|
13
|
15
|
14
|
12
|
10
|
|
|
|
A)
Find expected duration of each activity and their
variance
B)
Draw the project network and expected duration of the
project.
C)
Find variance of activities on critical path and its
standard Deviation
Ans:- Critical Path 1-2-5-6 or 1-3-5-6& Duration 21days
Q3. A Project has the followings activities and characteristics
|
Activity
|
1-2
|
2-3
|
2-4
|
3-5
|
4-5
|
4-6
|
5-7
|
6-7
|
7-8
|
7-9
|
8-10
|
9-10
|
|
Optimistic
|
1
|
1
|
1
|
3
|
2
|
3
|
4
|
6
|
2
|
5
|
1
|
3
|
|
Most Likely
|
5
|
3
|
5
|
5
|
4
|
7
|
6
|
8
|
6
|
8
|
3
|
7
|
|
Pessimistic
|
1.5
|
2
|
3
|
4
|
3
|
5
|
5
|
7
|
4
|
6
|
2
|
5
|
Required :-
Construct a PERT Network. Find the critical path and variance for each even.
Find the project duration at 95% probability
Ans:- Critical Path 1-2-4-6-7-9-10 Duration 28 1/6days
Probability
at 95% X=30.57 days
Q4. A Project has the followings activities and characteristics
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
|
|
|
|
Preceding
|
-
|
-
|
A
|
A
|
C
|
D
|
B
|
EF
|
G
|
|
|
|
|
Optimistic
|
1
|
1
|
1
|
3
|
2
|
3
|
4
|
6
|
2
|
|
|
|
|
Most Likely
|
5
|
3
|
5
|
5
|
4
|
7
|
6
|
8
|
6
|
|
|
|
|
Pessimistic
|
1.5
|
2
|
3
|
4
|
3
|
5
|
5
|
7
|
4
|
|
|
|
Required a) Draw the PERT Network
(b) Critical Path
(c) Prepare
Activity Schedule for the Project
(d) Find the Probability that the project is
completed in 36 weeks
(e) if the project managers
wishes to be 99% sure that the project is completed on June 2001, when should
he start the project work.
Ans:- Critical Path 1-2-4-6-8 (A-C-E-H) Duration
37days and variance of the critical path is 25 days, Z=42.07% , X=48.65.
Q5. Given the data below find the following (i) The expected task
times and their variance (ii) The earliest and latest expected time to reach
each node:
|
Activity
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
K
|
|
|
Least time
|
4
|
5
|
8
|
2
|
4
|
6
|
8
|
5
|
3
|
5
|
6
|
|
|
Greatest time
|
8
|
10
|
12
|
7
|
10
|
15
|
16
|
9
|
7
|
11
|
13
|
|
|
Most Likely time
|
5
|
7
|
11
|
3
|
7
|
9
|
12
|
6
|
5
|
8
|
9
|
|
Precedence relationship : A,C,D
can start immediately; (E>B,C; FG>D; HI>EF; J>I,G; K>H; B>A)
Sign > is to be interpreted as
“depends upon” also draw the network and critical path.
Ans:- Critical Path 1-2-3-5-7-8 (A-B-E-H-K)
Duration 35days
Q6. A project consist of activity A,B,C,D,_ _ _ H,I. The notation
X<Y mean that the activity X must be completed before Y can start &
X,Y<W means that W will start only after the completion of activities
X&Y with this notation.
a) Construct the network diagram for the following constraints
A<D,
A<E, B<F, C<G, D<HE, F<I
The
project has the following time schedule of the above activities
|
Task
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
|
Least time
|
5
|
18
|
26
|
16
|
15
|
6
|
7
|
7
|
3
|
|
Greatest time
|
10
|
22
|
40
|
20
|
25
|
12
|
12
|
9
|
5
|
|
Most Likely time
|
8
|
20
|
33
|
18
|
20
|
9
|
10
|
8
|
4
|
b) Determine the following 1.
Expected task time and their variance
2. Earliest and latest expected time to
reach each node 3. Critical Path 4. The Probability of a node occurring at the proposed completion
date if the original contract time of completing the project is 41.5 weeks.
Ans: Critical path 1-4-7 (C-G) 42.80 days
