Formulating a network model

The first stage in creating a network model is to represent the activities and their interrelationships as a graph. In CPM we do this by representing activities as links (arrowed lines) in the graph - the nodes (circles) representing the events of activities starting and finishing.

In Chapter 2 we saw how Amanda used her Product Breakdown to obtain an activity network. Figure 6.7 shows the fragment of her network that was discussed in that chapter and Figure 6.8 shows how this network would look represented as a critical path network.

Case Study Example

Specify overall system

Figure 6.7 The IOE maintenance group accounts project activity network



module A

module A i



module B

module B


Code/test v

module C

module C

Integrate/test system


Code/test [

module D

module D

Figure 6.7 The IOE maintenance group accounts project activity network fragment with a checkpoint activity added.

©Specify overall system

Specify module A Specify module B

Specify module C Specify module

Check specifications module A

Desig module C

Codetest module A

Code/test module B

Codelest module C

Code/test module D


test system

Figure 6.8 The IOE maintenance group accounts project activity network fragment represented as a CPM network.

Constructing CPM networks

Before we look at how CPM networks are used, it is worth spending a few moments considering the rules for their construction.

CPM networks are examples of directed graphs.

A project network may have only one start node The start node (node 1 in Figure 6.8) designates the point at which the project may start. All activities coming from that node may start immediately resources are available - that is, they do not have to wait for any other activities to be completed.

A project network may have only one end node The end node designates the completion of the project and a project may only finish once! The end node for the project fragment shown in Figure 6.8 is the one numbered 10.

A link has duration A link represents an activity and, in general, activities take time to execute. Notice, however, that the network in Figure 6.8 does not contain any reference to durations. The links are not drawn in any way to represent the activity durations. The network drawing merely represents the logic of the project - the rules governing the order in which activities are to be carried out.

Nodes have no duration Nodes are events and, as such, are instantaneous points in time. The source node is the event of the project becoming ready to start and the sink node is the event of the project becoming completed. Intermediate nodes represent two simultaneous events - the event of all activities leading in to a node having been completed and the event of all activities leading out of that node being in a position to be started.

In Figure 6.9 node 3 is the event that both coding and data take-on have been completed and activity program testing is free to start. Installation may be started only when event 4 has been achieved, that is, as soon as program testing has been completed.

Figure 6.9 Fragment of a CPM network.

Time moves from left to right If at all possible, networks are drawn so that time moves from left to right. It is rare that this convention needs to be flouted but, in any case, the arrows on the activity lines give a strong visual indication of the time flow of the project.

Nodes are numbered sequentially There are no precise rules about node numbering but nodes should be numbered so that head nodes (those at the 'arrow' end of an activity) always have a higher number than tail events (those at the 'non-arrow' end of an activity. This convention makes it easy to spot loops.

A network may not contain loops Figure 6.10 demonstrates a loop in a CPM network. A loop is an error in that it represents a situation that cannot occur in practice. While loops, in the sense of iteration, may occur in practice, they cannot be directly represented in a project network. Note that the logic of Figure 6.10 suggests that program testing cannot start until the errors have been corrected.

Figure 6.9 Fragment of a CPM network.

Program test


Figure 6.10 A loop represents an impossible sequence.

If we know the number of times we expect to repeat a set of activities, a test-diagnose-correct sequence, for example, then we can draw that set of activities as a straight sequence, repeating it the appropriate number of times. If we do not know how many times a sequence is going to be repeated then we cannot calculate the duration of the project unless we adopt an alternative strategy such as redefining the complete sequence as a single activity and estimating how long it will take to complete it.

A network may not contain dangles A dangling activity such as Write user manual in Figure 6.11 cannot exist, as it would suggest there are two completion points for the project. If, in Figure 6.11 node 5 represents the true project completion point and there are no activities dependent on activity Write user manual, then the network should be redrawn so that activity Write user manual starts at node 2 and terminates at node 5 - in practice, we would need to insert a dummy activity between nodes 3 and 5 as described in Section 6.9. In other words, all events, except the first and the last, must have at least one activity entering them and at least one activity leaving them and all activities must start and end with an event.

Precedents are the immediate preceding activities In Figure 6.9, the activity Program test cannot start until both Code and Data take-on have been completed and activity Install cannot start until Program test has finished. Code and Data take-on can therefore be said to be precedents of Program test, and Program test is a precedent of Install. Note that we do not speak of Code and Data take-on as precedents of Install - that relationship is implicit in the previous statement.

Dangles are not allowed in activity networks. Although undesirable, they are allowed in precedence networks (discussed in Chapter 9).

Figure 6.11 A dangle.

Exercise 6.1

Take a look at the networks in Figure 6.12. State what is wrong with each of them and where possible redraw them correctly.

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    4 years ago
  • Hamilcar
    What network model in software project?
    4 years ago

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