Using the Internet, and your own personal experiences, share one example of each of the following:
- A deterministic model
- A probabilistic model
- A situation in which you could use post optimality analysis (also known as sensitivity analysis).
Chapter 1
To accompany
Quantitative Analysis for Management, Eleventh Edition, by Render, Stair, and Hanna
Power Point slides created by Brian Peterson
Introduction to Quantitative Analysis
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Deterministic and Probabilistic Models – STAT: Quantitative Methods
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Learning Objectives
Describe the quantitative analysis approach
Understand the application of quantitative analysis in a real situation
Describe the use of modeling in quantitative analysis
Use computers and spreadsheet models to perform quantitative analysis
Discuss possible problems in using quantitative analysis
Perform a break-even analysis
After completing this chapter, students will be able to:
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Chapter Outline
1.1 Introduction
1.2 What Is Quantitative Analysis?
1.3 The Quantitative Analysis Approach
1.4 How to Develop a Quantitative Analysis Model
1.5 The Role of Computers and Spreadsheet Models in the Quantitative Analysis Approach
1.6 Possible Problems in the Quantitative Analysis Approach
1.7 Implementation — Not Just the Final Step
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Introduction
Mathematical tools have been used for thousands of years.
Quantitative analysis can be applied to a wide variety of problems.
It’s not enough to just know the mathematics of a technique.
One must understand the specific applicability of the technique, its limitations, and its assumptions.
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Examples of Quantitative Analyses
In the mid 1990s, Taco Bell saved over $150 million using forecasting and scheduling quantitative analysis models.
NBC television increased revenues by over $200 million between 1996 and 2000 by using quantitative analysis to develop better sales plans.
Continental Airlines saved over $40 million in 2001 using quantitative analysis models to quickly recover from weather delays and other disruptions.
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Quantitative analysis is a scientific approach to managerial decision making in which raw data are processed and manipulated to produce meaningful information.
What is Quantitative Analysis?
Raw Data
Meaningful
Information
Quantitative
Analysis
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Quantitative factors are data that can be accurately calculated. Examples include:
Different investment alternatives
Interest rates
Inventory levels
Demand
Labor cost
Qualitative factors are more difficult to quantify but affect the decision process. Examples include:
The weather
State and federal legislation
Technological breakthroughs.
What is Quantitative Analysis?
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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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Defining the Problem
Develop a clear and concise statement that gives direction and meaning to subsequent steps.
This may be the most important and difficult step.
It is essential to go beyond symptoms and identify true causes.
It may be necessary to concentrate on only a few of the problems – selecting the right problems is very important
Specific and measurable objectives may have to be developed.
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Developing a Model
Quantitative analysis models are realistic, solvable, and understandable mathematical representations of a situation.
There are different types of models:
$ Advertising
$ Sales
Y = b0 + b1X
Scale models
Schematic models
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Developing a Model
Models generally contain variables (controllable and uncontrollable) and parameters.
Controllable variables are the decision variables 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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Acquiring Input Data
Input data must be accurate – GIGO rule:
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
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Developing a Solution
The best (optimal) solution to a problem is found by manipulating the model variables until a solution is found that is practical and can be implemented.
Common techniques are
Solving equations.
Trial and error – trying various approaches and picking the best result.
Complete enumeration – trying all possible values.
Using an algorithm – a series of repeating steps to reach a solution.
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Testing the Solution
Both input data and the model should be tested for accuracy before analysis and implementation.
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 analysis determines how much the results will change if the model or input data changes.
Sensitive models should be very thoroughly tested.
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Implementing the Results
Implementation incorporates the solution into the company.
Implementation can be very difficult.
People may be resistant to changes.
Many quantitative analysis efforts have failed because a good, workable solution was not properly implemented.
Changes occur over time, so even successful implementations must be monitored to determine if modifications are necessary.
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Modeling in the Real World
Quantitative analysis models are used extensively by real organizations to solve real problems.
In the real world, quantitative analysis models can be complex, expensive, and difficult to sell.
Following the steps in the process is an important component of success.
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How To Develop a Quantitative Analysis Model
A mathematical model of profit:
Profit = Revenue – Expenses
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How To Develop a Quantitative Analysis Model
Expenses can be represented as the sum of fixed and variable costs. 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
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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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Pritchett’s Precious Time Pieces
Profits = sX – f – vX
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 = -f = –$1,000.
If sales = 1,000, profits = [(10)(1,000) – 1,000 – (5)(1,000)]
= $4,000
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Pritchett’s Precious Time Pieces
0 = sX – f – vX, or 0 = (s – v)X – f
Companies are often interested in the 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
f
s – v
X =
Fixed cost
(Selling price per unit) – (Variable cost per unit)
BEP =
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Pritchett’s Precious Time Pieces
0 = sX – f – vX, or 0 = (s – v)X – f
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
f
s – v
X =
Fixed cost
(Selling price per unit) – (Variable cost per unit)
BEP =
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.
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Advantages of Mathematical Modeling
Models can accurately represent reality.
Models can help a decision maker formulate problems.
Models can give us insight and information.
Models can save time and money in decision making and problem solving.
A model may be the only way to solve large or complex problems in a timely fashion.
A model can be used to communicate problems and solutions to others.
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Models Categorized by Risk
Mathematical models that do not involve risk are called deterministic models.
All of the values used in the model are known with complete certainty.
Mathematical models that involve risk, chance, or uncertainty are called probabilistic models.
Values used in the model are estimates based on probabilities.
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Computers and Spreadsheet Models
QM for Windows
An easy to use decision support system for use in POM and QM courses
This is the main menu of quantitative models
Program 1.1
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Computers and Spreadsheet Models
Excel QM’s Main Menu (2010)
Works automatically within Excel spreadsheets
Program 1.2
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Computers and Spreadsheet Models
Selecting Break-Even Analysis in Excel QM
Program 1.3A
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Computers and Spreadsheet Models
Break-Even Analysis in Excel QM
Program 1.3B
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Computers and Spreadsheet Models
Using Goal Seek in the Break-Even Problem
Program 1.4
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Possible Problems in the Quantitative Analysis Approach
Defining the problem
Problems may not be easily identified.
There may be conflicting viewpoints
There may be an impact on other departments.
Beginning assumptions may lead to a particular conclusion.
The solution may be outdated.
Developing a model
Manager’s perception may not fit a textbook model.
There is a trade-off between complexity and ease of understanding.
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Possible Problems in the Quantitative Analysis Approach
Acquiring accurate input data
Accounting data may not be collected for quantitative 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 validity
Analyzing the results in terms of the whole organization
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Implementation –
Not Just the Final Step
There may be an institutional lack of commitment and resistance to change.
Management may fear the use of formal analysis processes will reduce their decision-making power.
Action-oriented managers may want “quick and dirty” techniques.
Management support and user involvement are important.
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Implementation –
Not Just the Final Step
There may be a lack of commitment by quantitative analysts.
Analysts should be involved with the problem and care about the solution.
Analysts should work with users and take their feelings into account.
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Copyright
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America.
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