Tài liệu Project Planning and Control Part 3 pptx

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Precedence or activity on

node (AoN) diagrams

Some planners prefer to show the interrelation￾ship 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 con￾necting 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 advan￾tages 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 chang￾ing 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 11.25.

Project Planning and Control

Analysis and float calculation (see Chapter 15) 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 in.

A typical precedence network is shown in Figure 12.1, 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:

EF = ES + D

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

LS = LF – D

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.

The earliest start (ES) of activity F is 5 because it can start after activity D is

50% complete, i.e.

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Figure 12.1

Precedence or activity on node (AoN) diagrams

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 12.2). 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 12.3.

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 12.4 which is the precedence

representation of Figure 11.25.

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

11.24.

2 In a precedence diagram all the important information of an activity is

shown in a neat box.

A close inspection of the precedence diagram (Figure 12.5), 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.

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Figure 12.2 Figure 12.3

Project Planning and Control

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 12.5.

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

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Figure 12.4

Figure 12.5