Computing Critical Path

The first step in computing the critical path in PERT network is to reduce the three-time activity durations estimate into single expected time estimate. The rest of the procedure for computing critical path of PERT network is exactly the same as of the CPM network. The steps involved in computing critical path are as follows:

a)    Estimate the expected activity duration

It is given by the following formula:

        

           T₀ + 4T_m + T_p

T_e  =  -----------------

                   6

Where, T_e = Expected activity duration

            T₀ = Optimistic time, assuming that everything goes extremely well with no delays.

         T_p = Pessimistic time, assuming that everything occurs at its worst, with the exception being delays   due to acts which cannot be foreseen.

           T_m  = Most likely time, assuming the normal prevailing conditions.

As an example, consider PERT network outlined in fig. Using the three-time activity duration estimation formula, the expected activity timings can be calculated as in table.

b)    Convert PERT network into deterministic model

It is done by changing the three-time activity durations in PERT to the one-time expected estimates as show in fig.

c)     Transfer deterministic model into PERT network

This is achieved by replacing the one-time estimate with the three-time activity estimates, and marking the critical path as shown in fig.

Note: If more than one critical path is discovered during the analysis, then the path having the maximum level of uncertainty is termed as the critical path.