1 APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS DECISIONS UNDER CERTAINTY...
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Transcript of 1 APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS DECISIONS UNDER CERTAINTY...
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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
M
AX
IMIZ
E O
VE
RA
LL
VA
LU
E
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