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Mutli-Attribute Decision Making. Scott Matthews Courses: 12-706 / 19-702/ 73-359. Admin Issues. Projects - look good so far. Some comments coming Early evaluations? Lecture. Dominance. To pick between strategies, it is useful to have rules by which to eliminate options

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mutli attribute decision making

Mutli-Attribute Decision Making

Scott Matthews

Courses: 12-706 / 19-702/ 73-359

admin issues
Admin Issues
  • Projects - look good so far.
    • Some comments coming
  • Early evaluations?
  • Lecture

12-706 and 73-359

dominance
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
Dominance Example #1
  • CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

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slide5
But..
  • Need to be careful of “when” to eliminate dominated alternatives, as we’ll see.

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multi objective methods
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
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 everything
      • Assumes all B/C quantifiable
    • BCA still important : economic efficiency

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mcdm terminology
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
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
Example Objective

Objective:

Minimize air emissions

Sub-objectives:

Min. SO2

Min. NOx

tons SO2/yr

tons NOx/yr

Measures:

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
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
Structuring Objectives

Choose a college

  • Making this tree is useful for
    • Communication (for DM process)
    • Creation of alternatives
    • Evaluation of alternatives

Atmosphere

Reputation

Cost

Academic

Social

Tuition

Living

Trans.

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key issues
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
Choosing a Car
  • Car Fuel Eff (mpg) Comfort
  • Index
  • Mercedes 25 10
  • Chevrolet 28 3
  • Toyota 35 6
  • Volvo 30 9
  • Which 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
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
Tradeoff of Car Problem

1) What is tradeoff between Mercedes and Volvo?

Comfort

M

10

V

T

2) What can we see graphically

about dominated alternatives?

5

C

0

10

Fuel Eff

20

30

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tradeoff of car problem1
Tradeoff of Car Problem

Comfort

M(25,10)

10

-1

V(30,9)

5

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.

T

5

C

0

10

Fuel Eff

20

30

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tradeoff of car problem2
Tradeoff of Car Problem

Comfort

M(25,10)

10

-1

V(30,9)

5

Would you give up one unit of comfort for 5 more fuel economy?

-3

T (35,6)

5

5

THEN Would you give up 3 units of comfort for 5 more fuel economy?

0

10

Fuel Eff

20

30

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mcdm with decision trees
MCDM with Decision Trees
  • Incorporate uncertainties as event nodes with branches across possibilities
    • See “summer job” example in Chapter 4.

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slide21
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
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
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
Next time: Advanced Methods
  • More ways to combine tradeoffs and weights
  • Swing weights
  • Etc.

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how to solve mcdm problems
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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