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Chapter 1 Introduction to Quantitative Analysis To accompany Quantitative Analysis for Management ,  Tenth Edition ,   by Render, Stair, and Hanna   Power Point slides created by Jeff Heyl © 2009 Prentice-Hall, Inc.
Learning Objectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],After completing this chapter, students will be able to:
Chapter Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Introduction ,[object Object],[object Object],[object Object],[object Object]
Need for Operations Management ,[object Object],[object Object],[object Object],[object Object]
Need for OM ,[object Object],[object Object],[object Object],[object Object]
Need for OM ,[object Object],[object Object],[object Object]
Need for OM ,[object Object],[object Object]
Need for OM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Need for OM ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Examples of Quantitative Analyses ,[object Object],[object Object],[object Object]
[object Object],What is Quantitative Analysis? Meaningful Information Quantitative Analysis Raw Data
[object Object],[object Object],[object Object],What is Quantitative Analysis?
The Quantitative Analysis Approach Figure 1.1 Implementing the Results Analyzing the Results Testing the Solution Developing a Solution Acquiring Input Data Developing a Model Defining the Problem
Defining the Problem ,[object Object],[object Object],[object Object],[object Object],[object Object]
Developing a Model ,[object Object],There are different types of models $ Advertising $ Sales Y  =  b 0  +  b 1 X Schematic models Scale models
Developing a Model ,[object Object],[object Object],[object Object]
Acquiring Input Data ,[object Object],Data may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling Garbage In Process Garbage Out
Developing a Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Testing the Solution ,[object Object],[object Object],[object Object]
Analyzing the Results ,[object Object],[object Object],[object Object],[object Object],[object Object]
Implementing the Results ,[object Object],[object Object],[object Object],[object Object],[object Object]
Modeling in the Real World ,[object Object],[object Object],[object Object]
How To Develop a Quantitative Analysis Model ,[object Object],[object Object],Profit = Revenue – Expenses
How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit 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 per unit)(Number of units sold)] Profit = sX  – [ f   +   vX ] Profit = sX  –  f  –   vX where s  = selling price per unit v  = variable cost per unit f  = fixed cost X  = number of units sold
How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit 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 per unit)(Number of units sold)] Profit = sX  – [ f   +   vX ] Profit = sX  –  f  –   vX where s  = selling price per unit v  = variable cost per unit f  = fixed cost X  = number of units sold The  parameters  of this model are  f ,  v , and  s  as these are the inputs inherent in the model The  decision variable  of interest is  X
Bagels ‘R Us ,[object Object],Profits   =   $1*Number Sold  - $100 - $.50*Number Sold Assume you are the new owner of Bagels R Us and you want to develop a mathematical model for your daily 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)   ,[object Object]
Breakeven Example f=$100, s=$1,  v=$.50 X=f/(s-v) X=100/(1-.5) X=200 At this point, Profits are 0
Pritchett’s Precious Time Pieces ,[object Object],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. s  = 10 f  = 1,000 v  = 5 Number of spring sets sold =  X If sales = 0, profits =  – $1,000 If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)] = $4,000
Pritchett’s Precious Time Pieces ,[object Object],Companies are often interested in their  break-even point  (BEP). The BEP is the number of units sold that will result in $0 profit. Solving for  X , we have f  = ( s  –  v ) X X  =  f s  –  v BEP =  Fixed cost (Selling price per unit) – (Variable cost per unit)
Pritchett’s Precious Time Pieces ,[object Object],Companies are often interested in their  break-even point  (BEP). The BEP is the number of units sold that will result in $0 profit. Solving for  X , we have f  = ( s  –  v ) X X  =  f s  –  v BEP =  Fixed cost (Selling price per unit) – (Variable cost per unit) BEP for Pritchett’s Precious Time Pieces BEP = $1,000/($10  –  $5) = 200 units Sales of less than 200 units of rebuilt springs will result in a loss Sales of over 200 units of rebuilt springs will result in a profit
Advantages of Mathematical Modeling ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Models Categorized by Risk ,[object Object],[object Object],[object Object],[object Object]
Computers and Spreadsheet Models ,[object Object],[object Object],[object Object],Program 1.1
Computers and Spreadsheet Models ,[object Object],[object Object],Program 1.2A
Computers and Spreadsheet Models Excel QM’s Main Menu (2007)  Program 1.2B
Computers and Spreadsheet Models Excel QM for the Break-Even Problem Program 1.3A
Computers and Spreadsheet Models Excel QM Solution to the Break-Even Problem Program 1.3B
Computers and Spreadsheet Models Using Goal Seek in the Break-Even Problem Program 1.4
Possible Problems in the Quantitative Analysis Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Possible Problems in the Quantitative Analysis Approach ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Implementation –  Not Just the Final Step ,[object Object],[object Object],[object Object],[object Object]
Implementation –  Not Just the Final Step ,[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Summary ,[object Object],[object Object],[object Object],[object Object]

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Intro to Quantitative Analysis Modeling for Profits

  • 1. Chapter 1 Introduction to Quantitative Analysis To accompany Quantitative Analysis for Management , Tenth Edition , by Render, Stair, and Hanna Power Point slides created by Jeff Heyl © 2009 Prentice-Hall, Inc.
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  • 14. The Quantitative Analysis Approach Figure 1.1 Implementing the Results Analyzing the Results Testing the Solution Developing a Solution Acquiring Input Data Developing a Model Defining the Problem
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  • 25. How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit 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 per unit)(Number of units sold)] Profit = sX – [ f + vX ] Profit = sX – f – vX where s = selling price per unit v = variable cost per unit f = fixed cost X = number of units sold
  • 26. How To Develop a Quantitative Analysis Model Expenses can be represented as the sum of fixed and variable costs and variable costs are the product of unit 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 per unit)(Number of units sold)] Profit = sX – [ f + vX ] Profit = sX – f – vX where s = selling price per unit v = variable cost per unit f = fixed cost X = number of units sold The parameters of this model are f , v , and s as these are the inputs inherent in the model The decision variable of interest is X
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  • 28. Breakeven Example f=$100, s=$1, v=$.50 X=f/(s-v) X=100/(1-.5) X=200 At this point, Profits are 0
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  • 36. Computers and Spreadsheet Models Excel QM’s Main Menu (2007) Program 1.2B
  • 37. Computers and Spreadsheet Models Excel QM for the Break-Even Problem Program 1.3A
  • 38. Computers and Spreadsheet Models Excel QM Solution to the Break-Even Problem Program 1.3B
  • 39. Computers and Spreadsheet Models Using Goal Seek in the Break-Even Problem Program 1.4
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