Pert method - excel
domev
PERTShortPPT.pdf
3 - 1Copyright © 2017 Pearson Education, Inc.
► CPM assumes we know a fixed time estimate for each activity and there is no variability in activity times
► PERT uses a probability distribution for activity times to allow for variability
Variability in Activity Times
3 - 2Copyright © 2017 Pearson Education, Inc.
► Three time estimates are required
► Optimistic time (a) – if everything goes according to plan
► Pessimistic time (b) – assuming very unfavorable conditions
► Most likely time (m) – most realistic estimate
Variability in Activity Times
3 - 3Copyright © 2017 Pearson Education, Inc.
Estimate follows beta distribution
Variability in Activity Times
Expected activity time:
Variance of activity completion times:
t = (a + 4m + b)/6
v = [(b – a)/6]2
3 - 4Copyright © 2017 Pearson Education, Inc.
Expected activity time:
Variance of activity completion times:
t = (a + 4m + b)/6
v = [(b – a)/6]2
Estimate follows beta distribution
Variability in Activity Times
t = (a + 4m + b)/6
v = [(b − a)/6]2Probability of 1 in 100 of > b occurring
Probability of 1 in 100 of < a occurring
P ro
b a
b ili
ty
Optimistic Time (a)
Most Likely Time (m)
Pessimistic Time (b)
Activity Time
Figure 3.11
3 - 5Copyright © 2017 Pearson Education, Inc.
Computing Variance
TABLE 3.4 Time Estimates (in weeks) for Milwaukee Paper's Project
ACTIVITY OPTIMISTIC
a
MOST
LIKELY m
PESSIMISTIC b
EXPECTED TIME t = (a + 4m + b)/6
VARIANCE
[(b – a)/6]2
A 1 2 3 2 .11
B 2 3 4 3 .11
C 1 2 3 2 .11
D 2 4 6 4 .44
E 1 4 7 4 1.00
F 1 2 9 3 1.78
G 3 4 11 5 1.78
H 1 2 3 2 .11
3 - 6Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
Project variance is computed by summing the variances of critical activities
s2 = Project variance
= (variances of activities on critical path)
p
3 - 7Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
Project variance is computed by summing the variances of critical activitiesProject variance
s2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11
Project standard deviation
sp = Project variance
= 3.11 = 1.76 weeks
p
3 - 8Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
PERT makes two more assumptions:
► Total project completion times follow a normal probability distribution
► Activity times are statistically independent
3 - 9Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
Standard deviation = 1.76 weeks
15 Weeks
(Expected Completion Time)
Figure 3.12
3 - 10Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
What is the probability this project can be completed on or before the 16 week deadline?
Z = – /sp
= (16 weeks – 15 weeks)/1.76
= 0.57
Due Expected date date of completion
Where Z is the number of standard deviations the due
date or target date lies from the mean or expected date
3 - 11Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
What is the probability this project can be completed on or before the 16 week deadline?
Z = − /sp
= (16 wks − 15 wks)/1.76
= 0.57
due expected date date of completion
Where Z is the number of standard deviations the due
date or target date lies from the mean or expected date
.00 .01 .07 .08
.1 .50000 .50399 .52790 .53188
.2 .53983 .54380 .56749 .57142
.5 .69146 .69497 .71566 .71904
.6 .72575 .72907 .74857 .75175
From Appendix I
3 - 12Copyright © 2017 Pearson Education, Inc.
Probability of Project
Completion
Time
Probability
(T ≤ 16 weeks)
is 71.57%
Figure 3.13
0.57 Standard deviations
15 16
Weeks Weeks
3 - 13Copyright © 2017 Pearson Education, Inc.
Determining Project
Completion Time
Probability of 0.01
Z
Figure 3.14
From Appendix I
Probability of 0.99
2.33 Standard deviations
0 2.33
3 - 14Copyright © 2017 Pearson Education, Inc.
Variability of Completion Time
for Noncritical Paths
► Variability of times for activities on noncritical paths must be considered when finding the probability of finishing in a specified time
► Variation in noncritical activity may cause change in critical path
3 - 15Copyright © 2017 Pearson Education, Inc.
What Project Management Has
Provided So Far
1. The project’s expected completion time is 15 weeks
2. There is a 71.57% chance the equipment will be in place by the 16 week deadline
3. Five activities (A, C, E, G, and H) are on the critical path
4. Three activities (B, D, F) are not on the critical path and have slack time
5. A detailed schedule is available
