Multi-Criteria Decision Making

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Multi-Criteria Decision Making

• Decision Making and Risk, Sp2006 Session 6

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Notebook Computer Decision

• Consumer is interested in buying a notebook
  computer.
• Goes to electronics store.
• Sees the following options.
• How should she go about buying one?

3




 
 



 
Choices
Brand and Model Price Processor Speed RAM HD Screen
Model A 699 1.8 GHz 256 MB 100 GB 15.4
Model B 749 1.9 GHz 256 MB 100 GB 15
Model C 599 1.4 GHz 512 MB 60 GB 12
Model D 799 1.7 GHz 256 MB 80 GB 14.1


 

How would you proceed if you were the one making
the choice?
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Types of MCDM Rules

• Compensatory
• Simple compensatory
• Linear (integration and valuation)
• Non-linear (linear integration, non-linear
  valuation)
• Non-compensatory
• Screening
• Conjunctive
• Disjunctive
• Selection
• Elimination by aspects
• Lexicographic
• Heuristics

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Simple Compensatory Rule

• Alternative with the most number of top of class
  performance.

Brand and Model Price Processor Speed RAM HD Screen
Model A 699 1.8 GHz 256 MB 90 GB 15.4 1
Model B 749 1.9 GHz 256 MB 100 GB 15.4 3
Model C 599 1.4 GHz 512 MB 60 GB 12 2
Model D 799 1.7 GHz 256 MB 80 GB 14.1 0
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Approach 1

• Imagine n objects, with m attributes each.
• For the ith object
• Declare attribute importance for each of the m
  attributes (wj).
• Determine how much you like the level of the
  attribute in the ith product (aij)
• Combine attribute importance with attractiveness
  of the attribute level featured in the product.
• Add the above combinations.
• For the ith object, Vi Sj1 to n (wj aij),
  akin to expected utility.
• Repeat this for all i objects.
• Pick i such that, i Max (V1, V2, V3..Vn)

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Illustration Linear Compensatory Decision Rules
Price CPU RAM HD Screen
A 3 3 1 3 4 3.1
B 2 4 1 4 4 2.8
C 4 1 4 1 1 2.5
D 1 2 1 2 2 1.5
Wt 0.3 0.25 0.2 0.15 0.2
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Non-linear Compensatory Decision Rules

• Valuation of additional unit is not identical
  across the range of the levels.
• 60G to 80G is more consequential compared to 100
  to 120G
• However, integration across attributes of the
  alternatives is still linear.

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Summary of Compensatory

• Simple compensatory No relative valuation of
  attribute levels other than best/not best, equal
  weight for all attributes.
• Linear Compensatory Equal valuation of
  attributes levels, linear combination of
  valuation through attribute-specific weights.
• Non-linear Compensatory Unequal valuation of
  attribute levels, linear combination of valuation
  through attribute-specific weights.

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Non-Compensatory Decision Rules

• Screening Rules
• Conjunctive decision rule
• Disjunctive decision rule
• Choice Rules
• Elimination by aspects
• Lexicographic decision rule

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Elimination by Aspects

• Elimination By Aspects
• Start with minimum cutoff on most important
  attribute.
• Eliminate those that do not clear cutoff.
• Take the next most important attribute, and
  repeat steps above.
• Stop when you have one brand.
• Elimination rule, rather than selection rule.

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Conjunctive

• Eliminate alternatives that dont meet/exceed
  cutoff on every attribute.

Brand Price CPU RAM HD Screen Size
Compaq A 3 3 1 4 4
Compaq B 2 4 1 3 3
Compaq C 4 1 4 1 1
Compaq D 1 2 1 2 2
Min Cutoff 2 2 1 2 2


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Disjunctive

• Accept any alternative that exceeds minimum
  cutoff on at least one attribute.

Brand Price CPU RAM HD Screen Size
Compaq A 3 3 1 3 4
Compaq B 2 4 1 3 4
Compaq C 4 1 4 1 1
Compaq D 1 2 1 4 2
Cutoff 3 2 1 2 2
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Elimination By Aspects
Brand Price CPU RAM HD Screen Size
Compaq A 3 3 1 3 4
Compaq B 2 4 1 3 4
Compaq C 4 1 4 1 1
Compaq D 1 2 1 4 2
Cutoff lt2 N/A lt2



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Lexicographic

• Select best option on the most important
  attribute.

Brand Price CPU RAM HD Screen Size
Compaq A 3 3 1 3 4
Compaq B 2 4 1 3 4
Compaq C 4 1 4 1 1
Compaq D 1 2 1 4 2
Weight .3 .2 .2 .1 .2
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Comparing Compensatory and Non-compensatory
Decision Rules

• Compensatory Decision Rules
• Strengths of one attribute can overcome weakness
  of another.
• Selection rules
• Effortful
• Non-Compensatory Decision Rules
• Strength of one attribute cannot overcome
  weakness of another.
• Elimination rules
• Easier
• Often decision makers use hybrid rules

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Highlights

• What happens when decision options come with
  multiple attributes?
• Reduce them to a single attribute
• Deal with multiple attributes
• Compensatory
• Weighted attribute utility approach
  (compensatory)
• Non-compensatory
• EBA (sequential elimination)
• Lexicographic (selection by reduction to single
  attributerepeat if necessary)
• Conjunctive (inclusion based on thresholds for
  every attribute)
• Assists in narrowing the consideration set
• Disjunctive (inclusion based on threshold for at
  least one attribute)
• Assists in broadening the consideration set
• Different strategies at different stages.
• Vary in effort and data required.
• Regret may be a function of the type of decision
  strategy.
• Thresholds are the result of past experiences,
  negatives leave a stronger imprint.

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Heuristics

• Decision rules, shortcuts.
• Sometimes, they are meta-decisions.
• Some Examples
• What I did the last time around?
• What does the expert think?
• The price-quality relationship is
• Bogus, so, look for the relatively less expensive
  option.
• Valid, so, look for the relatively more expensive
  option.
• Minimize decision effort/cost.
• Minimize regret.
• Maximize effectiveness.