Title: MultiAttribute Value Analysis Value Assessment
1Multi-Attribute Value AnalysisValue Assessment
2Multiple 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
3Weight Elicitation Theory Techniques
4Elicitation 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
5Swing 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
6Example 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
7Attribute 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
8Attribute 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
9Attribute 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
10Networking Strategy - Alternative Values
11Combining 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 !!
12Value (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)
13Normalizing 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.
14Normalizing (Proportional Scale)
- not the actual evaluation measure score
- proportion of the way along the range of that
evaluation measure - Linear Utility functions only
15Determining 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
16Networking Strategy - Alternative Values
17Example 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
18Value Function Graphs
- The Productivity Increase and Security Piecewise
Value Functions are graphed below
19Cost 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.
20Swing 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
21Swing 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
22Swing Weights - Example (Cont.)
23Value Function and Weights - Example
24Backups
25Swing 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