mutli-attribute decision making
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Mutli-Attribute Decision Making
Scott MatthewsCourses: 12-706 / 19-702/ 73-359
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Admin Issues
Projects - look good so far. Some comments coming
Early evaluations?Lecture
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Dominance
To pick between strategies, it is useful to have rules by which to eliminate options
Let’s construct an example - assume minimum “court award” expected is $2.5B (instead of $0). Now there are no “zero endpoints” in the decision tree.
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Dominance Example #1
CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.
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But..
Need to be careful of “when” to eliminate dominated alternatives, as we’ll see.
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Multi-objective Methods
Multiobjective programming Mult. criteria decision making (MCDM)Is both an analytical philosophy and a
set of specific analytical techniques Deals explicitly with multi-criteria DM Provides mechanism incorporating values Promotes inclusive DM processes Encourages interdisciplinary approaches
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Decision Making
Real decision making problems are MC in nature Most decisions require tradeoffs E.g. college-selection problem BCA does not handle MC decisions well
It needs dollar values for everythingAssumes all B/C quantifiable
BCA still important : economic efficiency
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MCDM Terminology
Non-dominance (aka Pareto Optimal) Alternative is non-dominated if there is
no other feasible alternative that would improve one criterion without making at least one other criterion worse
Non-dominated set: set of all alternatives of non-dominance
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More Defs
Measures (or attributes) Indicate degree to which objective is achieved or
advanced Of course its ideal when these are in the same order of
magnitude. If not, should adjust them to do so.
Goal: level of achievement of an objective to strive for
Note objectives often have sub-objectives, etc.
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Example Objective
Minimize air emissionsObjective:
Min. SO2 Min. NOxSub-objectives:
Measures: tons SO2/yr tons NOx/yr
Potential Goal: reduce SO2 emissions by 50%!
This implies the need for an objective hierarchy or value tree
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Desirable Properties of Obj’s
Completeness (reflects overall objs)Operational (supports choice)Decomposable (preference for one is
not a function of another)Non-redundant (avoid double count)Minimize size
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Structuring Objectives
Choose a college
Reputation Cost Atmosphere
Academic SocialTuitionLivingTrans.Making this tree is useful for
Communication (for DM process) Creation of alternatives Evaluation of alternatives
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Key Issues
Specification - objectives need to be specified to allow measures to be specified ‘Max air quality’ not good enough! Find a balance between enough spec. to
allow measure and ‘too much’ spec.Means v. Ends - Hierarchy should
only include ‘ends objectives’
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Choosing a Car
Car Fuel Eff (mpg) Comfort IndexMercedes 25 10Chevrolet 28 3Toyota 35 6Volvo 30 9Which dominated, non-dominated?
Dominated can be removed from further consideration
BUT we’ll need to maintain their values for ranking
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Conflicting Criteria
Two criteria ‘conflict’ if the alternative which is best in one criteria is not the best in the other Do fuel eff and comfort conflict? Usual. Typically have lots of conflicts.
Tradeoff: the amount of one criterion which must be given up to attain an increase of one unit in another criteria
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Tradeoff of Car Problem
Fuel Eff
Comfort
10
5
0 10 20 30
MV
T
C
1) What is tradeoff between Mercedes and Volvo?
2) What can we see graphicallyabout dominated alternatives?
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Tradeoff of Car Problem
Fuel Eff
Comfort
10
5
0 10 20 30
M(25,10)V(30,9)
T
C
-15
The slope of the line between M and V is -1/5, i.e., you must trade one unit less of comfort for 5 units more of fuel efficiency.
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Tradeoff of Car Problem
Fuel Eff
Comfort
10
5
0 10 20 30
M(25,10)V(30,9)
T (35,6)
-15
Would you give up one unit of comfort for 5 more fuel economy?
-3
5
THEN Would you give up 3 units of comfort for 5 more fuel economy?
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MCDM with Decision Trees
Incorporate uncertainties as event nodes with branches across possibilities See “summer job” example in Chapter
4.
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Still need special (external) scales. And need to value/normalize them Typically give 100 to best, 0 to worst,
find scale for everything between (job fun)
Get both criteria on 0-100 scales!
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Next Step: Weights
Need weights between 2 criteria Don’t forget they are based on whole scale e.g., you value “improving salary on scale 0-
100 at 3x what you value fun going from 0-100”. Not just “salary vs. fun”
If choosing a college, 3 choices, all roughly $30k/year, but other amenities different.. Cost should have low weight in that example
In Texaco case, fact that settlement varies across so large a range implies it likely has near 100% weight
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Notes
While forest job dominates in-town, recall it has caveats: These estimates, these tradeoffs, these
weights, etc. Might not be a general result.
Make sure you look at tutorial at end of Chapter 4 on how to simplify with @RISK
Read Chap 15 Eugene library example!
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Next time: Advanced Methods
More ways to combine tradeoffs and weights
Swing weightsEtc.
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How to solve MCDM problems
All methods (AHP, SMART, ..) return some sort of weighting factor set Use these weighting factors in
conjunction with data values (mpg, price, ..) to make value functions
In multilevel/hierarchical trees, deal with each set of weights at each level of tree
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