Decision making considering multi-attributes

Copyright ©2012 by Pearson Education, Inc.
Upper Saddle River, New Jersey 07458
All rights reserved.
Engineering Economy, Fifteenth Edition
By William G. Sullivan, Elin M. Wicks, and C. Patrick Koelling
Engineering Economy
Chapter 14: Decision Making
Considering Multiattributes

The objective of Chapter 14 is to
present situations in which a
decision maker must recognize
and address multiple problem
attributes.

Few decisions are based strictly on
dollars and cents.
• We will address how diverse, nonmonetary
considerations (attributes), that arise from
multiple objectives can be explicitly
considered.
• Nonmonetary means there is no formal
mechanism to establish value.

Value is difficult to define.
• Seven classes of value: economic, moral,
aesthetic, social, political, religious, judicial
• Only economic value is measured in monetary
units.
• Economic value can be established through use
value (properties that provide a unit of work) and
esteem value (properties that make something
desirable).
• Use and esteem value defy precise quantification
in monetary terms.

Buying a car is a multiattribute decision.
What are some of the things you consider when
purchasing a car? A car enthusiast may care about
the following.
Attribute Car A Car B Car C
Horsepower 195 320 230
Transmission automatic automatic manual
Color red blue gray
Body style sedan coupe sedan
Brand import domestic import
Gas mileage 26 mpg 18 mpg 21 mpg
Dealer Reputation Excellent Fair Poor

The same data may bring different
values to different decision makers.
• While one may be able to assign a dollar amount
to gasoline mileage, the other attributes are not
nearly as clean.
• Some drivers would rate an automatic
transmission as “good,” while others would rate it
as “bad,” or at least less desirable.
• Do you have a favorite color? Do you “buy
American”?
• Many decision problems in industry are similar.

Choosing the “right” attributes is critical.
• Each attribute should distinguish at least two
alternatives.
• Each attribute should capture a unique dimension
of the decision problem (i.e., attributes are
independent and nonredundant).
• All attributes, collectively, are assumed sufficient
for selecting the “best” alternative.
• Differences in values for each attribute are
meaningful in distinguishing among alternatives.

Choosing attributes is a subjective
process.
• It is usually the result of group consensus.
• The final list is heavily influenced by the decision
problem and by an intuitive feel for which
attributes will discriminate among alternatives.
• Too many attributes is unwieldy, too few limits
discrimination.
• Attributes must have sufficient specificity to be
measured and therefore useful.

Measurement scales must be selected for
each attribute.
• The measurement scale for monetary
attributes is easy to define, less so perhaps
for other attributes.
• Some attributes may be measurable, such as
horsepower or mileage, but that may not
directly translate into value.
• Sometimes gradation measures such as
“good,” “fair,” or “poor” are used.

The dimensionality of the problem
dictates solution methods.
• All attributes can be collapsed into a single
dimension (single-dimension analysis) such as
dollar equivalents, or a utility equivalent perhaps
ranging from 0 to 100. It might be difficult to
assign such to a color.
• This is popular in practice because a complex
problem can be made computationally tractable.
• Single-dimension models are termed
compensatory models (allowing trade-offs among
attributes).

Full-dimension analysis retains the
individuality of all attributes.
• No attempt is made to create a common
scale.
• This approach is especially good for
eliminating inferior alternatives from further
analysis.
• Models for full-dimension analysis are
termed noncompensatory (no trade-offs
among attributes).

Noncompensatory models attempt to
select the best alternative considering the
full-dimensionality of the problem
• Dominance: screening to eliminate inferior alternatives.
• Satisficing: when all attributes meets a minimum
threshold.
• Disjunctive resolution: when at least one attribute meets a
minimum threshold.
• Lexicography: Choose the alternative with the “best” value
for a particular attribute. If there is a tie, consider scores
for the next most-valuable attribute, etc. So, the attributes
must be ranked in order of preference.

Revisiting the car problem.
Attribute Car A Car B Car C Preference Minimum
Horsepower 195 320 230 Higher 200
Transmission Automatic Automatic Manual Automatic Manual
Color Red Blue Gray B, G, R R
Body style Sedan Coupe Sedan Sedan Coupe
Brand Import Domestic Import Domestic Import
Gas mileage 26 mpg 18 mpg 21 mpg Higher 20 mpg
Dealer reputation Excellent Fair Poor Better rep. Fair

Pairwise comparison to determine
dominance.
Attribute Car A vs. Car B Car A vs. Car C Car B vs. Car C
Horsepower Worse Worse Better
Transmission Same Better Better
Color Worse Worse Better
Body style Better Same Worse
Brand Worse Same Better
Gas mileage Better Better Worse
Dealer reputation Better Better Better
Dominance? No No No

Assessing the alternatives using
noncompensatory methods.
• Dominance: None of the alternatives is
dominated (each is a “winner” for at least
one attribute).
• Satisficing: None meet the minimum
threshold in all categories. Car A does not
meet horsepower, Car B does not meet mpg,
and Car C does not meet dealer reputation.

Assessing the alternatives using
noncompensatory methods.
• Disjunctive resolution: All of the
alternatives meet at least one minimum
threshold.
• Lexicography: If we rank horsepower as
most important, Car B is selected. If we
select mileage, then Car A is selected. If
body style, then color, Car C is selected.

Compensatory models require attributes to be
converted to a common measurement scale.
• The scale may be, for example, dollars or utiles (a
dimensionless unit of worth).
• This conversion allows one to construct an overall
index value for each alternative, which can then be
directly compared.
• The construction of the overall index can take
many forms depending on the decision situation.
• Good performance in one attribute can
compensate for poor performance in another.

Converting attribute values to
nondimensional form.
• Nondimensional scaling converts all attribute
values to a scale with a common range (e.g., 0 to
1, 0 to 100). Otherwise, attributes will contain
implicit weights.
• All attributes should follow the same trend with
respect to desirability; most preferred values
should be either all small, or all large.
• Assessing each alternative can be as simple as
adding the individual scaled attribute values.

Converting original data to
nondimensional ratings
When original data are numerical values, the following
conversions can be used. First, when larger numerical
values are undesirable,
Then, when larger numerical values are desirable.

Rating horsepower and mileage in the
car example.
In each case, more is considered better. For example,
the rating for 230 horsepower would be
The ratings for these attributes for each car are below.
Horsepower 0.0 1.0 0.28
Gas mileage 1.0 0.0 0.38

For non-numerical attribute values, a
ranking process can be used.
Attributes can be ranked from 1 to n, where there are n
possible values of the attribute, and 1 is considered best.
Then the following formula can be used for rating.
The next slide provides ratings for the five non-
numerical attributes in the car example.

Attribute Value Relative Rank
Nondimensional
Value
Transmission Manual 1 0.00
Automatic 2 1.00
Color Red 1 0.00
Gray 2 0.50
Blue 3 1.00
Body style Coupe 1 0.00
Sedan 2 1.00
Brand Import 1 0.00
Domestic 2 1.00
Dealer reputation Poor 1 0.00
Fair 2 0.33
Good 3 0.67
Excellent 4 1.00

Nondimensional data for the car buying
decision. Car B is the “best” choice!
Horsepower 0.00 1.00 0.28
Transmission 1.00 1.00 0.00
Color 0.00 1.00 0.50
Body style 1.00 0.00 1.00
Brand 0.00 1.00 0.00
Gas mileage 1.00 0.00 0.38
Dealer Reputation 1.00 0.33 0.00
Sum of ratings 4.00 4.33 2.16

The additive weighting technique allows
some attributes to be more “important”
than others.
• An ordinal ranking of the problem attributes yields
attribute weights that can be multiplied by the
nondimensional attribute values to produce a
partial contribution to the overall score, for a
particular alternative.
• Summing the partial contributions results in a total
score for each alternative, which are then
compared to select the “best” one.

Establishing and using attribute weights.
1. Rank attributes from 1 to n based on position, with higher
numbers indicating greater importance. n may be the
number of attributes, indicating constant and difference
(importance) between attributes, or it may be larger
allowing for uneven spacing between attributes.
2. Normalize the relative ranking numbers by dividing each
by the sum of all rankings.
3. Multiply an attribute’s weight by the alternative’s rating
for that attribute to get the partial contribution.
4. Sum the partial contributions to obtain an alternative’s
total score to be used for comparison.

Weighting factors for the car example.
Attributes Relative Rank Normalized Rank
Horsepower 7 0.16
Transmission 11 0.24
Color 1 0.02
Body style 10 0.22
Brand 8 0.18
Gas mileage 6 0.13
Dealer reputation 2 0.05
45 1.00

Combining weights with nondimensional data for the
car buying decision. Car A is now the best choice!
Car A Car B Car C
Attribute Weight Rate Score Rate Score Rate Score
Horsepower 0.16 0.00 0.00 1.00 0.16 0.28 0.04
Transmission 0.24 1.00 0.24 1.00 0.24 0.00 0.00
Color 0.02 0.00 0.00 1.00 0.02 0.50 0.01
Body style 0.22 1.00 0.22 0.00 0.00 1.00 0.22
Brand 0.18 0.00 0.00 1.00 0.18 0.00 0.00
Gas mileage 0.13 1.00 0.13 0.00 0.00 0.38 0.05
Dealer rep. 0.05 1.00 0.05 0.33 0.02 0.00 0.00
Sum of score 0.64 0.62 0.32

Decision making considering multi-attributes

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