Networks
Network Analysis
The general term dealing with sequencing activities/tasks is network analysis.
Network analysis is a generic term for a family of related techniques developed to aid management in
the planning and control of projects. These techniques show the inter-relationship of the various jobs or
tasks which make up the overall project and clearly identify the critical parts of the project. They can
provide planning and control information on the time, cost and resource aspects of a project.
Network analysis is likely to be of most value where projects are:
 Complex
they contain many related and interdependent activities; and/or
 Large
where many types of facilities, high capital investments, many personnel are involved; and /or
 Where restrictions exist
where projects have to be completed within stipulated time or cost limits, or where some or all
of the resources (material, labour) are limited.
Background
A basic form of network analysis was being used in the UK and USA in the mid- l950's in an attempt to
reduce project times. In 1958 the US Naval Special Projects Office set up a team to devise a technique
to control the planning of complex projects. The outcome of the team's efforts was the development of
the network technique known as PERT (Programme Evaluation and Review Technique).
PERT was used to plan and control the development of the Polaris missile and was credited with saving
two years in the missile's development.
Since 1958 the technique has been developed and nowadays many variants exist which handle, in
addition to basic time factors, costs, resources, probabilities and combinations of all these factors. A
variety of names exist and some of the more commonly used are:
Critical Path Planning
CPP

Critical Path Analysis
CPA

Critical Path Scheduling
CPS

Critical Path Method
CPM
 Programme Evaluation and Review Technique
PERT, PERT/COST, …

Project Evaluation and Review TechniquePERT
Basic terminology
Activity - This is the task or job of work which takes time and resources.
An activity is represented in a network by an arrow, the head indicating where the task ends and the tail
where it begins. It normally points left-to-right and is seldom to scale.
Critical to network analysis is establishing what activities are involved, the relationship between them,
and estimates of the duration (and possibly costs, resources, probabilities, etc.)
Event - This is a point in time and indicates the start or finish of an activity.
An event is represented in a network by a circle or node.
Dummy Activity - This is an activity which does not consume time or resources, but is merely used to
show clear logical dependencies between activities so as not to violate the rules for drawing networks;
it is shown by a dotted arrow.
Activities may be identified in several ways. Typical of the methods to be found are:

Shortened description of the job e.g. Plaster wall. order timber etc.

Alphabetic or numeric code, e.g.. A, B, C etc. or 100, 101, 108 etc.

Identification by the tail and head event numbers e.g. 1--2, 2--3, 25 etc.
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Networks
Rules for drawing networks
The following rules are all logically based and should be thoroughly learned before attempting to draw
networks.






A complete network should have only one point of entry - a START event and only one point
of exit - a FINISH event.
Every activity must have one preceding or 'tail' event and one succeeding or ‘head' event.
Note that many activities may use the same tail event and many may use the head event.
However an activity must not share the same tail event AND the same head event with any
other activities (this is dealt with in detail in Dummies) .
No activity can start until its tail event is reached.
An event is not complete until all activities leading in to it are complete. This is an important
rule and invariably has to be applied in examination questions.
'Loops' i.e. a series of activities which lead back to the same event are not allowed because the
essence of networks is a progression of activities always moving onwards in time.
All activities must be tied into the network i.e. they must contribute to the progression or be
discarded as irrelevant. Activities which do not link into the overall project are termed
'danglers'.
Conventions for drawing networks
In addition to the Rules above, which must not be violated, certain conventions are usually observed:

Networks proceed from left to right.

Networks are not drawn to scale i.e. the length of the arrow does not represent time elapsed.

Arrows need not be drawn in the horizontal plane but unless it is totally unavoidable they
should proceed from left to right.
If they are not already numbered, events or nodes should be progressively numbered from left to right.
Simple networks may have events numbered in simple numeric progression i.e. 0, 1, 2, 3 etc. but larger,
more realistic networks may be numbered in 'fives' i.e. 0, 5, 10, 15 etc. or 'tens' i.e. 0, 10, 20, 30 etc.
This enables additional activities to be inserted subsequently without affecting the numbering sequence
of the whole project.
Exercise - Project XXX: building a boat
Activity Preceding Activity
A
--B
--C
A
D
A
E
A
F
C
G
C
H
C
J
B, D
K
F, J
L
E, H, G, K
M
E, H
N
L, M
Activity Description
Design Hull
Prepare Boat Shed
Design Mast and Mast mount
Obtain Hull
Design Sails
Obtain Mast Mount
Obtain Mast
Design rigging
Prepare Hull
Fit Mast Mount to Hull
Step Mast
Obtain Sails and Rigging
Fit sails and Rigging
Draw the network
NB. The shape of the network is unimportant, but the logic must be correct.
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Networks
Exercise - Service station.
The following tasks are to be completed on vehicles at a service station. Assume that all the jobs must
be done, and that an unlimited number of people are available. The radiator, sump and battery are all
located under the bonnet for the benefit of the exercise. Draw a network diagram.
TASKS (Not necessarily in order)
Preceding Task
A
Driver arrives and stops
NONE
B
Driver selects brands of oil and petrol
A
C
Fill petrol tank
B
D
Prepare bill
C and L
E
Receive payment and give stamps
D
F
Wash windscreen
A
G
Polish windscreen
F
H
Check tyre pressure
A
J
Inflate tyres
H
K
Open bonnet
A
L
Check oil requirement
K
M
Add oil
B and L
N
Add distilled water to battery
K
P
Fill radiator
K
Q
Close bonnet
M, N and P
R
Driver departs from forecourt
E, G, J and Q
Time Analysis
The main objective of network analysis is to establish the overall completion time of projects by
calculating what is known as the Critical Path.
Assessing The Time
Once the logic has been agreed and the outline network drawn it can be completed by inserting the
activity duration times.
Time estimates.
The analysis of project times can be achieved by using;

Single time estimates for each activity. These estimates would be based on the judgement of the
individual responsible or by technical calculations using data from similar projects, or

Multiple time estimates for each activity.
The most usual multiple time estimates are three estimates for each activity:
Optimistic
(O),
Most Likely
(ML)
Pessimistic
(P)
These three estimates are combined to give an expected time and the accepted formula is:
Expected time = (O + P + 4 ML) / 6
For example, assume that the three estimates for an activity are
Optimistic
11 days
Most likely
15 days
Pessimistic
18 days
then
Expected Time = (11 + 18+4*(15)) / 6
= 14. 8 days
Use of time estimates
As the three time estimates are converted to a single time estimate there is no fundamental difference
between the two methods as regards the basic time analysis of a network. However? on completion of
the basic time analysis, projects with multiple time estimates can be further analysed to give an
estimate of the probability of completing the project by a scheduled date.
Time units
Time estimates may be given in any unit i.e. minutes, hours, days, weeks, depending on the project.
All times estimates within a project must be in the same units otherwise confusion is bound to occur
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Networks
Critical Path
However sophisticated the time analysis becomes, a basic feature is always the calculation of the
project duration which is the duration of the critical path.
The critical path of a network gives the shortest time in which the whole project can be completed.
It is the chain of activities with the longest duration times. There may be more than one critical path in
a network and it is possible for the critical path to run through a dummy.
Earliest start times (EST)
Once the activities have been timed it is possible to assess the total project time by calculating the
EST's for each activity. The EST is the earliest possible time at which a succeeding activity can start.
Calculating EST (termed the FORWARD PASS)
The EST of a head event is obtained by adding onto the EST of the tail event the linking
activity duration starting from Event 0, time 0 and working forward through the network.
Where two or more routes arrive at an event the LONGEST route time must be taken, e.g..
Activity F depends on completion of D and E. E is completed by day 5 but D is not complete
until day 7 so F cannot start before day 7.
The EST in the finish event is the project duration and is the shortest time in which the whole
project can be completed.
Latest start times (LST).
To enable the critical path to be isolated, the LST for each activity must be established. The LST is the
latest possible time at which a preceding activity can finish without increasing the project duration.
Calculating LST (termed the BACKWARD PASS).
Starting at the finish event, insert the LST and work backwards through the network deducting
each activity duration from the previously calculated LST.
Where the tails of two activities join an event, the lowest number is taken as the LST for that
event otherwise the project would be delayed.
Critical Path
The critical path is the chain of activities which has the longest duration.
The critical path can be indicated on the network either by a different colour or by two small transverse
lines across the arrows along the path.
The activities along the critical path are vital activities which must be completed by their EST's/LST's
otherwise the project will be delayed. The non-critical activities have spare time or float available
If it is required to reduce the overall project duration then the time of one or more of the
activities on the critical path must be reduced perhaps by using more labour, or more or better
equipment or some other method of reducing job times.
A Crash Schedule is used to shorten the project
by using overtime (or anything else?) regardless of cost.
Note that for simple networks the critical path can be found by inspection, i.e. looking for the longest
route, but the above procedure is necessary for larger projects and must be understood.
The procedure is similar to that used by most computer programs dealing with network analysis.
Float
Float or spare time can only be associated with activities which are non-critical (since, by definition,
activities on the critical path cannot have float.)
There are three types of float, Total Float, Free Float and Independent Float.
Total Float. This is the amount of time a path of activities could delayed without affecting the overall
project duration.
Total Float = Latest Head time - Earliest Tail time - Activity Duration
Free Float. This is the amount of time an activity can be delayed without affecting the commencement
of a subsequent activity at its earliest start time, but may affect float of previous activity.
Free Float = Earliest Head time - Earliest Tail time - Activity Duration
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Networks
Independent float. This is the amount of time an activity an be delayed when all preceding activities
are completed as late as possible and all succeeding activities completed as early as possible.
Independent float therefore does not affect float of either preceding or subsequent activities.
Independent float = Earliest Head time - Latest Tail time - Activity Duration
The most important type of float is Total Float because it is involved with the
overall project duration. On occasions the term 'Float' is used without qualification. In such cases
assume that Total Float is required.
Slack
This is the difference between the EST and LST for each event.
Strictly it does not apply to activities but on occasions the terms are confused and unless the context
makes it abundantly clear that event slack is required, it is likely that some form of activity float is
required. Events on the critical path have zero slack.
Exercise - Service station
The earlier problem, but with the times for the activities added.
In addition, calculate the total float and free float for all activities.
The following tasks are to be completed on vehicles at a service station. Assume that all the jobs must
be done, and an unlimited number of people are available. The radiator, sump and battery are all
located under the bonnet for the benefit of this exercise.
TASKS (not necessarily in order)
Time (Seconds) Preceding Task
A
Driver arrives and stops
20
NONE
B
Driver selects brands of oil and petrol
10
A
C
Fill petrol tank
100
B
D
Prepare bill
50
C and L
E
Receive payment and give stamps
50
D
F
Wash windscreen
20
A
G
Polish windscreen
20
F
H
Check tyre pressures
100
A
J
Inflate tyres
90
H
K
Open bonnet
20
A
L
Check oil requirement
80
K
M
Add oil
20
B and L
N
Add distilled water to battery
30
K
P
Fill radiator
30
K
Q
Close bonnet
10
M,N and P
F
Driver departs from forecourt
20
E, G, J and Q
Exercise - Delta Limited
Delta Ltd., in planning to introduce a new product, has listed the following necessary activities:
Activity Preceding Activity
Expected Time (weeks)
A
-6
B
-3
C
A
5
D
A
4
E
A
3
F
C
3
G
D
5
H
B,D,E
5
I
H
2
J
F, G, I
3
Draw the critical path network for the project and determine the critical path and its duration.
If the start of activity B is delayed by 3 weeks, activity E by 2 weeks and activity G by 2 weeks, how is
the total time for the project affected?
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