1 APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS DECISIONS UNDER CERTAINTY Professor L. Robin Keller Multi-objective Decision Under.

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APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS

DECISIONS UNDER CERTAINTY

Professor L. Robin KellerMulti-objective Decision Under Certainty

Class 2

The INFORMS Merger Decision

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DECISIONS UNDER CERTAINTY

MUST CHOOSE AMONG SET OF ALTERNATIVES

EACH ALTERNATIVE DESCRIBED BY SEVERAL OBJECTIVES, EACH LOWEST LEVEL OBJECTIVE MEASURED BY A SPECIFIED SCALE (aka “Attribute Scale”)

DO NOT INCLUDE PROBABILISTIC UNCERTAINTY IN MODEL

USE WEIGHT AND RATE TECHNIQUE TO CHOOSE BEST ALTERNATIVE

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MULTI-OBJECTIVE MEASURABLEVALUE FUNCTIONS STRUCTURE OBJECTIVES IN HIERARCHICAL TREE DIRECTLY JUDGE VALUE RATINGS OF HOW WELL AN

ALTERNATIVE DOES ON EACH LOWEST LEVEL OBJECTIVE (or ASSESS SINGLE OBJECTIVE MEASURABLE VALUE FUNCTION FOR RATING EACH OBJECTIVE)

ASSESS WEIGHTS FOR LOWEST LEVEL OBJECTIVES FOR EACH ALTERNATIVE, COMPUTE WEIGHTED

AVERAGE OF VALUE RATINGS BY MULTIPLYING AN OBJECTIVES’S WEIGHT TIMES THAT OBJECTIVE’S VALUE RATING AND SUMMING OVER ALL LOWEST LEVEL OBJECTIVES

MODEL RECOMMENDS CHOICE OF ALTERNATIVE WITH HIGHEST WEIGHTED AVERAGE

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MERGER APPLICATION MULTI-OBJECTIVE ADDITIVE MEASURABLE VALUE FUNCTION IN ANALYSIS OF POTENTIAL

MERGER OF OPERATIONS RESEARCH SOCIETY OF AMERICA (ORSA)

AND THE INSTITUTE OFMANAGEMENT SCIENCES (TIMS)

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EVALUATION OF ORSA/TIMS MERGER ALTERNATIVES

AS OF DECEMBER 1993

I CHAIRED A COMMITTEE TO EVALUATE ALTERNATIVES (aka OPTIONS)

ARIZONA STATE’S DECISION ANALYSIS PROF. CRAIG KIRKWOOD WAS ON COMMITTEE

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ORSA/TIMS MERGER TREE

FIVE MAIN CATEGORIES

IMPROVE COST EFFICIENCY

ENHANCE QUALITY OF PRODUCTS

ESTABLISH STRONG EXTERNAL IMAGE

MAINTAIN SCOPE/DIVERSITY OF FIELD

IMPROVE OPERATIONS

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ADD BRANCHES TO MAIN CATEGORIES

IMPROVE COST EFFICIENCY

MAINTAIN ALLOCATE WELL MAINTAINEFFICIENT REVENUES AND EFFICIENTUSE OF FUNDS EXPENSES USE OF

TIME

EXPLOIT BALANCE DUES REMOVEECONOMIES RATE & FEE- DOUBLEDOF SCALE FOR-SERVICE DUES

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1. Improve cost efficiency ofTIMS/ORSA operations

2. Enhance the quality of ORSAand TIMS products

3. Establish a strong & coherentexternal image of field

4. Manage the scope and diversityof the field

5. Maintain/improve effectivenessof ORSA and TIMS operations

1.1 Maintain efficient use of funds

1.2 Allocate well revenues/expenses toactivities/entities

1.3 Maintain efficient use of time of volunteers

2.1 Provide high quality main and specialtyconferences

2.2 Provide high quality publications

2.3 Provide appropriate career services

2.4 Provide support for sub-units

2.5 Provide other member services

3.1 Increase visibility and clout of OR and MS

3.2 Foster professional identity

4.1 Maintain/improve membership composition

4.2 Create strong relationships with other societies

5.1 Maintain/improve quality of governance process

5.2 Maintain/improve quality of operation output

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Description of the final objectives used by the Cost/Benefit Committee

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ASSESS SINGLE OBJECTIVE VALUE RATINGS or FUNCTIONS

FOR RATING PERFORMANCE ON EACH OBJECTIVE

CHOOSE CONVENIENT ARBITRARY SCALE, CAN BE – WORST IS 0 AND BEST IS 1.0– WORST IS -2 AND BEST IS 2

OR CAN ASSESS A FUNCTIONAL FORM

vOBJECTIVE 1 (level of OBJECTIVE 1)

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VALUE RATING SCALE

2: SEEN BY AVERAGE MEMBER AS IMPROVED

1: SEEN BY OFFICERS AS IMPROVED BUT NOT BY AVERAGE MEMBER

0: NO CHANGE

-1: SEEN BY OFFICERS AS WORSE

-2: SEEN BY AVERAGE MEMBER AS WORSE

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INTERPRETATION OF MEASURABLE VALUE FUNCTION

STRENGTH OF PREFERENCES IS REFLECTED IN DIFFERENCES OF VALUES

DEGREE OF IMPROVEMENT

FROM 0 TO 1IS THE SAME AS

FROM 1 TO 2

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ORSA/TIMS COOPERATION ALTERNATIVES

SEP: SEPARATION OF ORSA & TIMS

SQ: STATUS QUO PARTNERSHIP

SM: SEAMLESS MERGER

M2: MERGE WITH ORSA/TIMS AS SUB-UNITS

M3: MERGE WITH NO ORSA/TIMS SUB-UNITS; SUB-UNITS ARE REPRESENTED ON BOARD

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JUDGED VALUE RATING SCORES

JUDGED VALUE RATING

ON ALTERNATIVES

OBJECTIVES SEP SQ SM M2 M3

1. IMPROVE COST EFFICIENCY

1.1 MAINTAIN EFFICIENT USE OF FUNDS

1.1.1 EXPLOIT ECONOMIES OF SCALE -2 0 1 -1 1

1.1.2 BALANCE DUES RATE AND

FEE-FOR-SERVICE-2 0 1 -1 1

1.1.3 REMOVE DOUBLED DUES -1 0 2 1 2

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WEIGHTS FOR OBJECTIVES

SUM OF WEIGHTS IS 1OO% FOR ALL LOWEST LEVEL OBJECTIVES

OBJECTIVE’S WEIGHT DEPENDS ON RANGE ATTAINABLE ON OBJECTIVE

DECISION MAKER JUDGES WEIGHTS ON OBJECTIVES

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Evaluation Judged Cooperation Alternative

Considerations Weight SEP SQ SM M2 M3

1. Improve cost efficiency of TIMS/ORSA operations

1.1 Maintain efficient use of funds

1.2 Allocate well revenues/expenses to activities/entities

1.3 Maintain efficient use of time of volunteers

2. Enhance the quality of ORSA and TIMS products

2.1 Provide high quality main and specialty conferences

2.2 Provide high quality publications

2.3 Provide appropriate career services

2.4 Provide support for sub-units

2.5 Provide other member services

3. Establish a strong & coherent external image of field

3.1 Increase visibility and clout of OR and MS

3.2 Foster professional identity

4. Manage the scope and diversity of the field

4.1 Maintain/improve membership composition

4.2 Create strong relationships with other societies

5. Maintain/improve effectiveness of ORSA and TIMS operations

5.1 Maintain/improve quality of governance process

5.2 Maintain/improve quality of operation output

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COMPUTE WEIGHTED AVERAGE OF VALUE RATINGS

MULTIPLY OBJECTIVE’S WEIGHT TIMES VALUE RATING ON EACH OBJECTIVE

SUM UP OVER ALL OBJECTIVES

RECOMMENDED OPTION IS ONE WITH HIGHEST OVERALL VALUE

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USE OF MERGER EVALUATION FORM

COMMITTEE MEMBERS AND ORSA/TIMS OFFICERS WERE GIVEN THE EXPANDED FORM

THEY FILLED IN OWN JUDGMENTS ON FORM:– ASSESSED WEIGHTS ON 52 LOWEST LEVEL

OBJECTIVES– JUDGED VALUE RATINGS FOR 5

ALTERNATIVES ON 52 OBJECTIVES

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MY MERGER EVALUATION

NEXT I SHOW MY OWN JUDGMENTS FILLED IN ON THE EVALUATION FORM, SEE EXCEL FILE HANDOUT

WE DID NOT REQUIRE PEOPLE TO REVEAL THEIR OWN JUDGMENTS, THEY USED THE FORM TO FOCUS CONTINUED DISCUSSIONS AND NEGOTIATIONS

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RESULTS OF MERGER DECISION ANALYSIS

OFFICERS TENDED TO PREFER MERGER3 ALTERNATIVE, WITH SUB-UNIT BOARD REPRESENTATION

VOCAL OPPONENTS WOULD COMPROMISE ON SEAMLESS MERGER, WITHOUT SUB-UNIT BOARD REPRESENTATION, AS LONG AS NEW NAME RETAINS “OPERATIONS RESEARCH”

Ask me about tea bags

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OUTCOME OF DECISION OFFICERS PRESENTED SEAMLESS MERGER

RECOMMENDATION TO MEMBERS MEMBERS VOTED TO MERGE MERGER TOOK PLACE JAN. 1ST, 1995 NAME IS INSTITUTE FOR OPERATIONS

RESEARCH AND THE MANAGEMENT SCIENCES (INFORMS)

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KEY POINTSTHE DECISION ANALYSIS WAY OF THINKING CAN BE APPLIED INFORMALLY IN MANY SITUATIONS

FORMAL OR INFORMAL DECISION ANALYSIS IS MEANT TO AID THE DECISION MAKER & PROVIDE INSIGHTS

Try to limit number of objectives (52 is too many)

Terms vary: Alternatives/options/ActionsObjectives//evaluation considerations/Attributes and attribute scales

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What do weights mean? Are weights priorities/importance?What is more important health or wealth?

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Swing Weight Technique to Assess Weights on Objectives

Most important point: OBJECTIVES’S WEIGHT DEPENDS ON RANGE OF PERFORMANCE ON OBJECTIVE

A person (Dilbert’s boss?) can’t say which objective is most important without knowing the range

SUM OF Normalized WEIGHTS IS 1OO% or 1.0 FOR ALL LOWEST LEVEL OBJECTIVES (conventionally)

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Swing Weight Method- Step 1 Think of starting with all 4 objectives (i.e., for a new apartment) at their worst levels. That will be the “benchmark worst option=alternative.”

We’ll make 4 hypothetical options, each with only one objective at best level, other objectives at worst.

Which is the “most important” objective, the first one which we’d choose to swing the level from worst to best? It is at its best level in the 1st ranked option. Give this best option a rating of 100. Assign other options ratings between 100 and 0.

Normal- ized

Raw Weight Benchmark

weights 1st rank 2nd rank 3rd rank 4th rank all worst

Most important objective 1 0 0 0 0

2nd most imp. objective 0 1 0 0 0

3rd most imp. objective 0 0 1 0 0

Least imp. objective 0 0 0 1 0

Directly rate overall value of each option Best = 100 90 70 20 Worst = 0

Options with one objective at best level, others at worst

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Swing Weight Method- Step 2 The direct ratings of the options (on a scale from 100 to 0) can be used to infer the “raw weights” on each objective. Remember an overall rating is computed by multiplying each objective’s weight times its rating and summing. Since the four hypothetical options have ratings of 0 for all but one objective, their overall rating is calculated by the raw weight on the objective at its best level times the rating, which is 1.

V(1st rank option) = 100 = raw weightmost important objective x ratingmost imp.objective + 0V(1st rank option) = 100 = raw weightmost important objective x 1 + 0

Normal- ized

Raw Weight Benchmark

weights 1st rank 2nd rank 3rd rank 4th rank all worst

Most important objective 100 1 0 0 0 02nd most imp. objective 90 0 1 0 0 03rd most imp. objective 70 0 0 1 0 0Least imp. objective 20 0 0 0 1 0

Directly rate overall value of each option

Best = 100 90 70 20

Worst = 0

Options with one objective at best level, others at worst

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Swing Weight Method- Step 3 The “raw weights” on each objective can be used to calculate normalized weights that sum up to 1. The raw weights sum up to 280 in this example. Divide each raw weight by sum = 280 to get normalized weights which sum to 1.0.

Normal- ized

Raw Weight Benchmark

weights 1st rank 2nd rank 3rd rank 4th rank all worst

Most important objective 100/sum 100 1 0 0 0 02nd most imp. objective 90/sum 90 0 1 0 0 03rd most imp. objective 70/sum 70 0 0 1 0 0Least imp. objective 20/sum 20 0 0 0 1 0

Sum of weights 1280= sum

Directly rate overall value of each option

Best = 100 90 70 20

Worst = 0

Options with one objective at best level, others at worst

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Swing Weight Method- general “short-cut” summary of all stepsStart with a benchmark option with all k objectives at their worst levels. Make k hypothetical options, each with only one objective at best level, others at worst. List first the most important objective for which we’ll swing the level from worst to best. That objective is at its best level in the first ranked hypothetical option. The 1st ranked option has a rating of 100, so the raw weight on the most important objective is 100. Assign other options ratings between 100 and 0. Compute sum of raw weights and then compute normalized weights by dividing raw weights by their sum.

For large numbers of objectives, direct judgements of the weights will likely be used.

The Most Important Objective swings first from its worst to best level

The Second Most Important Objective swings second from its worst to best level

The Least Important Objective swings last from its worst to best level

The benchmark option has all objectives at worst level

RANK of Rating=option w/ this RAWobjective at top level WEIGHT

NORMALIZEDWEIGHT

100

90

. . .

20 0

SUM = ?

. . .

100/sum

90/sum

20/sum 0

= 1.0

1st

2nd

LastBenchmark

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Swing Weight Practice AssessmentChoose 1st or 2nd & fill in the blank cells

Option Health Wealth Rank Directly Rate = raw

weight,

With 100 for best

Normalized weight

Raw weight/SUM =

Horrible Bad health

Low $ Benchmark Fixed to be 0

Healthy Poor Great health

Low $ 1st or 2nd?

Wealthy Sick Bad health

High $ 1st or 2nd?

SUM=

_____? = 1.0

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Swing Weight Practice AssessmentSample answer

Option Health Wealth Rank Directly Rate = raw weight,

With 100 for best

Normalized weight

Raw weight/SUM =

Horrible Bad health

Low $ Benchmark Fixed to 0

Healthy Poor Great health

Low $ 1st or 2nd?

FIRST 100 100/150 =

Wh = 2/3Wealthy Sick Bad

health High $ 1st or 2nd?

SECOND 50 50/150 =

W$= 1/3

SUM=

150 = 1.0

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Now compute overall value of 4 different health/wealth options with assessed swing weights

Name of

Option

Rating of

v(Health)

Multiply by

Weight wh on health

Rating of

V(Wealth)

Multiply by

Weight w$ on wealth

Overall

Multi-objective Value

Horrible v(Bad health) =

0 X__ +v(Low $) =

0 X__ =0 x wh+ 0 x w$ =

0Healthy Poor

v(Great health) =

1 X__ +V(Low $) =

0 X__ =Wealthy sick

v(Bad health) =

0 X__ +V(High $) =

1 X__ =Healthy and Wealthy

v(Great health) =

1 X__ +V(High $) =

1 X__ =1 x wh+ 1 x w$ =

1.0

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REFERENCES• L. ROBIN KELLER AND CRAIG W. KIRKWOOD,

“The Founding of INFORMS: A Decision Analysis Perspective,” Operations Research, Vol. 47, No. 1, January-February 1999, 16-28.

• http://www.informs.org