Use the Triple Time Estimate table below to determine the critical path and comp
ID: 432970 • Letter: U
Question
Use the Triple Time Estimate table below to determine the critical path and completion time for the project
(note: times are in weeks).
Task description
optimistic
Likely
Pessimistic
Period 1
Period 2
A
Task a
1
3
5
B
Task b
2
5
11
A
C
Task c
4
7
13
A
D
Task d
5
10
12
B
c
E
Task e
4
5
6
C
f
Task f
3
3
3
d
__________15a) What steps comprise the “critical path”?
__________15b) What is the minimum completion time?
__________15c) What is the probability of completing the project in less than 25 weeks?
__________15d) If TASK B can be completed in half the time for a small fee, would it be worthwhile
Task description
optimistic
Likely
Pessimistic
Period 1
Period 2
A
Task a
1
3
5
B
Task b
2
5
11
A
C
Task c
4
7
13
A
D
Task d
5
10
12
B
c
E
Task e
4
5
6
C
f
Task f
3
3
3
d
Explanation / Answer
The precedence diagram of activities as follows :
A
B
C
D
E
F
Please find below table highlighting expected durations as well as Variances of each activity.
Expected duration = ( Optimistic time + 4 x Most likely time + Pessimistic time ) / 6
Variance = ( Pessimistic time – Optimistic time ) ^2/36
Activity
To
tm
tp
te = ( to + 4.tm+tp)/6
Variance ( tp-to)^2/36
A
1
3
5
3
0.44
B
2
5
11
5.5
2.25
C
4
7
13
7.5
2.25
D
5
10
12
9.5
1.36
E
4
5
6
5
0.11
F
3
3
3
3
0.00
The expected durations of all parallel paths as follows :
A-B-D-F = 3 + 5.5 + 9.5 + 3 = 21
A-C-D-F = 3 + 7.5 + 9.5 + 3 = 23
A-C-E = 3 + 7.5 + 5 = 15.5
Out of above , A-C-D-F has the longest duration and hence forms the critical path.
Since minimum completion time of a project will be same as duration of the critical path, minimum completion time will be 23 weeks
STEPS COMPRISING CRITICAL PATH = ACDF
MINIMUM COMPLETION TIME = 23 WEEKS
Variance of the critical path’s duration
= Sum of variances of A,C,D,F
= 0.44 + 2.25 + 1.36+ 0
= 4.05 weeks
Therefore,
Standard deviation of duration of critical path = Square root ( Variance ) = Square root ( 4.05) = 2.01
Let z value corresponding to probability of completing the project in maximum 25 weeks =Z1
Therefore ,
Expected duration of critical path + Z1 x Standard deviation of duration of critical path = 25
Or, 23 + 2.01.Z1 = 25
Or, Z1 = 2/2.01 = 1 ( approx.)
Corresponding probability for Z= 1 as derived from standard normal distribution table is 0.84134.
PROBABILITY OF COMPLETING THE PROJECT FOR LESS THAN 25 WEEKS = 0.84134
Since task B does not lie on the critical path, shortening its duration will not help to reduce minimum completion time of the project. Therefore, it is not worthwhile to pay a small fee to complete task B in half the time.
A
B
C
D
E
F
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