## Precedence or activity on node AoN diagrams

Some planners prefer to show the interrelationship of activities by using the node as the activity box and interlinking them by lines. Because the durations are written in the activity box, dummy activities are eliminated. In a sense, each connecting line is, of course, a dummy because it is timeless. The network produced in this manner is called variously a 'precedence diagram', a 'circle and link diagram' or an 'activity on node diagram'. Precedence diagrams have a number of advantages over arrow diagrams in that

1 No dummies are necessary;

2 They may be easier to understand by people familiar with flow sheets;

3 Activities are identified by one number instead of two so that a new activity can be inserted between two existing activities without changing the identifying node numbers of the existing activities;

4 Overlapping activities can be shown very easily without the need for the extra dummies shown in Figure 20.25.

Analysis and float calculation (see Chapter 21) is identical to the methods employed for arrow diagrams and, if the box is large enough, the earliest and latest start and finishing times can be written

A typical precedence network is shown in Figure 22.1, where the letters in the box represent the description or activity numbers. Durations are shown above-centre and the earliest and latest starting and finish times are given in the corners of the box, as explained in the key diagram. The top line of the activity box gives the earliest start (ES), duration (D) and earliest finish (EF). Therefore:

The bottom line gives the latest start and the latest finish. Therefore:

The centre box is used to show the total float.

ES is, of course, the highest EF of the previous activities leading into it, i.e. the ES of activity E is 8, taken from the EF of activity B.

LF is the lowest LS of the previous activity working backwards, i.e. the LF of A is 3, taken from the LS of activity B.

Early start -(ES)

0 I 3 I 3

3 I 5 I 8

8 I 4 |12

151 4 |19

A

-i

B

-i

C

G

0 I 0 I 3

3 I 0 I 8

11| 3 |15

Total float

Early

Late

Duration

3 I 4 I 7

8 I 7 |15

D

E

4 I 1 I 8

Early

 5 5 10 F 10 5 1b

Figure 22.1 AoN diagr

The earliest start (ES) of activity F is 5 because it can start after activity D is 50% complete, i.e.

ES of activity D is 3 Duration of activity D is 4 Therefore 50% of duration is 2 Therefore ES of activity F is 3 + 2 = 5

Sometimes it is advantageous to add a percentage line on the bottom of the activity box to show the stage of completion before the next activity can start (Figure 22.2). Each vertical line represents 10% completion. Apart from showing when the next activity starts, the percentage line can also be used to indicate the percentage completion of the activity as a statement of progress once work has started, as in Figure 22.3.

There are two other advantages of the precedence diagram over the arrow diagram.

1 The risk of making the logic errors is virtually eliminated. This is because each activity is separated by a link, so that the unintended dependency from another activity is just not possible.

This is made clear by referring to Figure 22.4 which is the precedence representation of Figure 22.5.

As can be seen, there is no way for an activity like 'level bottom' in Stage I to affect activity 'Hand trim' in Stage III, as is the case in Figure 22.4.

2 In a precedence diagram all the important information of an activity is shown in a neat box.

 3 4 7 D 4 1 8 3

Figure 22.3 Progress indication

Figure 22.3 Progress indication

Stage II

Stage III

Stage II

Stage III

Figure 22.4 Logic to precedence diagr
F.F. = 0 (11-11)

0

6

6

6

5

11

11

9

20

D

E

F -,

—I

0

0

6

6

0

11

12

1

F.F. = 3 (20-17)

13

4

17

20

5

25

H

J

17

4

21

—I

21

1

Figure 22.5 Total and free float calculation

A close inspection of the precedence diagram (Figure 22.5), shows that in order to calculate the total float, it is necessary to carry out the forward and backward pass. Once this has been done, the total float of any activity is simply the difference between the latest finishing time (LF) obtained from the backward pass and the earliest finishing time (EF) obtained from the forward pass.

On the other hand, the free float can be calculated from the forward pass only, because it is simply the difference of the earliest start (ES) of a subsequent activity and the earliest finishing time (EF) of the activity in question.

### This is clearly shown in Figure 22.5.

Despite the above-mentioned advantages, which are especially appreciated by people familiar with flow diagrams as used in manufacturing industries, many prefer the arrow diagram because it resembles more closely a bar chart. Although the arrows are not drawn to scale, they do represent a forward-moving operation and, by thickening up the actual line in approximately the same proportion as the reported progress, a 'feel' for the state of the job is immediately apparent.

One major disadvantage of precedence diagrams is the practical one of size of box. The box has to be large enough to show the activity title, duration and earliest and latest times, so that the space taken up on a sheet of paper reduces the network size. By contrast, an arrow diagram is very economical, since the arrow is a natural line over which a title can be written and the node need be no larger than a few millimetres in diameter - if the coordinate method is used.

The difference (or similarity) between an arrow diagram and a precedence network is most easily seen by comparing the two methods in the following example. Figure 22.6 shows a project programme and Figure 22.7 the same programme as a precedence diagram. The difference in area of paper required by the two methods is obvious (see also Chapter 33).

Figure 22.7 shows the precedence version of Figure 22.6.

In practice, the only information necessary when drafting the original network is the activity title, the duration and of course the interrelationships of the activities. A precedence diagram can therefore be modified by drawing ellipses just big enough to contain the activity title and duration, leaving the computer (if used) to supply the other information at a later stage. The important thing is to establish an acceptable logic before the end date and the activity floats are computed. In explaining the principles of network diagrams in text books (and in examinations), letters are often used as activity titles, but in practice when building up a network, the real descriptions have to be used.

An example of such a diagram is shown in Figure 22.8. Care must be taken not to cross the nodes with the links and to insert the arrowheads to ensure the correct relationship.

One problem of a precedence diagram is that when large networks are being developed by a project team, the drafting of the boxes takes up a lot of time and paper space and the insertion

Figure 22.6 Arrow (AoA) network

Figure 22.6 Arrow (AoA) network

Figure 22.7 Precedence (AoN) network

of links (or dummy activities) becomes a nightmare, because it is confusing to cross the boxes, which are in effect nodes. It is necessary therefore to restrict the links to run horizontally or vertically between the boxes, which can lead to congestion of the lines, making the tracing of links very difficult.

When a large precedence network is drawn by a computer, the problem becomes even greater, because the link lines can sometimes be so close together that they will appear as one thick black line. This makes it impossible to determine the beginning or end of a link, thus nullifying the whole purpose of a network, i.e. to show the interrelationship and dependencies of the activities. See Figure 22.9.

For small networks with few dependencies, precedence diagrams are no problem, but for networks with 200-400 activities per page, it is a different matter. The planner must not feel restricted by the drafting limitations to develop an acceptable logic, and the tendency by some irresponsible software companies to advocate eliminating the manual drafting of a network altogether must be condemned. This manual process is after all the key operation for developing the project network and the distillation of the various ideas and inputs of the team. In other words, it is the thinking part of network analysis. The number crunching can then be left to the computer.

Figure 22.9 Computer generated AoN diagram