BIT 2016-2017
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Network Analysis
Northern College Programme
Business Information Technology
Project Management: Network Analysis
by Nigel R Hartland
Network Analysis involves looking at projects to determine how long they will
take to complete as well as how the intermediate steps of a project link together
to affect the overall duration of the project.
A project can range in simplicity from deciding on the processes (or activities) to
decorate a room to building a skyscraper. What they do have in common is that
they have a number of activities to perform which will have some time value
attributed to them (e.g. hours, days, weeks etc.).
These activities will often have a bearing on when other activities can be started.
For example: Building a house.
Some of the steps involved could include:
Building a House
Activity Duration (days)
Build walls
5
Build roof
3
Put on Doors
1
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etc.
The walls would need to be built first before the roof is put on, so the roof needs
the walls activity to be completed before it can start.
Some activities can occur at the same time if resources allow them to be
performed. For example, the doors could be put on the house whilst the roof is
being built etc.
This allows a reduction in the overall length of time (duration) that the project
takes to complete. One of the most difficult parts of project management is
deciding on the intermediate steps and how they relate to others.
Action planning
This is closely related to project management in that it involves determining some
future goal to aspire to, setting an aim (build a house) and objectives to reach
that aim that are measurable (build walls etc.) and amending the plan in the light
of changing circumstances.
Network diagrams can be constructed to show how activities relate to each other.
Further network analysis....
Constructing an network arrow diagram.
Before constructing a diagram, some definitions need to be made:
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Activity: These are a task or a job that takes up time denoted by:
Events: This is the point where an activity starts or ends. Denoted by:
also called nodes on the network arrow diagram. Some rules:
1. A diagram showing the project will flow from left to right. Each diagram will
start from one single event and end at a single event (the start and end events).
2. The activity arrows start and end at events, as such activities can be defined
by the events that go into and out of them, in the example below activity C can
also be labelled 2,4. Some computer programs label activities in this way.
3. Activities and Events depend on each other.
4. Events are numbered left to right with the number on the right being bigger
than that on the left.
5. The length of any activity arrow has no bearing on its duration but is often
drawn for simplicity.
In addition, the lines are always straight (not bent or curved)
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The example below shows a network diagram.
This shows activities and events and how they interact, such that, in this
example, A and B can be performed at the same time, so can C and D, and E
and F, but all must finish before G.
Further network analysis....
Dummy
This is an activity with no time attributed to it. It uses the notation:
There are two types of dummy: identification and logic.
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Network Analysis
Identification dummies
These dummies help with the identification process in avoiding having 2 activities
being given the same description.
For example, in the previous process, two activities could have the same
description: Add sugar or Add milk as they both go form events 5 to 6.
(Note only part of the diagram has been shown for simplicity)
so using an identification dummy:
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Add sugar is now uniquely identified as events 5-6 and Add milk is now
uniquely identified as events 5-7.
Logic dummies
Dummies can also maintain the logical flow of the network, where a logic
dummy would be used.
For instance, in the following table how can activities A, B and C be shown to be
completed before D starts?
Logic dummy example
Activity Preceding Activity
A
-
B
-
C
-
D
A, B, C
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Logical dummies are used:
Often when first drawing a network diagram, dummies are included and then
removed once the logic of the network diagram has been found.
Naming the dummies as identification or logic is NOT NECESSARY
Further network analysis....
Critical paths
Once the network diagram has been drawn, durations of time are usually added
to the activities.
In this way the time taken to follow a certain path through the diagram can be
calculated, many paths may exist.
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The path that has the longest time will give the total duration of the project.
Items on this path are critical to the completion of the project on time, this path is
known as the critical path and every diagram will have at least one.
The total duration therefore of a project can be calculated by adding the
durations of the activities on this critical path.
A number of methods can be used to determine the critical path(s) within the
network diagram the following being most suitable for arrow diagrams:
This involves the calculation of Earliest Event Times (EET) and Latest Event
Times (LET).
Earliest Event Times EET
These are the earliest times that an event can be completed.
The EET of the first event is ZERO and the EET of the last event determines the
overall duration of the project.
Latest Event Times LET
These are the latest times that an event must be completed by.
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Critical Paths
To determine the critical path it can be where:
(very simply) EET=LET for each event and
where the LET (end event) - EET (start event) = Duration of the activity or
LET (end event) - EET (start event) - Duration of the activity = 0
Using the following example:
Example 1
The following table gives the activities, their preceding activities and durations.
The aim is to construct an network arrow diagram, calculate the critical path and
determine the duration of the project.
Example 1 table of data
Activity Duration (Days) Preceding Activity
A
2
-
B
4
-
C
2
A
D
4
B
E
3
C, D
F
3
E
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For ease of use the symbols
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Network Analysis
are often used to show the
earliest event and latest event times.
The diagram is constructed by adding the activities and following the relationship
between them from the table. Durations are then added.
Network Diagram for example 1
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Further network analysis....
Example 1 continued.
click here to
load the network diagram for example 1 into a new window which you
can then drag and reposition on the screen.
Earliest event times are first added to the diagram:
Earliest Event Times Calculation for example 1
Event EET (days)
Explanation
1
0
Start event always zero
2
2
event 1 + duration of A (0+2) = 2
3
4
event 1 + duration of B (0+4) = 4
4
8
A choice exists:
event 2+ duration C (2+2) = 4 or
event 3 + duration D (4+4) = 8
choose biggest since all activities must be completed before E starts
5
11
event 4 + duration E (8+3) = 11
6
14
event 5 + duration F (11+3) = 14
Where a choice exists for the earliest event times, the biggest number is chosen
as all activities that belong to the event must be completed before the next event
can occur.
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The final event shows the duration of the project is 14 days.
Then latest event times can be added.
These are calculated by working back from the final event (the final event
assumes that the EET=LET), subtracting activity durations from the events.
Where a choice exists for the latest event times the smaller value is chosen
because the event has to be completed before the next event(s) start time(s).
Latest Event Times Calculation for example 1
Event
LET (days)
Explanation
6
14
End event = 14 (EET=LET)
5
11
event 6 - duration F (14-3) = 11
4
8
event 5 - duration E (11-3) = 8
3
4
event 4 - duration D (8-4) = 4
2
6
event 4 - duration C (8-2) = 6
1
0
A choice exists:
event 3 - duration B (4-4)= 0 or
event 2 - duration A (6-2)= 4
choose smallest
The critical path is where EET=LET for each event, and
LET (end event) - EET (start event) - Duration of the activity = 0
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See activities table for this example (click to open the table)
Activities table for example 1
LET end event - EET start event -DURATION of activity =REMAINDER
LET
EET
End
Start
Activity
event
event
A
6
0
2
4
B
4
0
4
0
C
8
2
2
4
D
8
4
4
0
E
11
8
3
0
F
14
11
3
0
If remainder = 0 the activity is
Duration
of activity Remainder
CRITICAL
Critical path therefore: B, D, E, F
thus it is B, D, E, F
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Further network analysis....
Using the next example:
Example 2 - using a dummy and calculating money
Using the example of a house, if the other activities are added and their
preceding activities, a diagram can be constructed.
If building costs are £500 per day what is the cost of the project?
Example 2 table of data
Activity
Description
Duration (Days) Preceding Activity
A
dig ground
5
-
B
obtain materials
1
-
C
build walls
5
A, B
D
put on doors
1
C
E
build roof
3
C
F
paint the building
3
D, E
From this the critical path can be calculated to determine the overall duration of
the project.
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Network Diagram for example 2
Further network analysis....
Example 2 continued.
click here to
load the network diagram for example 2 into a new window which you
can then drag and reposition on the screen.
As in the previous example, the EET's and LET's can be calculated.
Note the presence of a dummy increases the options for event times, but a
dummy has no time duration.
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Earliest Event Times Calculation for example 2
Event
EET
Explanation
(days)
1
0
Start event always zero
2
5
event 1 + duration of A (0+5) = 5
3
5
A choice exists:
event 1 + duration of B (0+1) = 1 or
event 2 + duration of dummy (5+0) = 5
choose biggest value i.e. 5 days as A must be completed
before C starts.
4
10
event 3 + duration of C = (5+5) = 10
5
11
event 4 + duration D (10+1) = 11
6
13
A choice exists:
event 4 + duration E (10+3) = 13 or
event 5 + duration of dummy (11+0) = 11
choose biggest i.e. 13 days as E must be completed before F
starts.
7
16
event 6 + duration F (13+3) = 16
The dummies provide alternate event times, however the largest times must be
chosen to ensure that the following events can start on time.
The duration (from the last event) is found to be 16 days, at £500 per day
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= £8000 which would be the cost of the project.
Latest event times can now be calculated, working back from the end event at
time 16 days and subtracting the duration of activities leading into the event(s).
Latest Event Times Calculation for example 2
Event
LET (days)
Explanation
7
16
End event = 16 (EET=LET)
6
13
event 7 - duration F (16-3) = 13
5
13
event 6 - duration of dummy (13-0) = 13
4
10
A choice exists:
event 6 - duration E (13-3) = 10 or
event 5 - duration D (13-1) = 12
choose smallest i.e. 10
3
5
event 4 - duration C (10-5) = 5
2
5
event 3 - duration of dummy (5-0) = 5
1
0
A choice exists:
event 3 - duration B (5-1)= 4 or
event 2 - duration A (5-5)= 0
choose smallest i.e. 0
The smallest figures for events 1 and 4 are chosen as choosing the larger figures
would increase the duration of the project by delaying start times of following
activities.
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The critical path being where EET=LET for each event and
LET (end event) - EET (start event) - Duration of the activity = 0
See activities table for this example (click to open the table)
Activities table for example 2
LET end event - EET start event -DURATION of activity =REMAINDER
LET
EET
End
Start
Activity
event
event
A
5
0
5
0
B
5
0
1
4
Dummy 1
5
5
0
0
C
10
5
5
0
D
13
10
1
2
E
13
10
3
0
Dummy 2
13
11
0
2
F
16
13
3
0
If remainder = 0 the activity is
Duration
of activity Remainder
CRITICAL
Critical path therefore: A, Dummy 1, C, E, F
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it is therefore A, (dummy 1), C, E, F.
Further network analysis....
Other questions that could be asked
Q. If activity E was increased by one day what effect would it have on the
project?
A. As E is on the critical path any delay in its duration will affect the overall
duration, in this case adding an extra day to the overall time of the project.
Q. Could activity D be increased by some amount, and if so what, such that it
does not effect the overall project duration?
A. As activity D is not on the critical path there is scope for some increase in its
duration, it could be increased by 2 days at the most such that it was completed
at day 13 for activity F to start, any further delay will affect the overall project
duration.
Note if it was increased by 2 days there would be an additional critical path,
A, dummy 1, C, D, dummy 2, F.
Network Analysis can be extended such that resource implications of labour for
example can be added to the calculations and activity durations produced which
are not constant and some level of unpredictability built in.
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This module has assumed that the times are constant.
Network Analysis therefore involves a great deal of planning and logical thinking
on how activities relate to others, how the overall project duration can be
calculated and if there is any scope for extending the durations of certain
activities.
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