# Network Analysis: Part 2- Worked Example (CPM)

In the first article in this series, I provided a brief overview of Network Analysis. In this article, I will describe a specific example of Network Analysis. As mentioned earlier, the differences between PERT and CPM are now largely historical. The illustrative example describes how to determine the Critical Path using the Critical Path Method.

## Worked Example:

Let us assume that the project in question is that of constructing a residential building. We will assume that the land has already been purchased.

In general, one needs to first design the building, obtain necessary approvals and clearances, construct the superstructure, install the fittings and fixtures, plaster, and paint the surfaces.

Step 1

The first step is to list What has to be done. At this point the focus is on what must be done, not who will do what. The processes involved in a project are called Activities or Tasks.

An activity or task is represented by a rectangle:

Step 2

The next step is to decide the Order of the activities. This may be determined by the application of logic: we cannot install fixtures and fittings unless the walls have been erected.

The general order of activities involved in the construction of a residential building is shown below:

1. Designing (preparing the design of the building in consultation with an architect)
2. Obtaining approvals (typically from the town planning authority and local bodies)
3. Preparing site for construction
5. Laying foundation
6. Erecting walls
7. Laying roof
8. Installing doors, windows
9. Installing plumbing and electrical fixtures
10. Plastering walls
11. Painting

While some Activities can start only after a preceding activity is completed, some may be undertaken while other activities are underway. For simplicity, we will assume that activities only take place in sequence.

The above sequence of activities may be depicted as a network (Figure 1):

The activities are joined with arrows to show the sequence or precedence (the logical relationships between them).

One may alter the network to include additional activities that run in parallel to existing activities. The assumption in this step is that one has infinite resources, so that does not cloud thinking- one only needs to concentrate on the logic.

### Time Analysis

Duration

With the network completed, we can start analysis. First, we need to know the duration of each activity and enter that information in the network. We will write duration in days.

It is preferable to reduce the resource requirement to the duration needed for one person. This will offer maximum flexibility to add additional resources when the project starts running late. Where activities cannot be performed by a single person, consider the time taken for two people to complete the task when working together. (A single person cannot lift a heavy beam alone. This task requires two persons lifting the beam from either end. Adding more resources will not necessarily reduce the duration and may even slow the task down.)