Page 163 - DCAP601_SIMULATION_AND_MODELING

Unit 9: Simulation of a PERT Network (I)

4. The early finish time (EF) Notes

5. The late start time (LS)
6. The late finish time (LF)
7. The slack

In order to determine this information it is assumed that the activities and normal duration
times are given. The first step is to determine the ES and EF. The ES is defined as the maximum
EF of all predecessor activities, unless the activity in question is the first activity, for which the
ES is zero (0). The EF is the ES plus the task duration (EF = ES + duration).
1. The ES for start is zero since it is the first activity. Since the duration is zero, the EF is also
zero. This EF is used as the ES for a and b.
2. The ES for a is zero. The duration (4 work days) is added to the ES to get an EF of four. This
EF is used as the ES for c and d.
3. The ES for b is zero. The duration (5.33 work days) is added to the ES to get an EF of 5.33.
4. The ES for c is four. The duration (5.17 work days) is added to the ES to get an EF of 9.17.
5. The ES for d is four. The duration (6.33 work days) is added to the ES to get an EF of 10.33.
This EF is used as the ES for f.
6. The ES for e is the greatest EF of its predecessor activities (b and c). Since b has an EF of 5.33
and c has an EF of 9.17, the ES of e is 9.17. The duration (5.17 work days) is added to the ES
to get an EF of 14.34. This EF is used as the ES for g.
7. The ES for f is 10.33. The duration (4.5 work days) is added to the ES to get an EF of 14.83.

8. The ES for g is 14.34. The duration (5.17 work days) is added to the ES to get an EF of 19.51.
9. The ES for finish is the greatest EF of its predecessor activities (f and g). Since f has an EF of
14.83 and g has an EF of 19.51, the ES of finish is 19.51. Finish is a milestone (and therefore
has a duration of zero), so the EF is also 19.51.
Barring any unforeseen events, the project should take 19.51 work days to complete. The next
step is to determine the late start (LS) and late finish (LF) of each activity. This will eventually
show if there are activities that have slack. The LF is defined as the minimum LS of all successor
activities, unless the activity is the last activity, for which the LF equals the EF. The LS is the LF
minus the task duration (LS = LF - duration).
1. The LF for finish is equal to the EF (19.51 work days) since it is the last activity in the project.
Since the duration is zero, the LS is also 19.51 work days. This will be used as the LF for f
and g.
2. The LF for g is 19.51 work days. The duration (5.17 work days) is subtracted from the LF to
get an LS of 14.34 work days. This will be used as the LF for e.
3. The LF for f is 19.51 work days. The duration (4.5 work days) is subtracted from the LF to
get an LS of 15.01 work days. This will be used as the LF for d.
4. The LF for e is 14.34 work days. The duration (5.17 work days) is subtracted from the LF to
get an LS of 9.17 work days. This will be used as the LF for b and c.
5. The LF for d is 15.01 work days. The duration (6.33 work days) is subtracted from the LF to
get an LS of 8.68 work days.

6. The LF for c is 9.17 work days. The duration (5.17 work days) is subtracted from the LF to
get an LS of 4 work days.

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