Quantitative Analysis...Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Introduction to...
Transcript of Quantitative Analysis...Quantitative Analysis Dr. Abdallah Abdallah Fall Term 2014 1 Introduction to...
Quantitative Analysis
Dr. Abdallah Abdallah
Fall Term 2014
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Introduction to quantitative analysis
Ch. 1
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What‘s quantitative analysis?
QA-approach
Application of the scientific method to managerial decision making
Typically via mathematical laws
Basic procedure
Developing models and testing them
Considering both quantitative and qualitative factors
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-Develop a clear statement of the problem is the most important step -Develop specific measurable objectives
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-A model is a representation of reality -Mathematical models are relevant for QA, i.e., set of mathematical relationships -Basic terminology: variable=measurable entity that may vary (controllable vs. uncontrollable variables) parameter=measurable entity given by the problem -suitable input data should be available!
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-garbage in, garbage out! -make use of statistical sampling procedures
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-via solving equations, per trial and error, or through complete enumeration of solutions -accuracy of the solution is determined by the input data and by the model
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-before analyzing and implementing the results! -testing includes: a. Testing accuracy and
completeness of data b. Testing the model‘s internal
validity
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-sensitivity analysis, determining how different parameters and/ or data will change the solution
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The QA-approach Defining the
problem
Developing a model
Aquiring input data
Developing a solution
Testing the solution
Analyzing the results
Implementing the results
-it is not straithforward to implement the obtained solution into an organization -implementation should be closely monitored
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Example
Developing a profit model and calculate the break even point
Profit=revenues-expenses
=revenues-(fixed costs+variable costs)
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Basic terminology
QA: scientific approach using quantitative techniques as a tool in decision making
Model: representation of reality
Mathematical model: set of mathematical relations
Algorithm: set of logical and mathematical operations performed in a specific sequence
Deterministic model: a model in which all value used are known with certainty
Probabilistic (or stochastic) model: all values used involve some chance or risk (probability)
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Basic terminology
Variable vs. Parameter
Sensitivity analysis: a process involving the determination of how sensitive a solution is to changes in the formulation of the problem
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The Pies are then processed and sold to local grocery stores in order to generate a profit.
Example 1: Simon Pie
Two ingredients combine to make Apple Pies: Fruit and frozen dough
performance measure variable
Profit Start here:
Decompose this variable into the intermediate variables Revenue and Total Cost
Profit
Revenue Total Cost
Now, further decompose each of these intermediate variables into more related intermediate variables ...
Profit
Revenue Total Cost
Pies Demanded
Pie Price Unit Pie
Processing Cost Fixed Cost
Processing
Cost
Ingredient
Cost
Unit Cost
Filling
Unit Cost
Dough
Required
Ingredient
Quantities
Step 3: Model Construction
Based on the previous Influence Diagram, create the equations relating the variables to be specified in the spreadsheet.
Profit
Revenue Total Cost
Profit = Revenue – Total Cost
Profit
Revenue
Pie Price
Pies Demanded
Revenue = Pie Price * Pies Demanded
Fixed Cost
Processing
Cost
Ingredient
Cost
Profit
Total Cost
Total Cost =
Processing Cost + Ingredients Cost + Fixed Cost
Processing Cost =
Pies Demanded *
Unit Pie Processing Cost
Processing
Cost
Total Cost
Pies Demanded
Unit Pie
Processing Cost
Profit
Ingredients Cost =
Qty Filling * Unit Cost Filling +
Qty Dough * Unit Cost Dough Ingredient
Cost
Profit
Total Cost
Unit Cost
Filling
Unit Cost
Dough
Required
Ingredient
Quantities
Simon’s Initial Model Input Values
Pie Price
Pies Demanded and sold
Unit Pie Processing Cost ($ per pie)
Unit Cost, Fruit Filling ($ per pie)
Unit Cost, Dough ($ per pie)
Fixed Cost ($000’s per week)
$8.00
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$2.05
$3.48
$0.30
$12
Initial Simon Pie Weekly Profit Model
“What if?” Projection Allows you to determine what would happen if you used alternative inputs.
For example, what would the resulting Profit be if the Profit for Pie Price and Pies Demanded changed to $7.00 and 20,000 or $9.00 and 12,000, respectively.
Simply change the values of these parameters in the spreadsheet to view the resulting Profit.
What if we change the values of two parameters?
What effect will that have on Total Cost and Profit?
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Home work Problems 1 - 18 1 – 19 1 – 20 1 – 21