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Network Analysis
Introduction 1
Network is a technique used for planning and scheduling of large projects in the fields of
construction, maintenance, fabrication, purchasing, computer system instantiation, research
and development planning etc. There is multitude of operations research situations that can
be modeled and solved as network. Some recent surveys reports that as much as 70% of
the real-world mathematical programming problems can be represented by network related
models. Network analysis is known by many names _PERT (Programme Evaluation and
Review Technique), CPM (Critical Path Method), PEP (Programme Evaluation Procedure),
LCES (Least Cost Estimating and Scheduling), SCANS (Scheduling and Control by
Automated Network System), etc
This chapter will present three of algorithms.
1. PERT & CPM
2. Shortest- route algorithms
3. Maximum-flow algorithms
The Basic Terminology
Network
It is a graphical representation of logical and sequentially connected activities and events of
a project. Network is also called arrow diagram. PERT (Programme Evolution Review
Technique) and (Critical Path Method) are the two most widely applied techniques.
Network
Techniques
PERT CPM
Project
A project is defined as a combination of interrelated activities which must be executed in a
certain order in for its completion.
Project Management Process
Network analysis is the general name given to certain specific techniques which can be used
for the planning, management and control of projects
Activity
Any individual operation, which utilizes resources and has an end and a beginning, is called
activity.
A task or a certain amount of work required in the project
Requires time to complete
Represented by an arrow
These are usually classified into four categories:
Predecessor activity
Successor activity
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Network Analysis
Concurrent activity
Dummy activity 2
Dummy Activity
It Indicates only precedence relationships and does not require any time of effort
PERT(Program Evaluation and Review Technique) is a method to analyze the involved
tasks in completing a given project, especially the time needed to complete each task, and
identifying the minimum time needed to complete the total project.
PERT is based on the assumption that an activity’s duration follows a probability distribution
instead of being a single value
Three time estimates are required to compute the parameters of an activity’s duration
distribution:
1. Pessimistic time (t ) - the time the activity would take if things did not go well
p
2. Most likely time (t ) - the consensus best estimate of the activity’s duration
m
3. Optimistic time (to ) - the time the activity would take if things did go well.
Mean (expected time) = (tp 4tm to)
6
t t 2
2 p o
Variance ( )= 6
Probability computation: Determine probability that project is completed within specified
time Z X
Where = project mean time
= project standard mean time
x = (proposed) specified time
Float:
Float of an activity represents the excess of available time over its duration.
Total Float (Ft)
The amount of time by which the completion of an activity could be delay beyond the
earliest expected completion time without affecting the overall project duration.
i.e. Tf= (Latest start-Earliest start) for activity(i-j), or,(Tf)ij=(LS)jj-(ES)ij
Free Float (Ff)
The time by which the completion of an activity can be delayed beyond the earliest finish
time without affecting the earliest start of a subsequent (succeeding) activities.
Situations in network diagram
1. A must finish before either B or C can start
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Network Analysis
3
2. Both A and B must finish before C can start
3. Both A and C must finish before either of B or D can start
4. A must finish before B can start both A and C must finish before D can start
Benefits of CPM/PERT
1) Useful at many stages of project management
2) Mathematically simple
3) Give critical path and slack time
4) Provide project documentation
5) Useful in monitoring costs
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Network Analysis
Distinguish Between PERT and CPM? WBUT-08 4
PERT CPM
(Programme Evaluation Review (Critical Path Method)
Technique)
1. PERT is event oriented. 1. CPM is activity oriented.
2. PERT is probabilistic. 2. CPM is deterministic.
3. PERT is primarily concerned with time 3. CPM places dual emphasis on project
only. time as well cost.
4. PERT is generally used for projects
where time required to complete the 4. CPM is used for projects which are
activities is not known a priori. Thus repetitive in nature and comparatively
PERT is used for large, R&D type of small in size.
projects. 5.One time estimate is possible for activities
5. Three time estimates are possible for (No allowance is made for uncertainty)
activities linking up two events.
Example: 02. The following table gives the activities of a construction project and other
relevant information.
Activities Normal duration Crash duration Crashing cost
(i-j) (days) (days) (Rs. per day)
1-2 9 6 20
1-3 8 5 25
1-4 15 10 30
2-4 5 3 10
3-5 10 6 15
4-5 2 1 40
A. What is the normal project length and minimum project length?
B. Determine the minimum crashing costs of schedule ranging from length down to and
the minimum length schedule.
C. What is the optimal length schedule duration of each job for your solution?
Given that over head cost total Rs. 60 per day.
DJ
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