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Introduction to Quantitative Analysis

Chapter 1Ms.Atiya Masood


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.


Chapter Outline

1.1 Introduction1.2 What Is Quantitative Analysis (QA)?1.3 The QA Approach1.4 How to Develop a QA Model


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.


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.


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.


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


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.


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).


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


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.


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).


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


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


Implement the ResultsResults Implementation:The incorporation of the solutioninto the company and the monitoring ofthe results.


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


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?


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)


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)


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


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


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


Question time

• __________ determines how the solutions will change with a different model or different input data

• Testing • Variation analysis • Sensitivity analysis


Question time

• Quantitative analysis uses a(n) __________ approach to decision making.

• qualitative • Scientific • common sense • judgmental

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