1. 1 APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS DECISIONS UNDER CERTAINTY Professor L. Robin Keller Multi-objective Decision Under Certainty Class 2 The INFORMS Merger Decision

2. 2 DECISIONS UNDER CERTAINTY u MUST CHOOSE AMONG SET OF ALTERNATIVES u EACH ALTERNATIVE DESCRIBED BY SEVERAL OBJECTIVES, EACH LOWEST LEVEL OBJECTIVE MEASURED BY A SPECIFIED SCALE (aka “Attribute Scale”) u DO NOT INCLUDE PROBABILISTIC UNCERTAINTY IN MODEL u USE WEIGHT AND RATE TECHNIQUE TO CHOOSE BEST ALTERNATIVE

3. 3 MULTI-OBJECTIVE MEASURABLE VALUE FUNCTIONS u STRUCTURE OBJECTIVES IN HIERARCHICAL TREE u 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) u ASSESS WEIGHTS FOR LOWEST LEVEL OBJECTIVES u 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 u MODEL RECOMMENDS CHOICE OF ALTERNATIVE WITH HIGHEST WEIGHTED AVERAGE

4. 4 MERGER APPLICATION u MULTI-OBJECTIVE ADDITIVE MEASURABLE VALUE FUNCTION u IN ANALYSIS OF POTENTIAL MERGER OF OPERATIONS RESEARCH SOCIETY OF AMERICA (ORSA) AND THE INSTITUTE OF MANAGEMENT SCIENCES (TIMS)

5. 5 EVALUATION OF ORSA/TIMS MERGER ALTERNATIVES u AS OF DECEMBER 1993 u I CHAIRED A COMMITTEE TO EVALUATE ALTERNATIVES (aka OPTIONS) u ARIZONA STATE’S DECISION ANALYSIS PROF. CRAIG KIRKWOOD WAS ON COMMITTEE

6. 6 ORSA/TIMS MERGER TREE u FIVE MAIN CATEGORIES IMPROVE COST EFFICIENCY ENHANCE QUALITY OF PRODUCTS ESTABLISH STRONG EXTERNAL IMAGE MAINTAIN SCOPE/DIVERSITY OF FIELD IMPROVE OPERATIONS

7. 7 ADD BRANCHES TO MAIN CATEGORIES IMPROVE COST EFFICIENCY MAINTAIN ALLOCATE WELL MAINTAIN EFFICIENT REVENUES AND EFFICIENT USE OF FUNDS EXPENSES USE OF TIME EXPLOIT BALANCE DUES REMOVE ECONOMIES RATE & FEE- DOUBLED OF SCALE FOR-SERVICE DUES

8. 8 1. Improve cost efficiency of TIMS/ORSA operations 2. Enhance the quality of ORSA and TIMS products 3. Establish a strong & coherent external image of field 4. Manage the scope and diversity of the field 5. Maintain/improve effectiveness of ORSA and TIMS 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 2.1 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 3.1 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 MAXIMIZE OVERALL VALUE Description of the final objectives used by the Cost/Benefit Committee

9. 9 ASSESS SINGLE OBJECTIVE VALUE RATINGS or FUNCTIONS u FOR RATING PERFORMANCE ON EACH OBJECTIVE u CHOOSE CONVENIENT ARBITRARY SCALE, CAN BE –WORST IS 0 AND BEST IS 1.0 –WORST IS -2 AND BEST IS 2 u OR CAN ASSESS A FUNCTIONAL FORM v OBJECTIVE 1 ( level of OBJECTIVE 1 )

10. 10 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

11. 11 INTERPRETATION OF MEASURABLE VALUE FUNCTION u STRENGTH OF PREFERENCES IS REFLECTED IN DIFFERENCES OF VALUES u DEGREE OF IMPROVEMENT FROM 0 TO 1 IS THE SAME AS FROM 1 TO 2

12. 12 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

13. 13 JUDGED VALUE RATING SCORES JUDGED VALUE RATING ON ALTERNATIVES OBJECTIVES SEPSQSMM2M3 1. IMPROVE COST EFFICIENCY 1.1 MAINTAIN EFFICIENT USE OF FUNDS 1.1.1 EXPLOIT ECONOMIES OF SCALE -201 1 1.1.2 BALANCE DUES RATE AND FEE-FOR-SERVICE -201 1 1.1.3 REMOVE DOUBLED DUES 02 1 2

14. 14 WEIGHTS FOR OBJECTIVES u SUM OF WEIGHTS IS 1OO% FOR ALL LOWEST LEVEL OBJECTIVES u OBJECTIVE’S WEIGHT DEPENDS ON RANGE ATTAINABLE ON OBJECTIVE u DECISION MAKER JUDGES WEIGHTS ON OBJECTIVES

15. 15

16. 16 COMPUTE WEIGHTED AVERAGE OF VALUE RATINGS u MULTIPLY OBJECTIVE’S WEIGHT TIMES VALUE RATING ON EACH OBJECTIVE u SUM UP OVER ALL OBJECTIVES u RECOMMENDED OPTION IS ONE WITH HIGHEST OVERALL VALUE

17. 17 USE OF MERGER EVALUATION FORM u COMMITTEE MEMBERS AND ORSA/TIMS OFFICERS WERE GIVEN THE EXPANDED FORM u THEY FILLED IN OWN JUDGMENTS ON FORM: –ASSESSED WEIGHTS ON 52 LOWEST LEVEL OBJECTIVES –JUDGED VALUE RATINGS FOR 5 ALTERNATIVES ON 52 OBJECTIVES

18. 18 MY MERGER EVALUATION u NEXT I SHOW MY OWN JUDGMENTS FILLED IN ON THE EVALUATION FORM, SEE EXCEL FILE HANDOUT u WE DID NOT REQUIRE PEOPLE TO REVEAL THEIR OWN JUDGMENTS, THEY USED THE FORM TO FOCUS CONTINUED DISCUSSIONS AND NEGOTIATIONS

19. 19 RESULTS OF MERGER DECISION ANALYSIS u OFFICERS TENDED TO PREFER MERGER3 ALTERNATIVE, WITH SUB-UNIT BOARD REPRESENTATION u VOCAL OPPONENTS WOULD COMPROMISE ON SEAMLESS MERGER, WITHOUT SUB-UNIT BOARD REPRESENTATION, AS LONG AS NEW NAME RETAINS “OPERATIONS RESEARCH” u Ask me about tea bags

20. 20 OUTCOME OF DECISION u OFFICERS PRESENTED SEAMLESS MERGER RECOMMENDATION TO MEMBERS u MEMBERS VOTED TO MERGE u MERGER TOOK PLACE JAN. 1ST, 1995 u NAME IS INSTITUTE FOR OPERATIONS RESEARCH AND THE MANAGEMENT SCIENCES (INFORMS)

21. 21 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

22. 22 What do weights mean? Are weights priorities/importance? What is more important health or wealth?

23. 23 Swing Weight Technique to Assess Weights on Objectives u Most important point: OBJECTIVES’S WEIGHT DEPENDS ON RANGE OF PERFORMANCE ON OBJECTIVE u A person (Dilbert’s boss?) can’t say which objective is most important without knowing the range u SUM OF Normalized WEIGHTS IS 1OO% or 1.0 FOR ALL LOWEST LEVEL OBJECTIVES (conventionally)

24. 24 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 1 st ranked option. Give this best option a rating of 100. Assign other options ratings between 100 and 0.

25. 25 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 weight most important objective x rating most imp.objective + 0 V(1st rank option) = 100 = raw weight most important objective x 1 + 0

26. 26 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.

27. 27 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 1 st 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 RAW objective at top level WEIGHT NORMALIZED WEIGHT 100 90... 20 0 SUM = ?... 100/sum 90/sum 20/sum 0  = 1.0 1st 2 nd Last Benchmark

28. 28 Swing Weight Practice Assessment Choose 1 st or 2 nd & fill in the blank cells OptionHealthWealthRank Directly Rate = raw weight, With 100 for best Normalized weight Raw weight/SUM = HorribleBad health Low $Benchmark Fixed to be 0 Healthy PoorGreat health Low $1 st or 2 nd ? Wealthy SickBad health High $1 st or 2 nd ? SUM= _____?  = 1.0

29. 29 Swing Weight Practice Assessment Sample answer OptionHealthWealthRank Directly Rate = raw weight, With 100 for best Normalized weight Raw weight/SUM = HorribleBad health Low $ Benchmark Fixed to 0 Healthy PoorGreat health Low $1 st or 2 nd ? FIRST 100 100/150 = W h = 2/3 Wealthy SickBad health High $1 st or 2 nd ? SECOND 50 50/150 = W $ = 1/3 SUM= 150  = 1.0

30. 30 Now compute overall value of 4 different health/wealth options with assessed swing weights Name of Option Rating of v(Health) Multiply by Weight w h 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 w h + 0 x w $ = 0 Healthy 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 w h + 1 x w $ = 1.0

31. 31 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