Mutli-Attribute Decision Making

1. Mutli-Attribute Decision Making Scott Matthews Courses: 12-706 / 19-702/ 73-359

2. Admin Issues • Projects - look good so far. • Some comments coming • Early evaluations? • Lecture 12-706 and 73-359

3. Dominance • To pick between strategies, it is useful to have rules by which to eliminate options • Let’s construct an example - assume minimum “court award” expected is $2.5B (instead of $0). Now there are no “zero endpoints” in the decision tree. 12-706 and 73-359

4. Dominance Example #1 • CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other. 12-706 and 73-359

5. But.. • Need to be careful of “when” to eliminate dominated alternatives, as we’ll see. 12-706 and 73-359

6. Multi-objective Methods • Multiobjective programming • Mult. criteria decision making (MCDM) • Is both an analytical philosophy and a set of specific analytical techniques • Deals explicitly with multi-criteria DM • Provides mechanism incorporating values • Promotes inclusive DM processes • Encourages interdisciplinary approaches 12-706 and 73-359

7. Decision Making • Real decision making problems are MC in nature • Most decisions require tradeoffs • E.g. college-selection problem • BCA does not handle MC decisions well • It needs dollar values for everything • Assumes all B/C quantifiable • BCA still important : economic efficiency 12-706 and 73-359

8. MCDM Terminology • Non-dominance (aka Pareto Optimal) • Alternative is non-dominated if there is no other feasible alternative that would improve one criterion without making at least one other criterion worse • Non-dominated set: set of all alternatives of non-dominance 12-706 and 73-359

9. More Defs • Measures (or attributes) • Indicate degree to which objective is achieved or advanced • Of course its ideal when these are in the same order of magnitude. If not, should adjust them to do so. • Goal: level of achievement of an objective to strive for • Note objectives often have sub-objectives, etc. 12-706 and 73-359

10. Example Objective Objective: Minimize air emissions Sub-objectives: Min. SO2 Min. NOx tons SO2/yr tons NOx/yr Measures: Potential Goal: reduce SO2 emissions by 50%! This implies the need for an objective hierarchy or value tree 12-706 and 73-359

11. Desirable Properties of Obj’s • Completeness (reflects overall objs) • Operational (supports choice) • Decomposable (preference for one is not a function of another) • Non-redundant (avoid double count) • Minimize size 12-706 and 73-359

12. Structuring Objectives Choose a college • Making this tree is useful for • Communication (for DM process) • Creation of alternatives • Evaluation of alternatives Atmosphere Reputation Cost Academic Social Tuition Living Trans. 12-706 and 73-359

13. Key Issues • Specification - objectives need to be specified to allow measures to be specified • ‘Max air quality’ not good enough! • Find a balance between enough spec. to allow measure and ‘too much’ spec. • Means v. Ends - Hierarchy should only include ‘ends objectives’ 12-706 and 73-359

14. Choosing a Car • Car Fuel Eff (mpg) Comfort • Index • Mercedes 25 10 • Chevrolet 28 3 • Toyota 35 6 • Volvo 30 9 • Which dominated, non-dominated? • Dominated can be removed from further consideration • BUT we’ll need to maintain their values for ranking 12-706 and 73-359

15. Conflicting Criteria • Two criteria ‘conflict’ if the alternative which is best in one criteria is not the best in the other • Do fuel eff and comfort conflict? Usual. • Typically have lots of conflicts. • Tradeoff: the amount of one criterion which must be given up to attain an increase of one unit in another criteria 12-706 and 73-359

16. Tradeoff of Car Problem 1) What is tradeoff between Mercedes and Volvo? Comfort M 10 V T 2) What can we see graphically about dominated alternatives? 5 C 0 10 Fuel Eff 20 30 12-706 and 73-359

17. Tradeoff of Car Problem Comfort M(25,10) 10 -1 V(30,9) 5 The slope of the line between M and V is -1/5, i.e., you must trade one unit less of comfort for 5 units more of fuel efficiency. T 5 C 0 10 Fuel Eff 20 30 12-706 and 73-359

18. Tradeoff of Car Problem Comfort M(25,10) 10 -1 V(30,9) 5 Would you give up one unit of comfort for 5 more fuel economy? -3 T (35,6) 5 5 THEN Would you give up 3 units of comfort for 5 more fuel economy? 0 10 Fuel Eff 20 30 12-706 and 73-359

19. MCDM with Decision Trees • Incorporate uncertainties as event nodes with branches across possibilities • See “summer job” example in Chapter 4. 12-706 and 73-359

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21. Still need special (external) scales. • And need to value/normalize them • Typically give 100 to best, 0 to worst, find scale for everything between (job fun) • Get both criteria on 0-100 scales! 12-706 and 73-359

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24. Next Step: Weights • Need weights between 2 criteria • Don’t forget they are based on whole scale • e.g., you value “improving salary on scale 0-100 at 3x what you value fun going from 0-100”. Not just “salary vs. fun” • If choosing a college, 3 choices, all roughly $30k/year, but other amenities different.. Cost should have low weight in that example • In Texaco case, fact that settlement varies across so large a range implies it likely has near 100% weight 12-706 and 73-359

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29. Notes • While forest job dominates in-town, recall it has caveats: • These estimates, these tradeoffs, these weights, etc. • Might not be a general result. • Make sure you look at tutorial at end of Chapter 4 on how to simplify with @RISK • Read Chap 15 Eugene library example! 12-706 and 73-359

30. Next time: Advanced Methods • More ways to combine tradeoffs and weights • Swing weights • Etc. 12-706 and 73-359

31. How to solve MCDM problems • All methods (AHP, SMART, ..) return some sort of weighting factor set • Use these weighting factors in conjunction with data values (mpg, price, ..) to make value functions • In multilevel/hierarchical trees, deal with each set of weights at each level of tree 12-706 and 73-359