Table 2
Event No.
Alternative paths
0-2345
1
35
35 + 47
35 + 70
820 or 35+ 28 or 105 + 0 105 17 or 105 +50
3 repeats Fig. 1, but activity dura- tions are added; events are numbered for easy reference and circled to dis tinguish them from the durations and times written on the diagram during analysis.
Analysis
How soon an event can occur is found by inspecting the alternative paths leading to it. No event can be reached (or new activity started) until all preceding activities are completed. Given a start time of 0 the earliest an event can occur is given by the longest alternative path to it. Table 1 sets out the lengths of the alternative paths to each event; of these the longest is call- ed the earliest time of event.
Event 5 marks the completion of the simple scheme shown in Figs. 1 and 3. The longest path to this event (through events 0, 1, 3, 4 and 5) is called the Critical Path since it defines the duration of the project as 155 working hours.
In such a simple diagram the Criti- cal Path can be found by inspection but for more complex diagrams it is necessary to determine the latest time for each event to find the Critical Path. The latest time of event is that time which allows all outgoing activity chains to be completed inside the pro- ject duration already determined. It is found by working backwards through the arrow diagram using similar calcu- lations to those above. The Critical Path then passes through those events whose earliest and latest times are equal. Critical activities associated with these events are indicated heavy arrows in Fig 4.
partitions
(35)
Fig. 4.
26
plumbers’fittings
(47) (23)
(0)
window surrounds
42
(50)
(28)
carporters' fi
(70) Q
internal painting
floor finish
(17)
by
Earliest time
of event (hours after
start)
Event
Earliest
No.
time
Latest time
0
35
82
105
12345
35
35
82
105
105
105
105
105
155
155
105 155
A complete project might contain thousands of arrows but the method of analysis is just the same. Critical activities form only a small proportion of the total in a complex arrow dia- gram.
The extent to which non-critical activities can be delayed without af fecting the project duration is found by comparing earliest and latest times for each event, as in Table 2.
The maximum time available for activity 1,2 is the difference between the earliest time for event 1 and the latest time for event 2, that is 70 hours. But activity 1,2 is estimated to take 47 hours, hence the total float for the activity is 23 hours. Total float times for each activity are shown in squares in Fig. 4.
Final scheduling
If the project duration given by the analysis is excessive then either one or more of the critical activities can be shortened or an alternative sequence examined. Re-analysis of the amended diagram will indicate the effects of any changes made.
When an acceptable project dura- tion has been obtained the resources required can be examined. The esti- mated times for activities will be relat- ed to their individual requirements for manpower and plant. A total resource requirement (with each activity start- ing as early as it can) can then be cal- culated. If jobs in parallel on the dia- gram require the same resource the total resources required may exceed those available.
By delaying non-critical jobs up to the limit of their float the need for extra resources can be minimized. Should the schedule obtained in this way still require more resources, at certain times, than are available, then an increase in the project duration is unavoidable.
As a result of this scheduling, a programme is obtained defining the
time at which each activity will be per- formed.
Project control
As work proceeds, PNA can help to control the project by:
on
1. indicating where management attention should be concentrated the critical activities,
2. determining the effects of what has happened to date by re-analysis of the diagram,
3. minimizing the effects of any delays that may have occurred by re- planning the remaining activities,
4. carrying out 2 and 3 at regular intervals throughout the project.
The above example, though simple, is sufficient to illustrate the basic method and indicate what it can achieve, without going into the varia- tions and refinements appropriate to the nature or size of particular projects and the needs of the planning team.
To recapitulate, PNA enables:
1. All activities to be identified and inter-related in a planned sequence.
2. All activities to be scheduled and their effects upon the duration of the project thereby distinguished as criti- cal or non-critical.
Example – a house
A modest example, showing the structure and finishing stages of a house, is presented in three alternative forms in Figs. 5, 6 and 7.
For the labour force assumed, the earliest completion date is 45 working days from dpc level, this time having been determined by the sequence of critical activities. A different labour force or method of construction may well modify the outlines of these dia- grams, without changing the basic PNA approach in any way. Fig. 5 shows and arrow presentation; Fig. 6 the flow chart form.
Fig. 7 presents the schedule in the form of a bar chart. The information
Far East BUILDER, June 1971