EP 331 – Management & Control of Quality
Laboratory Module
LAB 4
NETWORK (ARROW) DIAGRAM
1.0
OBJECTIVE
1.0 Understand one of the new tools for management.
2.0 To discuss and illustrate some practical issue in the implementation of network
diagram.
2.0
INTRODUCTION AND THEORY
Network planning methods can help managers monitor and control project. These
methods treat a project as a set of interrelated activities that can be visually display in a
network diagram. A Network Diagram visually displays the interrelated activities using
nodes (circles) and arcs (arrows) that depict the relationships between activities. Two
network planning methods (PERT & CPM) were originally distinctive, but today the
differences are minor and will be jointly referred to as PERT/CPM.
PERT (Program Evaluation and Review Technique) was utilized when activity
times involved risk.
CPM (Critical Path Method) was used when activity times were certain.
These methods offer several benefits to project managers, including the following:
1. Considering projects as a network forces project team to identify and organize the
data required and to identify the interrelationships between activities.
2. Networks enable project managers to estimate the completion time of projects.
3. Report highlight the activities that are crucial to completing projects on schedule.
4. Network methods enable project managers to analyze the time and cost
implication of resource trade-offs.
5.
Diagramming the projects as a network requires establishing the precedence relationship
between activities. A Precedence relationships determine a sequence for undertaking
activities, and specify that any given activity cannot start until a preceding activity has
been completed. In the AON approach, the nodes (circles) represent activities, and the
arcs represent the precedence relationships between them.
S & T must be completed
before U can be started.
U cannot begin until S & T have been
completed. V cannot begin until T has been
completed.
S
U
S
U
T
V
T
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EP 331 – Management & Control of Quality
Laboratory Module
Paths are the sequence of activities between a project’s start and finish. The critical path
is the longest path.
I
Path
Time (wks)
A
A-I-K
A-F-K
A-C-G-J-K
B-D-H-J-K
B-E-J-K
33
28
67
69
43
Start
B
F
K
C
G
D
H
Finish
J
E
The project team must make time estimates for each activity.
Activity times may be risky, in which case a probability distribution can be used
(CPM).
Activity slack is the maximum length of time that an activity can be delayed without
delaying the entire project.
Free slack is the amount of time an activity’s earliest finish time can be delayed
without delaying the earliest start time of any activity that immediately follows.
Activities on the critical path have zero slack and cannot be delayed without delaying the project
completion.
For the above example, we can’t go beyond 69 weeks.
Earliest Start Time (ES) is the latest earliest finish time of the immediately preceding
activities.
Earliest Finish Time (EF) is an activity’s earliest start time plus its estimated duration.
Latest Start Time (LS) is the latest finish time minus the activity’s estimated duration.
Latest Finish Time (LF) is the earliest latest start time of the activities that
immediately follow.
For simplicity, all projects start at time zero.
Determined by the earliest finish time
of the precedent activity. If there are
two or more precedent activities, this
time is the same as precedent activity
with the latest “Earliest Finish” time.
Slack is the difference, if any, between
the earliest start and latest start times
(or the earliest finish and latest finish
times).
S = LS – ES or S = LF– EF
Slack
Activity
This is the Latest
Finish time minus the
activity time.
Earliest
Start
Earliest
Latest
Start Activity
Duration
Latest
Finish
The earliest you can complete an
activity -- determined by adding
the activity time to the earliest
start time.
Finish
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The latest you can finish an activity
without delaying the project
completion date. It is the same as
the Latest Start time of the next
activity. If there are two or more
subsequent activities, this time is the
same as the earliest of those “Latest
Start” times.
EP 331 – Management & Control of Quality
Laboratory Module
The Statistical Analysis approach requires that activity times be stated in terms of three
reasonable time estimates for each activity.
1.Optimistic Time (a) is the shortest time in which a activity can be completed if all goes
exceptionally well.
2.Most Likely Time (m) is the probable time for an activity.
3.Pessimistic Time (b) is the longest time required.
The expected time and variance for an activity thus becomes…
te =
a + 4m + b
2 =
6
(b – a )
2
6
Probabilities of completing project by certain date becomes….
T – TE
2 =  (variances of activities)
z =
T = due date for the project
2


TE = Expected activities time on critical path)
3.0
EXAMPLE & PROCEDURE
Construct the network diagram and calculate the probability of completing the project
within 23 week.
1)
2)
3)
4)
5)
Calculate the expected time and variance.
Construct the network diagram.
Calculate the ES, LS, EF and LF for each activity.
Determine the critical path.
Calculate the Z value.
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EP 331 – Management & Control of Quality
Laboratory Module
Result:
4.0
D
16.0
Finish
8.0 12.0 20.0
0.0
A
4.0
9.0
E
15.5
4.0
4.0
8.0
9.0
6.5
15.5
Star
t
5.5
C
9.0
5.5
3.5
9.0
0.0
B
5.5
15.5
G
20.0
0.0
5.5
5.5
15.5
4.5
20.0
5.5
F
14.5
6.5
9.0
15.5
Using the Normal Distribution appendix,
we find that the probability of completing
the project in 23 weeks or less is 0.9357.
Page 4 of 6
EP 331 – Management & Control of Quality
4.0
Laboratory Module
TUTORIAL
To complete the wing assembly for an experimental aircraft, Jim Gilbert has laid out the
seven major activities involved. These activities have been labeled A through G in the
following table, which also show their estimated completion times (in weeks) and
immediate predecessors. Construct the complete network diagram and calculate the
probability of completing the project in 20 weeks or less.
Activity
A
B
C
D
E
F
G
a
1
2
4
8
2
4
1
m
2
3
5
9
5
5
2
b
3
4
6
10
8
6
3
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Immediate predecessors
------A
B
C, D
D
E
EP 331 – Management & Control of Quality
Laboratory Module
LAB 5
NETWORK (ARROW) DIAGRAM
Lab Result
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DATE OF EXPERIMENT :___________________________
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