UI = [ (1 - (Qbest - Qi) x N) / Pi ] x Pbest
UI = Utility Index
Qbest = Quality score of the quotation with the highest quality score
Qi = Quality of the registration
N = WQ / WP (quality/price ratio)
WQ = Weighing quality (in %)
WP = Price weighting (in %)
Pi = Subscription price
Pbest = Price of the quotation with the lowest price
"Value for Money (expressed in Utility of U)
The Utility index is a method to determine EMVI which is also called "Value for Money" in professional literature; Dividing quality by price; or Q/P. The highest resulting number (UI) is the best quotation. The higher the Q, the better, but also, the lower the P, the better. A 10% higher quality justifies a 10% higher price compared to another quotation. This makes the index intuitive and proportional.
Each supplier achieves a score of a minimum of 0 and a maximum of 100% on the qualitative part of the quotation. The Q value per quotation is established in the formula in the part:
1 - (Qbest - Qi)
The quality score of the quotation with the highest quality score (Qbest) scores 1 (=100%) on Q because for this quotation Qbest - Qi = 0. The difference between the best and other quotations (Qbest - Qi) is subtracted from 100% to determine the score of other quotations.
Adjustment in case quality and price are not equally important (N)
For Q / P applies; price and quality are just as important, 1% more Q may 1% more P 'cost'. To be able to apply a weighting in case quality is more important than price (e.g. 1% more Q may cost 2% more P) or vice versa, N has been included in the formula. The difference between the quotation with the best quality and the quality of another quotation ("i") is multiplied by a factor N. N = weight quality / weight price. In case price and quality are equally important, then N = 1. But if price is 4 times more important, then N = 0.25 (20%/80% = 0.25). In general: if price is more important, then N < 1 applies, if quality is more important, then N > 1 applies.
Multiply index by lowest price (×Pbest)
A second adjustment (irrelevant for the result) has been made to give the result UI a meaningful value. Because of this adjustment the maximum UI is 100%. This is obtained when an offer has the highest quality and the lowest price. The adjustment is to multiply the Q/P value by the price of the offer with the lowest price. Note that this does not make the formula "relative" to the lowest price (because all U's are multiplied with this same value).
The quotation with the highest U, a value greater than 0% and up to 100%, is the winning quotation.
Full ranking: From U to Price Deficient
On the determination of the highest U, a second step follows: determining the ranking of the other bids. Because the UI can potentially become negative at a high weight of quality (> 50%), the ranking of all UI's does not give a correct representation; Example how (1 - (Qbest - Qi) x N ) becomes negative: 1 - ( 0.9 - 0.5 ) x 4 = 1 - 1.6 = - 0.6
That's why we look at how many euros each quote would have to drop in price (Price deficiency) to score equal to the winning quote. The lower the price shortfall, the better the quotation. This is graphically shown below.
Numbers example for 3 quotes:
Quote A B C
Quality score Q 90.0% 80.0% 60.0%
Price P 1000.00 875.00 600.00
Weight Quality 60% and Price 40%, resulting in N = 1.5
Ua = [ (1 - (0.9 - 0.9) × 1.5 ) / 1000 ] × 600 =
= [ ( 1 – 0 ) / 1000 ] ×600 =
= 1/1000 × 600 =
= 0,600 (= 60%)
Ub = [ (1 - (0.9 - 0.8) × 1.5 ) / 875 ] × 600 =
= [ ( 1 – 0,1 × 1,5 ) / 875 ] × 600 =
= 0,85 / 875 × 600 =
= 0, 5829 (= 58,29%)
Uc = [ (1 - (0.9 - 0.6) ×1.5 ) / 600 ] × 600 =
= [ ( 1 – 0,3 × 1,5 ) / 600 ] × 600 =
= 0,55 / 600 × 600 =
= 0,5500 (= 55,00%)
Ua has the highest index (U) with 60%, so offers the most "Value for Money" and is therefore the most favorable offer.
Now the ranking of the other offers
The price at which a provider would be equivalent to the favorable offer is easy to calculate via:
UI / Ubest ×Pi
For B this is: 0, 5829 / 0.600 × 875 = € 850
With a price of € 850 B would have been equivalent to A. So the price deficiency of B is € 875 - € 850 = € 25, or too, B is € 25 "too expensive" to be equivalent to A.
For C this is: 0.5500 / 0.600 × 600 = € 550
With a price of € 550 C would have been equivalent to A. So the price deficiency of C is € 600 - € 550 = € 50.
Quotation A B C
Quality score Q 90.0% 80.0% 60.0%
Price P € 1000,00 € 875,00 € 600,00
Price deficit ("too expensive") - € 25 € 50
rank 1 2 3