Chapter 1

Introduction to Quantitative AnalysisPrepared by Lee Revere and John Large

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Learning ObjectivesStudents will be able to:Describe the quantitative analysis (QA) approach.Understand the application of QA in a real situation.Describe the use of modeling in QA.Use computers and spreadsheet models to perform QA.Discuss possible problems in using quantitative analysis.Perform a break-even analysis.

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Chapter Outline1.1 Introduction1.2 What Is Quantitative Analysis (QA)?1.3 The QA Approach1.4 How to Develop a QA Model1.5 The Role of Computers and Spreadsheet Models in the QA Approach1.6 Possible Problems in the QA Approach1.7 Implementation - Not Just the Final Step

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IntroductionMathematical 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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Overview of Quantitative AnalysisQuantitative Analysis:A scientific approach to managerial decisionmaking whereby raw data are processed and manipulated resulting in meaningful information.Raw DataQuantitativeAnalysisMeaningfulInformationQualitative 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 1.1Define the problemDevelop a modelAcquire input dataDevelop a solutionTest the solutionAnalyze the resultsImplement the results

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Define the ProblemProblem 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 ModelQuantitative Analysis Model:A realistic, solvable, and understandable mathematical statement showing the relationshipbetween variables. salesrevenuesy = mx + bModels 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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Acquire DataModel 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.

Garbage InGarbage Out=

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Develop a SolutionModel 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!

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Analyze the ResultsResults Analysis:Understanding actions implied by thesolution and their implications, as well as conducting a sensitivity analysis (a change to input values or the model) to evaluate the impact of a change in model parameters.

Sensitivity analyses allow the what-ifs to be answered.

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

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Modeling in the Real WorldReal World Models can be:Complex,expensive, anddifficult to sell.

BUTReal world models are used in the realworld by real organizations to solvereal problems!

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Possible Pitfalls in Using ModelsPrior to developing and implementing models,managers should be aware of the potential pitfalls.Define the ProblemConflicting viewpointsDepartmental impactsAssumptionsDevelop a ModelFitting the modelUnderstanding the modelAcquire Input Data Availability of dataValidity of data

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Possible Pitfalls (Continued)Develop a SolutionComplex mathematicsSolutions become quickly outdatedTest the SolutionIdentifying appropriate test proceduresAnalyze the ResultsHolding all other conditions constantIdentifying cause and effectImplement the SolutionSelling the solution to others

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Bagels R Us QA Model ExampleProfits = Revenue - ExpensesProfits = $1Q - $100 - $.5QAssume 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 ExampleBreakeven point occurs when Revenue = ExpensesWhere, Q = quantity of bagels sold F = fixed cost per day of operation V = variable cost/bagelSo, $1Q = $100 + $.5Q

Solve for Q

$1Q - .5Q = 100 => Q = 200

Breakeven Quantity = F/(P-V)

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ConclusionsModels can help managers:Gain deeper insight into the nature of business relationships.Find better ways to assess values in such relationships; andSee a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions.

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Conclusions (continued)Models:Are less expensive and disruptive than experimenting with real world systems, but may be expensive to develop and test.Allow What if questions to be asked.Are built for management problems and encourage input, but may be misunderstood due to the mathematical complexity.Enforce consistency in approach.Require specific constraints and goals, but tend to downplay qualitative information.Help communicate problem solutions to others, but may oversimplify assumptions and variables.

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Models: The Up SideModels:accurately represent reality.help a decision maker understand the problem.save time and money in problem solving and decision making.help communicate problems and solutions to others.provide the only way to solve large or complex problems in a timely fashion.

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Models: The Down SideModels:may be expensive and time-consuming to develop and test.are often misused and misunderstood (and feared) because of their mathematical complexity.tend to downplay the role and value of nonquantifiable information.often have assumptions that oversimplify the variables of the real world.

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QM for Windows

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QM for Windows

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Excel QM

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Excel QMs Main Menu of Models

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Excel QMs Main Menu of Models continuedThe highlighted area shows forecasting models

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