MONTE CARLO ANALYSIS

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V2.0

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Three-Point Estimate 2

 Pessimistic, most likely, and optimistic  Optimistic = opportunity  Pessimistic = threats  Optimistic < Most likely < Pessimistic

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Probability Distribution of 3-point Estimates 3

P

Optimistic

Most Likely

Duration / Cost

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Pessimistic

Total Project Cost Distribution 4

 Summing “most likely” is not an option  May not be value of original estimate  Research shows sum of most likely is not project mean  Each estimate can vary randomly  Method of Moments (MOM)  Monte Carlo is best

Source: Book, S (2004) Do Not Sum Most Likely Cost Estimates Copyright 2013 – Graywood Consulting Group, Inc.

Statistical Methods 5

 Total project “expected” or mean = sum of 3-point

estimate means

 3-point estimate mean = P = Pessimistic  M = Most likely  O = Optimistic 

𝑃+4∗𝑀+𝑂 6

where:

 Total project cost standard deviation = ∑( Copyright 2013 – Graywood Consulting Group, Inc.

𝑃−𝑂 2 ) 6

Total Project Cost Distribution 6

 Example (values in thousand $) Project Element

Optimistic

Most Likely

Pessimistic

Mean

Variance

Element A

25

36

82

42

90

Element B

18

26

54

29

36

Element C

115

128

135

127

11

Element D

98

118

129

117

27

308

Mean =>

315

164

Total

Standard Deviation Copyright 2013 – Graywood Consulting Group, Inc.

12.81

Total Project Cost Distribution (cont.) 7

Mean (μ) = $315k Std. Dev. (σ)= $12.81k 80th Percentile = 𝜇 + .84 ∗ 𝜎 = $325.44k

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Total Project Cost Distribution (cont.) 8

 Assumes a normal distribution  50% probability of achieving mean  Total project cost estimate based on probability can

be determined  80th percentile is recommended for proper contingency

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Monte Carlo Simulation 9

 Creates a virtual population of “similar” projects  Summary statistics provide insight  Begins with 3-point estimates for each element  Iterates the various combinations of P, M, and O for

each project element  

Selects each cost at random from the cumulative distribution implied by 3-point estimate Random number between 0 and 1 (probability) to determine specific cost

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3-Point Estimates for Cost Risk 10

Project Element

Optimistic

Most Likely

Pessimistic

Element A

30

40

75

Element B

90

100

200

Element C

210

250

400

Element D

250

300

500

Element E

750

800

1000

Element F

125

150

300

Total

1640 Copyright 2013 – Graywood Consulting Group, Inc.

Selecting a Cost Value for a Specific Iteration 11

• Cumulative and triangular distributions for Element E • Using the cumulative distribution, if the random number selection is .7 then the cost for that iteration would be $877.5 million.

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Estimate vs. Monte Carlo 12 Project Element

Estimate

Iteration 1

Iteration 2

Iteration 3

Iteration 4

Iteration 5

Element A

40

68

51

55

32

58

Element B

100

116

148

103

120

99

Element C

250

265

300

311

321

220

Element D

300

390

324

380

285

346

Element E

800

919

819

796

912

873

Element F

150

213

173

181

264

186

Total

1640

1961

1815

1826

1934

1782

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Technical Considerations of Using Monte Carlo 13

 Determining the number of iterations  More iterations mean more accuracy  Typically 5,000 to 10,000 for accuracy  More iterations can produce diminishing results  Input data is not particularly accurate  Seed value initializes random number generator  Same seed value produces same random number series

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Results of Monte Carlo Simulation 14

Percentile

Forecast Values

0%

$1566

10%

$1732

20%

$1770

30%

$1800

40%

$1828

50%

$1853

60%

$1878

70%

$1907

80%

$1941

90%

$1987

100%

$2270

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Calculating Project Contingency Reserve 15

Total Project Estimate

Contingency Reserve

Percentile

Forecast

Dollar

Percent

0%

1566

-74

-5%

10%

1732

92

6%

20%

1770

130

8%

30%

1800

160

10%

40%

1828

188

11%

50%

1853

213

13%

60%

1878

238

15%

70%

1907

267

16%

80%

1941

301

18%

90%

1987

347

21%

100%

2270

630

38%

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Monte Carlo Simulation vs MOM 16

Mean

Std. Dev.

80th

Method of Moments

1857

96.4

1938

Monte Carlo Simulation

1857

13.49

1941

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Sensitivity Analysis 17

 What if the results are not acceptable at desired

probability?  Example: 

P-80 requires additional 301 million / 18%

 Is the cost of mitigation worth it?  Cross-your-fingers project management  Which uncertain element has most correlation to

cost?  Answer: Sensitivity analysis

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Summary and Discussion 18

 Monte Carlo simulation creates a total project cost

probability distribution considering many possible iterations  Results of the simulation are various descriptive statistics, charts and graphs  The cumulative distribution allows for calculating percentiles and associated costs  Monte Carlo and MOM calculations can be similar but MOM is still limited

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Thank you! 19

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