Construction of network

Construction of network:

Rules for constructing network

For the construction of a network, generally, the following rules are followed:

(i) Each activity is represented by one and only one arrow.(i.e) only one activity can connect any two nodes.

(ii) No two activities can be identified by the same head and tail events.

(iii) Nodes are numbered to identify an activity uniquely. Tail node (starting point) should be lower than the head node (end point) of an activity.

(iv) Arrows should not cross each other.

(v) Arrows should be kept straight and not curved or bent.

(vi) Every node must have atleast one activity preceding it and atleast one activity following it except for the node at the beginning and at the end of the network.

Numbering the Events

After the network is drawn in a logical sequence, every event is assigned a number. The number sequence must be such as to reflect the flow of the network. In event numbering, the following rules should be observed:

(i) Event numbers should be unique.

(ii) Event numbering should be carried out on a sequential basis from left to right.

(iii) The initial event is numbered 0 or 1.

(iv) The head of an arrow should always bear a number higher than the one assigned at the tail of the arrow.

(v) Gap should be left in the sequence of event numbering to accommodate subsequent inclusion of activities, if necessary.

Remark: The above procedure of assigning numbers to various events of a network is known as Fulkerson’s Rule.

Example 10.9

Draw the logic network for the following:

Activities C and D both follow A , activity E follows C , activity F follows D , activity E and F precedes B.

Solution:

The required network for the above information.

Example 10.10

Develop a network based on the following information:

Solution:

Using the immediate precedence relationships and following the rules of network construction, the required network is shown in following figure

Dummy activity:

An activity which does not consume any resource or time, but merely depict the technological dependence is called a dummy activity. It is represented by dotted lines.

Example 10.11

Draw a network diagram for the project whose activities and their predecessor relationships are given below:

Solution:

Using the precedence relationships and following the rules of network construction, the required network diagram is shown in following figure

Example 10.12

Construct a network diagram for the following situation:

A<D,E;       B, D<F;      C<G  and B<H.

Solution:

Using the precedence relationships and following the rules of network construction, the required network is shown in following figure