in the network one activity may connect any_ nodes
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Answer:
the network diagram shown below, for the problem we considered before, each node (circle) represents an activity and is labelled with the activity number and the associated completion time (shown in brackets after the activity number).
This network is an activity on node (AON) network.
In constructing the network we:
draw a node for each activity
add an arrow from (activity) node i to (activity) node j if activity i must be finished before activity j can start (activity i precedes activity j). Note here that all arcs have arrows attached to them (indicating the direction the project is flowing in).
One tip that I find useful in drawing such diagrams is to structure the positioning of the nodes (activities) so that the activities at the start of the project are at the left, the activities at the end of the project at the right, and the project "flows" from left to right in a natural fashion.
Once having drawn the network it is a relatively easy matter to analyse it (using a dynamic programming algorithm to find the critical path). However we will not consider this algorithm in any detail here but will instead use the computer package to solve the problem.
Note here one key point, the above network diagram assumes that activities not linked by precedence relationships can take place simultaneously (e.g. at the start of the project we could be doing activity 1 at the same time as we are doing activity 2).
Essentially the above diagram is not needed for a computer - a computer can cope very well (indeed better) with just the lists of activities and their precedence relationships we had before. The above diagram is intended for people. Consider what might happen in a large project - perhaps many thousands or tens of thousands of activities and their associated precedence relationships. Do you think it would be possible to list those out without making any errors? Obviously not - so how can we spot errors? Looking at long lists in an attempt to spot errors is just hopeless. With a little practice it becomes easy to look at diagrams such as that shown above and interpret them and spot errors in the specification of the activities and and their associated precedence relationships.