� Traditionally business decisions have been based on subjective factors
� Though mathematical tools have been used for thousands of years, the formal study of it to make management decisions
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study of it to make management decisions began in twentieth century
� Quantitative analysis is based on numeric data analysis, modeling and mathematical calculations
� Quantitative analysis can be used to solve a wide variety of problems in business, government, health care, education, …
Introduction
� It’s not enough to just know how the mathematics of a technique (model) works
� One must understand the specific applicability of the technique (model), its limitations, and its assumptions
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limitations, and its assumptions� The terms management science,
operations management or research, and quantitative analysis are often interchangeable
What is Operations Management ?
� A set of activities that creates value in the form of goods and services by carefully managing the business operations to produce and distribute products and services efficiently and effectively
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services efficiently and effectively� Increase profit …� Reduce cost …
� One of three major functions ( marketing, finance, and operations ) of any organization and is integrally related to all the other business functions
What is Operations Management ?
�Operations Management (OM) is such a costly part of an organization�A large percentage of the revenue of
most firms is spent in the OM function
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most firms is spent in the OM function�OM provides a major opportunity for an
organization to improve its profitability and enhance its service to society
What is Operations Management ?
� Operations management involves using quantitative analysis methods to help people analyze complicated business processes and make good
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business processes and make good decisions
� These techniques are especially useful for helping understand and deal with business complexity and uncertainty
Examples of Quantitative Analyses
� Taco Bell saved over $150 million using demand forecasting and employee scheduling quantitative analysis models
� NBC television increased revenues by over
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� NBC television increased revenues by over $200 million by using quantitative analysis to develop better sales plans for advertisers
� Continental Airlines saved over $40 million using quantitative analysis models to quickly recover from weather delays and other disruptions
Quantitative analysis (QA)Quantitative analysis (QA) is a scientific approach to managerial decision making – no whim, emotions and guesswork. The heart of QA is the processing and manipulating of raw data into meaningful information
What is Quantitative Analysis?
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data into meaningful information
MeaningfulInformation
QuantitativeAnalysisRaw Data
Qualitative analysisQualitative analysis involves the investigation of factors in a decision-making problem that cannot be quantified
In solving real problems, both quantitative and qualitative factors must be considered
Quantitative factorsQuantitative factors might be different investment alternatives, interest rates, inventory levels, demand, or labor cost
What is Quantitative Analysis?
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inventory levels, demand, or labor costQualitative factorsQualitative factors such as the weather condition, state and federal legislation, the outcome of an election, technology breakthroughs, etc.
� may be difficult to quantify but can affect the decision-making process
� In most cases quantitative analysis will be an aid to the decision-making process.
� The results of quantitative analysis
What is Quantitative Analysis?
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� The results of quantitative analysis will be combined with other (qualitative) information in making the final decisions.
Acquiring Input Data
Developing a Model
The Quantitative Analysis Approach
Defining the Problem
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Implementing the Results
Analyzing the Results
Testing the Solution
Developing a Solution
Acquiring Input Data
Figure 1.1
1. Defining the Problem
The first step is to develop a clear and concise statement of the problem that gives direction and meaning to the subsequent steps
� This may be the most important and difficult step� It is essential to go beyond the symptoms of the
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� It is essential to go beyond the symptoms of the problem and identify true causes
� Several problems may exist. It is necessary to concentrate on only a few of the problems –selecting the right problems is very important
� If the problem is difficult to quantify, specific a nd measurable objectives may have to be developed (e.g. inadequate hospital health care delivery ����
raise # of beds, doctors, reduce waiting time …)
2. Developing a Model
Quantitative analysis models are realistic, solvable, and understandable mathematical representations of a situation
$ S
ales Mathematic
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There are other types of models
$ Advertising
$ S
ales
Schematic models
Scale models
Mathematic models
2. Developing a Model
� QA Models generally contain variables(controllable and uncontrollable) and parameters
� Variables are measurable quantities that
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� Variables are measurable quantities that are subject to change and are generally unknown (e.g. $ sales, $ advertising)
� Controllable variables are generally the decision variables (e.g. $ advertising)
� Parameters are known quantities that are a part of the problem (e.g. cost per second rate for the ads)
3. Acquiring Input Data
Input data must be obtained for the model to make i t useful and they must be accurate – GIGO rule
Garbage In
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Data may come from a variety of sources such as company reports, company documents, interviews, on-site direct measurement, or statistical sampling
In
Process
Garbage Out
4. Developing a Solution
� The best (optimal) solution to a problem is found by manipulating the model until a solution is found that is practical and can be implemented
� Common techniques are
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Common techniques are�� SolvingSolving equations�� Trial and errorTrial and error – trying various approaches
and picking the best result�� Complete enumerationComplete enumeration – trying all possible
values� Using an algorithmalgorithm – a series of repeating
steps to reach a solution� The input data and model determine the
accuracy of the solution
5. Testing the Solution
Both input data and the model should be tested for accuracy before the solution can be analyzed and implemented
Collect additional data from a different
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� Collect additional data from a different source to validate the accuracy of both the model and model input data
� Results should be logical, consistent, and represent the real situation
6. Analyzing the Results
Determine the implications of the solution� Implementing results often requires actions
and changes in an organization� The impact of actions or changes needs to
be studied and understood before
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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
� A model is only an approximation of reality � Sensitive models should be very thoroughly
tested to ensure their accuracy and validity
7. Implementing the Results
Implementation incorporates the solution into the company
� Implementation can be very difficult� People can resist changes� Many quantitative analysis efforts have failed
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� 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
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
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models can be complex, expensive, and difficult to sell
� Following the steps of quantitative analysis is an important component of success, but not a guarantee
How To Develop a Quantitative Analysis Model
� Developing a model is an important part of the quantitative analysis approach
� Let’s look at a simple mathematical model of profit
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model of profit
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 o f unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)Profit = (Selling price per unit)(number of units
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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
wheres = selling price per unit v = variable cost per unitf = 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 o f unit costs times the number of units
Profit = Revenue – (Fixed cost + Variable cost)Profit = (Selling price per unit)(number of units
The parameters of this model are f, v, and s as these are the inputs inherent in the model
Profit and X are variables
The decision variable of
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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
wheres = selling price per unit v = variable cost per unitf = fixed cost X = number of units sold
The decision variable of interest is X
Pritchett’s Precious Time Pieces
The company buys, sells, and repairs old clocks and clock parts. 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
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Profits = sX – f – vX = 10X – 1000 – 5X
s = 10 f = 1,000 v = 5Number of spring sets sold = X
Companies are often interested in their breakbreak--even even pointpoint (BEP). The BEP is the number of units sold that will result in $0 profit.
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Solving for X, we havef = (s – v)X
X = f
s – v
BEP = Fixed cost
(Selling price per unit) – (Variable cost per unit)
Pritchett’s Precious Time Pieces
0 = sX – f – vX, or 0 = (s – v)X – f
Companies are often interested in their breakbreak--even even pointpoint (BEP). The BEP is the number of units sold that will result in $0 profit.BEP for Pritchett’s Precious Time Pieces
BEP = $1,000/($10 – $5) = 200 units
Sales of less than 200 units of rebuilt springs
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Solving for X, we havef = (s – v)X
X = f
s – v
BEP = Fixed cost
(Selling price per unit) – (Variable cost per unit)
Sales of less than 200 units of rebuilt springs will result in a lossSales of over 200 units of rebuilt springs will result in a profit
Bagels ‘R Us
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 da y and your variable costs are 0.50 per bagel (these are GREAT bagels). You charge $1 per bagel.
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Profits = $1*Number Sold– $100 – $.50*Number Sold
(Price per Unit) ×(Number Sold)
– Fixed Cost – (Variable Cost/Unit) ×
(Number Sold)
Profits = Revenue – Expenses
Bagels ‘R Us
f = $100, s = $1, v = $.50
BEP = f / (s – v)
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BEP = $100 / ($1 – $.50)
BEP = 200 units
When the number of units sold is equal to 200, the profit is 0.
Advantages of Mathematical Modeling
1. Models can accurately represent reality2. Models can help a decision maker
formulate problems3. Models can give us insight and information
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3. Models can give us insight and information4. Models can save time and money in
decision making and problem solving5. A model may be the only way to solve large
or complex problems in a timely fashion6. A model can be used to communicate
problems and solutions to others
Models Categorized by Risk
� Mathematical models that do not involve risk are called deterministic models� We know all the values used in the model with
complete certainty (the outcome is also certain)
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� E.g. – profit and break-even models
� Mathematical models that involve risk, chance, or uncertainty are called probabilistic models� Values used in the model are estimates based
on probabilities (the outcome is not certain)� E.g. – market for a new product:
good (60%), not good (40%)
� Developing a solution, testing the solution, and analyzing the results are important steps in quantitative analysis approach
� Since mathematical models are used, these steps require mathematical
Computers and Spreadsheet Models
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these steps require mathematical calculations.
� Two computer programs can be used to make these steps easier:1) QM for Windows2) Excel QM
Computers and Spreadsheet Models
QM for Windows� An easy to use
decision support system for use in POM and QM courses
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courses
� This is the main menu of quantitative models
Program 1.1
Computers and Spreadsheet Models
Excel QM’s Main Menu (2003)� Works automatically within Excel spreadsheets
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Program 1.2A
Computers and Spreadsheet Models
Excel QM’s Main Menu (2007)
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Program 1.2B
Computers and Spreadsheet Models
Excel QM for the Break-Even Problem
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Program 1.3A
Computers and Spreadsheet Models
Excel QM Solution to the Break-Even Problem
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Problem
Program 1.3B
Computers and Spreadsheet Models
Using Goal Seek in the Break-Even Problem
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Problem
Program 1.4
Possible Problems in the Quantitative Analysis Approach
(Inventory analysis example will be usedInventory analysis example will be used ) Defining the problem – problems are not
easily identified�Conflicting viewpoints – financial and
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�Conflicting viewpoints – financial and sales people have different view about the inventory
� Impact on other departments – inventory is tied with cash flows and production
�Beginning assumptions – problem implies solution, e.g. inventory is too low ?
�Solution outdated (the problem changed)
Possible Problems in the Quantitative Analysis Approach
Developing a model�Fitting the textbook models – they may
not fit a manager’s perception of a problem (e.g. reducing holding & ordering cost vs. cash flow & customer
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ordering cost vs. cash flow & customer satisfaction)
�Understanding the model – trade-off between the complexity and ease of understanding (e.g. assume the demand is known and constant, o.w. probability need to be used)
Possible Problems in the Quantitative Analysis Approach
Acquiring input data – not a simple task�Using accounting data – it may not
include holding & ordering costs�Validity of data – lack of “good & clean”
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�Validity of data – lack of “good & clean” data
Developing a solution�Hard-to-understand mathematics –
managers tend to remain silent instead of being critical
�Only one answer is limiting – no options
Possible Problems in the Quantitative Analysis Approach
Testing the solution�Complex models tend to give solutions
not so obvious to managers and tend to be rejected
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�A review process is necessary to convince the managers and correct any errors in the models
Analyzing the results�Even small changes in organization are
difficult to bring about
Implementation –Not Just the Final Step
Lack of commitment and resistance to change from management
� Management may fear the use of formal analysis processes will reduce their
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analysis processes will reduce their decision-making power or just feel uncomfortable about using them
� Action-oriented managers may want “quick and dirty” techniques
� Management support and user involvement are critical to the success (manager: 98%, user: 70%, QA: 40%)
Implementation –Not Just the Final Step
Lack of commitment by quantitative analysts
� Analysts should be involved with the problem and care about the solution
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problem and care about the solution – be an integral part of the department facing the problem
� Analysts should work with users and take their feelings into account (e.g. not insisting on the users to follow computer-calculated order quantities)
Summary
� Quantitative analysis is a scientific approach to decision making
� The approach includes�Defining the problem
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�Defining the problem�Developing a model�Acquiring input data�Developing a solution�Testing the solution�Analyzing the results� Implementing the results
Summary
� Potential problems include� Conflicting viewpoints� The impact on other departments� Beginning assumptions� Outdated solutions
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� Outdated solutions� Fitting textbook models� Understanding the model� Acquiring good input data� Hard-to-understand mathematics� Obtaining only one answer� Testing the solution� Analyzing the results
Summary
� Implementation is not the final step� Problems can occur because of
� Lack of commitment to the approach�Resistance to change
