Decision analysis by interval SMART/SWING

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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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### 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):

wi is the weight of attribute i

vi(xi) is the component value of an alternative x in respect of an attribute i

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
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
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
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
Simplified PAIRS
• PAIRS
• Constraints on any weight ratios

 Feasible region S

• Generalized ratio methods simplified cases of PAIRS
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
Interval SMART/SWING
• The reference attribute given any (exact) number of points
• Points to non-reference attributes given as intervals
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
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

Reference attribute
• A as a reference attribute
Feasible region
• A as a reference attribute
Reference attribute
• B as a reference attribute
Feasible region
• B as a reference attribute
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
Using an interval on the reference attribute
• Meaning of the intervals
• Ambiguity
• Constraints for the weight ratios:
• Every constraint is bounding the feasible region
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

WINPRE software
• Weighting methods
• Preference programming
• PAIRS
• Interval SMART/SWING
An example
• Vincent Sahid's job selection (Hammond, Keeney and Raiffa, 1999)
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
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
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