Chapter 13
Network analysis
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Learning objectives
After studying this chapter, you should be able to:
• Explain the circumstances under which network analysis can be used as a
tool to enhance project management.
• Distinguish between the different methods used in network analysis.
• Understand the different terminology used in network analysis.
• Draw a network diagram for a project.
• Make an estimate of the expected duration of activities using the PERT
method.
• Identify the critical path in a project and explain its significance.
• Calculate the slack for each activity and explain its significance.
• Calculate the cost slope and explain its significance.
• Understand how to accelerate a project.
• Understand the limitations of network analysis.
• Explain the benefits of using network analysis in project management.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Techniques
• There are various methods of network
analysis, but the following two most
common methods will be discussed in this
chapter:
• critical path method (CPM)
• program evaluation and review technique
(PERT).
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Procedure for network analysis
• The following steps can be followed when doing
network analysis:
• Identify the activities to be performed in order to
complete the project.
• Identify the sequence in which they should be
completed, including parallel activities, which are
activities that occur simultaneously with other
activities.
• Calculate the time required to complete each activity.
• Construct a network diagram.
• Calculate the duration of the project.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Network diagrams
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All the individual tasks to complete a project must be visualised in a network
of activities and events representing the network diagram for the project.
The network diagram is drawn using the activity on the node method, or
activity on the arrow method.
An event is a particular point in time which indicates the start or completion
of an activity.
An activity is an identifiable section of a project which takes time to complete
and utilises resources.
Tail of activity → Head of activity
The tail side represents the start of an activity, and the arrowhead represents
the completion of the activity.
Other activities are independent of certain activities. They are referred to as
parallel activities and can take place simultaneously.
A dummy activity only indicates the relationship between two activities. No
time is used, and no resources are consumed.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 13.1
The preconstruction activities and estimated durations for each activity in the
following table have been determined for project Build a Bear by SC
Construction’s management consultant.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Rules for constructing networks
The following rules apply when constructing a network diagram:
• A network diagram has only one point of entry and one point of exit.
• A network diagram flows from left to right.
• Networks are not drawn to scale, i.e. the length of the line does not represent the
duration of the activity.
• Events are progressively numbered from left to right through the network diagram,
i.e. the event indicating the conclusion of the preceding activity has a higher
number than the preceding event.
• All activities must be tied into the network, i.e. dangling activities are not allowed.
They must either contribute to the progression or be disregarded as irrelevant.
• A loop which is a series of activities that lead back to the same event, is not
allowed, as the network should progress forward.
• An event is not reached until all the activities leading to it have been concluded.
• Two or more activities may not have the same activity preceding and succeeding
them.
• A dummy activity has to be drawn.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Network terminology
• Critical path
• The path with the longest cumulative activity time
determines the duration of the project and the project’s
completion date.
• Slack
• Also known as float, is the amount of spare time that is
available on the activity without increasing the duration of
the project or the critical path.
• Activities on the critical path have a slack of zero, since
increasing the duration on any critical activity will increase
the critical path. All non-critical activities have a positive
slack.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Network terminology (cont.)
• The less slack on activity, the more critical the activity, and vice versa.
• The following terminology is used in the calculation of slack:
• The earliest starting time (EST) is the earliest possible time an activity can
commence. It is calculated by obtaining the longest path from the beginning of the
project up to the tail of the activity, i.e., the event which proceeds the predecessor
activity.
• The latest starting time (LST) is the latest possible time an activity can commence
without delaying the project. It is calculated by subtracting the duration of the
critical path and the longest path from the tail of the activity to the end of the
network.
• The earliest completion time (ECT) is the earliest possible time an activity can be
completed, giving allowance for preceding activities to be completed. It is calculated
by computing the longest path from beginning of the network to the head of the
activity or by taking the EST plus the duration of the activity.
• The latest completion time (LCT) is the latest possible time at which an activity can
be completed without causing an increase in the duration of the project. It is
calculated by subtracting the duration of the critical path and the longest path from
the head of the activity to the end of the network, or by taking the LST plus the
duration of the activity.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 13.3
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Network acceleration
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The normal duration of the project is based on the duration of its critical path. However, it is
possible to reduce a project’s time by a process called acceleration (crashing).
This process entails reducing the normal duration of the project by incurring additional costs
or by utilising available resources differently.
Acceleration will bring in the project ahead of schedule, but at the same time it will increase
the project’s cost.
Management must decide whether the additional cost is justified by the advantage which
acceleration of the project implies.
Projects can either be accelerated with the aim of:
– minimising total project cost: in this case a project will be accelerated as long as it is cost
effective
– minimising total project time: in this case the acceleration is focused on minimising time,
regardless of whether the project cost increases
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Prior to commencing with acceleration, the cost per time period, known as the cost slope,
must be determined.
The cost slope is the average additional variable cost that has to be incurred in order to
reduce the duration of an activity by one period of time. The following formula is used to
determine the cost slope:
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 13.4
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 13.5
Using the information for SC Construction’s project, Builda-Bear to include acceleration. In addition to the variable
costs presented in Table 13.3, discretionary fixed costs
amount to R25 000 per day.
Required:
a) Determine the amount that was tendered for the
project, assuming that a mark-up of 25% on cost was
required.
b) Determine the amount that could have been
tendered had the project’s cost been minimised.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Solution
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Program evaluation
and review technique
• When a project is undertaken for the first
time, or a considerable amount of time has
elapsed since the last similar project,
management is usually uncertain about the
duration of the activities in the project.
• PERT analysis provides for this uncertainty by
determining a weighted average time
estimate.
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Estimating the expected
duration of activities
• PERT is applied when there is uncertainty about activity
times. Three time estimates are determined:
• 1. The most optimistic duration (to) is the time required to
complete an activity under ideal circumstances.
• 2. The most likely duration (tm) is the time in which the
activity will be completed under normal circumstances, i.e.,
if everything goes according to plan.
• 3. The most pessimistic duration (tp) is the time required to
complete the activity if unforeseen delays occur, such as
poor weather conditions, employees being ill, etc.
• The expected activity time (te) of each activity is a weighted
average of these three estimates.
• Expressed as a formula:
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Standard deviation
• Another aim of PERT analysis is to determine the standard deviation of
each activity and also of the critical path.
• The standard deviation of each activity indicates the degree of uncertainty
regarding the duration of an activity.
• The measure of the standard deviation of activity time is calculated by
means of the following formula:
• It is as important to know what variability to expect in the time of the
critical path as it is in the time of an activity. The measure of the standard
deviation of the critical path is calculated by means of the following
formula:
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Illustrative example 13.7
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229
Solution
Cost and Management Accounting: Operations and Management – A southern African approach (3rd edition)
© Juta and Company Ltd 2021
ISBN 9781485131229