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

2. 12-706 and 73-3592 Admin Issues  Projects - look good so far.  Some comments coming  Early evaluations?  Lecture

3. 12-706 and 73-3593 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.

4. 12-706 and 73-3594 Dominance Example #1  CRP below for 2 strategies shows “Accept $2 Billion” is dominated by the other.

5. 12-706 and 73-3595 But..  Need to be careful of “when” to eliminate dominated alternatives, as we’ll see.

6. 12-706 and 73-3596 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

7. 12-706 and 73-3597 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

8. 12-706 and 73-3598 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

9. 12-706 and 73-3599 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.

10. 12-706 and 73-35910 Example Objective Minimize air emissions Objective: Min. SO2Min. NOxSub-objectives: Measures: tons SO2/yrtons NOx/yr Potential Goal: reduce SO2 emissions by 50%! This implies the need for an objective hierarchy or value tree

11. 12-706 and 73-35911 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. 12-706 and 73-35912 Structuring Objectives Choose a college ReputationCost Atmosphere AcademicSocial TuitionLivingTrans.  Making this tree is useful for  Communication (for DM process)  Creation of alternatives  Evaluation of alternatives

13. 12-706 and 73-35913 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’

14. 12-706 and 73-35914 Choosing a Car  CarFuel Eff (mpg) Comfort  Index  Mercedes2510  Chevrolet283  Toyota356  Volvo309  Which dominated, non-dominated?  Dominated can be removed from further consideration  BUT we’ll need to maintain their values for ranking

15. 12-706 and 73-35915 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

16. 12-706 and 73-35916 Tradeoff of Car Problem Fuel Eff Comfort 10 5 0 2030 M V T C 1) What is tradeoff between Mercedes and Volvo? 2) What can we see graphically about dominated alternatives?

17. 12-706 and 73-35917 Tradeoff of Car Problem Fuel Eff Comfort 10 5 0 2030 M(25,10) V(30,9) T C 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.

18. 12-706 and 73-35918 Tradeoff of Car Problem Fuel Eff Comfort 10 5 0 2030 M(25,10) V(30,9) T (35,6) 5 Would you give up one unit of comfort for 5 more fuel economy? -3 5 THEN Would you give up 3 units of comfort for 5 more fuel economy?

19. 12-706 and 73-35919 MCDM with Decision Trees  Incorporate uncertainties as event nodes with branches across possibilities  See “summer job” example in Chapter 4.

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21. 12-706 and 73-35921  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!

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24. 12-706 and 73-35924 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

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29. 12-706 and 73-35929 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!

30. 12-706 and 73-35930 Next time: Advanced Methods  More ways to combine tradeoffs and weights  Swing weights  Etc.

31. 12-706 and 73-35931 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