Transcript Introduction to Data Analysis and Decision Making

Introduction to Data Analysis
and Decision Making
Data Analysis
• Describing data and datasets
• Making inferences from data and datasets
• Searching for relationships in data and
datasets
Decision Making
• Optimization
• Decision analysis with uncertainty
• Sensitivity Analysis
Uncertainty
• Measuring uncertainty
• Modeling and simulation
What is Management Science?
• Logical, systematic approach to decision
making using quantitative methods.
• Science Scientific methods used to
solve business related problems.
• Goal for this class: logically approach and
solve many different problems.
Management Science Approach
to Problem Solving
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Observation
Definition of the Problem
Constructing the Model
Solving the Model/problem
Implementation of Solution
(process is never really complete)
Observation
• Identify the problem
• Problem does not imply that there is
something wrong with the process
• “Problem” could imply need for
improvement
Definition of the Problem
• Clearly define problem
• Prevents incorrect/inappropriate solution
• Listing goals could be helpful
Constructing the Model
• Represents the problem in abstract form
• Schematic, scale, mathematical
relationship between variables (equation)
• Ex: Income = Hours Worked * Pay
Components of the Model
• Variable/Decision Variables
– Independent
– Dependent
• Objective Function
• Parameter
• Constraints
Model Solution
• Same as solving the problem:
• Ex:
Z = $20X – 5X
subject to
4X = 100
• Solution:
X=25 Z = $375
Implementation of Solution
• Solution aids us in making a decision but
does not constitute the actual decision
making.
Example
Blue Ridge Hot Tubs manufactures and sell hot tubs.
The company needs to decide how many hot tubs to
produce during the next production cycle. The company
buys prefabricated fiberglass hot tub shells from a local
supplier and adds pump and tubing to the shells to
create his hot tubs. The company has 200 pumps
available. Each hot tub requires 9 hours of labor. The
company expects to have 1,566 production labor hours
during the next production cycle. A profit of $350 will be
earned on each hot tub sold. The company is confident
that all of the hot tubs will sell. The question is, how
many should be produced if the company wants to
maximize profits during the next production cycle?
Msci Approach to Problem Solving
• Problem: Determine # of hot tubs to produce
• Definition: Maximize profit within the constraints
of the labor hours and materials available
• Model: Max Z = $350X
subject to
9X  1,566 labor hours
• Solution: X = 174; Z = 350(174) = $60,900
• Implementation: Recommend making 174 hot
tubs
A Generic Mathematical Model
Y = f(X1, X2, …, Xk)
Where:
Y = dependent variable (a bottom line performance measure)
Xi = independent variables (inputs having an impact on Y)
f(.) = function defining the relationship between the Xi and Y
Categories of Mathematical Models
Model
Category
Prescriptive
Predictive
Form of f(.)
Independent
Variables
OR/MS
Techniques
known,
well-defined
known or under
decision maker’s
control
LP, Networks, IP,
CPM, EOQ, NLP,
GP, MOLP
unknown,
ill-defined
known or under
decision maker’s
control
Regression Analysis,
Time Series Analysis,
Discriminant Analysis
unknown or
Queueing,
Simulation, PERT,
Descriptive
known,
well-defined uncertain
Inventory Models
Example – Spring Mills
• 280 observations
• Three variables per observation
• Relatively large dataset
Background Information
• Spring Mills produces and distributes a wide
variety of manufactured goods. It has a large
number of customers.
• Spring Mills classifies these customers as
small, medium, or large, depending on the
volume of business each does with them.
• Recently they have noticed a problem with
accounts receivable. They are not getting
paid by their customers in as timely a manner
as they would like. This obviously costs them
money.
RECEIVE.XLS
• Spring Mills has gathered data on 280
customer accounts.
• For each of these accounts the data set lists
three variables:
– Size - The size of the customer (coded 1 for
small, 2 for medium, 3 for large).
– Days - The number of days since the customer
was billed.
– Amount - The amount the customer owes.
• What information can we obtain from this
data?
Summary Measures for
Combined Data
Scatterplot: Amount vs Days
All Customers
Scatterplot: Amount vs Days
Small Customers
Scatterplot: Amount vs Days
Medium Customers
Scatterplot: Amount vs Days
Large Customers
Analysis -- continued
• There is obviously a lot going on here and it is
evident form the charts. We point out the following:
– there are considerably fewer large customers than
small or medium customers.
– the large customers tend to owe considerably
more than small or medium customers.
– the small customers do not tend to be as long
overdue as the large and medium customers.
– there is no relationship between Days and Amount
for the small customers, but there is a definite
positive relationship between these variables for
the medium and large customers.
Findings
• If Spring Mills really wants to decrease receivables, it
might want to target the medium-sized customer
group, from which it is losing the most interest.
• Or it could target the large customers because they
owe the most on average.
• The most appropriate action depends on the cost
and effectiveness of targeting any particular
customer group. However, the analysis presented
here gives the company a much better picture of
what’s currently going on.
Modeling and Models
• Graphical models
• Algebraic models
• Spreadsheet models
The Modeling Process
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Define the problem
Collect and summarize data
Formulate a model
Verify the model
Select one or more suitable decisions
Present the results to the organization
Implement the model and update through time
Describing Data:
The Basics
Descriptive vs Inferential
Statistics
• Descriptive statistics:
– The process of applying a method of analysis
to a set of data in order to better understand
the information contained within.
• Inferential statistics:
– Using a (sub)set of data (a sample) to predict
behavior of a larger set of data (the
population).
Population
• Definition:
– Set of existing units (usually people, objects,
transactions, or events); or
– Every element in a group that is the subject of
interest
– Depends upon the problem or situation
• Examples:
– College students, Honda Accords, cash sales
Population Parameters and Sample Statistics
A population parameter is number calculated from all
the population measurements that describes some
aspect of the population.
The population mean, denoted , is a population
parameter and is the average of the population
measurements.
A point estimate is a one-number estimate of the value
of a population parameter.
A sample statistic is number calculated using sample
measurements that describes some aspect of the
sample.
Measures of Central Tendency
Mean, 
The average or expected value
Median, Md The middle point of the ordered
measurements
Mode, Mo
The most frequent value
The Mean
Population X1, X2, …, XN

Sample x1, x2, …, xn
x
Population Mean
Sample Mean
N
n

X
i =1
N
i
x
x
i =1
n
i
Relationships Among Mean,
Median and Mode
Variables
• Definition:
– Characteristic or property of an individual
population unit
– Particular characteristics or properties may
vary among units in a population
• Examples:
– Starting salary of MBA college graduates
– Price of peanut butter at grocery stores
Measurement
• Definition:
– The process of quantifying information
• Quantitative variables:
– Test scores, product and process
measurements, survey results, etc.
• Qualitative variables:
– Product rating, arbitrary scales, etc.
Sample
• Definition:
– Subset of the units of the population
• Example:
– 100 GPA’s from all finance majors
– Tool wear on 3 machines out of 45 machines
• Notes:
– A random sample implies no statistical bias
– A census includes all population members
Statistical Inference
• Definition:
– Estimation, prediction, or other generalizations
about a population based on information
contained in a sample.
• Example:
– Based on a 5 year sample of similar weather
patterns, predicting the chance of rain today.
Reliability of the Inference
• Four items discussed thus far allow for
statistical inference:
– A population, variable(s) of interest, a sample,
and an inference.
• Fifth Item: A measure of the reliability of
the inference.
– How good the inference is, i.e. how much
confidence can we place in the inference?
Example
• The approval rating of the President; what does
it really mean?
• Uses a sample from the population to infer the
percentage of the population that approves of
his overall performance.
• Implies that 55% of the population approves of
the president’s performance plus or minus 5%,
i.e. between 50% and 60%.
Process Statistics
• A process transforms inputs into outputs:
– A manufacturing process which transforms aluminum
sheet into aluminum cans.
– A service process which offers financial advice based
on a customer’s input.
• Samples are obtained from a process and
statistical procedures can then be applied to
make inferences about the process itself.
Sampling a Process
Process
A sequence of operations that takes inputs (labor, raw
materials, methods, machines, and so on) and turns them
into outputs (products, services, and the like.)
Inputs
Process
Outputs
A process is in statistical control if it displays constant
level and constant variation.
Types of Data
• Data can be classified into four types:
– Nominal
– Ordinal
– Interval
– Ratio
Nominal Data
• Classify the members of the sample into
categories (Categorical Data).
• Examples:
– An individual’s religious affiliation
– Gender of applicants
– An individual’s political party affiliation
• No mathematical properties, i.e. numerical
values are only codes.
Ordinal Data
• Units of the sample can be ordered with respect
to the variable of interest.
• Examples:
– Size of rental cars.
– Ranking of microbrews with respect to taste.
– Ranking of consumer preferences for a product.
• No mathematical properties in that the difference
between ranking values is meaningless.
Interval Data
• Sample measurements enable comparisons
between members of the sample, i.e. the
differences between samples has meaning.
• Examples:
– Temperature or pressure readings.
– Machine speeds
• Can add and subtract but cannot multiply or
divide; origin has no meaning.
Ratio Data
• Equal distance between numbers imply
equal distances between the values of the
characteristic being measured, i.e. zero
represents the absence of the characteristic
being measured.
• Examples:
– Sales revenue for a product or service.
– Unemployment rate.
Classes of Data
• Data can be classified as either being:
– Qualitative data - nominal, ordinal, or
– Quantitative data - interval, ratio.
• Numerical data can also be discrete (countable)
or continuous.
• Spreadsheet (or Database)
– Variable (or Field)
– Observation (or Record)
Describing Data:
Graphs and Tables
Displaying Data
• For both Qualitative and Quantitative Data:
– Pie Charts
– Bar Graphs (Bar Charts)
– Histograms
– Frequency Tables
– Stem and Leaf Diagrams
Pie Chart Example
• 1999 Cigarette Sales
(in billions) by
company
– Philip Morris, 211.8
– Reynolds, 189.7
– Brown and Williamson,
69.1
– Lorillard, 48.6
– American, 43.9
– Liggett, 29.8
1999 Cigarette Sales
(Billions of Cigarettes)
48.6
69.1
43.9
29.8
211.
8
189.
7
Philip Morris
Brown and Williamson
Reynolds
Lorillard
American
Liggett
Bar Graph Example
• 1999 Cigarette Sales
(in billions) by
company
– Philip Morris, 211.8
– Reynolds, 189.7
– Brown and Williamson,
69.1
– Lorillard, 48.6
– American, 43.9
– Liggett, 29.8
1999 Cigarette Sales
(Billions of Cigarettes)
Liggett
American
Lorillard
Brown and Williamson
Reynolds
Philip Morris
0
100 200 300
Histogram Example
• Percentage of Sales
Revenue spent on
Advertising for a sample
of 35 Fortune 500
companies:
–
–
–
–
–
1% to 3% (4)
3% to 5% (9)
5% to 7% (11)
7% to 9% (8)
9% to 11% (3)
12
11
10
9
8
8
6
4
2
0
4
3
Measurement Classes
• Intervals are called measurement classes:
– A count of the members of a measurement class is
the frequency.
– The proportion of members in a measurement class
is the relative frequency. For a given interval, this
proportion is calculated by dividing the frequency of
the measurement class by the sample size.
Relative Frequency
• Sample:
Sales
Sales
Company Revenue Company Revenue
1
3.1
19
6.2
2
7.4
20
8.4
3
2.2
21
1.9
4
10.9
22
5.8
5
4.5
23
4.9
6
8.6
24
6.4
7
3.7
25
3.6
8
6.3
26
7.9
9
7.6
27
3.2
10
5.4
28
8.5
11
2.3
29
6.2
12
5.8
30
9.7
13
4.2
31
7.1
14
6.1
32
5.9
15
9.1
33
5.7
16
5.5
34
4.4
17
4.8
35
2.9
18
8.9
• Frequency Table:
Range
1% to 3%
3% to 5%
5% to 7%
7% to 9%
9% to 11%
Count
4
9
11
8
3
Proportion
0.114
0.257
0.314
0.229
0.086
– Divide range into intervals
of equal size.
– Count the number of
sample members that fall
within the ranges.
Relative Frequency Histogram
Example
• Percentage of Sales
Revenue spent on
Advertising for a sample
of 35 Fortune 500
companies:
–
–
–
–
–
1 to 3% (4/35=0.114)
3 to 5% (9/35=0.257)
5 to 7% (11/35=0.314)
7 to 9% (8/35=0.229)
9 to 11% (3/35=0.086)
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
Stem and Leaf Diagrams
• Data is displayed
graphically:
– The stem is the portion of
the data to the left of the
decimal point.
– The leaf is the portion of
data to the right of the
decimal point.
• Graphical representation
much like Histogram.
• From our previous
data:
Stem
Leaf
19
2239
31267
424589
5457889
612234
71469
84569
917
10 9
Key: Leaf units are tenths.
The Effect of Measurement
Class Size on a Histogram
• A Histogram showing
greater detail can be
obtained by:
– Decreasing class size
(which increases the
number of classes), or
– Increasing sample size
(which increases the
number of members in
each class).
7
6
6
5
5
4
4
2
2
0
4 4
3
3
1
5
1
1
Excel and StatPro Add-in
Demonstration
• Frequency tables
• Histograms
• Scatterplots
• Time series plots