June_1967 — Page 27

careful inspection of all the paths leading to the event. The earliest event time is the longest of these various paths. The process is clearly stated in the following rule. Rule-To the earliest event time of

the preceding event, add the durations of the activities con- necting it and select the highest of the values obtained.

When these earliest times have been computed, they should be entered on the diagram. In order that they are

easily distinguished, they are often en- closed in squares.

Latest Event Times

These are the latest times which events must be reached if the over-a!! project time is to be unaffected. The method of calculation is similar to that used in calculating earliest event times, with two important differences.

Calculations are made working backwards through the diagram start- ing at the last activity.

From the examination of the various paths leading to events the lowest of the values obtained should be used. Again this can be expressed in the following rule. Rule-Working backwards down the

arrows, subtract the duration of the job from the preceding event time and use the lowest of the values obtained. The values obtained are entered on the diagram. To distinguish them,

Reinforcement to Cols 5

Fmwk to cols

8 Conc Cols

70

80

(3)

Concrete Slab

and Stairs

(3)

Bwk to root leve!

2

12

Cure and Strike

50

(60)

90

(2)

(10)

17

100

(4)

Fmwk

Reinforcement

to

Kitchen area

(7)

7 to

[(110)]

Kitchen area

11

(120)

Concrete to Kitchen area

(4)

(6)

Fig. 7.

they can be enclosed in triangles.

Figure 7 shows a section of a net- work for a framed building with the events numbered and earliest and latest event times calculated. The first event has been numbered 50 and given an arbitrary time zero.

Critical Paths

Once earliest and latest event times have been calculated, the determina- tion of critical activities is simple. In an example of the size of that shown in Fig. 7, the critical activities may well have been obvious before finding earliest and latest times, but in a diag- ram with only a small increase in size this would not have been possible. In these circumstances it should be noted that, for activities on the critical path. the earliest and latest event times at

the start and completion of an activity are equal. Also the difference be- tween the earliest start and latest finish time equals the activity dura- tion.

The critical path on this diagram is indicated by a double black line. As mentioned earlier, there must always be at least one critical path. In this particular example, it would only need a slight increase in the duration of certain activities to form two critical paths.

References

To be continued

(1) D.R. Fulkerson (1962) Opera-

tions Research No. 10.

(2) F.E. Grubbs, D.R. Fulkerson, C.E. Clarke (1962) Operations Research No. 10.

THE ALLEN 16-60 TRENCHER

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Full details of this fine machine will be sent by the manufacturers:

ALLEN

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Far East Architect & Builder June, 1967

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