MultiAttribute Value Analysis Value Assessment

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Multi-Attribute Value AnalysisValue Assessment
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Multiple Objectives

• We often find ourselves with multiple objectives
• Fun
• Profit
• We have to come up with a common measure
• Otherwise we compare apples oranges
• Utility provides a common scale
• However, 0.7 on one utility scale might not be
  the same as 0.7 on the other
• We need to weight the comparative importance

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Weight Elicitation Theory Techniques
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Elicitation Techniques

• Swing Weighting Emphasizes the Range of
  Variation of variables
• Independent comparison of importance
• Relatively easy to elicit
• Trade-Offs A Derivative of Swing Weighting in
  Logical Decisions
• Zero sum game
• Easy to elicit

Courtesy Dr. Dan Maxwell
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Swing Weighting

• Based on comparing ranges of variation of
  attributes
• Can be used for non-quantitative attributes
• Method
• (1) Find Worst Conceivable Alternative
• - Lowest score in each attribute
• - May be imaginary
• (2) Pick attribute that gives greatest
  improvement when swings to highest level -
  remember increase
• (3) Pick attribute that gives next highest
  increase when swung
• - by percentage - how does it compare with the
  first?
• - never greater than 1 since first is best

Courtesy Dr. Dan Maxwell
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Example Networking Strategy

• A company is deciding what strategy to follow
  with respect to networking its personal
  computers. It will consider the following
  alternative strategies
• Status Quo (remain with old systems)
• Low cost / Low quality
• Medium Cost / Medium Quality
• High cost / High quality
• The company has selected three evaluation
  measures
• Productivity Enhancement,
• Cost Increase, and
• Security.
• Cost Increase is the net present value of the
  increased cost for an alternative relative to the
  current situation (measured in K)
• Productivity Enhancement and Security each have
  constructed scales.

Example is from Kirkwood, Craig Strategic
Decision Making, Duxbury Press, 1997 - Chapt 4
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Attribute Scale Productivity

• -1 User group productivity is diminished
  sufficiently that noticeably longer time or more
  resources are required to provide the same level
  of service.
• 0 No change in user group productivity is
  perceived.
• 1 User group productivity is enhanced to the
  extent that group members are perceived by their
  clients to be providing better service, or
  somewhat fewer resources are required to provide
  service at the same level as before the network
  was installed.
• 2 There is significant and easily perceived
  increase in user group productivity. Indicators
  of this could include a significant reduction in
  the staffing level required to carry out user
  group activities or considerable improvement in
  the financial performance of the group.
• Although subjective, the design team is sure that
  they can rate the productivity enhancement from
  each alternative network design according to this
  scale

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Attribute Scale Security

• -2 The addition of the network causes a
  potentially serious decrease in system control
  and security for the use of data or software.
• -1 There is a noticeable but acceptable
  diminishing of system control and security.
• 0 There is no detectable change in system
  control or security.
• 1 System control or security is enhanced by
  addition of a network.
• Cost is measured in dollars from 0 to (High
  Cost)
• Note that all of the scales are defined so that
  the status quo (that is, not adding a network)
  has a score of zero on each scale.
• However, the scales are not equivalent going
  from 0 to 1 on one scale is not necessarily
  the same as going from 0 to 1 on another
  scale. This is typical of constructed
  (artificial) scales

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Attribute Scale Security

• Cost is measured in dollars from 0 to (High
  Cost)
• Note that all of the scales are defined so that
  the status quo (that is, not adding a network)
  has a score of zero on each scale.
• However, the scales are not equivalent going
  from 0 to 1 on one scale is not necessarily
  the same as going from 0 to 1 on another
  scale. This is typical of constructed
  (artificial) scales

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Networking Strategy - Alternative Values
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Combining the Values
What is the best way to combine the three value
functions?

• Simple Averaging
• Status Quo (0-00)/30 (Best)
• High Quality/High Cost (2 - 125 0.5)/3
  -40.83
• Medium Quality/Medium Cost (1 - 95 0)13
  -31.33
• Low Quality/Low Cost (0.5 - 65 - 1)/3 -21.83
• Suppose that we measure Cost Increase in millions
  of dollars instead of thousands of dollars
• Status Quo (0 - 0 0)/3 0
• High Quality/High Cost (2 - 0.125 0.5)/3
  0.79
• Medium Quality/Medium Cost (1 - 0.095 0)/3
  0.30
• Low Quality/Low Cost (0.5 - 0.065 - 1)/3 -0.19

Problem !!
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Value (Utility) Functions

• Value functions convert measures into a common
  scale
• Usually we map to values between zero and one
• Proportional (simplest, most common with natural
  measures)
• Piecewise linear
• Other (e.g., exponential)

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Normalizing Formula

• For an evaluation measure where higher scores are
  more preferred
• For an evaluation measure where lower scores are
  more preferred
• This can still give us problems if we change the
  relative ranges of the measures
• However, this is an appropriate formula to use
  when we have proportional value functions
  (linear).
• Typically, natural scales such as Cost, Weight,
  etc.

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Normalizing (Proportional Scale)

• not the actual evaluation measure score
• proportion of the way along the range of that
  evaluation measure
• Linear Utility functions only

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Determining Value Functions - Example

• Example Productivity Enhancement evaluation
  measure.
• Suppose that the value increment between XP 0
  and XP 1 is the smallest increment between any
  two neighboring scores on the Productivity
  Enhancement scale.
• This value increment is the same as between XP
  1 and XP 2.
• The value increment between XP -1 and XP 0
  is greater than that between XP 0 and XP 1.
  Specifically, this value increment is twice as
  great as that between XP 0 and XP 1.
• ThenLet x represent the smallest value increment
  (from 0 to 1). Then the increment going from 1 to
  2 is also x, and the increment going from -1 to 0
  is 2x. Thus the sum of all the value increments
  is 2x x x. Hence, 2x x x 1, or 4x 1.
  Thus, x 1/4 0.25.

vp(-1) 0 (since this is the least preferred
level) vp(0) 0 2x 0.00 2 ? 0.25
0.50 vp(1) 0 2x x 0.00 2 ? 0.25 0.25
0.75 vp(2) 0 2x x x 0.00 2 ? 0.2
0.25 0.25 1.00
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Networking Strategy - Alternative Values
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Example Security Value Function

• Suppose that
• The value increment between XS -1 and XS 0
  is twice as large as that between XS 0 and XS
  1
• The value increment between XS -2 and XS -1
  is three times as large as that between XS 0
  and XS 1.
• Then, since the value increments must sum to 1,
  it is true that 3v 2v v 6v 1, where v
  represents the value increment between XS 0 and
  XS 1. Hence, v 1/6, and thus

vS (-2) 0 vS (-1) 0.00 3v 0.00 3 x
(1/6) 0.50 vS (0) 0.00 3v 2v 0.00 3 ?
(1/6) 2 ? (1/6) 0.83 vS (l) 0.00 3v 2v
v 0.00 3 ? (1/6) 2 ? (1/6) (1/6) 1.00
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Value Function Graphs

• The Productivity Increase and Security Piecewise
  Value Functions are graphed below

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Cost Increase Value Function

• Suppose that the Cost Increase Value Function is
  Exponential with the following formula

Then the value function will curve downward as
shown. This formula is used when bigger is worse.
is the value function used when bigger is better.
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Swing Weights - Example (Cont.)

• Swing Weighting corrects for the following
  problems
• The evaluation results depend on the range of
  variation that is specified for each evaluation
  measure, and
• The procedure assumes that variations on each
  evaluation measure from the worst to the best
  specified score are of equal importance.
• We use the following procedure
• 1. Consider increase in value from swinging each
  measure from min to max
• 2. Quantitatively scale each value increment as a
  multiple of the smallest
• 3. Set smallest value increment such that the
  total of all increments is 1
• 4. Use the results of (3) to determine the
  weights for all evaluation measures

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Swing Weights - Example (Cont.)

• Suppose that the swing over Productivity
  Enhancement (from -1 to 2) has the smallest value
  over all of the 3 criteria, followed by Cost
  (150 to 0) and then Security (-2 to 1).
• This is a subjective evaluation!
• Suppose also that
• Swing over Cost has 1.5 times the value as swing
  over Productivity Enhancement
• Swing over Security is 1.25 times the value as
  swing over Cost

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Swing Weights - Example (Cont.)
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Value Function and Weights - Example
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Backups
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Swing Weights (Cont.)

• (4) Repeat for rest of attributes
• (5) Assess weights by noting that

Solve for the ks
where ki weight of attribute i, and pi1
percentage of improvement compared with attribute
1
Courtesy Dr. Dan Maxwell