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© Yanbu University College
YANBU UNIVERSITY COLLEGEWomen’s Campus
© Yanbu University College
Introduction to Quantitative Analysis
Chapter 1Ms.Atiya Masood
© Yanbu University College
Learning Objectives
Students will be able to:1. Describe the quantitative analysis
(QA) approach.2. Understand the application of QA in
a real situation.3. Describe the use of modeling in QA.4. Discuss possible problems in using
quantitative analysis.5. Perform a break-even analysis.
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Chapter Outline
1.1 Introduction1.2 What Is Quantitative Analysis (QA)?1.3 The QA Approach1.4 How to Develop a QA Model
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Introduction
Mathematical tools have been used for thousands of years.
QA can be applied to a wide variety of problems.
One must understand the specific applicability of the technique, its limitations, and its assumptions.
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Examples of Quantitative AnalysesTaco Bell saved over $150 million using
forecasting and scheduling QA models.
NBC increased revenues by over $200 million by using QA to develop better sales plans.
Continental Airlines saved over $40 million using QA models to quickly recover from weather and other disruptions.
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Quantitative Analysis:A scientific approach to managerial decision making whereby raw data are processed and manipulated resulting in meaningful information.
Raw Data
Quantitative
Analysis
MeaningfulInformatio
n
Overview of Quantitative Analysis
Qualitative Factors:Information that may be difficult to quantify but can affect the decision-making process such as the weather, state, and federal legislation.
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The QA Approach: Fig 1.1
Define the
problem
Develop a model
Acquire input data
Develop a
solution
Test the
solution
Analyze the
results
Implement the results
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Define the Problem
Problem Definition:A clear and concise statement that givesdirection and meaning to the subsequent QA stepsand requires specific, measurable objectives.
THIS MAY BE THE MOST DIFFICULT STEP!…because true problem causes must be identified and the relationship
of the problem to other organizational processes must be considered.
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Develop the Model
Quantitative Analysis Model:A realistic, solvable, and understandable
mathematical statement showing the relationship
between variables.
Models contain both controllable (decision variables) and uncontrollable variables and parameters. Typically, parameters are known quantities (salary of sales force) while variables are unknown (sales quantity).
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Develop the Model
• Models generally contain variables (controllable and uncontrollable) and parameters
• Controllable variables are generally the decision variables and are generally unknown
• Parameters are known quantities that are a part of the problem
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Acquire Data
Model Data:Accurate input data that may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement,or statistical sampling.
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Develop a Solution
Model Solution:The best model solution is found by manipulating the model variables until a practical and implemental solution is obtained.
Manipulation can be done by solving the equation(s), trying various approaches (trial and error), trying all possible variables (complete enumeration), and/or implementing an algorithm (repeating a series of steps).
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Test the SolutionModel Testing: The collection of data from a different source to validate the accuracy and completeness and sensibility of both the model and model input data ~ consistency of results is key!– New data can be collected to test the model– Results should be logical, consistent, and represent the real
situation
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Analyzing the Results
Determine the implications of the solution– Implementing results often requires change in
an organization– The impact of actions or changes needs to be
studied and understood before implementation
Sensitivity analysisSensitivity 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
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Implement the ResultsResults Implementation:The incorporation of the solutioninto the company and the monitoring ofthe results.
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How To Develop a Quantitative Analysis Model
Development is an important part of the quantitative analysis approach
Let’s look at a simple mathematical model of profit
Profit = Revenue – ExpensesProfit = Sx - f -Vxs: selling price per unitf: fixed costV: variable cost X: number or quantity of units sold
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Breakeven Example
• The company buys, sells, and repairs old clocks. Rebuilt springs sell for $10 per unit. Fixed cost of equipment to build springs is $1,000. Variable cost for spring material is $5 per unit.
• Calculate the profit when X is 1000?
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Bagels R Us QA Model Example
Profits = Revenue - Expenses
Profits = $1X - $100 - $.5X
Assume you are the new owner of Bagels R Us and you want to develop a mathematical model for yourdaily profits and breakeven point. Your fixed overhead is $100 per day and your variable costs are 0.50 per bagel (these are GREAT bagels). You charge $1 per bagel.
(Price per Unit) × (Number Sold)
- Fixed Cost - (Variable Cost/Unit) × (Number Sold)
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Bagels R Us QA Model Breakeven Example
Breakeven point occurs Breakeven point occurs when when Revenue = ExpensesRevenue = Expenses
Where, X= quantity of bagels sold F = fixed cost per day of operation V = variable cost/bagel
So, $1X= $100 + $.5X
Solve for X
$1X- .5X= 100 => X= 200
Breakeven Quantity = F/(P-V)Breakeven Quantity = F/(P-V)
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Question
• The company buys, sells, and repairs old TV. Rebuilt Winter sell for $100 per unit. Fixed cost of equipment to build springs is $1,000. Variable cost for spring material is $50 per unit.
• A) develop a model of profit and BEP• B) If X= 100, profits
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Summary
• Quantitative analysis is a scientific approach to decision making
• The approach includes – Defining the problem– Acquiring input data– Developing a solution– Testing the solution– Analyzing the results– Implementing the results
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Question time
Accuracy of the output is determined by the accuracy of the __________ and the __________.
•model, input data •result data, software used test• graph judgment, intuition
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Question time
• __________ determines how the solutions will change with a different model or different input data
• Testing • Variation analysis • Sensitivity analysis
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Question time
• Quantitative analysis uses a(n) __________ approach to decision making.
• qualitative • Scientific • common sense • judgmental
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THE ENDQ & A