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


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

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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

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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

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Generating Confidence

Calculate each ―Area increment‖

Δ value x p

Δ value p f(v)


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


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?



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



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


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


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

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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


Includes effects of non-

working days


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

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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


3/23/99 3/31/99 4/9/99

Name: Task 1.4

1.0

0.5

4/9 3/23 3/31



Budgets?

• Are the effects on budget totals any different when adding up a

string of $budgets from the WBS work packages?



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?




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




•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




Confidence degrades

Shift right to recover confidence

Milestone, m


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




Probability ‗center of gravity‘ shifts right

EV increases from 3.6 to 4.2

Critical path may change

Milestone, m


0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6

EV


Date: 3/9/99 10:30:27 PM

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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


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


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

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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


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


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


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


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


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


―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


―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


Task 1

Task 2

20d Critical Path = 50d

5d 15d

30d

Rule # 1: CP work begins at project beginning

Resources on the CP


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


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


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


Project manager’s mission:

To defeat an unfavorable forecast and deliver

customer value, taking reasonable risks to do so


Graphic Earned Schedule, ES

Schedule AT = actual time

ES = earned schedule

ES Variance

Value

Cumulative


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


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

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Quantitative methods schedule