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Transcript of Quantitative methods schedule
Copyright 2010, John C Goodpasture, All Rights Reserved 1
Mitigating Risk in Schedules
Quantitative Methods in Project Management
Produced by
Square Peg Consulting, LLC
John C. Goodpasture
Managing Principal www.sqpegconsulting.com
Copyright 2010, John C Goodpasture, All Rights Reserved
About Confidence
• Likelihood an event will occur within a range
• A number from 0 to 1
• Cumulative summation of probabilities within the range
Copyright 2010, John C Goodpasture, All Rights Reserved
Confidence ―S‖ Curve
Normalized cumulative probability from ‗bell‘ curve
0.25
0.5
0.75
1
0
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
Normalized value
Value / Standard deviation, σ
Cu
mu
lati
ve
Pro
ba
bilit
y
Copyright 2010, John C Goodpasture, All Rights Reserved
Confidence ―S‖ Curve
2
2
1
1
1. 68% confidence: value between -1 to +1
2. 16% confidence: value > 1
3. 84% confidence: value < 1
3
0.25
0.5
0.75
1
0
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5
Cu
mu
lati
ve
Pro
ba
bilit
y
Copyright 2010, John C Goodpasture, All Rights Reserved
Area = Height (probability) X
width (Δ Value)
f(v)
Probability Distribution
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Normalized random variable value
Pro
bab
ilit
y
Generating Confidence
Calculate each ―Area increment‖
Δ value x p
Δ value p f(v)
Copyright 2010, John C Goodpasture, All Rights Reserved
Sum & Plot area increments
F(v)
Value
Area increments summed
F(v) is the area under the f(v) curve
f(v)Δv
F(v) = 1 is the limiting value
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6
What is to be expected at the milestone?
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8 9 10 11 12
EV
EV
EVmilestone = Sum (EV in tandem)
Convolved task probabilities
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 1
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3 4 5 6 7 8 9 10 11 12
Value =
Sum values at a constant confidence
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10 11 12
Copyright 2010, John C Goodpasture, All Rights Reserved
1/1
2/12
1/21
3/25
3/15
1.1
1.2
1.3
1.4
Risk Parameters for each Task:
• Risk distribution: Triangular
• Most optimistic: -10% of ML duration
• Most pessimistic: +25% of ML duration
• ML finish dates shown
Date
Monte Carlo simulation
12 weeks, 60 work days
Copyright 2010, John C Goodpasture, All Rights Reserved
Completion Std Deviation: 2.4d
Each bar represents 1d.
Completion Probability Table
Prob Date 0.05 3/25/99 0.10 3/25/99 0.15 3/26/99 0.20 3/26/99 0.25 3/29/99 0.30 3/29/99 0.35 3/29/99 0.40 3/30/99 0.45 3/30/99 0.50 3/30/99
Prob Date 0.55 3/31/99 0.60 3/31/99 0.65 4/1/99 0.70 4/1/99 0.75 4/1/99 0.80 4/2/99 0.85 4/2/99 0.90 4/5/99 0.95 4/6/99 1.00 4/9/99
1/1
2/12
1/21
3/25
3/15
1.1
1.2
1.3
1.4
Date
Date: 3/9/99 10:30:27 PM
Sam
ple
Count
Cu
mu
lati
ve
Pro
ba
bil
ity
17
34
51
68
85
102
119
136
153
170
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date range
3/23/99 3/31/99 4/9/99
Name: Task 1.4
1.0
0.5
4/9 3/23 3/31
Monte Carlo simulation
Includes effects of non-
working days
Copyright 2010, John C Goodpasture, All Rights Reserved
1/1
2/12
1/21
3/25
3/15
1.1
1.2
1.3
1.4
Risk Evaluation: 3/25 CPM date is
about 10% probable
Date
Date: 3/9/99 10:30:27 PM
Sam
ple
Count
Cu
mu
lati
ve
Pro
ba
bil
ity
17
34
51
68
85
102
119
136
153
170
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date range
3/23/99 3/31/99 4/9/99
Name: Task 1.4
1.0
0.5
4/9 3/23 3/31
Monte Carlo simulation
Copyright 2010, John C Goodpasture, All Rights Reserved
Budgets?
• Are the effects on budget totals any different when adding up a
string of $budgets from the WBS work packages?
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
1 2 3 4 5 6
What happens at the milestone?
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 2
What happens at the milestone?
Lots of combinations—36 possible outcomes
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 30 36
Series1
Duration value
‗12‘ combo milestone value could be 4 or 6
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 2
What happens at the milestone?
•Confidence at the milestone is
the product of the confidences
of the joining paths
Milestone, m
Durations, d1 and d2
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 2
What happens at the milestone?
Confidence degrades
Shift right to recover confidence
Milestone, m
Durations, d1 and d2
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6
Copyright 2010, John C Goodpasture, All Rights Reserved
Schedule Network Architecture 2
What happens at the milestone?
Probability ‗center of gravity‘ shifts right
EV increases from 3.6 to 4.2
Critical path may change
Milestone, m
Durations, d1 and d2
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6
EV
Copyright 2010, John C Goodpasture, All Rights Reserved
Date: 3/9/99 10:30:27 PM
Sam
ple
Count
Cu
mu
lati
ve
Pro
ba
bilit
y
17
34
51
68
85
102
119
136
153
170
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date range
3/23/99 3/31/99 4/9/99
Name: Task 1.4
1.0
0.5
4/9 3/23 3/31
• Milestone distribution for each
independent path
• 50% confidence of 3/30 completion
2/12 1/21
3/25
3/15
1/1
2/12 1/21
3/25
3/15
Monte Carlo Simulation
Copyright 2010, John C Goodpasture, All Rights Reserved
Probability of 3/30 =
0.5 x 0.5 = 0.25, or less
Monte Carlo Simulation
3/25
3/15
3/25
3/15 C
um
ula
tive
Pro
ba
bili
ty
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Completion Date 3/24/99 4/1/99 4/12/99
Date: 3/8/99 9:31:06 PM Number of Samples: 2000 Unique ID: 12 Name: Finish Milestone
Completion Probability Table
Prob Date 0.05 3/29/99 0.10 3/29/99 0.15 3/30/99 0.20 3/30/99 0.25 3/30/99 0.30 3/31/99 0.35 3/31/99 0.40 3/31/99 0.45 3/31/99 0.50 4/1/99
Prob Date 0.55 4/1/99 0.60 4/1/99 0.65 4/2/99 0.70 4/2/99 0.75 4/2/99 0.80 4/2/99 0.85 4/5/99 0.90 4/5/99 0.95 4/6/99 1.00 4/12/99
Join independent
paths at milestone
Copyright 2010, John C Goodpasture, All Rights Reserved
Event Chain Methodology
• Extension of Monte Carlo simulation method.
• Events occur at probabilistic nodes
• Probabilistic nodes can be in the middle of the task and lead to
task delay, restart, cancellation
• Events can cause other events and generate event chains
Baseline outcome
Alternative Probabilistic node
p = 0.8
p = 0.2
Copyright 2010, John C Goodpasture, All Rights Reserved
Build a path
A(12)
B(11)
C(15) G(20) I(8)
D(21)
E(15)
F(18)
H(3)
J(13) L(12)
O(9)
K(21) M(14)
N(20)
Task Duration is shown in days (#):
Start End
Float = 25d
Float = 33d
80 days for the path shown
Copyright 2010, John C Goodpasture, All Rights Reserved
Build a network schedule
A(12)
B(11)
C(15) G(20) I(8)
D(21)
E(15)
F(18)
H(3)
J(13) L(12)
O(9)
K(21) M(14)
N(20)
CP = 80 days; Additional paths are 49, 57, or 63, 73 days < 82 days
Start End
A(12) Every network at least one Critical Path
Float = 25d
Float = 33d
Copyright 2010, John C Goodpasture, All Rights Reserved
Critical path shifts with variation
A(12)
B(12)
C(15) G(20) I(8)
D(21)
E(17)
F(18)
H(3)
J(13) L(12)
O(10)
K(23) M(16)
N(20)
Former path at 50%; new path at 80%
Start End
B(11) Critical path is 81.5 days
Float = 25d
Float = 33d
Copyright 2010, John C Goodpasture, All Rights Reserved
Critical path shifts with variation
A(12)
B(12)
C(15) G(20) I(8)
D(21)
E(17)
F(18)
H(3)
J(13) L(12)
O(10)
K(23) M(16)
N(20)
Start End
Three milestones will shift the END & change CP probabilities
Float = 25d
Float = 33d
Copyright 2010, John C Goodpasture, All Rights Reserved
―Critical Chain‖ buffers uncertainty
10 days
15 days 10 days
Task on the critical path
Project Buffer
Critical chain is a concept developed in the book
Critical Chain (Goldratt, 1997)
Project buffer
protects final
milestone
from variation
Copyright 2010, John C Goodpasture, All Rights Reserved
―Critical Chain‖ buffers uncertainty
Critical chain is a concept developed in the book
Critical Chain (Goldratt, 1997)
Buffer 11 days 10 days
15 days 10 days
Task on the critical path
Task with risky duration, not on critical path
1 2
Project Buffer 12 days
Path buffer mitigates
“shift right” at the
milestone of joining
path
Copyright 2010, John C Goodpasture, All Rights Reserved
Task 1
Task 2
20d Critical Path = 50d
5d 15d
30d
Rule # 1: CP work begins at project beginning
Resources on the CP
Copyright 2010, John C Goodpasture, All Rights Reserved
Rule # 2: Resource CP first and then level
Resources on the CP
Task 1
Task 2
Mary 20d
Mary
5d John 15d
John 30d Critical Path = 65d
Float
Copyright 2010, John C Goodpasture, All Rights Reserved
Rule # 3: Reorganize the network logic
Task 1
Task 2
Mary 20d
Mary
5d John 15d
John 30d Critical Path = 55d
CP responds to constraints
Work does not begin first on the CP
Copyright 2010, John C Goodpasture, All Rights Reserved
Resource consequences
• Resource dependencies
lengthen the schedule
• In fact, any loss of
independence from any
cause will lengthen the
schedule!
• Resource constraints may
require work begin off the CP
Copyright 2010, John C Goodpasture, All Rights Reserved
Project manager’s mission:
To defeat an unfavorable forecast and deliver
customer value, taking reasonable risks to do so
Copyright 2010, John C Goodpasture, All Rights Reserved
Graphic Earned Schedule, ES
Schedule AT = actual time
ES = earned schedule
ES Variance
Value
Cumulative
Copyright 2010, John C Goodpasture, All Rights Reserved
Graphic Earned Schedule, ES
Schedule AT
ES
ES Variance
EV = PV
• ES will never be 0 for a late project
• EV schedule variance, EV – PV, will
always be 0 for a completed project
Value
Cumulative
Copyright 2010, John C Goodpasture, All Rights Reserved
What‘s been learned?
• Confidence expresses probability over a range
• Confidence is based on the cumulative probability, a.k.a. the ‗area
under the curve‘
• Confidence is constant in tandem strings, whether budget or
schedule, but degrades rapidly at a parallel join
• Monte Carlo simulations give results very close to calculated
‗ideals‘
• Earned schedule will not have a 0 variance when all value is
earned