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Operations
Research (MTH601)
42
Expected
length of a critical
path:
The
expected length of a sequence of
independent activities is simply the
sum of their separate
expected
lengths.
This gives us the expected
length of the entire
project. We have to calculate
the expected length te of
every
activity
with the weights attached to
the three time estimates
and find the critical
path in the manner
described
previously.
The expected length of the
entire project denoted by
Te is
the length of the critical
path (i.e.) the sum
of
the,
te's
of all activities along the
critical path.
In
the same way, the
variance of a sum of independent
activity times is equal to
the sum of their
individual
variances.
Since Te is
the is the sum of te's
along the critical path,
then variance of Te equals the sum of
all the
variances
of the critical activities. The
standard deviation of the
expected project duration is
the square root of the
of
the
variance Te as
calculated above.
At
this juncture, consider the
following example to illustrate the
application of these
formulae.
Example
2
1,1,7
1,1,1
1
1,4,7
3
2,5,14
5
3,6,15
2,2,8
4
6
2,5,8
Fig.
20
Activity
Expected
time (te)
Std.
deviation
Variance
1-2
(1+4+7)/6
= 2
(7-1)/6
= 1
1
1-3
(1+16+7)/6
= 4
(7-1)/6
= 1
1
1-4
(2+8+8)/6
= 3
(8-2)/6
= 1
1
2-5
(1+4+1)/6
= 1
(1-1)/6
= 0
0
3-5
(2+20+14)/6
= 6
(14-2)/6
= 2
4
4-6
(2+20+8)/6
= 5
(8-2)/6
= 1
1
5-6
(3+24+15)/6
= 7
(15-3)/6
= 2
4
For
each activity, the
optimistic mostly likely and
pessimistic time estimates
are labeled in the same
order.
Using
PERT formulae for te and St
tabulate
the results as above.
To
calculate the critical path,
list all the three
paths with their expected
time of completion from figure
21.
1-2-5-6
=
10
42
Operations
Research (MTH601)
43
1-3-5-6
= 17
1-4-6
=8
43