#### Transcript Decision Technology

```Decision Technology
Modeling, Software and
Applications
Matthew J. Liberatore
Robert L. Nydick
John Wiley & Sons, Inc.
Chapter 9
Introduction to Decision Making
INTRODUCTION
Classical decision analysis and the Analytic
Hierarchy Process (AHP) provide structure and
making complex decisions.
Examples include:
Which job offer should I accept?
Where should my company locate a new service
facility?
Should my local government offer a tax amnesty
program to increase revenues?
INTRODUCTION
Decisions such as these are characterized by
uncertainty, conflicting multiple objectives,
and differing perspectives of the various
affected stakeholders.
The recommendations offered by decision
analysis should not be blindly accepted. The
process and its results should be viewed as an
important source of information for making
decisions.
INTRODUCTION
We distinguish between a good decision and a good
outcome.
Decision analysis improves your chances for a good
outcome and reduces your chances for an
unpleasant outcome.
INTRODUCTION
Why might decision analysis not produce a
good outcome?
There are a lot of reasons!
- you bought a car and got a lemon.
- when buying a car fuel economy was not
important to you, however, you were recently
transferred and now you have a 50 minute
commute.
CLASSICAL DECISION ANALYSIS
Suppose you inherited the following lottery.
CLASSICAL DECISION ANALYSIS
Suppose you inherited the following lottery.
0.50
\$1000
L1
0.50
\$0
CLASSICAL DECISION ANALYSIS
Suppose you inherited the following lottery.
0.50
\$1000
L1
0.50
\$0
What amount makes you indifferent between
selling the lottery or keeping the lottery and
playing?
CLASSICAL DECISION ANALYSIS
Suppose you inherited the following lottery.
0.50
\$1000
L1
0.50
\$0
Amount
1000
999
998
...
2
1
0
Decision
Sell
Sell
Sell
...
Keep
Keep
Keep
What amount makes you indifferent between
selling the lottery or keeping the lottery and
playing?
EXPECTED MONETARY VALUE
The expected monetary value (EMV) is a long
run average and is computed as:
EMV = (Pi)(Xi)
EMV = Expected monetary value
Pi = probability of event i
Xi = payoff of event i
EXPECTED MONETARY VALUE
For the above lottery:
EMV = (0.50)(1000) + (0.50)(0) = \$500
Most would sell for less than \$500.
EMV does not consider risk.
Many factors influence your attitude including
wealth and personal beliefs.
EXPECTED MONETARY VALUE
Example 1 (Lawsuit settlement): Choose one of
the following:
A1: \$100,000 gift, tax free, for sure;
Example 2 (Insurance): Choose one of the
following:
B1: \$1000 loss;
B2: 0.0006 chance of a \$1,000,000 loss and
0.9994 chance of no loss.
EXPECTED MONETARY VALUE
Example 3 (A paradox): Choose one of the
following:
C1: \$10,000 gift tax free, for sure;
C2: 2N cents, where N is the number of coin
flips until the first tails occurs.
Which alternatives do you prefer?
Most people would choose A1, B1, and C1.
However, EMV decision makers would prefer
A2, B2, and C2 (EMV(A2)=125000,
EMV(B2)=-\$600, and EMV(C2)=?).
Example 3 is known as the St. Petersburg
EXPECTED MONETARY VALUE
The EMV of the St. Petersburg Paradox.
N
p(N)
2N
Result
1
(1/2)1
21
T
2
(1/2)2
22
HT
3
(1/2)3
23
HHT
4
(1/2)4
24
HHHT
...
EXPECTED MONETARY VALUE
The EMV of the St. Petersburg Paradox.
N
p(N)
2N
Result
1
(1/2)1
21
T
2
(1/2)2
22
HT
3
(1/2)3
23
HHT
4
(1/2)4
24
HHHT
...
EMV= (1/2)1*21 + (1/2)2*22 + (1/2)3*23 +
(1/2)4*24 + ...
=
1 +
1 +
1 +
+ ...
= infinity!
1
UTILITY THEORY
EMV is a long run average and does not
consider risk.
Von Neumann and Morgenstern argued that
people maximize expected utility.
This assumes that a utility function can be
determined for each individual or group for a
given problem situation.
UTILITY THEORY
The utility function expresses an attitude
toward risk. In a given situation, some
people may be risk neutral, risk averse, or
risk loving.
Recall, the first lottery of a 50/50 chance of
winning \$0 or \$1000. Those that value the
lottery at \$500 are risk neutral EMVers.
Those that value the lottery at less than \$500
are risk averse, while those that value the
lottery at more than \$500 are risk loving.
UTILITY THEORY
A utility function for a risk averse person is
upward sloping and concave.
U(X)
0
X
ESTIMATING UTILITY FUNCTIONS
Utility functions can be estimated by developing a
series of indifference points between receiving a
certain amount and taking a gamble or lottery.
Reconsider the first lottery of a 50/50 chance of
winning \$0 or \$1000.
1. Set anchor utility values: U(1000)=1 and
U(0)=0.
2. Suppose you are indifferent between receiving
\$300 or keeping the lottery. This implies that:
U(300)=EU(lottery) = .5*U(1000) + .5*U(0) =
0.5
ESTIMATING UTILITY FUNCTIONS
3. Other points on the utility curve can be defined
by finding indifference values for other lotteries.
a.Consider the lottery of a 50/50 chance of
winning \$1000 or \$300. Suppose you are
indifferent for \$400. Then,
U(400)=EU(lottery)=.5*U(1000) + .5*U(300) =
0.75
b.Consider the lottery of a 50/50 chance of
winning \$300 or \$0. Suppose you are
indifferent for \$50. Then,
U(50)=EU(lottery)=.5*U(300) + .5*U(0) = 0.25
ESTIMATING UTILITY FUNCTIONS
Using these five points, a utility curve can be
drawn.
U(X)
Piecewise concave
1 utility curve
0.75
EMV
0.50
0.25
0 50
300 400
1000
X
PROBLEMS WITH UTILITY
There are several problems with utility theory that
1. It is assumed that the decision maker is
perfectly consistent in their beliefs about
utility.
From the utility curve that we just estimated, we
know that U(50)=0.25, U(300)=0.50, and
U(400)=0.75.
This implies that, U(300)=2*U(50),
U(400)=1.5*U(300), so U(400)=3*U(50).
PROBLEMS WITH UTILITY
This might be acceptable in some cases, but
suppose we have estimated a utility curve for
market share.
We find that: U(30%)=2*U(20%) and
U(20%)=1.5*U(15%).
Utility theory requires us to believe that
U(30%)=3*U(15%).
PROBLEMS WITH UTILITY
In fact, when considering this comparison, we
might find that U(30%) might be 4 or 5 times
U(15%).
Individuals are not always perfectly consistent in
their judgments and this does not mean that
they are illogical!
PROBLEMS WITH UTILITY
2. The use of lotteries to determine a utility
curve is artificial since individuals are asked
to make hypothetical choices and use this
information to solve real problems.
3. Utility functions must be anchored on a fixed
scale. What happens when phenomena must
be evaluated that are outside the range of the
scale?
PROBLEMS WITH UTILITY
4. Utility curves can only be developed if numbers
can be assigned to the relevant criteria.
How do you develop a utility curve to measure
intangible and highly subjective factors, such as
style, when deciding what car to purchase?
PROBLEMS WITH UTILITY
For these and other reasons, managers often make
decisions that are inconsistent with the
maximization of expected utility.
That is, expected utility often is not descriptive of
actual decision making behavior, even though it
is appealing from a prescriptive point of view.
Would you use expected utility to help make a
major business decision? A major personal
decision?
THE AHP
The Analytic Hierarchy Process (AHP) is an
alternate approach to expected utility.
AHP successfully addresses the limitations of
expected utility.
AHP is implemented using the software
package called Decision Lens.
THE AHP
What is the Analytic Hierarchy Process (AHP)?
The AHP, developed by Tom Saaty, is a
decision-making method for prioritizing
alternatives when multi-criteria must be
considered.
An approach for structuring a problem as a
hierarchy or set of integrated levels.
THE AHP
AHP problems are structured in at least three
levels:
The goal, such as selecting the best car to
purchase,
The criteria, such as cost, safety, and appearance,
The alternatives, namely the cars themselves.
THE AHP
The decision-maker:
measures the extent to which each alternative
achieves each criterion, and
determines the relative importance of the criteria
in meeting the goal, and
synthesizes the results to determine the relative
importance of the alternatives in meeting the
goal.
THE AHP
How does AHP capture human judgments?
AHP never requires you to make an absolute
judgment or assessment. You would never
be asked to directly estimate the weight of a
stone in kilograms.
AHP does require you to make a relative
assessment between two items at a time.
AHP uses a ratio scale of measurement.
APPROACH
Suppose the weights of two stones are being
assessed. AHP would ask: How much heavier
(or lighter) is stone A compared to stone B?
AHP might tell us that, of the total weight of
stones A and B, stone A has 65% of the total
weight, whereas, stone B has 35% of the total
weight.
APPROACH
Individual AHP judgments are called pairwise
comparisons.
These judgments can be based on objective or
subjective information.
For example, smoothness might be a subjective
criterion used to compare two stones.
Pairwise comparisons could be based on
touch.
APPROACH
However, suppose stone A is a diamond worth
\$1,000.00 and stone B is a ruby worth
\$300.00.
This objective information could be used as a
basis for a pairwise comparison based on the
value of the stones.
APPROACH
Consistency of judgments can also be measured.
Consistency is important when three or more
items are being compared.
Suppose we judge a basketball to be twice as
large as a soccer ball and a soccer ball to
be three times as large as a softball.
To be perfectly consistent, a basketball must be
six times as large as a softball.
APPROACH
AHP does not require perfect consistency,
however, it does provide a measure of
consistency.
We will discuss consistency in more detail later.
AHP APPLICATIONS
AHP has been successfully applied to a variety of
problems.
1. R&D projects and research papers;
2. vendors, transport carriers, and site locations;
3. employee appraisal and salary increases;
4. product formulation and pharmaceutical
licensing;
5. capital budgeting and strategic planning;
6. surgical residents, medical treatment, and
diagnostic testing.
AHP APPLICATIONS
The product and service evaluations prepared by
consumer testing services is another potential
application.
Products and services, such as self propelled
lawn mowers are evaluated.
Factors include: bagging, mulching, discharging,
handling, and ease of use.
An overall score for each mower is determined.
AHP APPLICATIONS
solely on this score?
Probably not! Some of the information will be
How important is each criterion?
Would you weigh the criteria the same way?
Are all of the criteria considered important to you?
Are there other criteria that are important to you?
Have you ever thought about these issues?
RANKING SPORTS RECORDS
The AHP has been used to rank outstanding
season, career, and single event records across
sports.
Season
1. Babe Ruth, 1920: .847 slugging average
2. Joe DiMaggio, 1944: 56 game hitting streak
3. Wilt Chamberlain, 1961-62: 50.4 points per
game scoring average
RANKING SPORTS RECORDS
Career
1. Johnny Unitas, 1956-70: touchdown passes in
47 consecutive games
2. Babe Ruth, 1914-35: .690 slugging average
3. Walter Payton, 1975-86: 16,193 rushing
yardage
Single event
1. Wilt Chamberlain, 1962: 100 points scored
2. Norm Van Brocklin, 1951: 554 passing yards
3. Bob Beamon, 1968: 29' 2.5" long jump
RANKING SPORTS RECORDS
How do we compare records from different
sports?
It all depends on the criteria that you select!
Golden and Wasil (1987) used the following
criteria:
1. Duration of record - years record has stood,
years expected to stand
2. Incremental improvement - % better than
previous record
3. Other record characteristics - glamour, purity
(single person vs. team)
RANKING SPORTS RECORDS
records?
Absolutely not!
In bars and living rooms across the country,
AHP provides a methodology to structure the
debate.
Different criteria and different judgments could
produce different results.
In reading the sports pages we often see
discussion of how well teams match up across
different positions.
These match-ups are often used to predict a
winner.
Match-ups are a pairwise comparison concept!
AHP APPLICATIONS
Our culture is obsessed with quantitative
rankings of all sorts of things.
There are many measurement problems
associated with rankings of products, sports
teams, universities, and the like.
Many of these issues are discussed on a web site
at:
http://www.expertchoice.com/annie.person
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from
childhood:
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from
childhood:
You can’t compare apples and oranges.
All you get is mixed fruit!
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from
childhood:
You can’t compare apples and oranges.
All you get is mixed fruit!
do you still believe this statement?
APPLES AND ORANGES
The discussion of how to compare records from
different sports recalls a saying from
childhood:
You can’t compare apples and oranges.
All you get is mixed fruit!
do you still believe this statement?
We hope not!!!
APPLES AND ORANGES
What criteria might you use when comparing
apples and oranges?
There are a vast set of criteria that may change
depending upon time of day or season of year:
taste,
ripeness,
shape,
cost.
texture,
juiciness,
weight,
Can you think of others?
smell,
nutrition,
color, and
APPLES AND ORANGES
The point is that people are often confronted with
the choice between apples and oranges.
Their choice is based on some psychological
assessment of:
relevant criteria,
their importance, and
how well the alternatives achieve the criteria.
Slippery Rock Number 1
In 1936 there was no consensus about the number 1 college
football team. Some experts argued that the University of
Minnesota should be number 1 while others argued that it
should be the University of Pittsburgh.
One expert thought that Slippery Rock, a small college in
western Pennsylvania, should be number 1. His reasoning
is:
–
–
–
–
–
Slippery Rock defeated West Virginia
West Virginia defeated Duquesne
Duquesne defeated Pitt
Pitt defeated Notre Dame
Notre Dame defeated Minnesota
Do you believe this argument?
In 1999 Zagat’s survey rated the Fountain as the number 1
restaurant in Philadelphia with perennial winner Le BecFin dropping to the number 2 spot.
How did this happen?
– Zagat relies on ordinary diners to rate restaurants
– Nearly 1000 people voted for Philadelphia restaurants
– People rated each of three categories (Food, Décor, and
Service) on a 0-3 scale, where 3 is perfection
– Zagat averages the numbers (An average of 2.6 translates
to a 26)
– The numbers are then rounded
The results:
Food
Décor
Service
Total
Le Bec-Fin
29.14 (29)
28.36 (28)
28.67 (29)
86.17 (86)
Fountain
28.88 (29)
28.68 (29)
28.59 (29)
86.15 (87)
Zagat rated the Fountain number 1 because their
rounded score beat Le Bec-Fin’s rounded score.
What do you think?
SUMMARY
This chapter provided an introduction to
decision making.
Specific topics covered include: Expected
Monetary Value, Utility Theory, and an
introduction to the Analytic Hierarchy
Process.
Copyright  2003Matthew J. Liberatore and Robert L. Nydick.
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```