Say there are 3 companies A, B and C. Each company has a quality rating from 0 to 100 and a price in USD.
Company Quality Price
A 80 7.9
B 70 8.0
C 75 8.1
How do I determine the best quality-price trade-off? What kind of analysis should I use?
The Keeney-Raiffa approach to Multi-attribute valuation theory is well-grounded practically and theoretically, has been successfully applied to many problems, and--when applied to problems with just two attributes--is particularly simple. It proceeds by systematically exploring the trade-offs you would actually make in hypothetical situations and uses those to deduce two things: (1) an appropriate way to re-express each attribute and (2) a linear combination of the re-expressed attributes that fully reflects an overall value.
Be careful when doing Web research on this. The vast majority of published models of this type appear to ignore (1), which is crucial, and often establish (2) in ad-hoc or arbitrary ways.
Another approach, consistent with (but inferior to) the Keeney-Raiffa theory, establishes an "efficient frontier." Plot quality on one axis and price on another for each of the available alternatives. If you do so with increasing quality to the right and decreasing price upwards, then points lying at the extreme right or above of all the others are the best candidates to consider. In effect this method ignores (1) and uses this "frontier" to avoid specifying the coefficients in (2). It is often used in financial applications where the two attributes are "alpha" (expected rate of return) and "beta" (variance of returns, a surrogate for risk). Modern portfolio theory uses a variant of this approach.
