N = Determined on the basis of the X / Y ratio.
Pi = Price tender submitted
Pref = Price reference quote
Qi = Quality of the tender submitted
Qref = Quality reference quote
The EMVI Super Formula is derived from the 'Super Formula' as devised by Johan Gielis, a Belgian mathematician and biologist. His formula describes the diversity of forms in nature.
To make the formula work in Negometrix3 it is necessary to enter the score of a reference quote. That is, a reference price (Pref) with associated reference quality (Qref). This reference quality must be between 50% and 100%. The user must also specify a price that would give an equal total score if a quotation were to score 100% quality.

Example:
Reference price (Pref) € 100,000
Reference quality (Qref) 70%
Price at Qi = 100% (Pmax) € 130,000
This means that purchasing with a quality score of 70% expects a price of € 100,000.

In addition, purchasing would, for example, consider a quotation of € 130,000 with 100% quality equivalent to the reference quotation. The values: € 100,000, 70%. and € 130,000 are entered in Negometrix3.
Negometrix3 calculates the variable n on the basis of this data. Further below is explained what the n means.

The interesting idea behind the method is that purchasing would like to receive a quote that is the same as the reference. A more expensive offer is only more attractive if extra (i.e. non-linear) "more quality" is offered. On the other hand, a quote with a lower quality score is only more attractive if it comes with an extra (again non-linear) low price. The method is "absolute".

The formula dissected

You could cut the super formula into small pieces to dissect it step by step. Firstly, the qualitative value is converted to Qscore after assessment. This is the following formula:

You can then determine the price using the following formula:

These score formulas have the property that there are no hidden weighting factors. If the Q (quality) of an offer is x% better than Qref, then the Q score is also x% better. Ditto for the price. Both applies to the Pscore and Qscore: the smaller the score, the better.

With both scores, the EMVI score is calculated using the following formula:

The variable n
The formula also contains the variable n. This variable is also indirectly determined by the buyer. The n determines to what extent other quotations with a different P and / or Q are equivalent to the reference quotation. How much do people want to pay more (x%) for better quality (y%)? And how much do people want to pay less (x%) with lesser quality (y%)?

For example, you want to pay 10% more for 20% more Quality or pay 20% less for 10% less Quality. The exponent n in the Super formula is determined by your choice of X and Y. See the table below that applies to Y = 10%.

Value of n if we want to pay 10% more for X% more Quality

When using the super formula, Negometrix3 recommends using the above table when entering the n. A practical value is X = 20%. At n = 5.68, people are willing to pay 10% more if 20% more quality is offered.
It is not recommended to use X = 10%. With n = 1 the formula makes the same choices as with Grant by Value or the (linear) Weighted Factor Method and is therefore not based on the reference values.

EMVI score
If a quotation precisely scores the reference value on price and quality, then the score is 1.00. If better, it has a score of <1.00. So the lower the better. The value determines the ranking, the tender with the lowest value is the best.

The above text is largely based on a document written by Ir. J.C. (Hans) Kuiper.