# PROCEDURE FOR NUMBERING THE EVENTS USING FULKERSON'S RULE - Quantitative Techniques for management

## Explain Fulkerson's rule of numbering events

An event represents the accomplishment of task. In a network diagram, beginning and ending of an activity are represented as events.

Step1: Number the start or initial event as 1.

Step2: From event 1, strike off all outgoing activities. This would have made one or more events as initial events (event which do not have incoming activities).
Number that event as 2.

Step3: Repeat step 2 for event 2, event 3 and till the end event. The end event must have the highest number.

Example : Draw a network for a house construction project. The sequence of activities with their predecessors is given in the following table, below.

Sequence of Activities for House Construction Project Solution: Network diagram representing house construction project.

The network diagram in the above figure shows the procedure relationship between the activities. Activity A (preparation of house plan), has a start event 1 as well as an ending event 2. Activity B (Construction of house) begins at event 2 and ends at event 3.

The activity B cannot start until activity A has been completed. Activities C and D cannot begin until activity B has been completed, but they can be performed simultaneously. Similarly, activities E and F can start only after completion of activities C and D respectively. Both activities E and F finish at the end of event 6.

Example : Consider the project given in the following table and construct a network diagram.

Sequence of Activities for Building Construction Project Solution: The activities C and D have a common predecessor A. The network representation shown in Figure Network representing the Error violates the rule that no two activities canbegin and end at the same events. It appears as if activity B is a predecessor of activity C, which is not the case. To construct the network in a logical order, it is necessary to introduce a dummy activity as shown in Figure.

Network representing the Error Correct representation of Network using Dummy Activity Example : Construct a network for a project whose activities and their predecessor relationship are given in Table.

Activity Sequence for a Project Solution: The network diagram for the given problem is shown in Figure with activities A, B and C starting simultaneously.

Network Diagram Example : Draw a network diagram for a project given in Table.

Project Activity Sequence Solution: An activity network diagram describing the project is shown in figure below:

Network Diagram Quantitative Techniques for management Topics