Chapter 1_ SP Introductionrsh_qam11_ch01 GE

8/12/2019 Chapter 1_ SP Introductionrsh_qam11_ch01 GE

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Ch ap ter 1

To accompanyQuant i ta tive Analys is for Management , Eleventh Edi t ion , Global Edi t ionby Render, Stair, and HannaPower Point slides created by Brian Peterson

In t ro du c t ion to

Quant i tat iv e A n alys is


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Copyright 2012 Pearson Education 1-2

L earn ing Ob ject iv es

1. Describe the quantitative analysis approach2. Understand the application of quantitative

analysis in a real situation3. Describe the use of modeling in quantitative

analysis4. Use computers and spreadsheet models to

perform quantitative analysis5. Discuss possible problems in using

quantitative analysis6. Perform a break-even analysis

After completing this chapter, students will be able to:


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Chapter Outl in e

1.1 Introduction1.2 What Is Quantitative Analysis?1.3 The Quantitative Analysis Approach

1.4 How to Develop a Quantitative AnalysisModel1.5 The Role of Computers and Spreadsheet

Models in the Quantitative AnalysisApproach

1.6 Possible Problems in the QuantitativeAnalysis Approach

1.7 Implementation Not Just the Final Step


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In t roduc t ion

Mathematical tools have been used forthousands of years.

Quantitative analysis can be applied toa wide variety of problems.Its not enough to just know themathematics of a technique.One must understand the specificapplicability of the technique, itslimitations, and its assumptions.


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Exam ples o f Quant i tat ive An alyses

In the mid 1990s, Taco Bell saved over $150million using forecasting and schedulingquantitative analysis models.

NBC television increased revenues by over$200 million between 1996 and 2000 by usingquantitative analysis to develop better salesplans.Continental Airlines saved over $40 million in2001 using quantitative analysis models toquickly recover from weather delays and otherdisruptions.


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MeaningfulInformation

QuantitativeAnalysis

Quant i ta t ive analys is is a scientific approachto managerial decision making in which rawdata are processed and manipulated toproduce meaningful information.

Wh at is Qu an t i tat ive A n alys is?

Raw Data


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Quant i ta t ive facto rs are data that can beaccurately calculated. Examples include:

Different investment alternativesInterest ratesInventory levelsDemandLabor cost

Quali tat ive factors are more difficult to

quantify but affect the decision process.Examples include:The weatherState and federal legislationTechnological breakthroughs.

Wh at is Qu an t i tat ive A n alys is?



Implementing the Results

Analyzing the Results

Testing the Solution

Developing a Solution

Acquiring Input Data

Developing a Model

The Quant i tat ive A nalys is A pp roach

Defining the Problem

Figure 1.1



Defin ing the Prob lem

Develop a clear and concise statement thatgives direction and meaning to subsequentsteps.

This may be the most important and difficultstep.It is essential to go beyond symptoms andidentify true causes.It may be necessary to concentrate on only afew of the problems selecting the rightproblems is very importantSpecific and measurable objectives may haveto be developed.


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Develop ing a Mo del

Quantitative analysis models are realistic,solvable, and understandable mathematicalrepresentations of a situation.

There are different types of models:

$ Advertising

$ S a

l e s

Schematicmodels

Scalemodels


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Develop ing a Mo del

Models generally contain variables(controllable and uncontrollable) andparameters.

Controllable variables are the decisionvariables and are generally unknown.

How many items should be ordered for inventory?Parameters are known quantities that are a

part of the model.What is the holding cost of the inventory?


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A cq uir ing Inp ut Data

Input data must be accurate GIGO rule:

Data may come from a variety of sources such ascompany reports, company documents, interviews,on-site direct measurement, or statistical sampling.

GarbageIn

ProcessGarbage

Out


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Develop ing a Solut io n

The best (optimal) solution to a problem isfound by manipulating the model variablesuntil a solution is found that is practicaland can be implemented.

Common techniques areSolv ing equations.Trial and erro r trying various approachesand picking the best result.Com plete enum erat ion trying all possiblevalues.Using an a lgor i thm a series of repeatingsteps to reach a solution.


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Test ing the Solu t ion

Both input data and the model should betested for accuracy before analysis andimplementation.

New data can be collected to test the model.Results should be logical, consistent, andrepresent the real situation.


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A naly zing the Resu l ts

Determine the implications of the solution:Implementing results often requires change inan organization.The impact of actions or changes needs to bestudied and understood beforeimplementation.

Sens i t ivi ty analys is determines how muchthe results will change if the model orinput data changes.

Sensitive models should be very thoroughlytested.


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Im plem ent ing the Resu l t s

Implementation incorporates the solutioninto the company.

Implementation can be very difficult.

People may be resistant to changes.Many quantitative analysis efforts have failedbecause a good, workable solution was notproperly implemented.

Changes occur over time, so evensuccessful implementations must bemonitored to determine if modifications arenecessary.


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Mod el ing in th e Real Wo rld

Quantitative analysis models are usedextensively by real organizations to solvereal problems.

In the real world, quantitative analysismodels can be complex, expensive, anddifficult to sell.Following the steps in the process is animportant component of success.


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How To Develop a Qu an t i tat iveA nalys i s Model

A mathematical model of profit:

Profit = Revenue Expenses


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Expenses can be represented as the sum of fixed andvariable costs. Variable costs are the product of unitcosts times the number of units.

Profit = Revenue (Fixed cost + Variable cost)Profit = (Selling price per unit)(number of units

sold) [Fixed cost + (Variable costs perunit)(Number of units sold)]

Profit = sX [f + vX ]

Profit = sX f vX

wheres = selling price per unit v = variable cost per unitf = fixed cost X = number of units sold


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Expenses can be represented as the sum of fixed andvariable costs and variable costs are the product ofunit 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 perunit)(Number of units sold)]

Profit = sX [f + vX ]

Profit = sX f vX

wheres = selling price per unit v = variable cost per unitf = fixed cost X = number of units sold

The parameters of this modelare f , v , and s as these are theinputs inherent in the model

The decis ion var iab le ofinterest is X


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Pritchetts Precious Time Pieces

Profits = sX f vX

The company buys, sells, and repairs old clocks.Rebuilt springs sell for $10 per unit. Fixed cost ofequipment to build springs is $1,000. Variable costfor spring material is $5 per unit.

s = 10 f = 1,000 v = 5Number of spring sets sold = X

If sales = 0, profits = - f = $1,000 .If sales = 1,000, profits = [(10)(1,000) 1,000 (5)(1,000)]

= $4,000


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0 = sX f vX, or 0 = ( s v )X f

Companies are often interested in the break-evenp o i n t (BEP). The BEP is the number of units soldthat will result in $0 profit.

Solving for X , we havef = (s v )X

X =

f

s v

BEP =Fixed co s t

(Sell ing pric e per unit) (Variable co st per u nit)


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0 = sX f vX, or 0 = ( s v )X f

Companies are often interested in their break-evenp o i n t (BEP). The BEP is the number of units soldthat will result in $0 profit.

Solving for X , we havef = (s v )X

X =

f

s v

BEP =Fixed co s t

(Sell ing pric e per unit) (Variable co st per u nit)

BEP for Pritchetts Precious Time Pieces

BEP = $1,000/($10 $5) = 200 units

Sales of less than 200 units of rebuilt springswill result in a loss.Sales of over 200 units of rebuilt springs will

result in a profit.


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A dv antages o f Mathem at ical Mod el ing

1. Models can accurately represent reality.2. Models can help a decision maker

formulate problems.3. Models can give us insight and information.4. Models can save time and money in

decision making and problem solving.5. A model may be the only way to solve large

or complex problems in a timely fashion.6. A model can be used to communicate

problems and solutions to others.


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Mod els Catego r ized b y Risk

Mathematical models that do not involverisk are called determinis t ic models.

All of the values used in the model areknown with complete certainty.

Mathematical models that involve risk,chance, or uncertainty are calledprobabi l i s t ic models.

Values used in the model are estimatesbased on probabilities.


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Com pu ters and Spreads heet Models

QM for WindowsAn easy to usedecision supportsystem for use in

POM and QMcoursesThis is the mainmenu ofquantitativemodels

Program 1.1


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Excel QMs Main Menu (2010) Works automatically within Excel spreadsheets

Program 1.2


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SelectingBreak-EvenAnalysis inExcel QM

Program 1.3A


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Break-EvenAnalysisin Excel

QM

Program 1.3B


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Using GoalSeek in theBreak-Even

Problem

Program 1.4


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Pos s ib le Prob lem s in theQuant i tat ive A nalys i s Ap pro ach

Defining the problemProblems may not be easily identified.There may be conflicting viewpointsThere may be an impact on otherdepartments.Beginning assumptions may lead to aparticular conclusion.The solution may be outdated.

Developing a modelManagers perception may not fit a textbookmodel.There is a trade-off between complexity andease of understanding.


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Pos s ib le Prob lem s in theQuant i tat ive A nalys i s Ap pro ach

Acquiring accurate input dataAccounting data may not be collected forquantitative problems.

The validity of the data may be suspect.Developing an appropriate solution

The mathematics may be hard to understand.

Having only one answer may be limiting.Testing the solution for validityAnalyzing the results in terms of the whole

organization


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Implementa t ion Not J u s t th e Final Step

There may be an institutional lack ofcommitment and resistance to change.

Management may fear the use of formalanalysis processes will reduce theirdecision-making power.Action-oriented managers may wantquick and dirty techniques. Management support and userinvolvement are important.


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Implementa t ion Not J u s t th e Final Step

There may be a lack of commitmentby quantitative analysts.

Analysts should be involved with theproblem and care about the solution.Analysts should work with users andtake their feelings into account.


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Chapter 1_ SP Introductionrsh_qam11_ch01 GE