## Arithmetical Analysis

This method is the classical technique and can be performed in a number of ways. One of the easiest methods is to add up the various activity durations on the network itself, writing the sum of each stage in a square box at the end of that activity, i.e. next to the end event (Figure 21.1). It is essential that each route is examined separately and where the routes meet, the largest sum total must be inserted in the box. When the complete network has been summed in this way, the earliest starting will have been written against each event.

Now the reverse process must be carried out. The last event sum is now used as a base from which the activities leading into it are subtracted. The result of these subtractions are entered in triangular boxes against each event (Figure 21.2). As with the addition process for calculating the earliest starting times, a problem arises when a node is reached where two routes or activities meet. Since the latest starting times of an activity are required, the smallest result is written against the event.

The two diagrams are combined in Figure 21.3. The difference between the earliest and latest times gives the 'float', and if this difference is zero (i.e. if the numbers in the squares and triangles are the same) the event is on the critical path. Figure 21.1 Forward pass Figure 21.2 Backward pass The equivalent precedence (AoN) diagram is shown in Figure 21.6. A table can now be prepared setting out the results in a concise manner (Table 21.1) 