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Decision analysis by interval SMART/SWING

Decision analysis by interval SMART/SWING. Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi. Multiattribute Value Tree Analysis. Value tree: Value of an alternative x (additive): w i is the weight of attribute i

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Decision analysis by interval SMART/SWING

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  1. Decision analysis by interval SMART/SWING Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi

  2. Multiattribute Value Tree Analysis • Value tree: • Value of an alternative x (additive): wi is the weight of attribute i vi(xi) is the component value of an alternative x in respect of an attribute i

  3. Ratio methods in weight elicitation Questions of interest - new alternative ways: • Reference attribute (Are there other than worst/best = SMART/SWING?) • Relationship to direct weighting? • Uncertain replies modelled as intervals • Uncertain reference considered as an interval • Behavioral and procedural benefits and problems

  4. Attribute weighting SWING • 100 points to the most important attribute change from its lowest level to the highest level • Fewer points to other attributes denoting their relative importance • Weights elicited by normalizing the sum of the points to one SMART • 10 points to the least important attribute

  5. Interval decision analysis methods • Intervals used to describe impreciseness • Preference Programming (Interval AHP) • Arbel, 1989; Salo and Hämäläinen 1995 • PAIRS (Preference assessment by imprecise ratio statements) • Salo and Hämäläinen, 1992 • PRIME (Preference ratios in multiattribute evaluation) • Salo and Hämäläinen, 1999

  6. Generalizing SMART and SWING • Relaxing the reference attribute to be any attribute • Allowing the DM to reply with intervals instead of exact point estimates • Allowing also the reference attribute to be an interval

  7. Generalizing SMART and SWING

  8. Simplified PAIRS • PAIRS • Constraints on any weight ratios  Feasible region S • Generalized ratio methods simplified cases of PAIRS

  9. Relaxing the reference attribute to be any attribute • Generalization of SMART/SWING or direct weighting • Weight ratios calculated as ratios of the given points  Technically no difference to SMART and SWING • Possibility of behavioral biases • Proper guidance to the DMs • More research needed

  10. Interval SMART/SWING • The reference attribute given any (exact) number of points • Points to non-reference attributes given as intervals

  11. Interval SMART/SWING • Max/min ratios of points constraint the feasible region of weights • Values calculated with PAIRS • Pairwise dominance • A dominates B pairwisely, if the value of A is greater than the value of B for every feasible weight combination

  12. An example • Three attributes: A, B, C • Preferences of the DM: • Two cases considered: 1. A chosen as reference attribute (100 points)  Other attributes (B, C) given 50-200 points 2. B chosen as reference attribute (100 points)  A given 50-200 points, C given 100 points

  13. Reference attribute • A as a reference attribute

  14. Feasible region • A as a reference attribute

  15. Reference attribute • B as a reference attribute

  16. Feasible region • B as a reference attribute

  17. Choice of the reference attribute • Only the weight ratio constraints including the reference attribute are given  Feasible region depends on the choice of the reference attribute • Choice of the reference attribute? • Attribute with least uncertainty • Easily measurable attribute, e.g. money

  18. Using an interval on the reference attribute • Meaning of the intervals • Ambiguity • Constraints for the weight ratios: • Every constraint is bounding the feasible region

  19. Using an interval on the reference attribute • An example

  20. Using an interval on the reference attribute • Feasible region S

  21. Using an interval on the reference attribute • Are the DMs able to compare the intevals? • The final step of generalizations is to relax the weight ratio constraints to be any constraints  PAIRS method

  22. WINPRE software • Weighting methods • Preference programming • PAIRS • Interval SMART/SWING

  23. An example • Vincent Sahid's job selection (Hammond, Keeney and Raiffa, 1999)

  24. Value Tree

  25. Imprecise rating of the alternatives

  26. Interval SMART/SWING weighting

  27. PAIRS

  28. The results

  29. The results • Jobs C and E dominated  Eliminated from subsequent analyses • Process could be continued by defining the attributes more accurately • Easier as fewer alternative

  30. Conclusions • Interval SMART/SWING • An easy method to model uncertainty by intervals • Linear programming algorithms involved • Software needed • WINPRE introduced • Does the DMs understand the intervals? • More research needed

  31. References Arbel, A., 1989. Approximate articulation of preference and priority derivation, European Journal of Operational Research 43, 317-326. Hammond, J.S., Keeney, R.L., Raiffa, H., 1999. Smart Choices. A Practical Guide to Making Better Decisions, Harvard Business School Press, Boston, MA. Salo, A., Hämäläinen, R.P., 1992. Preference assessment by imprecise ratio statements, Operations Research 40 (6) 1053-1061. Salo, A., Hämäläinen, R.P., 1995. Preference programming through approximate ratio comparisons, European Journal of Operational Research 82, 458-475. Salo, A., Hämäläinen, R.P., 1999. PRIME - Preference ratios in multiattribute evaluation. Manuscript. Downloadable at http://www.sal.hut.fi/ Publications/pdf-files/Prime.pdf

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