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**© 2008 Prentice-Hall,
Inc.**

*Chapter 1*

**To accompany
**

**Power Point slides
created by Jeff Heyl**

*Introduction to
Quantitative Analysis*

**© 2009 Prentice-Hall,
Inc. **

**© 2009 Prentice-Hall,
Inc. 1 – 2 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 3 **

*Need for Operations
Management*

**The increased complexity of running a successful business.****Many large companies with complex business processes have used OM for years to help executives and managers make good strategic and operational decisions.****American Airlines and IBM have incredibly complex operations in logistics, customer service and resource allocation that are built on OM technologies.****As the trend of increased business complexity moves to smaller enterprises, OM will play vital operational and strategic roles.**

**© 2009 Prentice-Hall,
Inc. 1 – 4 **

*Need for OM*

**Lots of information, but no decisions.****Enterprise resource planning (ERP) systems and the Web have contributed to a pervasive information environment; decision-makers have total access to every piece of data in the organization.****The problem is that most people need a way to transform this wealth of data into actionable information that helps them make good tactical and strategic decisions.****The role of OM decision methods is to help leverage a company��s investment in information technology infrastructure by providing a way to convert data into actions.**

**© 2009 Prentice-Hall,
Inc. 1 – 5 **

*Need for OM*

**A large nationwide bank is using OM techniques to configure complicated financial instruments for their customers.****A process that previously required a human agent and took minutes or hours to perform is now executed automatically in seconds on the bank��s Intranet.****The resulting financial products are far superior to those produced by the manual process.**

**© 2009 Prentice-Hall,
Inc. 1 – 6 **

*Need for OM*

**A major retail enterprise is using OM methodology for making decisions about customer relationship management (CRM).****They are using mathematical optimization to achieve the most profitable match between a large number of customer segments, a huge variety of products and services, and an expanding number of marketing and sales channels such**

**© 2009 Prentice-Hall,
Inc. 1 – 7 **

*Need for OM*

**Sears, Roebuck and Company****Manages a U.S. fleet of more than 1,000 delivery vehicles, some company owned and some not.****The company makes more than 4 million deliveries a year of 21,000 uniquely different items.****It has 46 routing offices and provides the largest home delivery service of furniture and appliances in the United States.****The company also operates a U.S. fleet of 12,500 service vehicles, together with an associated staff of service technicians.****Service demand is on the order of 15 million calls per year and revenue generated is approximately $3 billion.**

**© 2009 Prentice-Hall,
Inc. 1 – 8 **

*Need for OM*

**OM researchers designed a system to deal with such variables as customer schedules and requested performance times, time estimates for the required service, vehicles and personnel available, skills needed, parts and product availability and so on.****The system was designed to automatically schedule all facets of performance in such a way as to****Provide accurate and convenient time windows for the Sears customer****Minimize costs****Maximize certain objective measures of task performance, including customer satisfaction.****This effort generated a one time cost reduction of $9 million as well as ongoing savings of $42 million per year.**

**© 2009 Prentice-Hall,
Inc. 1 – 9 **

*Examples of Quantitative
Analyses*

**Taco Bell saved over $150 million using forecasting and scheduling quantitative analysis models****NBC television increased revenues by over $200 million by using quantitative analysis to develop better sales plans****Continental Airlines saved over $40 million using quantitative analysis models to quickly recover from weather delays and other disruptions**

**© 2009 Prentice-Hall,
Inc. 1 – 10 **

**Meaningful**

**Information**

**Quantitative**

**Analysis**

*Quantitative analysis*** is a scientific approach to managerial decision
making whereby raw data are processed and manipulated resulting in meaningful
information**

**Raw Data**

* What is Quantitative
Analysis?*

**© 2009 Prentice-Hall,
Inc. 1 – 11 **

*Quantitative factors*** might be different investment alternatives,
interest rates, inventory levels, demand, or labor cost**

*Qualitative factors ***such as the weather, state and federal legislation,
and technology breakthroughs should also be considered**

**Information may be difficult to quantify but can affect the decision-making process**

* What is Quantitative
Analysis?*

**© 2009 Prentice-Hall,
Inc. 1 – 12 **

**Implementing the Results**

**Analyzing the Results**

**Testing the Solution**

**Developing a Solution**

**Acquiring Input Data**

**Developing a Model**

*The Quantitative
Analysis Approach*

**Defining the Problem**

**Figure 1.1**

**© 2009 Prentice-Hall,
Inc. 1 – 13 **

*Defining the Problem*

**Need to develop a clear and concise
statement that gives direction and meaning to the following steps**

**This may be the most important and difficult step****It is essential to go beyond symptoms and identify true causes****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**

**© 2009 Prentice-Hall,
Inc. 1 – 14 **

*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* =
*b*_{0}** +
b**

**Schematic models**

**Scale models**

**© 2009 Prentice-Hall,
Inc. 1 – 15 **

*Developing a Model*

**Models generally contain variables (controllable and uncontrollable) and parameters****Controllable variables are generally the decision variables and are generally unknown****Parameters are known quantities that are a part of the problem**

**© 2009 Prentice-Hall,
Inc. 1 – 16 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 17 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 18 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 19 **

*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 of the analysis
will change if the model or input data changes**

**Sensitive models should be very thoroughly tested**

**© 2009 Prentice-Hall,
Inc. 1 – 20 **

*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 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**

**© 2009 Prentice-Hall,
Inc. 1 – 21 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 22 **

*How To Develop a
Quantitative Analysis Model*

**An important part of the quantitative analysis approach****Let��s look at a simple mathematical model of profit**

**Profit = Revenue – Expenses **

**© 2009 Prentice-Hall,
Inc. 1 – 23 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 24 **

*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 **

**The
decision variable of interest is **

**© 2009 Prentice-Hall,
Inc. 1 – 25 **

*Bagels ��R Us*

Profits = Revenue - Expenses

**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)

- Fixed Cost

- (Variable Cost/Unit) (Number Sold)

**© 2009 Prentice-Hall,
Inc. 1 – 26 **

*Breakeven Example*

**f=$100, s=$1, v=$.50**

**X=f/(s-v)**

**X=100/(1-.5)**

**X=200**

**At this point, Profits are 0**

** **

**© 2009 Prentice-Hall,
Inc. 1 – 27 **

*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 = ****–$1,000**

**If sales = 1,000, profits = [(10)(1,000)
– 1,000 – (5)(1,000)]**

**=
$4,000 **

**© 2009 Prentice-Hall,
Inc. 1 – 28 **

*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*

*X*** = **

*f*

*s*
– *v*

**BEP = **

*Fixed cost*

*(Selling price per
unit) – (Variable cost per unit)*

**© 2009 Prentice-Hall,
Inc. 1 – 29 **

*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*

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 30 **

*Examples*

**Selling price $1.50, cost/bagel $.80, fixed cost $250 Breakeven point?****Seeking a profit of $1,000, selling price $1.25, cost/bagel $.50, 100 sold/day. What is fixed cost?****What selling price is needed to achieve a profit of $750 with a fixed cost of $75 and variable cost of $.50**

**© 2009 Prentice-Hall,
Inc. 1 – 31 **

*Examples*

*Seeing a need for childcare in
her community, Sue decided to launch her own daycare service. Her service
needed to be affordable, so she decided to watch each child for $12
a day. After doing her homework, Sue came up with the following financial
information: *

**Selling
Price **(per child per day) **$12 **

**Operating Expenses **
(per month)

Insurance 400 + Rent 200 = Total OE $600

**Costs
of goods sold $4.00 per unit **

Meals 2 @ $1.50 (breakfast & lunch)

Snacks 2 @ $0.50

*How many children will she need
to watch on a monthly basis to breakeven?*

**© 2009 Prentice-Hall,
Inc. 1 – 32 **

*Examples*

Applying the formula, we have:

**$600/($12-$4) = 75**

**She has to have a total of 75 children
in her program over the month to breakeven.**

**If she is open only 20 days per month
then she needs **

**75/20=3.75 children per day on the
average.**

**Expenses per month $600 + 75*$4.00
= $900**

**Revenue per month 75*$12 = $900**

**© 2009 Prentice-Hall,
Inc. 1 – 33 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 34 **

*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****Mathematical models that involve risk, chance, or uncertainty are called***probabilistic***models****Values used in the model are estimates based on probabilities**

**© 2009 Prentice-Hall,
Inc. 1 – 35 **

*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**

**© 2009 Prentice-Hall,
Inc. 1 – 36 **

*Computers and Spreadsheet
Models*

**Excel QM��s Main Menu (2003)**

**Works automatically within Excel spreadsheets**

**Program 1.2A**

**© 2009 Prentice-Hall,
Inc. 1 – 37 **

*Computers and Spreadsheet
Models*

**Excel QM��s Main Menu (2007) **

**Program 1.2B**

**© 2009 Prentice-Hall,
Inc. 1 – 38 **

*Computers and Spreadsheet
Models*

**Excel QM for the Break-Even Problem**

**Program 1.3A**

**© 2009 Prentice-Hall,
Inc. 1 – 39 **

*Computers and Spreadsheet
Models*

**Excel QM Solution to the Break-Even
Problem**

**Program 1.3B**

**© 2009 Prentice-Hall,
Inc. 1 – 40 **

*Computers and Spreadsheet
Models*

**Using Goal Seek in the Break-Even
Problem**

**Program 1.4**

**© 2009 Prentice-Hall,
Inc. 1 – 41 **

*Computers and Spreadsheet
Models*

**Using Goal Seek in the Break-Even
Problem**

**Program 1.4**

**© 2009 Prentice-Hall,
Inc. 1 – 42 **

*Possible Problems
in the Quantitative Analysis Approach*

**Defining the problem**

**Problems are not easily identified****Conflicting viewpoints****Impact on other departments****Beginning assumptions****Solution outdated**

**Developing a model**

**Fitting the textbook models****Understanding the model**

**© 2009 Prentice-Hall,
Inc. 1 – 43 **

*Possible Problems
in the Quantitative Analysis Approach*

**Acquiring input data**

**Using accounting data****Validity of data**

**Developing a solution**

**Hard-to-understand mathematics****Only one answer is limiting**

**Testing the solution**

**Analyzing the results**

**© 2009 Prentice-Hall,
Inc. 1 – 44 **

*Implementation –
Not Just the Final Step*

**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**

**© 2009 Prentice-Hall,
Inc. 1 – 45 **

*Implementation –
Not Just the Final Step*

**Lack of commitment by quantitative
analysts**

**An 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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