CPM
explained
T
HE chief merit of Critical Path Methods is a simple logic which imposes a clear and systematic ap- proach to programming and which is equally well suited to smaller building projects as it is to complex schemes requiring electronic puters for analysis.
com-
What is it? It is a method of planning and controlling projects by recording their analysis in a diagram- matic form which enables each fundamental problem involved to be tackled separately.
What does it do? It employs a network diagram to show the jobs to be done and their interrelations. From this diagrammatic "method statement" and estimates of time taken to do individual jobs, it cal- culates the project duration, the Critical Path (that sequence of jobs which defines project duration) and the float (or permissible delay) for non-critical jobs. A schedule programme for the whole project is thus devised.
Advantages
or
The advantages to be gained from CPM are as follows:
1. It separates (a) the sequence of jobs from (b) scheduling times for the jobs.
2. It shows the inter-relationships between jobs (not possible with a bar chart) and enables people to see not merely the overall plan, but the ways in which their own activities depend upon, or influence, those of others.
3. By setting out the complete plan for examination by everyone involved in the project it is easier to assess its soundness and so prevent unrealistic or superficial planning.
4. The effect on the project of alternative methods or individual job times can be examined at the outset.
5. The total
of requirements manpower and plant can be readily calculated. By delaying or slowing down non-critical jobs, that is those not immediately affecting the dura- tion of the project, a schedule may be devised which makes the best allowance for any limitations in available resources.
6. The identification of the Criti- cal Path has two immediate advant- ages: (a) If the completion date has to be advanced, attention can be concentrated on speeding up the relatively few "critical" jobs, and (b) money is not wasted on speeding up non-critical jobs.
what it is
what it does
how it is used
on
7. Schedules may be based considerations of costs so as to com- plete projects in a given time at mimimum expense.
Utilisation
All projects consist of separate operations or jobs (called here activities). The activities are inter- related technical or logical con- siderations will define a certain sequence in which the activities must be performed.
Stage 1-The sequence of activities
The first step is to decide which activities are involved, and their sequence. This requires care, thought and a good knowledge of the project in hand. In CPM the sequence is presented as a network, of which the commonest form is the arrow dia- gram, each activity being represented by an
Figure 1 shows a typical sequence of activities forming part of a building project.
PARTITIONS
Fig. 1
arrow.
PLUMBERS Fittings
WWDOW
SURROUNDS
CARPENTERS FISING
INTERMAL PRINTING
FLOOR FINISH
I. The duration of activities is not considered at this stage, so the arrow diagram is not drawn to a time scale. The arrows indicate the direction of time flow only.
2. The two unnamed broken arrows (called 'dummy' arrows) do not repre- sent real activities; they merely help clarify the sequence by showing, for example, that internal painting follows the completion of carpenter's fixing as well as of window surrounds,
3.
The junctions of arrows are called events, Sometimes an event corresponds to a well-defined stage, for example the completion of foundations, but usually an event serves no more useful a pur- pose than the separation of one activity from another.
an
4. Only one rule is needed to interpret arrow diagram: at every event all activities represented by incoming arrows must be complete before any activity represented by an outgoing arrow start.
can
Figure 1 is thus a more concise re- presentation of the following method statement: When the partitions are completed, the plumber's fittings and carpenter's fixing can be started, and
Far East Architect & Builder March, 1965
also the window surrounds. The floor finish can be started when the carpenter's fixing is complete and the internal painting can commence when carpenter's fixing, plumber's fittings and window surrounds are finished.
In practice, the necessary opera- tions or activities are listed and the arrow diagram drawn by asking of each activity in turn:
(i) what activities must precede it? (ii) what activities must follow it? what activities can be done at the same time?
Stage 2--Estimated job durations
Once the sequence is known, estimated times for each activity are added:
Fig. 2
(F)
(0)
(15)
(20)
(50)
(0)
(7)
This figure repeats Fig. 1, leaving out descriptions of activities for the sake of clarity, and including their durations instead. Events can be num- hered for easy reference and circled as shown to distinguish them from the durations and times written on diagram during analysis.
Stage 3- Analysis
the
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 called the earliest event time.
Table 1
Event
No.
Alternative paths
Earliest event time
0
0
35
35
2
3
35+47 35+70
82
105
4 82+0 or 35+28 or 105+0 105 105+17 or 105+50 155
5
Event 5 marks the completion of the simple scheme shown in Figs. 1 and 2. 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 а simple diagram the Critical Path can be found by inspec- tion, but for more complex diagrams it is necessary to determine the latest time for each event to find the Critical Path. The latest event time
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