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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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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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  • 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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