Network Analysis: CPM

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Network analysis is an important part of project management. Project management involves the proper management of the activities in the projects. Proper management includes planning, scheduling and controlling the activities of a project in such a way that the project will complete on time. Network analysis is the analysis of the project network. these networks are the connection of the different activities of the projects.

Network analysis can be carried out with the help of many methods, including CPM. Nowadays, CPM and PERT are the methods that are more popular for network analysis. This article contains fundamental notes on the Network Analysis topic of the “Construction Planning and Management” subject.

What is Network Analysis in Project Management?

Project management is evolved to coordinate and control all project activities efficiently and cost-effectively. In project management, a network connects the different activities or tasks. Let’s understand the features of project management. Here some features of project management are listed below. These features of the project will help in the network analysis. Let’s understand these features:

  • A project has identifiable beginning and endpoints.
  • Each project can be broken down into several identifiable activities, which will consume time and other resources during their completion.
  • A project is scheduled to be completed by a target date.
  • A project is usually large and complex and has many interrelated activities.
  • The execution of the project activities is always subjected to some uncertainties and risks.

Network Analysis Techniques

There are many network analysis techniques available, including CPM and PERT. These network analysis techniques are the Gantt chart, Bar chart, etc. These techniques are discussed one by one.

Gantt Chart

The predecessor to network techniques, the Gantt Chart, was developed, during world war I, by Henry L Gantt, for production scheduling. Here an example of a Gantt chart is shown below.


The Gantt chart was later modified to a bar chart, which was an important tool in the project and production schedule.

Bar Chart

The bar chart is a modification of the Gantt Chart. Here an example of the Bar chart is shown below.


Milestone chart

The bar charts then developed into milestone charts and network techniques such as CPM and PERT. The bar chart didn’t give information about critical activity and interdependence among activities. A bar chart is activity-oriented, while a milestone chart is event-oriented.


Network Construction

A network is the graphical representation of the project activities arranged in a logical sequence, depicting all the interrelationships among them. A network consists of activities and events. Network construction is the foremost step of network analysis. Here different terms of a network are explained below.


An activity is a physically identifiable part of a project which consumes both time and resources. An arrow in a network diagram represents activity. The head of an arrow represents the start of the activity, and the tail of the arrow represents its end. The activity description and its estimated completion time are written along the arrow. Activity in the network can be represented in several ways: (i) by numbers of its head and tail events (i.e., 10-20 etc.), and (ii) by a letter code (i.e., A, B etc.). All those activities, which must be completed before the start of the activity under consideration, are called their predecessor activities. All those activities, which must follow the activity under consideration, are called their successor activities.


An activity used to maintain the pre-defined precedence relationship only during the construction of the project network is called a dummy activity. A dotted arrow represents a dummy activity and does not consume time and resources.


An unbroken chain of activities between any two events is called a path.


An event represents the accomplishment of some task. In a network diagram, the beginning and end of an activity are represented as events. Each event is represented as a node in a network diagram. An event does not consume any time or resources. Each network diagram starts with an initial event and ends at a terminal event.


Each node is represented by a circle and numbered using Fulkerson’s Rule. The following steps are involved in the numbering of the nodes.

  • The initial event, which has all outgoing arrows and no incoming arrow, is numbered 1.
  • Delete all the arrows from the node just numbered (i.e., 1). This step will create some more nodes (at least one) in the initial events. Number these events in ascending order (i.e., 2, 3 ­etc.).
  • Continue the process until the final or terminal node with all arrows coming in, with no arrow going out, is numbered.

As a recommendation, it must be noted that most of the projects are liable for modifications, and hence there should be scope for adding more events and numbering them without causing any inconsistency in the network. This is achieved by skipping the numbers (i.e., 10, 20, 30).

Rules for Drawing a Network Diagram

As we know, drawing a network diagram is the foremost step of network analysis. Network analysis is required to determine the project’s critical duration and path. Here some rules for the drawing of a network diagram are given below.

Rule 1: Each activity is represented by one and only one arrow in the network.

Rule 2: No two activities can be identified by the same end events.

Rule 3: Precedence relationships among all activities must always be maintained.

Rule 4: Dummy activities can only be used to maintain precedence relationships when required. Their use should be minimized in the network diagram.

Use of Dummy Activities


Rule 5: Looping among the activities must be avoided.


Critical Path Method(CPM)

This is based on the deterministic approach in which only a one-time estimate is made for activity completion. The CPM (critical path method) networking system is used when the activity time estimates are deterministic. For each activity, a single time required for its execution is estimated. Time estimates can easily be converted into cost data in this technique. CPM is an activity-oriented technique. Here are some features of the Critical Path Method of Network Analysis.

  1. A network diagram in CPM is activity-oriented.
  2. Cost is the most important criterion. The minimum is found to correspond to the optimum time.
  3. There is only a single time estimate for each activity.
  4. The probability of activity completion in this estimated duration is 100%.
  5. It is based on a deterministic approach.
  6. Suitable for the repetitive type of work.
  7. The normal distribution is followed.

Activity times


(i) Earliest start time


(ii) Earliest Finish time

EFT = EST + Activity time

EFT = EST + tij

(iii) Latest finish time

LFT = TL of head event

LFT = Tj

(iv) Latest start time

LST = LFT – tij

LST = TjL – tij


Float denotes the range within which activity time or its finish time may fluctuate without affecting the project’s completion.

(i) Total Float (FT)

FT = LST – EST or FT = LFT – EFT

FT = TjL – TiE – tije

(ii) Free Total (FF)

FF = TiE – TjE – tije or FF = FT – Sj

Where Sj = Head event slack

(iii) Independent Float (FID)

FID = TjE – TiL – tije

FID = FF – Si

FID = FT – Sj – Si

Where Si = Tail event slack

FT = 0 – for Critical path

FT > 0 – for Subcritical path

FT < 0 – for Supercritical path

(iv) Interfering float (FIN)

It is another name for head event slack.

FIN = Sj = FT – FF

CPM Systems

Mainly two systems are used in CPM analysis:

  1. A-O-A System (Activity on arrow system)

An arrow graphically represents an activity.

The arrow’s tail end and head end represent the start and finish of the activity, respectively.


  1. A-O-N System (Activity on node system or precedence diagram). A circle or node represents activity. Events have no places. Arrows are used only to show the dependency relationship between activity nodes.

When two or more activities start parallel, an activity called DEBUT (D0) is provided at the beginning. Likewise, a finish activity (F0) is provided at the end when more than one activities finish parallel. Activity D & F have zero duration.


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