Critical Path Analysis – Introduction

Critical path analysis allows you to determine the best way of arranging activities. The typical question to answer is “what is the minimum time required for a process?”

Performing activities one after the other as you come to them might not be the best way of organising a project. If more than one activity can be worked on at the same time you will need to decide when to start each one. Below, in table 1, are the activities needed to build a house with durations given in days. We are going to perform a critical path analysis on the process of house construction.

AExcavate foundations2
BPour concrete1
CBuild walls3
DConstruct roof sections7
EPut up roof sections1
FTile roof3
GInstall plumbing4
HInstall electrics3
IInstall windows and doors2
JPaint ceilings2
KPaint walls3
LLay carpets2
Table 1: Activities involved in building a house

The first thing that we need to do is to decide which of the activities depend on other activities:

  • B requires that A be complete.
  • C requires that B be complete.
  • E requires that C and D be complete.
  • F requires that E be complete.
  • G, H, and I all require that F be complete.
  • J and K require that G, H, and I be complete.
  • L requires that J and K be complete.

With this information we can draw an activity network. In an activity network the edges represent activities, such as those listed above. The nodes represent events. An event is the start and/or finish of one or more activities. The activity network for the house building example is shown in figure 1.

Figure 1: The activity network for house building.
Figure 1: The activity network for house building.

The activity network shows that there are 12 events involved in the building of this house, and that 12 activities (plus 3 dummy activities) are required before the house is complete.

As you can see, there are a few activities that can occur concurrently. Later we will use this example to find the critical path through the operation (finding a critical path). It is the longest path and determines the minimum length of time that is necessary to complete the house.