introduction to modeling introduction management models simulate business activities and decisions...

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


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


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


• 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



Models

Physical Analog Symbolic

Non-decisionDecision

Symbolic

Decision


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


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


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


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.


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


•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


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


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


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


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


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


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


Forecast: B1

Outcome Frequency Chart - Lognormal Distribution


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


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


Forecast: B1


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


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

introduction to modeling introduction management models simulate business activities and decisions...

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