Definition

Network Analysis in Operations Research: Definition, Components, Applications, CPM and PERT

Introduction of Network Analysis

Many real-life projects are made up of a large number of activities that are connected to one another. Some activities can be started only after certain other activities have been completed, while some activities can be carried out at the same time.

Examples include constructing a building, installing a new plant, developing a new product, conducting a research project, implementing a computer system, or carrying out a major maintenance project.

When a project contains many interrelated activities, it becomes difficult to plan and control the entire project simply by using a list of activities. Network analysis provides a systematic way of representing these relationships and analyzing the project.

Network Analysis in Operations Research: Definition, Components, Applications

In Operations Research, network models are also used more broadly for problems involving connections between nodes and links. They can be used to study problems such as shortest paths, flows, and other network optimization problems. Project planning and scheduling are important applications of network techniques.

In this article, we learn about:

What is Network Analysis? In Simple Words for Students with Example
Definition: What is Network Analysis in Operations Research?
What is a Project?
Basic Components of a Project Network

Activities or Tasks,
Events or Nodes,
Links or Arrows,
Precedence Relationships

Objectives of Network Analysis
Applications of Network Analysis
Why is Network Analysis Needed?
What is a Path?
Why is the Critical Path Important?
What is Float or Slack?
Major Network Techniques in Project Management
CPM
PERT
CPM vs PERT
What will uou actually study in Network Analysis?
One Important Point: Network Analysis is Broader than CPM/PERT
The Whole Concept in One Picture
Network Analysis and Decision-Making
Advantages of Network Analysis
Limitations of Network Analysis
Example of Network Analysis in Operations Research
Common Questions Answered by Network Analysis
Important Terms to Remember
FAQs

What is Network Analysis? In Simple Words for Students with Example

First, forget the complicated mathematical terminology and consider a real-world example.

Suppose a company wants to complete a construction project. The project may contain many activities:

Prepare the design
Purchase materials
Build the foundation
Construct walls
Install electricity
Install plumbing
Build the roof
Paint the building

These activities are not independent. For example, you cannot construct the walls before completing the foundation.

Similarly, you cannot paint the building before the walls are ready.

So, there is a particular order or relationship among activities.

Network Analysis is a group of Operations Research techniques used to represent these activities in the form of a network and analyze the project systematically.

The main questions are:

What activities have to be performed?
In what order should they be performed?
How long will the project take?
Which activities are most important?
Which activities cannot be delayed?
Where is there some flexibility?
Can we finish the project earlier?

Think of a Network as a Road Map

This is the easiest way to understand it.

Imagine you are travelling from City A to City D. There may be several routes:

A ─── B ─── D
\ /
\─── C ───

A network in OR works in a similar way.

But instead of cities and roads, we have

Events and Activities. For example:

Start → Design → Construction → Painting → Finish

This represents the sequence of work in a project.

Definition: What is Network Analysis in Operations Research?

Definition: Network analysis is a group of Operations Research techniques used to represent and analyze systems or projects that can be described in terms of connected activities, events, nodes, or links.

In project management, network analysis represents the logical relationships among project activities and helps in:

planning,
scheduling,
monitoring,
controlling large and complex projects,
completing projects efficiently.

A network provides a graphical representation of the relationships within a project. Depending on the convention used (AOA - Activity on Arrow or AON - Activity on Node), activities and events are represented by nodes and directed links or arrows. The set of nodes connected by edges is defined as a network, where something flows along the edges. This graphical representation simplifies understanding the execution order—it is decided which tasks will be completed simultaneously and which will be completed sequentially.

Network models in Operations Research play a broader role in solving network optimization problems, such as finding shortest paths, maximal flow, and minimum spanning trees. Standard OR texts treat network models as a major area that includes several types of network optimization problems in addition to project-related analysis.

The managerial applications of network analysis are as follows:

Assembly Line Scheduling,
Research and Development,
Inventory Planning and Control,
Shifting of manufacturing plant from one plant to another,
Launch of new products and advertising campaigns,
Developing long-range planning and staffing plans, etc.

What is a Project?

A project is a collection of interrelated activities that must be completed in a planned sequence to achieve a specific objective.

Each project has a definite objective and normally requires limited resources such as:

Time
Money
Labour
Materials
Equipment

Examples of projects include:

Construction of a building or bridge
Setting up a new manufacturing plant
Installation of machinery
Development of a new product
Research and development projects
Software or computer-system implementation
Major maintenance projects
Launch of a new product or service

A Project such as setting up of a new plant, research and development in an organization, development of a new product, marketing of a product etc. is a combination of interrelated activities (tasks) which must be executed in a certain order before the entire task can be completed.

A project is generally considered successful when it is completed within the required time and approved budget and meets the specified technical or performance requirements.

Basic Components of a Project Network

A project network mainly describes the relationships among project activities.

1. Activities

What is an Activity (Task)? An activity is a specific task or job that forms part of a project. Normally for any project, one may be interested in answering questions such as,

What will be the expected time of project completion?
What is the effect of delay of any activity on the overall completion of a project?
How to reduce the time to perform certain activities in case of the availability of additional funds?
What is the probability of completion of the project in time

That is, an activity normally:

requires time for completion,
may require resources,
has a definite beginning and end, and
has logical relationships with other activities.

For example, in a building construction project, activities may include site preparation, foundation work, construction of walls, installation of electrical systems, and finishing work.

In simple words, an activity is a task or job that requires time and, in many cases, resources for completion.

In a network diagram, an activity is commonly represented by an arrow.

A → B
Activity

Activities are often related through precedence relationships. This means that one activity may have to be completed before another activity can begin. For example, the foundation of a building must be completed before certain construction activities can start.

Hence, the activities are interrelated in a logical sequence in such a way that the same activities can not start until some others are completed. An activity in a project is usually viewed as a job requiring resources for its completion.

Some activities, however, can be performed simultaneously when their precedence relationships permit it.

Activity in Network Diagram: Types & Use of Dummy Activity

2. Events or Nodes

What is an Event? An event represents a significant point in the progress of a project, such as the start or completion of one or more activities.

In network diagrams, nodes are commonly used to represent events or activities depending on the network representation being used.

In simple words, an event represents a point in time or a milestone. It does not itself consume time. For example:

(1) → (2)
Here:
(1) = starting event
(2) = ending event
arrow = activity

Suppose the activity is “Build Foundation.” Then:

(1) ── Build Foundation → (2)

Event 1 means: Foundation work can start.

Event 2 means: Foundation work has been completed.

So remember:

Activity = work
Event = milestone/state

3. Links or Arrows

Links or arrows are used to show relationships between elements of a network. Their exact meaning depends on the network representation and convention being used.

4. Precedence Relationships

Precedence relationships specify the order in which activities can be performed.

They answer questions such as:

Which activity must be completed before another activity can begin?

Understanding these relationships is essential for preparing a correct project network.

Objectives of Network Analysis

The main objectives of network analysis in project management include:

Determining the sequence of project activities.
Estimating project completion time.
Identifying critical activities.
Identifying activities that have scheduling flexibility.
Monitoring project progress.
Detecting activities that may cause project delays.
Supporting efficient allocation and use of resources.
Helping management take corrective action when necessary.
Reducing unnecessary delays and conflicts.
Supporting timely and economical project completion.

Applications of Network Analysis

Network analysis is useful in many areas where a project consists of interrelated activities.

1. Construction Projects

It can be used for planning and scheduling the construction of buildings, bridges, roads, and other large structures.

2. Plant Installation

Network techniques can help plan the installation and commissioning of a new manufacturing plant or major equipment.

3. Research and Development

Research projects often involve a sequence of related activities. Network analysis can help organize and schedule these activities.

4. Product Development

The development of a new product may involve design, testing, procurement, production preparation, and other activities that must be properly coordinated.

5. Maintenance Projects

Large maintenance and shutdown projects contain many activities that must be completed in a planned sequence.

6. Software and System Implementation

Network planning can be used to organize activities involved in developing and implementing computer-based systems.

7. New Product Launch

Activities related to product preparation, production, distribution, advertising, and launch can be coordinated using project network techniques.

8. Engineering Projects

Large engineering projects often contain many interdependent activities and can benefit from systematic network planning.

Why is Network Analysis Needed?

Why Do We Need a Network Diagram? — Suppose a project has only four activities:

Activity	Description	Time
A	Design	3 days
B	Foundation	5 days
C	Construction	7 days
D	Painting	4 days

And the order is:

A → B → C → D

Then:

Start
↓
A (3 days)
↓
B (5 days)
↓
C (7 days)
↓
D (4 days)
↓
Finish

The total project time is: 3+5+7+4=19 days. So the project requires 19 days.

This is a very simple network.

But Real Projects Are More Complicated.

A large project may contain hundreds or even thousands of activities. Managing such a project using only a simple list of tasks can make it difficult to determine which activities are most important to the overall completion time.

Network analysis helps managers obtain a clearer picture of the project. It can help answer questions such as:

What is the expected project completion time?
Which activities are critical to the completion of the project?
What will be the effect of delaying a particular activity?
How much flexibility is available for non-critical activities?
Can the project completion time be reduced?
Which activities require special attention from management?
How should available resources be planned and controlled?
In probabilistic project analysis, what is the likelihood of completing the project within a specified time?

Example: Now suppose that after the foundation is completed, two activities can start simultaneously:

Electrical work = 6 days

Plumbing = 4 days

The network may look like:

Notice something important. Electrical and plumbing can be performed at the same time. Therefore, we do not simply add:

6+4=10

Instead, we have to wait until both activities are finished. So this part of the project takes:

Max (6, 4) = 6 days.

This idea leads us to one of the most important concepts in Network Analysis: Critical Path.

What is a Path?

A path is a sequence of connected activities from the beginning of a project to its completion.

Suppose we have:

Path 1:
A → B → C
Path 2:
A → D → E

Suppose their durations are:

Path 1 = 3 + 5 + 4 = 12 days
Path 2 = 3 + 7 + 6 = 16 days

The project cannot be completed until all necessary paths are completed. Therefore, the project duration is: 16 days.

The longer path determines the project duration. That path is called the Critical Path.

The critical path is the longest-duration path from the start of the project to its finish.

This is one of the most important ideas in CPM.

Why is the Critical Path Important?

Suppose the critical path is:

A → D → E

and activity D takes 7 days.

If D is delayed by 2 days, the entire project may be delayed by 2 days. Therefore, activities on the critical path require special attention and control.

But be careful:
“Critical” does not mean that the activity is the most difficult activity.

It means that its timing directly affects the project completion time.

What is Float or Slack?

Now suppose another activity can be delayed by 3 days without delaying the entire project. That 3-day flexibility is called Float or Slack.

In simple words:

Float is the amount of time by which an activity can be delayed without causing a specified delay in the project.

For a basic CPM problem:

Critical activities generally have zero total float. So:

Critical Activity
↓
Float = 0

while a non-critical activity may have:

Non-critical Activity
↓
Float > 0

Major Network Techniques in Project Management

Two important network-based techniques used in project planning and scheduling are:

CPM – Critical Path Method
PERT – Program Evaluation and Review Technique

Nowadays we use CPM and PERT as technical tools for planning, scheduling and controlling stages of projects. Both techniques are used to analyze project activities and relationships, but they differ in their treatment of activity times and uncertainty.

Commonly used project management techniques are:

Critical Path Method (CPM) and
Project Evaluation and Review Technique (PERT)
Several network technologies as given below have been developed in recent times:
Resource Allocation and Multi-Project Scheduling (RAMS)
Program Evolution Process (PEP)
Critical Operating Production Allocation Control (COPAC)
Manpower Allocation Process (MAP)
Resource Planning and Scheduling Method (RPSM)
Least Cost Selection (LCS)
Multi-Operation Scheduling System (MOSS)
Project Control System (PCS)
Graphical Evaluation Review Technique (GERT)

Critical Path Method (CPM)

CPM stands for Critical Path Method.

It is a network-based project management technique used to plan and schedule activities and identify the critical path of a project.

The critical path is the sequence of activities that determines the project completion time under the assumptions of the particular CPM model.

A delay in a critical activity can delay the project completion time unless appropriate corrective action is taken.

The basic idea is:

Activities
↓
Network
↓
Calculate activity times
↓
Find paths
↓
Find Critical Path
↓
Find Project Duration
↓
Find Floats

CPM is particularly associated with deterministic activity-time estimates and is also useful in analyzing time-cost trade-offs in project planning. It is useful when activity times can reasonably be treated as known or fixed estimates.

Program Evaluation and Review Technique (PERT)

PERT stands for Program Evaluation and Review Technique.

PERT is a network-based project planning and scheduling technique developed for situations in which activity times are uncertain.

Instead of assuming a single certain duration for each activity, PERT uses multiple time estimates to represent uncertainty in activity duration.

The important difference is that PERT deals explicitly with uncertainty in activity times.

Suppose you are developing a completely new product. You cannot say with certainty: “This activity will definitely take exactly 10 days.” It may take:

6 days in the best case
10 days under normal conditions
18 days in the worst case

The traditional three time estimates are:

Optimistic time — The shortest reasonable time.
Most likely time — The time most likely to occur.
Pessimistic time — The longest reasonable time under unfavorable conditions.

PERT is therefore particularly useful when activity durations are uncertain, as in many research, development, and other projects.

CPM vs PERT — Basic Idea

Feature	CPM	PERT
Full form	Critical Path Method	Program Evaluation and Review Technique
Main use	Project planning and scheduling	Project planning and scheduling under uncertainty
Activity times	Traditionally treated as deterministic	Traditionally represented using uncertain time estimates
Focus	Critical path and project schedule	Project completion under uncertain activity times
Common use	Construction, production, maintenance and similar projects	Research, development and projects with uncertain activity durations

The distinction should not be overstated: modern project-management practice can use ideas from both approaches, but the traditional textbook distinction is useful for students.

Both are based on the same basic idea:

Represent a project as a network and analyze its activities and relationships.

What Will You Actually Study in Network Analysis?

When you study this topic seriously, you will encounter:

Basic concepts

Activity
Event
Network
Path
Precedence relationship
Dummy activity

CPM

Forward Pass
Earliest Start Time
Earliest Finish Time
Backward Pass
Latest Start Time
Latest Finish Time
Critical Path
Project Duration
Float/Slack

Advanced CPM

Normal time
Crash time
Normal cost
Crash cost
Cost slope
Crashing
Time-cost trade-off

PERT

Optimistic time
Most likely time
Pessimistic time
Expected time
Variance
Standard deviation
Probability of completing the project by a specified date

One Important Point: Network Analysis Is Broader Than CPM/PERT

In Operations Research, network models are not limited to project scheduling.

The Whole Concept in One Picture

The most important thing for you right now

Don't start by memorizing formulas. First understand these seven words:

Activity → Event → Network → Path → Critical Path → Float → Project Duration

Once these seven concepts become clear, Forward Pass, Backward Pass, CPM and PERT will become much easier.

Next, the best lesson to study is “Activity, Event, Dummy Activity and how to construct a Network Diagram” with 2–3 very small examples. That is the proper starting point before doing any CPM numerical problem.

Network Analysis and Decision-Making

Network analysis does not replace the project manager or decision-maker.

Instead, it provides a structured way to analyze the project and its activities.

The results can help management decide:

which activities require close monitoring,
where delays may create serious consequences,
where additional resources may be useful,
how the project schedule can be improved, and
where corrective action should be taken.

Therefore, network analysis is a decision-support approach rather than a substitute for managerial judgment.

Advantages of Network Analysis

Network analysis offers several practical advantages:

Better project planning: It provides a systematic view of project activities and their relationships.
Clear activity sequence: It shows which activities must precede others.
Identification of critical activities: It helps management focus attention on activities that have a major effect on project completion.
Time estimation: It helps estimate project completion time under the assumptions of the selected technique.
Progress monitoring: The network can be used to compare planned and actual progress.
Resource planning: It provides useful information for planning the use of project resources.
Early identification of delays: Activities that may affect project completion can be identified and monitored.
Improved coordination: It helps different teams understand how their activities are related.

Limitations of Network Analysis

Network analysis also has some limitations:

Quality of results depends on the model and input information. Incorrect activity relationships or unreliable time estimates can lead to misleading results.
Large projects can produce complicated networks. As the number of activities increases, the network may become difficult to prepare and interpret.
Real projects may change. Changes in resources, priorities, costs, technology, or activity durations may require the network and schedule to be updated.
Human factors are not completely captured by the network. Motivation, communication, management decisions, and other qualitative factors may influence project performance.
A network does not guarantee project success. It supports planning and control, but successful project management also requires proper execution, monitoring, communication, and managerial judgment.

An Example of Network Analysis in Operations Research

Suppose a project consists of the following activities:

Activity A: Project planning
Activity B: Material procurement
Activity C: Equipment installation
Activity D: Testing
Activity E: Final commissioning

If equipment installation cannot begin until the required materials have been procured, then there is a precedence relationship between procurement and installation.

Similarly, testing may have to wait until installation is completed.

A network diagram can represent these relationships and help determine:

which activities can be performed simultaneously,
which activities must be performed sequentially,
which sequence determines project completion, and
where a delay could affect the entire project.

This simple representation becomes especially valuable when a project contains hundreds of interrelated activities.

Common Questions Answered by Network Analysis

A project manager may use network analysis to answer questions such as:

Q. When will the project be completed?

The network and the selected project-scheduling technique can be used to determine the planned or expected completion time.

Q. Which activities are critical?

The analysis identifies the activities or sequence of activities that determine the project completion time under the model assumptions.

Q. What happens if an activity is delayed?

The effect depends on the activity's position in the network and the amount of scheduling flexibility available.

Q. Can the project be completed earlier?

In appropriate project models, management can examine ways of reducing project duration, including the allocation of additional resources where justified.

Q. What is the probability of completing the project on time?

This question is particularly relevant to probabilistic project analysis such as traditional PERT.

Important Terms to Remember

Term	Meaning
Project	A collection of related activities undertaken to achieve a specific objective
Activity	A task or job that forms part of a project
Network	A graphical representation of relationships among connected elements
Precedence	The required order between related activities
Event	A significant point marking the beginning or completion of activities in certain network conventions
Critical Path	The path that determines the project completion time under the model
CPM	Critical Path Method
PERT	Program Evaluation and Review Technique
Feasibility	The ability of a proposed schedule or plan to satisfy the specified requirements and constraints

Frequently Asked Questions (FAQs)

Q. What is network analysis in Operations Research?

Network analysis is a set of OR techniques used to represent and analyze connected activities or network relationships. In project management, it is used for planning, scheduling, monitoring, and controlling projects.

Q. What is the main purpose of network analysis?

Its main purpose is to provide a systematic representation of a project or network so that activities, their relationships, project duration, and important scheduling issues can be analyzed.

Q. What are the two main project network techniques?

The two traditional techniques most commonly associated with project network analysis are CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique).

Q. What is CPM?

CPM stands for Critical Path Method. It is a network-based technique used for project planning and scheduling, particularly with deterministic activity-time estimates.

Q. What is PERT?

PERT stands for Program Evaluation and Review Technique. It is a network-based project planning and scheduling technique that explicitly considers uncertainty in activity durations.

Q. What is a critical path?

The critical path is the sequence of activities that determines the project completion time under the assumptions of the network model. Activities on the critical path require particular attention because delays in them can affect project completion.

Q. Is network analysis used only for projects?

No. Network models have a broader role in Operations Research. They are also used for network optimization problems such as shortest-path and flow-related problems. Project planning and scheduling are one important application of network techniques.

Conclusion

Network analysis is an important area of Operations Research for dealing with projects and other systems that can be represented through connected activities or network relationships.

In project management, a project is divided into activities and their precedence relationships are represented systematically. This helps managers understand the sequence of activities, estimate project duration, identify critical activities, monitor progress, and take corrective action when required.

CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique) are two important traditional techniques used for project planning and scheduling. CPM is commonly associated with deterministic activity times, while PERT is designed to handle uncertainty in activity durations.

Network analysis does not replace managerial judgment. Instead, it provides useful analytical information that helps managers plan, schedule, and control complex projects more effectively.

About the Author

Lata Agarwal

Mathematics, Science and Astronomy professional, M.Sc. and M.Phil. in Maths with 10+ years of experience as Assistant Professor and Subject Matter Expert.

Author at Prinsli.com

References

Hamdy A. Taha, Operations Research: An Introduction, 10th Edition, Pearson.
Frederick S. Hillier and Gerald J. Lieberman, Introduction to Operations Research, McGraw-Hill Education.
J. K. Sharma, Operations Research: Theory and Applications, Macmillan India.
Kanti Swarup, P. K. Gupta and Man Mohan, Operations Research, Sultan Chand & Sons.
S. D. Sharma, Operations Research, Kedar Nath Ram Nath.

Network Analysis in Operations Research: Definition, Components, Applications