From my doctoral course
This note comes from the doctoral course “Multi-Criteria Decision Making”. I rewrote the explanations in my own words and recomputed the numerical examples. Main source of the course: Asgharpour, Multi-Criteria Decision Making (University of Tehran).
The idea
After normalising and weighting, we build an overall score for each alternative and pick the highest. These methods are compensatory: a high score on one attribute can cover a low score on another.
SAW (simple additive weighting)
We normalise the matrix linearly (a negative attribute by its inverse). The score of each alternative = the sum of (weight × normalised value).
WPM (weighted product)
A product instead of a sum and a power instead of a multiplication. It is more sensitive to very low values: if an alternative is nearly zero on one attribute, its overall score is also nearly zero, so it behaves a little “more non-compensatory”.
WASPAS
Zavadskas et al. (2012) proposed combining both:
usually with (or optimised from the standard deviations). Its accuracy is higher than either alone.
Example: four laptops
| Price (million) | Performance | Battery | |
|---|---|---|---|
| A | 40 | 8 | 7 |
| B | 55 | 9 | 9 |
| C | 35 | 6 | 6 |
| D | 60 | 10 | 8 |
Weights ; price is negative and the rest positive.
| SAW | WPM | WASPAS (λ=0.5) | |
|---|---|---|---|
| A | 0.824 | 0.823 | 0.823 |
| B | 0.820 | 0.804 | 0.812 |
| C | 0.777 | 0.756 | 0.767 |
| D | 0.806 | 0.783 | 0.795 |
In this example all three put “A” first, but the gap between A and B is only 0.004; so with a small change in the weights the ranking changes. That is why sensitivity analysis is part of the method, not decoration.
When and why?
SAW and WPM are simple and excellent for explaining to a senior manager. Their critique is that they assume the attributes are independent and compensation is complete. If not, I move to TOPSIS or outranking.
Related: Weighting criteria.