1

Mutli-Attribute Decision Making

Scott MatthewsCourses: 12-706 / 19-702/ 73-359

12-706 and 73-359 2

Admin Issues

Projects - look good so far. Some comments coming

Early evaluations?Lecture

12-706 and 73-359 3

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.

12-706 and 73-359 4

Dominance Example #1

CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

12-706 and 73-359 5

But..

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

12-706 and 73-359 6

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

12-706 and 73-359 7

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

12-706 and 73-359 8

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

12-706 and 73-359 9

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.

12-706 and 73-359 10

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

12-706 and 73-359 11

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

12-706 and 73-359 12

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

12-706 and 73-359 13

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’

12-706 and 73-359 14

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

12-706 and 73-359 15

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

12-706 and 73-359 16

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?

12-706 and 73-359 17

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.

12-706 and 73-359 18

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?

12-706 and 73-359 19

MCDM with Decision Trees

Incorporate uncertainties as event nodes with branches across possibilities See “summer job” example in Chapter

4.

12-706 and 73-359 20

12-706 and 73-359 21

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!

12-706 and 73-359 22

12-706 and 73-359 23

12-706 and 73-359 24

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

12-706 and 73-359 25

12-706 and 73-359 26

12-706 and 73-359 27

12-706 and 73-359 28

12-706 and 73-359 29

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!

12-706 and 73-359 30

Next time: Advanced Methods

More ways to combine tradeoffs and weights

Swing weightsEtc.

12-706 and 73-359 31

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