GSBA 509
Multiple Attribute Decisions
• Some choice problems need more than one
measure to evaluate different outcomes
Multi-Attribute Decision Making
• Multiple attributes = multiple criteria to consider
when making decisions
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Example: Buy a home
Decision Approaches
• You want to buy a house and have narrowed
• To make a choice, a method is needed to
down to 2:
either
Attribute
Cost
Size
Neighborhood
Distance to work
Condition
(etc…)
House 1
455,000
455
000
3br, 1 ba
average
5 mi
good
ƒ Consider all attributes at the same time
House 2
520 000
520,000
4 br, 2 ba
nice
15 mi
average
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ƒ Decompose the problem and treat attributes
sequentially
(Note: Tradeoffs may be difficult to make)
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Three Decision Methods
Dominance
• Problems:
• 1. Dominance: if alternative A has
outcomes at least as good as those for
alternative B for each attribute, choose A
ƒ This doesn’t happen often, especially if the number
of criteria is large
ƒ If it does happen, decision problem becomes trivial
Example: if you want a smaller, inexpensive
house close to work and in good condition, and
don’t care about the neighborhood, choose
house 1
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Three Decision Methods
Satisficing
• Problems:
ƒ Solution may not be unique, or a solution may not
• 2. Satisficing: set minimum requirements
exist
for each attribute
ƒ Attributes must be independent (since they get
treated separately)
ƒ If not satisfactory on one or more attribute, discard
ƒ One slightly bad attribute can eliminate an otherwise
the alternative
good choice
Example: if you decide you need 4 bedrooms, discard all
houses with 3 or fewer bedrooms
Examples:
-- need: 4 br, good neighborhood, less than $470,000
…..no solution
-- need: at least 3 br, no more than 20 miles from job
…..nothing eliminated
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Three Decision Methods
Lexicographic procedure
• 3. Lexicographic procedure (ordering):
• Problems:
ƒ Rank attributes from most important to least
ƒ This may only use one or two attributes and ignore
important
the others
((doesn’t
’ allow bad performance
f
on one to be
made up by good outcomes on others)
ƒ Compare alternatives on most important attribute –
chose the best one. If still tied, use the next most
important attribute….continue until decision is made
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Trade-off Methods
Trade-off Methods
Method:
• Idea: create alternatives that are different only
1. Choose the “surviving” attribute
2. Choose a “base level” for the remaining
on one attribute (the “surviving” attribute)
attributes
3. Adjust
j
each alternative’s outcomes – change
g
all but the “surviving” attribute to base level,
then adjust the measure of the surviving
attribute so the new outcome is equivalent to
the old outcome
4. Choose preferred alternative by comparing
surviving attribute values
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Example
Steps
Example: 3 houses, 3 criteria:
Criteria
House 1
House 2
House 3
Cost:
Si
Size:
Nbrhd:
495,000
3b 2b
3br,
2ba
good
380,000
3b 1b
3br,
1ba
excellent
560,000
4b 2b
4br,
2ba
average
1. Let surviving attribute = cost
ƒ ($ values are easiest to adjust)
2. Choose “base level” for size and nbrhd:
ƒ Let size base level = 3 br
br, 2 ba
ƒ Let neighborhood base level = good
3. Adjust Cost to account for differences from
base
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Adjustments
Adjustments
• House 1:
•
• House 3:
ƒ no adjustment needed, base levels exist
House 2:
ƒ What would you accept to settle for only 1 bath
ƒ What would you pay for the extra bedroom?
(i.e., what is the marginal value of 1 extra bathroom from 1 to 2?)
$35 000
$35,000
$30,000
(example)
neighborhood?
$50 000
$50,000
(example)
ƒ What would you accept to settle for only an average
(example)
ƒ What would you pay for an excellent neighborhood?
(i.e., what is the marginal value of “good” to “excellent” neighborhood?)
$20,000
(example)
i.e., 560,000 – 30,000 + 50,000 = 580,000
cost – size adj. + nbrhd adj. = adjusted cost
i.e., 380,000 + 35,000 – 20,000 = 395,000
cost + size adj. – nbrhd adj. = adjusted cost
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After Adjustment
After Adjustment
Example: 3 houses, 3 criteria:
• Now these are easier to compare….
Criteria
House 1
House 2
House 3
Cost:
Size:
Nbrhd:
495,000
3br, 2ba
good
380,000
3br, 1ba
excellent
560,000
4br, 2ba
average
395,000
3br, 2 ba
good
580,000
3br, 2 ba
good
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• If these really represent your preferences and
values, you should pick House #2
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Another Scaling Technique
Scaling of Criteria Weights
MUST Criteria: No scaling necessary since these are
absolutely necessary
• Apply weights to individual criteria, then
compute a weighted score for each alternative
WANT Criteria: Scaling is necessary since these are not
equal in desirability
IGNORABLE Criteria: No scaling necessary since these
are not part of the decision problem
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Scaling of Criteria Weights
Scaling of Criteria Weights
MUST Criteria: No scaling necessary
MUST Criteria: No scaling necessary
WANT Criteria:
WANT Criteria:
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
Very Important
Important
Somewhat Important
Somewhat Unimportant
IGNORABLE Criteria: No scaling necessary
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Monthly Payment = 9
Important
Quality of schools = 5
Somewhat Important
Somewhat Unimportant
Air conditioning = 2
IGNORABLE Criteria: No scaling necessary
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Example
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MUST criteria
•
•
•
•
•
•
• A couple with two children must buy a new
home and move in within 30 days after arriving
in a city to start new jobs. Apartments have
been ruled out.
• First, the couple lists their MUST criteria:
Yandell – GSBA 509
Example Weights:
Very Important
•
•
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3 or more bedrooms
2 or more bathrooms
Available within 30 days
Not downtown
Not more than 30 minutes driving time to jobs
Monthly payment, including taxes, not more than
$2500
Down payment not more than $120,000
Must not have a swimming pool
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WANT criteria
•
•
•
•
•
•
•
•
IGNORE criteria
Weight
10
9
7
7
6
5
4
2
Monthly payment
Distance to jobs
Distance to kid’s school
Size of garage
Condition of home
Extra bedroom
Traffic and noise
View
•
•
•
•
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Age of home
Brick or wood exterior
Attached or separate garage
Fireplace
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Compare weighted scores
Compare Alternatives
House 1
Criterion
Monthly payment
Distance to jobs
Distance to school
Size of garage
Condition of home
Extra bedroom
Traffic and noise
View
Attribute
Score
2150
10 mi
4 blocks
2 car
good
no
fair
no
8
7
6
7
6
0
3
0
House 2
Attribute
Score
2300
5
15 mi
4
2 blocks 8
2 car
7
good
6
no
0
average 5
partial
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Σ(weight x score)
House 3
Attribute
• House 1:
Score
(10x8)+(9x7)+(7x6)+(7x7)+(6x6)+(5x0)+(4x3)+(2x0) = 282
2450
3
6 mi
9
3 blocks 7
3 car
10
average 3
yes
10
good
8
no
0
• House 2:
(10x5)+(9x4)+(7x8)+(7x7)+(6x6)+(5x0)+(4x5)+(2x4) = 255
• House 3:
(10x3)+(9x9)+(7x7)+(7x10)+(6x3)+(5x10)+(4x8)+(2x0) = 330
Best Choice
(Note: the 0-10 scale used to score individual
attributes is arbitrary, but consistent across houses)
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Summary
• Multi-Attribute Decision Models
ƒ Descriptive procedures
• Dominance
• Satisficing
• Lexicographic
ƒ Trade-off procedures
• Surviving attribute
• Weighted scores
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