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Introduction to Modeling Introduction
Management Models • Simulate business activities and decisions • Feedback about and forecast of outcomes• Minimal risk or cost
Why Model?
Implementation
Introduction to Modeling The Modeling Process
The Managerial Approach to decision making
Management Situation
Decision Payoff
Should our baking company make cookies in addition to cakes?
Owner has been a baker for 50 yearsand thinks the cookies will sell:
“Taip!”
The company spends 50,000 litae on newmachinery and advertising.
The cookies sell well!But fewer cakes can be baked
Net profit falls
Relying solely on intuition is riskyNo feedback until the final outcome
Introduction to Modeling The Modeling Process
The Managerial Approach to decision makingUsing a Model!
Managerial judgment - intuition - essential aspect of process
Management Situation
Decisions
Symbolic World
Real World
ModelA
bstr
actio
n
Inte
rpre
tatio
n
ResultsAnalysis
Intuition
ManagerialJudgment
Implementation
Introduction to Modeling The Modeling Process
Decision Payoff
The Managerial Approach to decision makingUsing a Model!
Interpretation of model results
Intuition of Management situation
Introduction to Modeling Types of Models
Model Type Characteristics Examples
Physical Model
Analog Model
Symbolic Model
Tangible Comprehend: Easy Duplicate/Share: Difficult Modify/Manipulate: Difficult Range of uses: Lowest
Intangible Comprehend: Harder Duplicate/Share: Easier Modify/ Manipulate: Easier Range of uses: Wider
Intangible Comprehend: Hardest Duplicate/Share: Easiest Modify/ Manipulate: Easiest Range of uses: Widest
Model Airplane Model House Model City
Road Map Speedometer Pie Chart
Simulation Model Algebraic Model Spread Sheet Model
Introduction to Modeling Formulation
TheModel
Decisions(Controllable)
Parameters(Uncontrollable)
Performance Measure(s)
Consequence Variables
Ex
og
en
ou
s
Va
riab
les
En
do
ge
no
us
Va
riab
les
{{Black Box View of the Model
TheModel
TheModel
TheModel
TheModel
TheModel
Introduction to Modeling Decision Models
Deterministic Probabilistic
Models
Physical Analog Symbolic
Non-decisionDecision
Symbolic
Decision
Deterministic Probabilistic
• Assumed: all elements known with certainty• Highest value: few uncertain uncontrolled model inputs
• Assumed: Some elements not known with certainty• Incomplete knowledge: Uncertainty must be incorporated into the model
• Optimization
• Forecasting
• Monte Carlo Simulation
• Decision Trees
Introduction to Modeling Decision Models
Deterministic Probabilistic
Models
Physical Analog Symbolic
Non-decisionDecision
Symbolic
Decision
Deterministic Probabilistic
Introduction to Modeling Decision Analysis
Decision Theory
Decision Vs. Nature
Decision Analysis Payoff Table
State of Nature
Decision
r11
1
d1
The result (return) of one decision depends on another player’s (nature’s) action over which you have no control
Introduction to Modeling Decision Analysis
Decision Theory
Decision Vs. Nature
Decision Analysis Payoff Table
State of Nature
Decision 1
r11d1
2
d2
r12
r21 r22
r13
r31
3
d3
r23
r32 r33
r1m
rn1
m
dn
r2m
rn2
r3m
rn3 rnm
The result (return) of one decision depends on another player’s (nature’s) action over which you have no control
Introduction to Modeling Decision Models
Decision Model
A
B
C
The outcome of nature
•Decisions Under Certainty
•Decisions Under Risk
•Decisions Under Uncertainty
Three Classes of Decision Models
Introduction to Modeling Decision Under Certainty
Decision Under Certainty occurs in situations where you know which state of nature will occur.
1
Decision Analysis Payoff Table
State of Nature
Decision
r11d1
d2 r21
r31d3
rn1dn
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 ofnature.
Decision Analysis Payoff Table
State of Nature
Decision 1
r11 = 50 Ltd1
2
d2
r12= 70 Lt
r21 r22
r13= 125 Lt
r31
3
d3
r23
r32 r33
r1m = 30 Lt
rn1
m
dn
r2m
rn2
r3m
rn3 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
High
Middle
Low
Risky
Safe
Safe
Safe
Risky
Risky
Start
24 possibilities after only one three-way
and 3 two-waydecisions
Assign probabilities at these points
Introduction to Modeling Monte Carlo Simulation
• Great teacher• Many situations• Deal with the unexpected•Thorough understanding of processes• Broader knowledge
• Expensive• Not always practical• Time consuming• Impossible for all situations• Can be complex
ConsPros
Experience
Introduction to Modeling Monte Carlo Simulation
•Expensive•Not always practical•Time consuming•Impossible for all situations•Can be complex
ConsPros
Experience
More Pros
•Expensive•Not always practical•Time consuming•Impossible for all situations•Can be complex
• Cheap• Flexible• Fast• Adaptable• Simplifying
Simulation
Provides“VirtualExperience”
• Great teacher• Many situations• Deal with the unexpected•Thorough understanding of processes• Broader knowledge
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
Assumption: A1
Normal distribution with parameters:Mean 3.00Standard Dev. 0.30
Selected range is from -Infinity to +InfinityMean value in simulation was 3.00
2.10 2.55 3.00 3.45 3.90
A1
Normal Distribution
• 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
CRYSTAL BALL:
EXAMPLE: Normal Distribution of random variables having a mean value of 3.0 generated by the equation is X2
Introduction to Modeling Monte Carlo Simulation
Generating Other Distributions
0.00 1.50 3.00 4.50 6.00
A1Triangle Distribution
0.74 0.89 1.04 1.19 1.34
A1Lognormal Distribution
0.90 0.95 1.00 1.05 1.10
A1Uniform Distribution
.000
.058
.115
.173
.231
2.00 2.50 3.00 3.50 4.00
A1Custom Distribution
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 distributions3) Define the forecasts4) Select number of trials5) Run the Monte Carlo Simulation6) Interpret the results7) Make decisions
Introduction to Modeling Monte Carlo Simulation
Distribution of Outcomes
Distribution of outcomes depends on the distributions chosen for the assumption variables
Frequency Chart
.000
.002
.005
.007
.010
0
24.75
49.5
74.25
99
5.00 7.50 10.00 12.50 15.00
10,000 Trials 85 Outliers
Forecast: B1
Outcome Frequency Chart - Normal Distribution
Frequency Chart
.000
.005
.011
.016
.021
0
5.25
10.5
15.75
21
0.00 1.25 2.50 3.75 5.00
1,000 Trials 28 Outliers
Forecast: B1
Outcome Frequency Chart - Lognormal Distribution
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.
Frequency Chart
.000
.003
.007
.010
.013
0
3.25
6.5
9.75
13
0.40 0.70 1.00 1.30 1.60
1,000 Trials 5 Outliers
Forecast: B1
Goal: Determine the likelihood that, given the normal distribution used, the resultwill equal at least 1.Result: Drag the arrow to where the frequency chart equals 1 and the probability will be calculated by Crystal Ball.
Frequency Chart
Certainty is 53.60% from -Infinity to 1.00
.000
.003
.007
.010
.013
0
3.25
6.5
9.75
13
0.40 0.70 1.00 1.30 1.60
1,000 Trials 5 Outliers
Forecast: B1
Introduction to Modeling Monte Carlo Simulation
Sensitivity Analysis and Risk
Probability that the result will equal at least 1 is 53.60%
Introduction to Modeling Decision Tree Analysis
Expected Sales Data/AssumptionsSales Forecast Percent Dollars
High Demand Survey ResultsHigh 65% 175000 Favorable 67% 105000
Marketing Cost Unfavorable 33% 54300Consumer 122000 25000
Survey 50% 35% 95000 Favorable Survey ResultsLow Demand Percent Dollars
105000 Marketing CostHigh Demand High 50% 25000
50% 45% 125000 Low 50% 1500088000 15000
Favorable Low Demand - High Marketing CostResults Marketing Cost 55% 85000 High 65% 17500067% Low Demand Low 35% 95000
Demand - Low Marketing CostHigh 45% 125000
88269 Low 55% 85000
Unfavorable Survey ResultsHigh Demand Percent Dollars
33% High 55% 105000 Marketing CostUnfavorable Marketing Cost High 65% 25000
Results 62000 25000 Low 35% 1500065% 45% 65000
Low Demand Demand - High Marketing Cost54300 High 55% 105000
High Demand Low 45% 6500035% 25% 85000
40000 15000 Demand - Low Marketing CostLow High 25% 85000
Marketing Cost 75% 45000 Low 75% 45000Low Demand
Introduction to Modeling Monte Carlo Simulation
Expected Sales Data/AssumptionsSales Forecast Probability Sales - Dollars
High Demand Survey ResultsHigh 65% 175000 Favorable 67% 105000
Marketing Cost Unfavorable 33% 54300Consumer 122000 25000
Survey 50% 35% 95000 Favorable Survey ResultsLow Demand Percent Dollars
105000 Marketing CostHigh Demand High 50% 25000
50% 45% 125000 Low 50% 1500088000 15000
Favorable Low Demand - High Marketing CostResults Marketing Cost 55% 85000 High 65% 17500067% Low Demand Low 35% 95000
Demand - Low Marketing CostHigh 45% 125000
88269 Low 55% 85000
Unfavorable Survey ResultsHigh Demand Percent Dollars
33% High 55% 105000 Marketing CostUnfavorable Marketing Cost High 65% 25000
Results 62000 25000 Low 35% 1500065% 45% 65000
Low Demand Demand - High Marketing Cost54300 High 55% 105000
High Demand Low 45% 6500035% 25% 85000
40000 15000 Demand - Low Marketing CostLow High 25% 85000
Marketing Cost 75% 45000 Low 75% 45000Low Demand