APPLICATIONS OF MULTI-OBJECTIVE DECISION MODELS FOR DECISION ANALYSIS DECISIONS UNDER CERTAINTY

1. 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

2. 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

3. 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

4. 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)

5. 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

6. ORSA/TIMS MERGER TREE • FIVE MAIN CATEGORIESIMPROVE COST EFFICIENCYENHANCE QUALITY OF PRODUCTSESTABLISH STRONG EXTERNAL IMAGEMAINTAIN SCOPE/DIVERSITY OF FIELDIMPROVE OPERATIONS

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

8. 1.1 Maintain efficient use of funds 1.2 Allocate well revenues/expenses to 1. Improve cost efficiency of activities/entities TIMS/ORSA operations 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. Enhance the quality of ORSA and TIMS products 2.4 Provide support for sub-units 2.5 Provide other member services MAXIMIZE OVERALL VALUE 3.1 Increase visibility and clout of OR and MS 3. Establish a strong & coherent external image of field 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

9. 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)

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

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. 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 FEE-FOR-SERVICE 1.1.3 REMOVE DOUBLED DUES -1 0 2 1 2 JUDGED VALUE RATING SCORES

14. 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

16. 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

17. 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

18. 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

19. 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

20. 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) inf orms

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

23. 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 NormalizedWEIGHTS IS 1OO% or 1.0 FOR ALL LOWEST LEVEL OBJECTIVES (conventionally)

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

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 weightmostimportant objective x ratingmostimp.objective + 0V(1st rank option) = 100 = raw weightmostimportant objective x 1 + 0

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. 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. RANK of Rating=option w/ this RAWobjective at top level WEIGHT NORMALIZEDWEIGHT 1st 2nd LastBenchmark 100/sum 90/sum 20/sum 0  = 1.0 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 100 90 . . . 20 0 SUM = ? . . . For large numbers of objectives, direct judgements of the weights will likely be used.

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

29. Swing Weight Practice AssessmentSample answer

30. Now compute overall value of 4 differenthealth/wealth options with assessed swing weights

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