5.3.4 Critical Path Analysis
Critical Path Analysis (CPA) or Critical Path Method (CPM) is part of a planning system called Network Analysis.
CPA uses the arrow diagram in which:
- A circle represents an event (or phase)
- The arrow points to the next event (or phase)
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Figure 3 The simplest critical path analysis

Figure 4 Four activities linking five events in a critical path analysis
Suppose we wanted to devise a Critical Path Analysis for planting a tree in our garden. First, we estimate the duration of each sub-activity or task:
TASK DURATION
1 - 2 Dig a hole 20 minutes
2 - 3 Position the tree 1 minute
3 - 4 Fill in hole 5 minutes
There are four critical points from start to finish and a total of 26 minutes duration. This can be represented as follows:

Figure 5 Critical path analysis activity network
Not all projects accomplish their phases sequentially. Some project phases are accomplished simultaneously thereby establishing a network.

Figure 6 Simple network critical path analysis
The Network critical path Analysis represents a slightly more complex project. Note that the network is more than a simple straight line sequence. Here, there are two paths that lead from the start to the finish. In fact, there is even a third path represented by the dotted line and called a "dummy" activity 4 to 3. Here, the start of activity 3 to 6 is dependent not only on completion of activity 2 to 3, but it must also await completion of activity 1 to 4. This means activity 3 to 6 cannot start until events 3 and 4 has both been achieved.
Now look at the numbers above the stages and along the arrows. Activity 1 to 2 takes 1 week. Activity 2 to 3 takes 2 weeks. 1 week plus 2 weeks = 3 week but note point 3 allows for 5 weeks! This is because activity 1 to 4 takes five weeks and so as we cannot proceed past 3 until 4 is completed, we can allow five weeks for 1 to 3 even though it only requires 3 weeks. This gives us 2 extra weeks up our sleeve during which time staff can be allocated to another task (possibly on another project). In fact, we can afford to delay activities by some weeks here because we have allowed time for other phases to catch up. This allows us a whole range of options. For example:
- Duration of Activity 5 to 6 = 2 weeks
- Earliest possible start = beginning of week 6
- Earliest possible finish (6+2) = end of week 8
- Latest permissible finish = end of week 9
- Total float (free time) = 1 week on activity 5 to 6.
"Float" or "slack" = the amount of leeway available for starting and finishing an activity.
When the float = 0 (no leeway allowed between earliest and latest time) = the critical path.
Too much slack time effectively means the project is progressing (in terms of cost and time) but no useful activity is performed to progress project completion. (Schonberger 1994:483)