ADVANCED EXCEL

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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

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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

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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

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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]2

Probability of 1 in 100 of > b occurring

Probability of 1 in 100 of < a occurring

Probability

Optimistic Time (a)

Most Likely

Time (m)

Pessimistic

Time (b)

Activity Time

Figure 3.11

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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

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Probability of Project Completion

Project variance is computed by summing the variances of critical activities

s2 = Project variance

= (variances of activities on critical path)

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Probability of Project Completion

Project variance is computed by summing the variances of critical activities

Project variance

s2 = .11 + .11 + 1.00 + 1.78 + .11 = 3.11

Project standard deviation

sp = Project variance

= 3.11 = 1.76 weeks

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Probability of Project Completion

PERT makes two more assumptions:

Total project completion times follow a normal probability distribution

Activity times are statistically independent

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Probability of Project Completion

Standard deviation = 1.76 weeks

15 Weeks

(Expected Completion Time)

Figure 3.12

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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

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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

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Probability of Project Completion

Time

Probability (T ≤ 16 weeks) is 71.57%

Figure 3.13

0.57 Standard deviations

15 16 Weeks Weeks

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Determining Project Completion Time

Probability of 0.01

Figure 3.14

From Appendix I

Probability of 0.99

2.33 Standard deviations

2.33

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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

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What Project Management Has Provided So Far

The project’s expected completion time is 15 weeks

There is a 71.57% chance the equipment will be in place by the 16 week deadline

Five activities (A, C, E, G, and H) are on the critical path

Three activities (B, D, F) are not on the critical path and have slack time

A detailed schedule is available

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