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The Activity Network Diagram (known as the PERT diagram in its full version- Program of Evaluation and Review Technique) is a planning assistance tool.

## Introduction

Activity Network Diagram is used to create the schedule, to identify the sequencing and critical path of the project. This simplified method comes from the PERT diagram (tool developed in the year 1950 by the US Navy to assist in the planning of its major projects).

In relation to the arrow diagram, the PERT asks to include in the diagram the dates at the earliest and at the latest and the durations of the steps, which is not necessary for an Activity Network Diagram.

The first step is to list all the stages of the project and define the antecedent of the stage and its duration. The table to be completed is as follows:

## 2-Build the graph

In the light of the preceding elements, the diagram is constructed according to the following rules:

• Each step is represented by a round
• Each step link is represented by an arrow
• We start from the left and finish the project on the right.

## 3-Determining the critical path

Last step is to calculate the critical path. For this, for each step, one determines:

• The earliest date: This is the date the task can be finished as soon as possible. This taking into account the dates as early as the previous steps. To determine it we go through the diagram from left to right
• the date at the latest: This is the date the task is to be finished if we do not want to delay the project. To calculate it, the diagram from right to left is traversed by subtracting the duration of the task.

The difference between the earliest date and the date at the latest is called the margin.

The critical path is the step sequence that has a zero margin. In the example below, the critical path is the continuation of steps 1, 2, 6, 7, and 8.

In contrast the optimistic time corresponds to the stage sequence having the largest margin. In our example below, the optimistic path is the continuation of steps 1, 3, 5, 7 and 8.

Representation as an Activity Network Diagram Representation as a PERT 