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Introduction to Simulation:
The Athematic of Uncertainty

May 15th, 2014
We	
  will	
  get	
  started	
  3	
  –	
  5	
  minutes	
  past	
  the	
  hour	
  
“Our	
  culture	
  encodes	
  a	
  strong	
  bias	
  either	
  to	
  neglect	
  or	
  ignore	
  VARIATION.	
  	
  	
  
	
  
We	
  tend	
  to	
  focus	
  instead	
  on	
  measures	
  of	
  central	
  tendency,	
  and	
  as	
  a	
  result	
  we	
  make	
  some	
  terrible	
  mistakes,	
  
o>en	
  with	
  considerable	
  prac?cal	
  import[ance].”	
  	
  	
  -­‐Stephen	
  Jay	
  Gould,	
  naturalist,	
  1941-­‐2002	
  
	
  	
  	
  
	
  	
  
	
  	
  
	
  
	
  	
  	
  
	
  	
  
	
  	
  
	
  
Presented by:
Andrew Pulvermacher
Director | Decision Sciences
in/drewpulvermacher	
  
Agenda	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
Value	
  of	
  Simula?on	
  Modeling	
  
	
  
•  What	
  is	
  it…	
  
•  Why	
  you	
  need	
  it…	
  
•  When	
  would	
  you	
  us	
  it…	
  
•  How	
  to	
  use	
  it…	
  
•  Which	
  Sim	
  Product	
  to	
  use…	
  
•  Who	
  uses	
  it…	
  
in/drewpulvermacher	
  
REASON FOR BEING
1:	
  Cure	
  for	
  the	
  Flaw	
  of	
  Averages	
  
2:	
  Embed	
  UNCERTAINTY	
  
3:	
  Enable	
  Risk	
  Management	
  
MEANINGFUL	
  INFORMATION	
  
4	
  Drew@PerformanceG2.com
Simulation Modeling
What	
  it	
  is….	
  
5	
  Drew@PerformanceG2.com
Simulation Modeling
Why	
  use	
  it….	
  
What-­‐If
What	
  Utilization	
  Rate	
  should	
  we	
  maintain	
  to	
  maximize	
  profit?
Profit	
  per	
  Unit: 10.00$	
  	
  	
  	
  
Missed	
  Order	
  Cost (5.00)$	
  	
  	
  	
  	
  
Plant	
  Capacity: 100	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
Utilization	
  Rate: 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Units	
  Produced -­‐	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   10	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   20	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   30	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   40	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   50	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   60	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   70	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   80	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   90	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   100	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
Product	
  Profit -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   100$	
  	
  	
  	
  	
  	
  	
  	
   200$	
  	
  	
  	
  	
  	
  	
  	
   300$	
  	
  	
  	
  	
  	
  	
  	
   400$	
  	
  	
  	
  	
  	
  	
  	
   500$	
  	
  	
  	
  	
  	
  	
  	
   600$	
  	
  	
  	
  	
  	
  	
  	
   700$	
  	
  	
  	
  	
  	
  	
  	
   800$	
  	
  	
  	
  	
  	
  	
  	
   900$	
  	
  	
  	
  	
  	
  	
  	
   1,000$	
  	
  	
  	
  	
  
Cost	
  of	
  Missed	
  Orders -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
  
Profit -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   100$	
  	
  	
  	
  	
  	
  	
  	
   200$	
  	
  	
  	
  	
  	
  	
  	
   300$	
  	
  	
  	
  	
  	
  	
  	
   400$	
  	
  	
  	
  	
  	
  	
  	
   500$	
  	
  	
  	
  	
  	
  	
  	
   600$	
  	
  	
  	
  	
  	
  	
  	
   700$	
  	
  	
  	
  	
  	
  	
  	
   800$	
  	
  	
  	
  	
  	
  	
  	
   900$	
  	
  	
  	
  	
  	
  	
  	
   1,000$	
  	
  	
  	
  	
  
6	
  
What-­‐If	
  Analysis	
  on	
  Steroids	
  
*With	
  beneficial	
  side	
  effects	
  
Input	
  
Variable	
  
Target	
  
TradiHonal	
  What-­‐If	
   SimulaHon	
  
Input:	
  #	
  to	
  	
  
7	
  
What-­‐If	
  Analysis	
  on	
  Steroids	
  
*With	
  beneficial	
  side	
  effects	
  
TradiHonal	
  What-­‐If	
   SimulaHon	
  
Outputs	
  =	
  Meaningless	
  
Inputs	
  =	
  Misleading	
   Inputs	
  =	
  ‘Mimic’	
  Real-­‐World	
  
Outputs	
  =	
  StaHsHcally	
  Meaningful	
  
•  Talk	
  in	
  terms	
  of	
  Probability	
  
•  Terms	
  of	
  Achieving	
  
•  Likelihood	
  of	
  Failure	
  
•  BeRer	
  idea	
  of	
  what	
  to	
  EXPECT	
  
$#&!	
  
8	
  
SCENARIO	
  
Today:	
  May	
  15,	
  2014	
  
Submit	
  Sales	
  Forecast	
  for	
  
Black	
  Friday	
  Event	
  
Why	
  don’t	
  we	
  use	
  simulaHon…	
  
WHY	
  SIMULATION?	
  
What	
  will	
  Black	
  Friday	
  sales	
  volume	
  be?	
  
$5.5	
  B	
  
80%	
  Confidence	
  
Level	
  
$8.2	
  B	
  
$3.9	
  B	
  Which	
  es?mate	
  do	
  we	
  use?	
  
(6	
  months	
  from	
  now….)	
  
POINT	
  ESTIMATE	
  
RANGE	
  
trying	
  to	
  hold	
  people	
  accountable?	
  establishing	
  a	
  budget?	
  
defending	
  an	
  audit	
  of	
  how	
  it	
  was	
  generated?	
  Leadership	
  does	
  not	
  have	
  
permission	
  to	
  be	
  uncertain!	
  
10	
  
“If	
  a	
  man	
  will	
  begin	
  in	
  certain1es	
  he	
  shall	
  end	
  in	
  doubts;	
  
but	
  if	
  he	
  will	
  be	
  content	
  to	
  begin	
  in	
  doubts	
  
he	
  shall	
  end	
  in	
  certain1es.”	
  
	
   	
   	
   	
   	
   	
   	
   	
  -­‐Sir	
  Francis	
  Bacon	
  
Es?mate	
  $5.5	
  B	
  
Combine	
  a	
  point	
  esHmate	
  with	
  a	
  likelihood	
  esHmate	
  
Chance	
  of	
  Missing	
  |	
  35%	
  
WHY	
  SIMULATION?	
  
What	
  will	
  Black	
  Friday	
  sales	
  volume	
  be?	
  
ASK	
  YOURSELF…	
  
MENTAL	
  BREAK	
  
Blackjack	
  
Dealer	
  
HIT	
  
70%	
  of	
  busHng	
  
Stay	
  
65%	
  of	
  busHng	
  
ASK	
  YOURSELF…	
  
401(k)	
  
Return:	
   Return:	
  25%	
   15%	
  
RiskP(<0%)	
   15%	
   5%	
  
Risk	
  
Tolerance	
  
Uncertainty	
  <>	
  Risk	
  
RiskP(<0%)	
  
CORE	
  CONCEPT	
  
Uncertainty	
  <>	
  Risk	
  
UNCERTAINTY	
  does	
  not	
  equal	
  RISK.	
  	
  	
  
	
  
By	
  recognizing	
  uncertainty	
  exists	
  and	
  by	
  modeling	
  
uncertainty	
  (simula8on),	
  you	
  know	
  enable	
  decision	
  
makers	
  to	
  bejer	
  manage	
  RISK.	
  
Es?mate	
  $5.5	
  B	
  
Chance	
  of	
  Missing	
  |	
  35%	
  
WHY	
  SIMULATION?	
  
Combine	
  a	
  point	
  esHmate	
  with	
  a	
  likelihood	
  esHmate	
  
$3.9B	
   $5.5B	
   $8.2B	
  
10%	
   35%	
   90%	
  
Black	
  Friday	
  Sales	
  Forecast	
  
16	
  
What-­‐If	
  Analysis	
  on	
  Steroids	
  
*With	
  beneficial	
  side	
  effects	
  
What-­‐If
What	
  Utilization	
  Rate	
  should	
  we	
  maintain	
  to	
  maximize	
  profit?
Profit	
  per	
  Unit: 10.00$	
  	
  	
  	
  
Missed	
  Order	
  Cost (5.00)$	
  	
  	
  	
  	
  
Plant	
  Capacity: 100	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
Utilization	
  Rate: 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Units	
  Produced -­‐	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   10	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   20	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   30	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   40	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   50	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   60	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   70	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   80	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   90	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
   100	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
Product	
  Profit -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   100$	
  	
  	
  	
  	
  	
  	
  	
   200$	
  	
  	
  	
  	
  	
  	
  	
   300$	
  	
  	
  	
  	
  	
  	
  	
   400$	
  	
  	
  	
  	
  	
  	
  	
   500$	
  	
  	
  	
  	
  	
  	
  	
   600$	
  	
  	
  	
  	
  	
  	
  	
   700$	
  	
  	
  	
  	
  	
  	
  	
   800$	
  	
  	
  	
  	
  	
  	
  	
   900$	
  	
  	
  	
  	
  	
  	
  	
   1,000$	
  	
  	
  	
  	
  
Cost	
  of	
  Missed	
  Orders -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
  
Profit -­‐$	
  	
  	
  	
  	
  	
  	
  	
  	
   100$	
  	
  	
  	
  	
  	
  	
  	
   200$	
  	
  	
  	
  	
  	
  	
  	
   300$	
  	
  	
  	
  	
  	
  	
  	
   400$	
  	
  	
  	
  	
  	
  	
  	
   500$	
  	
  	
  	
  	
  	
  	
  	
   600$	
  	
  	
  	
  	
  	
  	
  	
   700$	
  	
  	
  	
  	
  	
  	
  	
   800$	
  	
  	
  	
  	
  	
  	
  	
   900$	
  	
  	
  	
  	
  	
  	
  	
   1,000$	
  	
  	
  	
  	
  
Input	
  
Variable	
  
TradiHonal	
  What-­‐If	
  
SimulaHon	
  
75%	
  chance	
  producHon	
  will	
  be	
  less	
  
than	
  100	
  units.	
  
in/drewpulvermacher	
  
REAL WORLD RISKS
Pa?ent	
  Flow	
  
Mee?ng	
  an	
  Order	
  Due	
  Date	
  
Tampering	
  with	
  a	
  Stable	
  Process	
  
Modeling	
  Customer	
  Loyalty	
  
Long-­‐Term	
  Value	
  of	
  a	
  Customer	
  
Reducing	
  Churn	
  
Inventory	
  Modeling	
  
Es?ma?ng	
  Dynamic	
  Market	
  Share	
  
Warranty	
  Costs	
  for	
  a	
  Product	
  
When	
  would	
  you	
  use	
  SimulaHon	
  Modeling…	
  
Corporate	
  FP&A	
  
18	
  Drew@PerformanceG2.com
Simulation Modeling
How….	
  
19	
  
DEMO
NEWSVENDOR	
  
20	
  
DEMO
Office	
  of	
  Finance	
  
21	
  
Pa?ent	
  Flow	
  
22	
  
Why	
  SPSS…	
  
23	
  
Why	
  SPSS…	
  
Black	
  Friday….	
  
$65M	
  
$67M	
  
2012	
   2013	
  
Black	
  Friday….	
  
Black	
  Friday….	
  
$65M	
  
$67M	
  
2012	
   2013	
  
24	
  
Why	
  SPSS…	
  
25	
  Drew@PerformanceG2.com
Who	
  is	
  using	
  it…	
  
REAL WORLD RESULTS
26	
  26	
  
SimulaHon	
  Modeling:	
  TODAY	
  
Building Risk Management at Lego
August 5, 2013
Today,	
  the	
  sophis?ca?on	
  of	
  LEGO’s	
  Enterprise	
  Risk	
  Management	
  
(ERM)	
  framework	
  is	
  widely	
  recognized.	
  It	
  is	
  one	
  of	
  the	
  foremost	
  
companies	
  to	
  use	
  Monte	
  Carlo	
  simula?on	
  to	
  quan?fy	
  risk	
  and	
  present	
  
key	
  risk	
  informa?on	
  to	
  its	
  board	
  of	
  directors	
  for	
  decision-­‐making	
  
purposes.	
  	
  
This	
  gives	
  the	
  company	
  a	
  true	
  understanding	
  of	
  the	
  vola?lity	
  that	
  it	
  
believes	
  is	
  inherent	
  in	
  its	
  ac?vi?es,	
  in	
  order	
  that	
  it	
  can	
  act	
  to	
  pre-­‐empt	
  
it.	
  
in/drewpulvermacher	
  
YOU CAN DO THIS
& PerformanceG2 WILL HELP
Regression	
  
Mul?variate	
  Analysis	
  
Forecas?ng	
  
Op?miza?on	
  Modeling	
  
Markov	
  Chains	
  
Queuing	
  Theory	
  
War	
  Gaming	
  
Neural	
  Networks	
  
Linear	
  Networks	
  
Decision	
  Trees	
  
Bayesian	
  Networks	
  
ANALYTICS	
  
28	
  Drew@PerformanceG2.com
Q&A
Thank you for attending our webinar
29	
  Drew@PerformanceG2.com
"  Call us: 877.742.4276
"  	
  Email us: info@performanceg2.com or drew@performanceg2.com
"  	
  Visit our web site: performanceg2.com
"  	
  Read our Analytics blog: performanceg2.com/blog
"  	
  Follow us:
"  (Twitter) @performanceg2
"  (Facebook) /performanceg2
"  (YouTube) /performanceg2
"  (LinkedIn) /performanceg2-inc
Predictive Analytics Series
1.  Execu?ve	
  Introduc?on	
  
2.  Data	
  Modeling	
  
3.  Simula?on	
  
4.  Op?miza?on	
  –	
  June	
  2014	
  
5.  Data-­‐Driven	
  Leadership	
  

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Introduction to Simulation- Predictive Analytics

  • 1. Introduction to Simulation: The Athematic of Uncertainty May 15th, 2014 We  will  get  started  3  –  5  minutes  past  the  hour   “Our  culture  encodes  a  strong  bias  either  to  neglect  or  ignore  VARIATION.         We  tend  to  focus  instead  on  measures  of  central  tendency,  and  as  a  result  we  make  some  terrible  mistakes,   o>en  with  considerable  prac?cal  import[ance].”      -­‐Stephen  Jay  Gould,  naturalist,  1941-­‐2002                                   Presented by: Andrew Pulvermacher Director | Decision Sciences
  • 2. in/drewpulvermacher   Agenda                             Value  of  Simula?on  Modeling     •  What  is  it…   •  Why  you  need  it…   •  When  would  you  us  it…   •  How  to  use  it…   •  Which  Sim  Product  to  use…   •  Who  uses  it…  
  • 3. in/drewpulvermacher   REASON FOR BEING 1:  Cure  for  the  Flaw  of  Averages   2:  Embed  UNCERTAINTY   3:  Enable  Risk  Management   MEANINGFUL  INFORMATION  
  • 6. What-­‐If What  Utilization  Rate  should  we  maintain  to  maximize  profit? Profit  per  Unit: 10.00$         Missed  Order  Cost (5.00)$           Plant  Capacity: 100                     Utilization  Rate: 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Units  Produced -­‐                       10                           20                           30                           40                           50                           60                           70                           80                           90                           100                       Product  Profit -­‐$                   100$                 200$                 300$                 400$                 500$                 600$                 700$                 800$                 900$                 1,000$           Cost  of  Missed  Orders -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   Profit -­‐$                   100$                 200$                 300$                 400$                 500$                 600$                 700$                 800$                 900$                 1,000$           6   What-­‐If  Analysis  on  Steroids   *With  beneficial  side  effects   Input   Variable   Target   TradiHonal  What-­‐If   SimulaHon   Input:  #  to    
  • 7. 7   What-­‐If  Analysis  on  Steroids   *With  beneficial  side  effects   TradiHonal  What-­‐If   SimulaHon   Outputs  =  Meaningless   Inputs  =  Misleading   Inputs  =  ‘Mimic’  Real-­‐World   Outputs  =  StaHsHcally  Meaningful   •  Talk  in  terms  of  Probability   •  Terms  of  Achieving   •  Likelihood  of  Failure   •  BeRer  idea  of  what  to  EXPECT   $#&!  
  • 8. 8   SCENARIO   Today:  May  15,  2014   Submit  Sales  Forecast  for   Black  Friday  Event   Why  don’t  we  use  simulaHon…  
  • 9. WHY  SIMULATION?   What  will  Black  Friday  sales  volume  be?   $5.5  B   80%  Confidence   Level   $8.2  B   $3.9  B  Which  es?mate  do  we  use?   (6  months  from  now….)   POINT  ESTIMATE   RANGE   trying  to  hold  people  accountable?  establishing  a  budget?   defending  an  audit  of  how  it  was  generated?  Leadership  does  not  have   permission  to  be  uncertain!  
  • 10. 10   “If  a  man  will  begin  in  certain1es  he  shall  end  in  doubts;   but  if  he  will  be  content  to  begin  in  doubts   he  shall  end  in  certain1es.”                  -­‐Sir  Francis  Bacon  
  • 11. Es?mate  $5.5  B   Combine  a  point  esHmate  with  a  likelihood  esHmate   Chance  of  Missing  |  35%   WHY  SIMULATION?   What  will  Black  Friday  sales  volume  be?  
  • 12. ASK  YOURSELF…   MENTAL  BREAK   Blackjack   Dealer   HIT   70%  of  busHng   Stay   65%  of  busHng  
  • 13. ASK  YOURSELF…   401(k)   Return:   Return:  25%   15%   RiskP(<0%)   15%   5%   Risk   Tolerance   Uncertainty  <>  Risk   RiskP(<0%)  
  • 14. CORE  CONCEPT   Uncertainty  <>  Risk   UNCERTAINTY  does  not  equal  RISK.         By  recognizing  uncertainty  exists  and  by  modeling   uncertainty  (simula8on),  you  know  enable  decision   makers  to  bejer  manage  RISK.  
  • 15. Es?mate  $5.5  B   Chance  of  Missing  |  35%   WHY  SIMULATION?   Combine  a  point  esHmate  with  a  likelihood  esHmate   $3.9B   $5.5B   $8.2B   10%   35%   90%   Black  Friday  Sales  Forecast  
  • 16. 16   What-­‐If  Analysis  on  Steroids   *With  beneficial  side  effects   What-­‐If What  Utilization  Rate  should  we  maintain  to  maximize  profit? Profit  per  Unit: 10.00$         Missed  Order  Cost (5.00)$           Plant  Capacity: 100                     Utilization  Rate: 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Units  Produced -­‐                       10                           20                           30                           40                           50                           60                           70                           80                           90                           100                       Product  Profit -­‐$                   100$                 200$                 300$                 400$                 500$                 600$                 700$                 800$                 900$                 1,000$           Cost  of  Missed  Orders -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   -­‐$                   Profit -­‐$                   100$                 200$                 300$                 400$                 500$                 600$                 700$                 800$                 900$                 1,000$           Input   Variable   TradiHonal  What-­‐If   SimulaHon   75%  chance  producHon  will  be  less   than  100  units.  
  • 17. in/drewpulvermacher   REAL WORLD RISKS Pa?ent  Flow   Mee?ng  an  Order  Due  Date   Tampering  with  a  Stable  Process   Modeling  Customer  Loyalty   Long-­‐Term  Value  of  a  Customer   Reducing  Churn   Inventory  Modeling   Es?ma?ng  Dynamic  Market  Share   Warranty  Costs  for  a  Product   When  would  you  use  SimulaHon  Modeling…   Corporate  FP&A  
  • 20. 20   DEMO Office  of  Finance  
  • 23. 23   Why  SPSS…   Black  Friday….   $65M   $67M   2012   2013   Black  Friday….  
  • 24. Black  Friday….   $65M   $67M   2012   2013   24   Why  SPSS…  
  • 25. 25  Drew@PerformanceG2.com Who  is  using  it…   REAL WORLD RESULTS
  • 26. 26  26   SimulaHon  Modeling:  TODAY   Building Risk Management at Lego August 5, 2013 Today,  the  sophis?ca?on  of  LEGO’s  Enterprise  Risk  Management   (ERM)  framework  is  widely  recognized.  It  is  one  of  the  foremost   companies  to  use  Monte  Carlo  simula?on  to  quan?fy  risk  and  present   key  risk  informa?on  to  its  board  of  directors  for  decision-­‐making   purposes.     This  gives  the  company  a  true  understanding  of  the  vola?lity  that  it   believes  is  inherent  in  its  ac?vi?es,  in  order  that  it  can  act  to  pre-­‐empt   it.  
  • 27. in/drewpulvermacher   YOU CAN DO THIS & PerformanceG2 WILL HELP Regression   Mul?variate  Analysis   Forecas?ng   Op?miza?on  Modeling   Markov  Chains   Queuing  Theory   War  Gaming   Neural  Networks   Linear  Networks   Decision  Trees   Bayesian  Networks   ANALYTICS  
  • 29. Thank you for attending our webinar 29  Drew@PerformanceG2.com "  Call us: 877.742.4276 "    Email us: info@performanceg2.com or drew@performanceg2.com "    Visit our web site: performanceg2.com "    Read our Analytics blog: performanceg2.com/blog "    Follow us: "  (Twitter) @performanceg2 "  (Facebook) /performanceg2 "  (YouTube) /performanceg2 "  (LinkedIn) /performanceg2-inc
  • 30. Predictive Analytics Series 1.  Execu?ve  Introduc?on   2.  Data  Modeling   3.  Simula?on   4.  Op?miza?on  –  June  2014   5.  Data-­‐Driven  Leadership