Transcript INFORMS Merger - University of California, Irvine

Professor L. Robin Keller
Multi-objective Decision Under Certainty
Class 2
APPLICATIONS OF MULTI-OBJECTIVE DECISION
MODELS FOR DECISION ANALYSIS
DECISIONS UNDER CERTAINTY
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 MEASURABLE
VALUE 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 OF
MANAGEMENT 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 MAINTAIN
EFFICIENT
REVENUES AND EFFICIENT
USE OF FUNDS
EXPENSES
USE OF
TIME
EXPLOIT
ECONOMIES
OF SCALE
BALANCE DUES REMOVE
RATE & FEEDOUBLED
FOR-SERVICE
DUES
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1.1 Maintain efficient use of funds
1. Improve cost efficiency of
TIMS/ORSA operations
1.2 Allocate well revenues/expenses to
activities/entities
1.3 Maintain efficient use of time of volunteers
2.1 Provide high quality main and specialty
conferences
2. Enhance the quality of ORSA
and TIMS products
2.3 Provide appropriate career services
2.4 Provide support for sub-units
VALUE
MAXIMIZE OVERALL
2.2 Provide high quality publications
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
4.1 Maintain/improve membership composition
4. Manage the scope and diversity
of the field
4.2 Create strong relationships with other societies
5.1 Maintain/improve quality of governance process
5. Maintain/improve effectiveness
of ORSA and TIMS operations
5.2 Maintain/improve quality of operation output
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 1
IS 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
-2
0
1
-1
1
-1
0
2
1
2
FEE-FOR-SERVICE
1.1.3 REMOVE DOUBLED DUES
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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
Considerations
Weight
Cooperation Alternative
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”
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 Ask me about tea bags
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 POINTS
THE 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/Actions
Objectives//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
person (Dilbert’s boss?) can’t say which objective is most
important without knowing the range
A
 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- Raw
Options with one objective at best
ized
Weight
level, others at worst
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
70
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Worst =240
Directly rate overall value of each option
Best
= 100 90
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 + 0
V(1st rank option) = 100 = raw weightmost important objective x 1
+0
Normalized
weights
Most important objective
2nd most imp. objective
3rd most imp. objective
Least imp. objective
Raw
Weight
100
90
70
20
Directly rate overall value of each option
Options with one objective at best
level, others at worst
Benchmark
1st rank 2nd rank 3rd rank 4th rank all worst
1
0
0
0
Best
= 100
0
1
0
0
90
0
0
1
0
70
0
0
0
1
0
0
0
0
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Worst =
0
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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.
Normalized
weights
Most important objective
2nd most imp. objective
3rd most imp. objective
Least imp. objective
Sum of weights
Raw
Weight
100/sum 100
90/sum
90
70/sum
70
20/sum
20
1
Directly rate overall value of each option
Options with one objective at best
level, others at worst
Benchmark
1st rank 2nd rank 3rd rank 4th rank all worst
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
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Worst =
0
280=
sum
Best
= 100
90
70
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Swing Weight Method- general “short-cut” summary of all steps
Start 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.
RANK of
Rating=
option w/ this
objective at top level
RAW
WEIGHT
NORMALIZED
WEIGHT
1st
100
100/sum
The Second Most Important Objective swings second from its worst to
2nd
best level
90
90/sum
The Most Important Objective swings first from its worst to best level
.
.
.
.
.
.
The Least Important Objective swings last from its worst to best level
Last
The benchmark option has all objectives at worst level
Benchmark
20/sum
0
20
0
SUM = ?
 = 1.0
For large numbers of objectives, direct judgements of the weights will likely be
used.
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Swing Weight Practice Assessment
Choose 1st or 2nd & fill in the blank cells
Option
Horrible
Health
Wealth
Rank
Bad
health
Low $
Healthy Poor
Great
health
Low $
1st or 2nd?
Wealthy Sick
Bad
health
High $
1st or 2nd?
Directly
Rate = raw
weight,
With 100
for best
Normalized
weight
Raw
weight/SUM =
Benchmark Fixed to
be 0
SUM=
_____?
 = 1.0
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Swing Weight Practice Assessment
Sample answer
Option
Health Wealth
Rank
Directly Rate
= raw weight,
With 100 for
best
Horrible
Bad
health
Low $
Benchmark
Fixed to 0
Healthy Poor
Great
health
Low $
1st or 2nd?
FIRST
100
Wealthy Sick Bad
health
High $
1st or 2nd?
SECOND
50
SUM=
Normalized
weight
Raw
weight/SUM =
100/150 =
Wh = 2/3
50/150 =
W$= 1/3
 = 1.0
150
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Now compute overall value of 4 different
health/wealth options with assessed swing weights
Name of
Option
Horrible
Rating of
v(Health)
Multiply
by
Weight wh
on health
v(Bad health) =
0
Healthy
Poor
v(Great health) =
Wealthy
sick
v(Bad health) =
Healthy
and
Wealthy
v(Great health) =
1
0
1
Rating of
V(Wealth)
Multiply
Overall
by
Multi-objective
Weight w$
Value
on wealth
v(Low $) =
__ +
X
0
0 x wh+ 0 x w$ =
__ =
X
0
V(Low $) =
__ +
X
0
__ =
X
V(High $) =
__ +
X
1
__ =
X
V(High $) =
__ +
X
1
1 x wh+ 1 x w$ =
__ =
X
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
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