MONTE CARLO ANALYSIS
The PMI Registered Education Provider logo is a registered mark of the Project Management Institute, Inc.
V2.0
Copyright 2013 – Graywood Consulting Group, Inc.
Three-Point Estimate 2
Pessimistic, most likely, and optimistic Optimistic = opportunity Pessimistic = threats Optimistic < Most likely < Pessimistic
Copyright 2013 – Graywood Consulting Group, Inc.
Probability Distribution of 3-point Estimates 3
P
Optimistic
Most Likely
Duration / Cost
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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.
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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%
Copyright 2013 – Graywood Consulting Group, Inc.
Monte Carlo Simulation vs MOM 16
Mean
Std. Dev.
80th
Method of Moments
1857
96.4
1938
Monte Carlo Simulation
1857
13.49
1941
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
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
Copyright 2013 – Graywood Consulting Group, Inc.
Thank you! 19
201 Royal St. Suite F Leesburg, VA 20175 www.graywoodtraining.com
[email protected] 703-635-7682
Copyright 2013 – Graywood Consulting Group, Inc.