Transcript ETM 5241 Strategic Project Management

The Concept of Float
Activities that are not on the critical path
contain positive slack or float.
critical path activities have zero slack or float
Slack or float represents the amount by
which an activity can be delayed without
impacting the completion date of the
project.
the terms float and slack are interchangeable
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
1
The Concept of Float
(continued)
There are two types of float.
Total Float is the amount by which an activity
can be delayed without delaying the completion
of the project.
An activity with initial node i and terminal node j
TF(i,j) = LC(j) - ES(i) - D(i,j)
•
•
•
•
TF is total float
LC is latest completion
ES is earliest start
D is duration
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
2
The Concept of Float
(continued)
Free Float is the amount by which an activity
can be delayed without delaying the start of
at least one other activity in the network.
For an activity with initial node i and terminal
node j
FF(i,j) = ES(j) - ES(i) - D(i,j)
• FF is free float
• ES is earliest start
• D is duration
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
3
The Concept of Float
(continued)
Let’s re-examine our prior example and
calculate the total and free float.
Example to be shown in class
Use the Excel calculation template provided
in ADM_Float_Calcs.xls
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
4
Float Calculations
Excel Template
A
B
C
D
E=D-B-A
F=C-B-A
Activity
D(i,j)
ES(i)
ES(j)
LC(j)
TF(i,j)
FF(i,j)
(0,1)
2
(0,2)
3
(1,3)
2
(2,3)
3
(2,4)
2
(3,4)
0
(3,5)
3
(3,6)
2
(4,5)
7
(4,6)
5
(5,6)
6
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
5
The Concept of Float
(continued)
The following general observations can be
made regarding float calculations:
Free Float will always be less than or equal
to Total Float.
Free Float may be zero when Total Float is
non-zero.
Total Float for critical path activities will
always be zero
Free Float will also be zero
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
6
Why is Float Important ?
Float is flexibility (i.e., wiggle room).
Float tells us that we don’t need to worry
about some activities if they fall behind.
Float helps us separate the “trivial many”
from the “vital few”.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
7
Probability Considerations
Generally time estimates for activity
durations are not deterministic.
A common approach to incorporate nondeterministic durations is to develop three
time estimates for each activity
Optimistic time
Pessimistic time
Most Likely time
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
8
Time Estimates
Optimistic
time which will be required if execution goes
extremely well
Pessimistic
time which will be required if execution goes very
badly
Most Likely
time which will be required if execution is normal
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
9
Time Estimates
(continued)
It is important to note that the most likely
estimate does not have be the midpoint
between the optimistic and pessimistic.
At this point in the methodology it is
common to assume that the activity times
follow a Beta distribution.
This is largely based on empirical evidence.
Examples to be shown in class.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
10
Time Estimates
(continued)
Next we calculate the mean and variance
of each activity time under the Beta
assumption.
Mean = (opt + 4*ml + pess) / 6
Variance = ((pess - opt) / 6)^2
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
11
Mean and Variance of an
Activity Duration
Let’s work an example.
Assume that in our previous network
example, Activity (0,1) had the following
estimates
opt = 1; ml = 2; pess = 3
The resulting mean and variance are:
mean = (1 + 4*2 + 3) / 6 = 12/6 = 2.0
var = ((3 - 1) / 6)^2 = 0.33^2 = 0.11
Let's review the results in
ADM_Mean_Variance.xls
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
12
Results of Duration Mean
and Variance Calculations
Mean and Variance
Act
(0,1)
(0,2)
(1,3)
(2,3)
(2,4)
(3,4)
(3,5)
(3,6)
(4,5)
(4,6)
(5,6)
Strategic Project Management
opt
1.0
2.0
1.0
1.0
0.5
0.0
1.0
1.0
6.0
3.0
4.0
ml
2.0
2.0
2.0
1.5
1.0
0.0
2.5
2.0
7.0
4.0
6.0
pess mean
3.0
2.0
8.0
3.0
3.0
2.0
11.0
3.0
7.5
2.0
0.0
0.0
7.0
3.0
3.0
2.0
8.0
7.0
11.0
5.0
8.0
6.0
var
0.11
1.00
0.11
2.78
1.36
0.00
1.00
0.11
0.11
1.78
0.44
SPM Basic PERT/CPM (Part 2)
13
Probabilistic Completion
Times
We can now determine the critical path
based on the mean activity times.
We can also make probability statements
about the project completion time.
The expected time to completion of the
critical path is the sum of the mean
activity times for the activities on the
critical path.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
14
Expected Duration of the
Critical Path
The Critical Path is
(0,2)
(2,3)
(3,4)
(4,5)
(5,6)
with
with
with
with
with
mean
mean
mean
mean
mean
duration
duration
duration
duration
duration
of 3.0
of 3.0
of 0.0 (dummy)
of 7.0
of 6.0
The mean time to completion is 19.0
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
15
Probabilistic Completion
Times (continued)
The variance of the expected time to
completion of the critical path is the sum
of the variances of the activity times for
the activities on the critical path.
As we move forward, BE CAREFUL to
differentiate between the VARIANCE and the
STANDARD DEVIATION.
We will be using both and it is important that
you are using the correct one in each case.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
16
Critical Path Variance of
Expected Duration
The Critical Path is
(0,2)
(2,3)
(3,4)
(4,5)
(5,6)
with
with
with
with
with
variance
variance
variance
variance
variance
of 1.00
of 2.78
of 0.00 (dummy)
of 0.11
of 0.44
The variance of time to completion is 4.33
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
17
What Now?
We now have the mean and variance of
the time to complete the critical path.
Mean time to completion= 19.0
Variance of time to completion = 4.33
But what do we do now?
We can now make probability statements
about project completion.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
18
Probability Statements
about Project Completion
First, we invoke the Central Limit
Theorem
 We will assume that the distribution of
completion time is approximately Normal.
This is actually not a very risky assumption
since the sum of random variables quickly
approaches Normality.
We can now estimate the probability of
completing by specified times.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
19
Probability Statements
about Project Completion
In our example,
mean = 19.0, variance = 4.33
we will need the standard deviation (rather
than variance) of expected time to completion
std dev = SQRT(variance) = 4.33^0.5 =
2.08
We will also need “Standard Normal
Tables” found in most Statistics books
or in file: ADM_Standard_Normal_Table.xls
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
20
Probability Statements
about Project Completion
What is the probability of completing by
time 20.0?
Step 1: Convert to Standard Normal (also
known as a “z statistic”)
z = (point of interest - mean) / (std. dev.)
z = (20.0 -19.0) / 2.08 = 0.48
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
21
Probability Statements
about Project Completion
What is the probability of completing by
time 20?
Step 2: Look up the probability for the z
value in a standard Normal table
z = 0.48
Pr(z<0.48) = 0.6844
Probability of completing the project in 20.0
time units or less is 0.6844
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
22
Probability Statements
about Project Completion
What is the probability of completing by
time 19.0?
z = (19.0 - 19.0) / 2.08 = 0.0
Pr(z<0) = 0.5000
Probability of completing in 19 or less is 0.50
Conclusion: traditional critical path
calculations are optimistic! They actually give
us the 50/50 probability point.
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
23
Probability Statements
about Project Completion
By what time are we 90% sure we will be
complete?
Pr(z<?) = 0.9
search the standard Normal table
? = 1.28
(time-19)/2.08 = 1.28
time = 21.7
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
24
Probability Statements
about Project Completion
By what time are we 99% sure we will be
complete?
Pr(z<?) = 0.99
search the standard Normal table
? = 2.33
(time-19)/2.08 = 2.33
time = 23.8
Strategic Project Management
SPM Basic PERT/CPM (Part 2)
25