ppt day 1
DESCRIPTION
pls help meTRANSCRIPT
Introduction to Quantitative AnalysisPREPARED BY MERGA
MEKURIA2013
*
Quantitative analysis is a scientific approach to managerial decision making whereby raw data are processed and manipulated resulting in meaningful information
What is Quantitative Analysis?
Meaningful
Information
Quantitative
Analysis
is more of an art than a science
Quantitative Analysis
concentrates on the quantitative facts or data associated with the problem
develops mathematical expressions/ models that describe the objectives, constraints, and other relationships that exist in the problem
© 2009 Prentice-Hall, Inc. 1 – *
Qualitative factors such as the
weather,
technology breakthroughs should also be considered
Information may be difficult to quantify but can affect the decision-making process
PREPARED BY MERGA MEKURIA2013
*
5 Steps of Decision Making; 7 steps of Problem Solving
Define the problem.
Evaluate the alternatives.
-------------------------------------------------------------------
Implementing the Results
Analyzing the Results
Testing the Solution
Developing a Solution
Acquiring Input Data
Developing a Model
Defining the Problem
Defining the Problem
Need to develop a clear and concise statement that gives direction and meaning to the following steps
This may be the most important and difficult step
It is essential to go beyond symptoms and identify true causes
May be necessary to concentrate on only a few of the problems – selecting the right problems is very important
Specific and measurable objectives may have to be developed
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Three forms of models are:
Iconic models - physical replicas (scalar representations) of real objects
Analog models - physical in form, but do not physically resemble the object being modeled
Mathematical models - represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses
© 2009 Prentice-Hall, Inc. 1 – *
Objective Function – a mathematical expression that describes the problem’s objective, such as maximizing profit or minimizing cost
Constraints – a set of restrictions or limitations, such as production capacities
Uncontrollable Inputs/Parameters – factors that are not under the control of the decision maker
*
Mathematical Models
Deterministic Model – if all parameters to the model are known and cannot vary
Stochastic (or Probabilistic) Model – if any parameter is uncertain and subject to variation
© 2009 Prentice-Hall, Inc. 1 – *
Formulation and Construction of the Mathematical Model
Solution
An important part of the quantitative analysis approach
Let’s look at a simple mathematical model of profit
Profit = Revenue – Expenses
© 2009 Prentice-Hall, Inc. 1 – *
How To Develop a Quantitative Analysis Model
Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units sold) – [Fixed cost + (Variable costs per unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
How To Develop a Quantitative Analysis Model
Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units sold) – [Fixed cost + (Variable costs per unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold
PREPARED BY MERGA MEKURIA2013
The parameters of this model are f, v, and s as these are the inputs inherent in the model
The decision variable of interest is X
© 2009 Prentice-Hall, Inc. 1 – *
Illustration; ABC Publishing plc
Profits = $1*Number Sold - $100 - $.50*Number Sold
Assume you are the new owner of ABC PLC and you want to develop a mathematical model for your daily profits and breakeven point. Your fixed overhead is $100 per day and your variable costs are 0.50 per unit (these are news papers). You charge $1 per unit.
(Price per Unit) (Number Sold)
Fixed Cost
*
X=f/(s-v)
X=100/(1-.5)
X=200
PREPARED BY MERGA MEKURIA2013
*
Models can help a decision maker formulate problems
Models can give us insight and information
Models can save time and money in decision making and problem solving
A model may be the only way to solve large or complex problems in a timely fashion
A model can be used to communicate problems and solutions to others
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Models Categorized by Risk
Mathematical models that do not involve risk are called deterministic models
We know all the values used in the model with complete certainty
Mathematical models that involve risk, chance, or uncertainty are called probabilistic models
Values used in the model are estimates based on probabilities
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
PREPARED BY MERGA MEKURIA2013
$ Advertising
$ Sales
Input data must be accurate – GIGO rule
Data may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling
PREPARED BY MERGA MEKURIA2013
Garbage In
Developing a Solution
The best (optimal) solution to a problem is found by manipulating the model variables until a solution is found that is practical and can be implemented
Common techniques are
Solving equations
Trial and error – trying various approaches and picking the best result
Complete enumeration – trying all possible values
Using an algorithm – a series of repeating steps to reach a solution
PREPARED BY MERGA MEKURIA2013
*
Testing the Solution
Both input data and the model should be tested for accuracy before analysis and implementation
New data can be collected to test the model
Results should be logical, consistent, and represent the real situation
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Implementing results often requires change in an organization
The impact of actions or changes needs to be studied and understood before implementation
Sensitivity analysis determines how much the results of the analysis will change if the model or input data changes
Sensitive models should be very thoroughly tested
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Implementation can be very difficult
People can resist changes
Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented
Changes occur over time, so even successful implementations must be monitored to determine if modifications are necessary
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
*
Quantitative analysis is a scientific approach to managerial decision making whereby raw data are processed and manipulated resulting in meaningful information
What is Quantitative Analysis?
Meaningful
Information
Quantitative
Analysis
is more of an art than a science
Quantitative Analysis
concentrates on the quantitative facts or data associated with the problem
develops mathematical expressions/ models that describe the objectives, constraints, and other relationships that exist in the problem
© 2009 Prentice-Hall, Inc. 1 – *
Qualitative factors such as the
weather,
technology breakthroughs should also be considered
Information may be difficult to quantify but can affect the decision-making process
PREPARED BY MERGA MEKURIA2013
*
5 Steps of Decision Making; 7 steps of Problem Solving
Define the problem.
Evaluate the alternatives.
-------------------------------------------------------------------
Implementing the Results
Analyzing the Results
Testing the Solution
Developing a Solution
Acquiring Input Data
Developing a Model
Defining the Problem
Defining the Problem
Need to develop a clear and concise statement that gives direction and meaning to the following steps
This may be the most important and difficult step
It is essential to go beyond symptoms and identify true causes
May be necessary to concentrate on only a few of the problems – selecting the right problems is very important
Specific and measurable objectives may have to be developed
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Three forms of models are:
Iconic models - physical replicas (scalar representations) of real objects
Analog models - physical in form, but do not physically resemble the object being modeled
Mathematical models - represent real world problems through a system of mathematical formulas and expressions based on key assumptions, estimates, or statistical analyses
© 2009 Prentice-Hall, Inc. 1 – *
Objective Function – a mathematical expression that describes the problem’s objective, such as maximizing profit or minimizing cost
Constraints – a set of restrictions or limitations, such as production capacities
Uncontrollable Inputs/Parameters – factors that are not under the control of the decision maker
*
Mathematical Models
Deterministic Model – if all parameters to the model are known and cannot vary
Stochastic (or Probabilistic) Model – if any parameter is uncertain and subject to variation
© 2009 Prentice-Hall, Inc. 1 – *
Formulation and Construction of the Mathematical Model
Solution
An important part of the quantitative analysis approach
Let’s look at a simple mathematical model of profit
Profit = Revenue – Expenses
© 2009 Prentice-Hall, Inc. 1 – *
How To Develop a Quantitative Analysis Model
Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units sold) – [Fixed cost + (Variable costs per unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
How To Develop a Quantitative Analysis Model
Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)
Profit = (Selling price per unit)(number of units sold) – [Fixed cost + (Variable costs per unit)(Number of units sold)]
Profit = sX – [f + vX]
Profit = sX – f – vX
s = selling price per unit v = variable cost per unit
f = fixed cost X = number of units sold
PREPARED BY MERGA MEKURIA2013
The parameters of this model are f, v, and s as these are the inputs inherent in the model
The decision variable of interest is X
© 2009 Prentice-Hall, Inc. 1 – *
Illustration; ABC Publishing plc
Profits = $1*Number Sold - $100 - $.50*Number Sold
Assume you are the new owner of ABC PLC and you want to develop a mathematical model for your daily profits and breakeven point. Your fixed overhead is $100 per day and your variable costs are 0.50 per unit (these are news papers). You charge $1 per unit.
(Price per Unit) (Number Sold)
Fixed Cost
*
X=f/(s-v)
X=100/(1-.5)
X=200
PREPARED BY MERGA MEKURIA2013
*
Models can help a decision maker formulate problems
Models can give us insight and information
Models can save time and money in decision making and problem solving
A model may be the only way to solve large or complex problems in a timely fashion
A model can be used to communicate problems and solutions to others
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Models Categorized by Risk
Mathematical models that do not involve risk are called deterministic models
We know all the values used in the model with complete certainty
Mathematical models that involve risk, chance, or uncertainty are called probabilistic models
Values used in the model are estimates based on probabilities
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
PREPARED BY MERGA MEKURIA2013
$ Advertising
$ Sales
Input data must be accurate – GIGO rule
Data may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling
PREPARED BY MERGA MEKURIA2013
Garbage In
Developing a Solution
The best (optimal) solution to a problem is found by manipulating the model variables until a solution is found that is practical and can be implemented
Common techniques are
Solving equations
Trial and error – trying various approaches and picking the best result
Complete enumeration – trying all possible values
Using an algorithm – a series of repeating steps to reach a solution
PREPARED BY MERGA MEKURIA2013
*
Testing the Solution
Both input data and the model should be tested for accuracy before analysis and implementation
New data can be collected to test the model
Results should be logical, consistent, and represent the real situation
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Implementing results often requires change in an organization
The impact of actions or changes needs to be studied and understood before implementation
Sensitivity analysis determines how much the results of the analysis will change if the model or input data changes
Sensitive models should be very thoroughly tested
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *
Implementation can be very difficult
People can resist changes
Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented
Changes occur over time, so even successful implementations must be monitored to determine if modifications are necessary
PREPARED BY MERGA MEKURIA2013
© 2009 Prentice-Hall, Inc. 1 – *