1. 1 Multiple Criteria Decision Making Scott Matthews Courses: 12-706 / 19-702/ 73-359 Lecture 12 - 10/10/2005

2. 12-706 and 73-3592 Admin Issues  PS 3 returned  Average: 42/50  Joe and Pauli will give feedback and answers  Early Course Feedback  For Wed: Read Campbell Chapters, Kennywood Report  Lecture

3. 12-706 and 73-3593 Early Evaluation Comments - “Positive”  Goals clear  Grading criteria clear  Well Organized  Good examples in lecture  Responsive/answers questions  HW Hard but fun  Excel add-ins  Open-ended stuff is novel and interesting (thanks)  Analogies/stories/jokes good (try 1 per class)  Enthusiastic (that’s a new one)

4. 12-706 and 73-3594 Early Comments - “Negative” Not meant to be defensive  Equations in PPTs hard to read (good one)  Problems vague (I warned you!)  More feedback on point deductions/criteria (ok)  All these are odd since I have never received them before!  Minor adjustments on slides at last minute (ok)  Want to see links sooner (thus the problem - see above)  Hard to get textbook  Talk too fast and too quietly (tell me!)  Unsure of grading for three courses (different scales)  Prefer homeworks/projects to exams (everyone?)

5. 12-706 and 73-3595 Mid-Course Adjustments  Lecture Notes:  Thought a lot about this one. Sought advice.  Posting them for you is a service  “Best Guess” slides posted by 10am  They will likely change by 1-2 slides by class time (but not much more)  Ironically, we wont have many more lectures  Problems MAY NOT get more clear  Note all but one have been used before with no issues (except q4 of last one)  Midterm -> Homework, Final -> Project

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 Choosing a Car  CarFuel Eff (mpg) Comfort  Index  Mercedes2510  Chevrolet283  Toyota356  Volvo309  Which dominated, non-dominated?  Dominated can be removed from further analysis

10. 12-706 and 73-35910 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.  Tradeoff: the amount of one criterion which must be given up to attain an increase of one unit in another criteria

11. 12-706 and 73-35911 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?

12. 12-706 and 73-35912 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.

13. 12-706 and 73-35913 On Objectives  Specifying and using objectives is fundamentally important  Is the most important thing you do  Get it right, on the way to win-win  Get them wrong, in big trouble!  Objective (aka criterion): a statement of desirable performance which includes a direction or orientation (e.g. min air emissions)

14. 12-706 and 73-35914 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.

15. 12-706 and 73-35915 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

16. 12-706 and 73-35916 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

17. 12-706 and 73-35917 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’

18. 12-706 and 73-35918 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

19. 12-706 and 73-35919 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

20. 12-706 and 73-35920 MCDM with Decision Trees  Incorporate uncertainties as event nodes with branches across possibilities  See “summer job” example in Chapter 4.  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!  Also need WEIGHTS between 2 criteria (your preference, nobody else’s!)  Weights - based on ratio best to worst on each scale

21. 12-706 and 73-35921 Notes  Whether you normalize or not, the tradeoffs/weights need to consider any differences in scale. (eg if we hadnt normalized $ and fun then 2/3 and 1/3 might not be correct weights)