MODELING and ANALYSIS

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MODELING and ANALYSIS

• Model Variables
• Static vs. Dynamic (time)
• Deterministic vs. Stochastic (uncertainty)
• Influence Diagrams
• Spreadsheet Modeling
• Decision Analysis
• Optimization
• Simulation

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MODEL STRUCTURE
Independent Variables
Dependent Variables
Mathematical Relationships
Decision Variables
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EXAMPLE REGRESSION MODEL STRUCTURE

• Independent variables variables that come from
  outside the system and cannot be controlled
  (exogenous)
• Dependent variables Variables whose values
  depend on independent variables (decision
  variables)
• Mathematical relationships

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EXAMPLE REGRESSION MODEL STRUCTURE
Independent Variables POP INCOME
Dependent Variable SALES

• Decision Variables
• N/A

Math Relationship SALESt 3.45 .496POPt
.0092INCOMEt
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EXAMPLE OPTIMIZATION MODEL STRUCTURE

• PRODUCT MIX
• Given unit labor cost, unit production time, and
  unit profit, how many units of two products, WS-1
  and WS-2, should be manufactured in order to
  maximize the profit subject to labor and budget
  constraints?

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EXAMPLE OPTIMIZATION MODEL STRUCTURE
Constraints 300X1 500X2 lt 200,000 10,000X1
15,000X2 lt 8,000,000 X1, X2 gt 0
Dependent Variable Total Profit 8000X1
12000X2
Objective Function MAX(Total Profit) subject to
constraints

• Decision Variables
• X1 units of WS-1
• X2 units of WS-2

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STATIC VS. DYNAMIC MODELS

• A dynamic model has the time dimension explicitly
  included whereas a static model is a snapshot.
• Examples
• Regression example?
• Optimization example?
• Dynamic models tend to be considerably more
  complex in general.

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DETERMINISTIC VS. STOCHASTIC MODELS

• Deterministic models are not probabilistic, i.e.,
  every value is a point estimate with the
  assumption that the value is known with 100
  certainty.
• Stochastic models are probabilistic, wherein one
  or more values of a variable are pulled from a
  distribution.

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EXAMPLE FINANCIAL PLANNING PROBLEM

• Problem Whats going to happen to my profit
  margin over the next 4 years? Assumptions
• Initial sales volume of 1.3 million units
• Sales volume increase of 15 per year
• Unit production cost of 0.19
• Initial unit price of 0.32
• Price increase of 5 per year
• Costs will rise with inflation estimated at 4
  per year
• Overhead expenses of 42,000 also rising with
  inflation

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FINANCIAL PLANNING MODEL (DETERMINISTIC)

• SALES GROWTH RATE .15
• PRICE INCREASE RATE .05
• INFLATION RATE .08
• INITIAL PRICE .32
• SALES 130000, PREVIOUS SALES GROWTH RATE
• UNIT COST .19, PREVIOUS INFLATION RATE
• UNIT PRICE INITIAL PRICE, PREVIOUS PRICE
  INCREASE RATE
• REVENUES SALES UNIT PRICE
• COSTS SALES UNIT COST
• OVERHEAD 42000, PREVIOUS INFLATION RATE
• TOTAL EXPENSES COSTS OVERHEAD
• PROFIT BEFORE TAX REVENUES TOTAL EXPENSES
• PROFIT MARGIN PROFIT BEFORE TAX / REVENUES

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FINANCIAL PLANNING MODEL(DETERMINISTIC)
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FINANCIAL PLANNING MODEL(DETERMINISTIC) GOAL
SEEKING

• What Price Increase Schedule would we have to
  achieve to maintain this 2001s profit margin?
• Set Profit margin cells to desired value(s)
• Specify cell(s) to change (Price Increase Rate)
• Back calculate

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FINANCIAL PLANNING MODEL(STOCHASTIC) RISK
ANALYSIS

• Remove assumption that we know values with
  certainty
• Lets now assume that inflation rate is a random
  variable ranging from 8 to 10 likelihood with
  any value in this range possible in any year.
• 1.08
  1.10

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FINANCIAL PLANNING MODEL(STOCHASTIC) RISK
ANALYSIS

• SALES GROWTH RATE .15
• PRICE INCREASE RATE .05
• INFLATION RATE UNIRAND(.08, .10)
• INITIAL PRICE .32
• SALES 130000, PREVIOUS SALES GROWTH RATE
• UNIT COST .19, PREVIOUS INFLATION RATE
• UNIT PRICE INITIAL PRICE, PREVIOUS PRICE
  INCREASE RATE
• REVENUES SALES UNIT PRICE
• COSTS SALES UNIT COST
• OVERHEAD 42000, PREVIOUS INFLATION RATE
• TOTAL EXPENSES COSTS OVERHEAD
• PROFIT BEFORE TAX REVENUES TOTAL EXPENSES
• PROFIT MARGIN PROFIT BEFORE TAX / REVENUES

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FINANCIAL PLANNING MODEL(STOCHASTIC) RISK
ANALYSIS
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INFLUENCE DIAGRAMS

• A graphical way of understanding the structure of
  a model (either quantitative or qualitative) by
  tracing the causal effects between any pair of
  variables in the model
• Example
• Rectangle Decision Variable
• Circle Independent Variable
• Oval Dependent Variable
• designates Random variable
• Straight Arrows designate certainty
• Curly Arrows designate uncertainty
• Directionality implies effect

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INFLUENCE DIAGRAMS

• Example 1
• Profit Income Expenses
• Income Units Sold Unit Price
• Units Sold 0.5 Advertisement Expense
• Advertisement Expense UNIRAND(100K, 150K)
• Expenses Unit Cost Units Sold Fixed Cost

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INFLUENCE DIAGRAMSQUANTITATIVE MODEL
Fixed Cost
Expenses
Unit Cost

• Profit

Advertisement Expense
Units Sold
Income
Unit Price
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ANALYTICA PRODUCT FROM LUMINA, Inc.

• www.lumina.com

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INFLUENCE DIAGRAMSQUALITATIVE MODEL
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SIMULATION

• Imitation vs. Modeling
• Descriptive vs. Normative
• Complex and/or Stochastic applications

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ADVANTAGES/DISADVANTAGES OF SIMULATION

• ADVANTAGES
• Time compression
• Avoid costly real world testing (e.g., combat
  simulation, new products)
• Descriptive vs. normative gt what if
• DISADVANTAGES
• Optimum usually unattainable
• High setup costs
• Low reusability
• Special languages gt higher development costs

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TYPES OF SIMULATION

• Discrete event simulation
• Continuous simulation
• Animated simulation
• Agent-based simulation
• Multiple player business war games
• Single player games (e.g., SimCity)