Turban, Aronson, and Liang
Decision Support Systems and Intelligent Systems,
Seventh Edition
Decision Trees and Tables; LP
Modeling
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-1
Decision-Making
• The act of choosing from a set of
alternatives to obtain a goal
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-2
Decision-Making
• Certainty
– Assume complete knowledge
– All potential outcomes known
– Easy to develop
– Resolution determined easily
– Can be very complex
– example: the amount returned on an
investment with a constant rate (CD)
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-3
Decision-Making
• Uncertainty
– Several outcomes for each decision
– Probability of occurrence of each
outcome unknown
– Insufficient information
– Assess risk and willingness to take it
– Pessimistic/optimistic approaches
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-4
DM under uncertainty for a
maximization problem
• Optimistic – look at the best outcome
for each alternative, then choose the
“best of the best”
• Pessimistic – look at the worst
outcome for each alternative, then
choose the “best of the worst”
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-5
DM under uncertainty for a
minimization problem
• Optimistic – look at the smallest
payoff for each alternative, then
choose the “lowest of the lows”
• Pessimistic – look at the largest
payoff for each alternative, then
choose the “lowest of the highs”
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-6
Decision Tables
• Multiple criteria decision analysis
• Features include:
– Decision variables (alternatives)
– Uncontrollable variables
– Result variables
• Applies principles of certainty,
uncertainty, and risk
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-7
DM under uncertainty example 1 –
Driving to school
• To save on gasoline, Janet and Joe
agree to form a carpool for traveling
to and from school. After limiting the
travel routes to two alternatives, the
students cannot agree on the best
way to get to school. The students do
not know the condition of the freeway
ahead of time. If Janet is an optimist,
which route does she prefer? If Joe is
a pessimist, which does he prefer?
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-8
Janet and Joe Decision table
States of Nature
Decision
Alternatives
s1= light
s2 = heavy
freeway traffic freeway traffic
a1 = take
freeway
10 minutes
40 minutes
a2 = take
Walnut Ave.
20 minutes
20 minutes
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-9
Results of Janet and Joe
• Janet is optimisitic, therefore choose
the best of the best
– a1: 10 minutes*****
– a2: 20 minutes
Joe is pessimistic, therefore choose the
best of the worst
– a1: 40 minutes
– a2: 20 minutes*****
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-10
Naddol Toy Company Plant
Construction
•
•
•
•
See handout for problem
Set up the decision table
Why can we eliminate option 4?
Is the problem a maximization or
minimization problem?
• What alternative would you choose is
you were optimistic? Pessimistic?
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-11
NADDOL Decision Table
Decision
Alternatives
States of Nature
s1= low
demand
s2= medium
demand
s3= high
demand
a1 = build
small plant
$250,000
-$40,000
$0
a2 = build
moderate
plant
-$50,000
$350,000
$60,000
a3 = build
large plant
-$100,000
$80,000
$400,000
a4 = build
-$120,000
$75,000
$400,000
very large
plant
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-12
Decision-Making
• Probabilistic Decision-Making
– Decision under risk
– Probability of each of several possible
outcomes occurring
– Risk analysis
• Calculate value of each alternative
• Select best expected value (For each
alternative, mult. prob. of each SoN by the
expected outcome and add)
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-13
Naddol revisited under risk!
• Now look at the Naddol problem using
the following probabilities of each
state of nature:
• P(s1) = .3 = P(low demand)
• P(s2) = .6 = P(medium demand)
• P(s3) = .1 = P(high demand)
• Find the expected value for each
alternative and choose the best one
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-14
Decision Making Under Risk
Decision
Alternatives
States of Nature
s1= low
demand; .3
s2= medium
demand; .6
s3= high
demand; .1
a1 = build
small plant
$250,000
$75,000
-$40,000
-$24,000
$0
$0
a2 = build
moderate
plant
-$50,000
-$15,000
$350,000
$210,000
$60,000
$6,000
a3 = build
large plant
-$100,000
$30,000
$80,000
$48,000
$400,000
$40,000
a4 = build
very large
plant
-$120,000
$75,000
$400,000
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-15
Decision Tree
• Graphical representation of
relationships
• Multiple criteria approach
• Demonstrates complex relationships
• Cumbersome, if many alternatives
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-16
p(s1)=.3
xi(Payoff)
p(si)xi
$250K
$75K
$-40K
$-24K
p(s2)=.6
p(s3)=.1
$51K
0
0
a1 = small
p(s1)=.3
a2 = medium
$-50K
$-15K
$350K
$210K
p(s2)=.6
p(s3)=.1
$60K
$6K
$-100K
$-30K
$80K
$48K
$400K
$40K
$201K
a3 =large
p(s1)=.3
p(s2)=.6
$58K
p(s3)=.1
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-17
Modeling with Spreadsheets
• Flexible and easy to use
• End-user modeling tool
• Allows linear programming and
regression analysis
• Features what-if analysis, data
management, macros
• Seamless and transparent
• Incorporates both static and dynamic
models
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-18
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-19
MSS Mathematical Models
• Link decision variables, uncontrollable
variables, parameters, and result variables
together
– Decision variables describe alternative choices.
– Uncontrollable variables are outside decisionmaker’s control.
– Fixed factors are parameters.
– Intermediate outcomes produce intermediate
result variables.
– Result variables are dependent on chosen
solution and uncontrollable variables.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-20
MSS Mathematical Models
• Nonquantitative models
– Symbolic relationship
– Qualitative relationship
– Results based upon
• Decision selected
• Factors beyond control of decision maker
• Relationships amongst variables
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-21
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-22
Mathematical Programming
• Tools for solving managerial problems
• Decision-maker must allocate resources
amongst competing activities
• Optimization of specific goals
• Linear programming
– Consists of decision variables, objective
function and coefficients, uncontrollable
variables (constraints), capacities, input and
output coefficients
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-23
Sungold Paint LP problem
In preparing Sungold paint, it is required that the
paint have a brilliance rating of at least 300
degrees and a hue level of at least 250 degrees.
Brilliance and hue levels are determined by two
ingredients, Alpha and Beta. Both Alpha and
Beta contribute equally to the brilliance rating;
one ounce (dry weight) of either produces one
degree of brilliance in one drum of paint.
However, the hue is controlled entirely by the
amount of Alpha; one ounce of it producing 3
degrees of hue in one drum of paint. The cost of
Alpha is 45 cents per ounce, and the cost of
Beta is 12 cents per ounce. Assuming that the
objective is to minimize the cost of the
resources, then the problem is to find the
quantity of Alpha and Beta to be included in the
preparation of each drum of paint.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
4-24
Turban, Aronson, and Liang
Set-up of Sungold Paint LP
problem
• Decision variables
– A = quantity of Alpha to be included, in
ounces, per drum
– B = quantity of Beta to be included, in
ounces, per drum
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-25
Set-up of Sungold Paint LP
problem, 2
• Objective = to minimize cost of
ingredients for one drum
• Uncontrollable variables = price per
ounce of each ingredient
– Cost of Alpha = .45 per ounce (cents)
– Cost of Beta = .12 per ounce (cents)
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-26
Set-up of Sungold Paint LP
problem, 3
• S0, the objective function is displayed
as:
.45A + .12B with the goal of
minimizing the cost!
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-27
Set-up of Sungold Paint LP
problem, 4
•
Constraints – usually decided by the
situation
1. To supply brilliance rating of at least
300 degrees per drum, each ounce
of alpha or beta increases the
brilliance by 1 degree, so…
A + B >= 300
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-28
Set-up of Sungold Paint LP
problem, 5
2. To provide hue level of at least 250
degrees, the effect of alpha alone on
hue is…
3A + 0B >= 250
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-29
Set-up of Sungold Paint LP
problem, 6
3. Non-negativity constraints (neither
value can be 0 or less), so
A >= 0
B >= 0
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-30
Rapido Sports – try to set up for
HW
•
The advertising agency promoting the new Rapido sports
car wants to get the best possible exposure for the product
within the available $200,000 budget. To do so, the
agency must decide how much to spend on its two most
effective media: evening television spots and large
magazine ads. Each television spot costs $20,000 and a
magazine ad involves a $5000 expenditure. Fractional
spots and ads can be purchase from the media. By
processing industry’s ratings through the company’s media
evaluation information system, research staff have
estimated that 400,000people will be reached with each
television spot and 150,000 people will be reached with a
magazine ad.
•
Dawn Shaw, the agency director, knows from experience that it is
important to use both media. In this way, the advertising will
reach the broadest spectrum of potential Rapido customers. As
a result, she decides to contract for at least 4, but no more than
12, television spots and a minimum of 6 magazine ads.
© 2005 Prentice Hall, Decision Support Systems and Intelligent Systems, 7th Edition,
Turban, Aronson, and Liang
4-31