**The formula: **

Ui = [ (1 – (Qbest – Qi) x N) / Pi ] x Pbest

Ui : Utility Index

Qbest : Quality of the best tender

Qi : Quality of the tender

N : WQ / WP (quality/price ratio)

WQ : Weighting of quality (as a %)

WP : Weighting of price (as a %)

Pi : Price of the tender

Pbest : Price of the best tender

**‘Value for Money’ (expressed as Utility or U)**

The Utility index is a way of determining the MEAT which is also referred to in the professional literature as ‘Value for Money’: Dividing quality by Price; or Q / P. The highest resulting number (Ui) is the best offer. The higher the Q, the better, but also: the lower the P, the better. 10% higher quality justifies a price that is 10% higher than another offer. This makes the index intuitive and proportional. The difference with respect to the Value for Money 50/50 formula is in the price/quality ratio. This formula does allow a ratio to be set up.

**Qi: Quality**

Every supplier receives a score of minimum 0 and maximum 100% for the qualitative part of the offer.

The Q value per offer is reached in the formula in the section:

**1 - (Qbest - Qi)**

The best offer (Qbest) scores 1 (=100%) for Q because for this offer, Qbest - Qi = 0. The difference between the best and the other offers (Qbest - Qi) is subtracted from 100% in order to determine the score of the other offers.

**Adjustment if quality and price are not equally important (N)**

For Q / P: price and quality are exactly equally important, 1% more Q may cost 1% more P. In order to introduce weighting if quality is more important than price (for instance, 1% more Q may cost 2% more P) or vice versa, N is entered in the formula; The difference between the offer with the best quality and the quality of a different offer (‘i’) is multiplied by the factor N. N = weight of quality / weight of price. If price and quality are equally important, N = 1. But if price is 4 times as important, then N = 0.25 (20%/80% = 0.25). In general: if price is more important, then N < 1, if quality is more important, then N > 1.

**Multiply index by lowest price (x Pbest)**

A second adjustment (irrelevant for the result) is made to give the result Ui a meaningful value. This adjustment makes the maximum Ui 100%. This is received if an offer has both the highest quality and the lowest price. The adjustment is to multiply the Q/P value by the lowest price. Please note, this does not make the formula ‘relative’ compared to the lowest price (because all Us are multiplied by this same value).

__The offer with the highest U, a value greater than 0% and maximum 100%, is the winning offer.__

**Full ranking: From U to Price deficit**The determination of the highest U is followed by a second step: determining the ranking of the other offers. Because the Ui can potentially become negative if quality has a higher weight (> 50%), the ranking of all the Us does not give an accurate representation; Example of how (1 - (Qbest - Qi) x N ) can become negative: 1 - ( 0.9 – 0.5 ) x 4 = 1 – 1.6 = - 0.6 That is why you check by how many euros every offer would have to decrease (Price deficit) in order to score the same as the winning offer. The lower the price deficit, the better the offer. This is shown graphically below.

**Calculated example for 3 offers:**

Offer | A | B | C |

Quality score Q | 90.0% | 80.0% | 60.0% |

Price P | 1,000.00 | 875.00 | 600.00 |

Weight of Quality 60% and Price 40%; from which it follows that 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%)

At 60%, Ua has the highest index (U), offers the most ‘Value for Money’ therefore, and as such is the most advantageous offer.

**Now the ranking of the other offers:**

The price which an offeror would have to offer to be equal to the most advantageous offer can be easily calculated:

Ui / Ubest ×Pi

For B, this is: 0.5829 / 0.600 × 875 = € 850.

With a price of € 850, B would have ranked the same as A. The price deficit of B is therefore

€ 875 – € 850 = € 25, in other words, € 25 ‘too expensive’ compared to A.

For C, this is: 0.5500 / 0.600 × 600 = € 550.

With a price of € 550, C would have ranked the same as A. The price deficit of C is therefore

€ 600 – € 550 = € 50

Offer | A | B | C |

Quality score Q | 90.0% | 80.0% | 60.0% |

Price P | € 1,000.00 | € 875.00 | € -600.00 |

Price dificit ("too expensive") | - | € 25 | € 50 |

Ranking | 1 | 2 | 3 |