Mutli-Attribute Decision Making

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# Mutli-Attribute Decision Making - PowerPoint PPT Presentation

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

Scott Matthews

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

• Projects - look good so far.
• Early evaluations?
• Lecture

12-706 and 73-359

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
• 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
• 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

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
• 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

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

Atmosphere

Reputation

Cost

Social

Tuition

Living

Trans.

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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
• 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
• 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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1) What is tradeoff between Mercedes and Volvo?

Comfort

M

10

V

T

2) What can we see graphically

5

C

0

10

Fuel Eff

20

30

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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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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
• 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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