Transcript Modelling&Simulation

Introduction to Modeling
Introduction
Why Model?
Management Models
• Simulate business activities and decisions
• Feedback about and forecast of outcomes
• Minimal risk or cost
Introduction to Modeling
The Modeling Process
The Managerial Approach to decision making
Management
Situation
Decision
Implementation
Thebeen
cookies
sell well!
Owner has
a baker
for 50 years
TheShould
company
litae
on new
ourspends
baking 50,000
company
make
Butthinks
fewer the
cakes
can be
baked
and
cookies
will
sell:
machinery
and advertising.
cookies
in addition
to cakes?
Net“Taip!”
profit falls
Relying solely on intuition is risky
No feedback until the final outcome
Payoff
Introduction to Modeling
The Modeling Process
The Managerial Approach to decision making
Using a Model!
Analysis
Real World
Management
Situation
Results
Managerial
Judgment
Interpretation
Symbolic World
Abstraction
Model
Intuition
Decisions
Managerial judgment - intuition - essential aspect of process
Introduction to Modeling
The Modeling Process
The Managerial Approach to decision making
Using a Model!
Interpretation of model results
Decision
Intuition of Management situation
Implementation
Payoff
Introduction to Modeling
Types of Models
Model Type
Characteristics
Examples
Physical Model
 Tangible
 Comprehend: Easy
 Duplicate/Share: Difficult
 Modify/Manipulate: Difficult
 Range of uses: Lowest
 Model Airplane
 Model House
 Model City
Analog Model
 Intangible
 Comprehend: Harder
 Duplicate/Share: Easier
 Modify/ Manipulate: Easier
 Range of uses: Wider
 Road Map
 Speedometer
 Pie Chart
Symbolic Model
 Intangible
 Comprehend: Hardest
 Duplicate/Share: Easiest
 Modify/ Manipulate: Easiest
 Range of uses: Widest
 Simulation Model
 Algebraic Model
 Spread Sheet Model
Introduction to Modeling
Formulation
{
Decisions
(Controllable)
Parameters
(Uncontrollable)
The
Model
Performance
Measure(s)
Consequence
Variables
Endogenous
Variables
Exogenous
Variables
Black Box View of the Model
Introduction to Modeling
Decision Models
Models
Physical
Analog
Symbolic
Decision
Deterministic
• Assumed: all elements known with
certainty
• Highest value: few uncertain
uncontrolled model inputs
Non-decision
Probabilistic
• Assumed: Some elements not known
with certainty
• Incomplete knowledge: Uncertainty
must be incorporated into the model
Introduction to Modeling
Decision Models
Models
Physical
Analog
Symbolic
Decision
Deterministic
• Forecasting
• Optimization
Non-decision
Probabilistic
• Decision Trees
• Monte Carlo Simulation
Introduction to Modeling
Decision Analysis
Decision Theory
Decision Vs. Nature
The result (return) of one decision depends on another
player’s (nature’s) action over which you have no control
Decision Analysis Payoff Table
State of Nature
Decision
1
d1
r11
Introduction to Modeling
Decision Analysis
Decision Theory
Decision Vs. Nature
The result (return) of one decision depends on another
player’s (nature’s) action over which you have no control
Decision Analysis Payoff Table
State of Nature
Decision
1
2
3
m
d1
d2
d3
dn
r11
r21
r31
rn1
r12
r22
r32
rn2
r13
r23
r33
rn3
r1m
r2m
r3m
rnm
Introduction to Modeling
Decision Models
The outcome of nature
A
Decision Model
B
C
Three Classes of Decision Models
•Decisions Under Certainty
•Decisions Under Risk
•Decisions Under Uncertainty
Introduction to Modeling
Decision Under Certainty
Decision Under Certainty occurs in situations where
you know which state of nature will occur.
Decision Analysis Payoff Table
State of Nature
Decision
1
d1
d2
d3
dn
r11
r21
r31
rn1
Introduction to Modeling
Decision Under Risk
Decision Under Risk occurs in situations where
the decision maker can arrive at a probability estimate
for the occurrence for each of the various states of
nature.
Decision Analysis Payoff Table
State of Nature
Decision
1
2
3
m
d1
d2
d3
dn
r11 = 50 Lt
r21
r31
rn1
r12= 70 Lt
r22
r32
rn2
r13= 125 Lt
r23
r33
rn3
r1m = 30 Lt
r2m
r3m
rnm
Probabilities of States of Nature (SON)
P1 = .2 P2 = .45 P3 = .05 Pm = .3
R1 = .2(r11) + .45(r12) + .05(r13) + .3(r1m) = Expected Value
56.75Lt = .2(50) + .45(70) + .05(125) + .3(30)
Introduction to Modeling
Decision Under Risk
Risky
High
Safe
Risky
Start
Middle
Safe
Risky
Low
Safe
Assign probabilities at these points
24 possibilities after
only one three-way
and 3 two-way
decisions
Introduction to Modeling
Monte Carlo Simulation
Experience
Pros
Cons
• Great teacher
• Expensive
• Many situations
• Deal with the unexpected
•Thorough understanding of
processes
• Broader knowledge
• Not always practical
• Time consuming
• Impossible for all situations
• Can be complex
Introduction to Modeling
Monte Carlo Simulation
Simulation
Experience
Provides
“Virtual
Experience”
Pros
Cons
• Great teacher
•Expensive
• Many situations
• Deal with the unexpected
•Thorough understanding of
processes
• Broader knowledge
•Not always practical
•Time consuming
•Impossible for all situations
•Can be complex
•Expensive
• Cheap
•Not always practical
•Time consuming
•Impossible for all situations
•Can be complex
• Flexible
• Fast
• Adaptable
• Simplifying
Introduction to Modeling
Monte Carlo Simulation
Key Points of Simulation Models
• Allow for interactivity and experimentation by the modeler
• Generates a range of possibilities from criteria given rather than optimizing the
goal
• Applicable to short run, temporary and specific behavior
Analytic (statistical) models predict average, or steady state, long run behavior
• Deals well with uncertainty
• Can deal with ‘complicating factors’ that make analytical modeling difficult or
impossible to estimate: uncertainty, risk, multiple locations, volatile sales
• Inexpensive, relatively simple process using software like Excel and
Crystal Ball
Introduction to Modeling
Monte Carlo Simulation
Monte Carlo Simulation - named for the roulette wheels of Monte Carlo
As in roulette, variable values are known with uncertainty
Unlike roulette, specific probability distributions define the range of outcomes
Crystal Ball - an application specializing in Monte Carlo simulation
Introduction to Modeling
Monte Carlo Simulation
Generating Random Variables
CRYSTAL BALL:
Normal Distribution
A1
• Generates random variables across
a distribution specified by the user
• Lets users select distributions from
a gallery or generate their own
• Generates a report containing all of
the model’s assumptions
2 .1 0
2 .5 5
3 .0 0
3 .4 5
3 .9 0
Assumption: A1
EXAMPLE:
Normal Distribution of random
variables having a mean value of
3.0 generated by the equation is X2
Normal distribution with parameters:
Mean
Standard Dev.
3.00
0.30
Selected range is from -Infinity to +Infinity
Mean value in simulation was 3.00
Introduction to Modeling
Monte Carlo Simulation
Generating Other Distributions
Uniform Distribution
Triangle Distribution
A1
0 .9 0
0 .9 5
1 .0 0
A1
1 .0 5
1 .1 0
0 .0 0
1 .5 0
Custom Distribution
3 .0 0
4 .5 0
6 .0 0
Lognormal Distribution
A1
A1
.2 3 1
.1 7 3
.1 1 5
.0 5 8
.0 0 0
2 .0 0
2 .5 0
3 .0 0
3 .5 0
4 .0 0
0 .7 4
0 .8 9
1 .0 4
1 .1 9
1 .3 4
Introduction to Modeling
Monte Carlo Simulation
The User
• Defines distribution assumptions
• Selects the number of trials
• Sets the forecast variables
Crystal Ball
• Repeats the simulation for the predetermined number of trials
• Calculates forecast values for each trial
• Reports the results
Monte Carlo Simulation Via Crystal Ball
1) Specify the model’s equation(s)
2) Define the variable distributions
3) Define the forecasts
4) Select number of trials
5) Run the Monte Carlo Simulation
6) Interpret the results
7) Make decisions
Introduction to Modeling
Monte Carlo Simulation
Distribution of Outcomes
Distribution of outcomes depends on the distributions chosen for
the assumption variables
Outcome Frequency Chart - Normal Distribution
Outcome Frequency Chart - Lognormal Distribution
Forecast: B1
Forecast: B1
10,000 Trials
85 Outliers 1,000 Trials
Frequency Chart
Frequency Chart
28 Outliers
.010
99
.021
21
.007
74.25
.016
15.75
.005
49.5
.011
10.5
.002
24.75
.005
5.25
.000
0
.000
0
5.00
7.50
10.00
12.50
15.00
0.00
1.25
2.50
3.75
5.00
Introduction to Modeling
Monte Carlo Simulation
Sensitivity Analysis and Risk
One of Crystal Ball’s best features: it can easily and quickly perform
sensitivity and risk analysis.
Forecast: B1
1,000 Trials
Frequency Chart
5 Outliers
.013
13
.010
9.75
.007
6.5
.003
3.25
.000
0
0.40
0.70
1.00
1.30
1.60
Goal: Determine the likelihood that, given the normal distribution used, the result
will equal at least 1.
Result: Drag the arrow to where the frequency chart equals 1 and the
probability will be calculated by Crystal Ball.
Introduction to Modeling
Monte Carlo Simulation
Sensitivity Analysis and Risk
Forecast: B1
1,000 Trials
Frequency Chart
5 Outliers
.013
13
.010
9.75
.007
6.5
.003
3.25
.000
0
0.40
0.70
1.00
1.30
1.60
Certainty is 53.60% from -Infinity to 1.00
Probability that the result will equal at least 1 is 53.60%
Introduction to Modeling
Expected
Sales
Decision Tree Analysis
Sales
Forecast
Consumer
Survey
High
Marketing Cost
122000
25000
50%
High Demand
65%
35%
Low Demand
175000
95000
105000
88000
Favorable
Results
67%
50%
15000
Low
Marketing Cost
High Demand
45%
55%
Low Demand
125000
85000
88269
33%
Unfavorable
Results
High
Marketing Cost
62000
25000
65%
High Demand
55%
45%
Low Demand
105000
40000
35%
15000
Low
Marketing Cost
75%
Low Demand
Survey Results
Favorable
Unfavorable
67%
33%
Dollars
105000
54300
Favorable Survey Results
Percent
Dollars
Marketing Cost
High
50%
25000
Low
50%
15000
Demand - High Marketing Cost
High
65%
Low
35%
175000
95000
Demand - Low Marketing Cost
High
45%
Low
55%
125000
85000
Unfavorable Survey Results
Percent
Dollars
Marketing Cost
High
65%
25000
Low
35%
15000
65000
54300
High Demand
25%
Data/Assumptions
Percent
Demand - High Marketing Cost
High
55%
Low
45%
105000
65000
Demand - Low Marketing Cost
High
25%
Low
75%
85000
45000
85000
45000
Introduction to Modeling
Expected
Sales
Monte Carlo Simulation
Sales
Forecast
Consumer
Survey
High
Marketing Cost
122000
25000
50%
High Demand
65%
35%
Low Demand
175000
95000
105000
88000
Favorable
Results
67%
50%
15000
Low
Marketing Cost
High Demand
45%
55%
Low Demand
125000
85000
88269
33%
Unfavorable
Results
High
Marketing Cost
62000
25000
65%
High Demand
55%
45%
Low Demand
105000
40000
35%
15000
Low
Marketing Cost
75%
Low Demand
Survey Results
Favorable
Unfavorable
67%
33%
105000
54300
Favorable Survey Results
Percent
Dollars
Marketing Cost
High
50%
25000
Low
50%
15000
Demand - High Marketing Cost
High
65%
Low
35%
175000
95000
Demand - Low Marketing Cost
High
45%
Low
55%
125000
85000
Unfavorable Survey Results
Percent
Dollars
Marketing Cost
High
65%
25000
Low
35%
15000
65000
54300
High Demand
25%
Data/Assumptions
Probability Sales - Dollars
Demand - High Marketing Cost
High
55%
Low
45%
105000
65000
Demand - Low Marketing Cost
High
25%
Low
75%
85000
45000
85000
45000