MOORA (Multi-Objective Optimisation by Ratio Analysis)

MOORA is a ranking method for when you already hold a decision table filled with numbers and want the alternatives placed in a single order. Its output is a single score for every alternative, the net value of the ratio system, and the rank that score produces. Willem Brauers and Edmundas Zavadskas proposed the method in 2006, applying it to privatisation decisions in a transition economy. The "multi-objective" in its name comes from its ability to combine both "higher is better" and "lower is better" criteria in a single calculation. It produces no weights; it takes them from outside.

Brauers and Zavadskas defined MOORA not as a single calculation but as a pair of complementary approaches resting on the same normalised data: the ratio system and the reference point approach. The ratio system computes each alternative's share on every criterion, that share being its proportion of the criterion's total magnitude. It then produces a single net score by summing the shares on beneficial criteria and subtracting the shares on harmful criteria. This is the form DecisionMind applies and the one this card describes. The reference point approach follows a different logic. For every criterion it finds the largest, that is worst, distance from a reference point built out of the best values, and selects the alternative whose worst distance is smallest; this is close to the "limit the greatest regret" logic found in VIKOR. Brauers and Zavadskas showed that the two approaches often give the same order but need not always do so (Brauers and Zavadskas, 2009). Using both of these together with a third, fully multiplicative form, corresponds to a separate method, MULTIMOORA.

One consequence of this philosophy is that the ratio system is compensatory, like TOPSIS: a weak share on one criterion is balanced in the total by a strong share on another. Its difference from TOPSIS is that, rather than building two hypothetical extreme points (ideal/anti-ideal), it takes the algebraic difference of the beneficial and harmful ratios directly. This also makes MOORA one of the lightest ranking methods to compute.

The method proceeds through four steps (in the ratio-system form).

First, scale equalisation (normalisation). Criteria are in different units. MOORA divides every column by its own magnitude: each value in the column is divided by the square root of the sum of the squared values in that column, the same vector normalisation used in TOPSIS. Every column becomes unit-free and comparable as a result.

Second, weighting. Each equalised column is multiplied by the criterion's weight. Weights come from outside and must sum to 1.

Third, the ratio system. For every alternative, the sum of the weighted shares on the "lower is better" criteria is subtracted from the sum of the weighted shares on the "higher is better" criteria. This single operation does directly, by subtraction, the work that TOPSIS does by separately building an ideal/anti-ideal point and measuring distance.

Fourth, ranking. Alternatives are ranked from the highest net score to the lowest. The highest score belongs to the alternative whose share on the beneficial criteria is highest relative to its share on the harmful criteria.

The formulas behind each step, the intermediate tables and the citation formats, including the reference point approach, are given on the DecisionMind method page; this card carries no formulas.

A MOORA score shows an alternative's net advantage in its share of the beneficial criteria over its share of the harmful criteria; it says nothing more. The score itself is not a percentage or a probability and cannot be compared with a score from a different analysis, because normalisation in every analysis is carried out against that analysis's own alternative set. A positive score does not mean "good" and a negative score does not mean "bad"; it only shows relative position within this alternative set. A small score gap between two alternatives is not a robust ranking but one sensitive to the weights.

Thus instead of writing:

"MOORA found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative with the highest net score under the ratio system is this one; the order is sensitive to the weight on these criteria"

MOORA works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, one number per cell, no empty cells; direction information for every criterion; and criterion weights that sum to 1. MOORA does not produce weights, it asks for them. The seminal method is a weighted form; an unweighted application, giving every criterion an equal share, is not recommended, because it can produce a different order. You can take weights from subjective sources such as AHP, BWM or SWARA, or objective sources such as Entropy or CRITIC. DecisionMind holds fourteen MOORA family members alongside the base method. A minimum of two alternatives and two criteria is required, and three to twelve criteria work comfortably.

MOORA is a suitable choice if your criteria can be measured numerically, the table is complete, you accept that a weakness on one criterion may be offset by strength on another, and you want a fast ranking with a low computational burden. Its typical territory includes supplier and process-parameter selection, manufacturing decisions, and public-policy prioritisation.

There is a single case where it should not be used, and it follows from its own philosophy: where you will not compromise on one criterion. MOORA's ratio system does not prevent this on its own; sub-threshold alternatives must first be screened out and the remainder ranked with MOORA, or methods built on elimination logic should be used instead. Where both the ratio system and the reference point approach, along with the fully multiplicative form, need to be seen together, MULTIMOORA should be preferred to MOORA.

Numerical table, compensation accepted, the goal is a fast ranking → MOORA

The ratio system alone is not enough, a consensus among the three approaches is needed → MULTIMOORA

Not "the best" but "the compromise limiting the greatest regret" → VIKOR or MOORA's reference point approach

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → the ELECTRE family

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective) · Entropy, CRITIC (objective)

MOORA's most important advantage is its simplicity. After normalisation and weighting, the result is reached with a single addition-subtraction operation; this requires fewer computations than TOPSIS's building of two extreme points and measuring distance to them. Brauers and Zavadskas's own robustness analysis has shown that the method gives relatively stable results against small changes in the normalisation form (Brauers and Zavadskas, 2009). Being able to derive two different approaches, the ratio system and the reference point, from the same data offers the chance to cross-check the result rather than relying on a single calculation. According to Chakraborty and colleagues' 2023 review, the method has spread across a wide range of applications owing to its simplicity (Chakraborty et al., 2023).

Its limitations also follow from this same simplicity. First, choosing the square root of the sum of squares as the normalisation denominator is a convention, as in TOPSIS; different normalisation forms can give a different order (Chakraborty et al., 2023). Second, there is the full-compensation assumption: a serious weakness on one criterion can be papered over by others. Third, the ratio system and the reference point approach need not always give the same order; which one to use should be clarified in advance (Singh et al., 2024). Fourth, criteria are taken to be independent; where criteria influence one another, weight is implicitly counted twice. Fifth, the rank-reversal risk known generally in the MCDM literature also applies to MOORA; the order can change when the alternative set changes (Aires and Ferreira, 2018; see the MABAC card).

The most common mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," the addition and subtraction swap places in the ratio system and the order reverses. A second mistake is confusing an unweighted (equal-share) application of MOORA with the seminal weighted method; the two applications can give different orders and the report should state which was used. A third mistake is presenting the ratio system's result as "the objective truth" without cross-checking it against the reference point approach. If the two approaches give different orders, this shows the risk of relying on a single method. A fourth mistake is reading the MOORA score as a percentage or probability and comparing scores across different analyses. A fifth is choosing a compensatory method for a situation where one criterion can never be traded away.

The governing principle is this:

A MOORA result is a summary of the normalisation, the weights and the ratio system you chose; trusting a single order without also testing the same data with the reference point approach is a premature conclusion.