MARA (Magnitude of the Area for the Ranking of Alternatives)

MARA is a ranking method for when you already hold a numerical decision table and want the alternatives placed in a single order. Its output is an area score (R) for every alternative and the rank produced by that score from smallest to largest; the smallest area marks the best alternative. Gligorić and colleagues proposed it in 2022, for the problem of choosing an underground mine gallery support system. It takes weights from outside, it does not generate them.

MARA's idea is to compare two alternatives not through a single number, but through the area beneath two linear functions. The method first builds a hypothetical ideal alternative: made up of the best weighted value observed on every criterion, this alternative does not actually exist. It then splits the criteria of both the ideal and every real alternative into two groups: benefit criteria and cost criteria. For every alternative, a simple linear function is built from the sum of these two groups; this function represents, on an axis running from 0 to 1, "the alternative's position between benefit and cost." The area between the two functions, the ideal's function and the real alternative's function, shows how far the alternative sits from the ideal.

This idea has one consequence: MARA is compensatory, because benefit and cost criteria are summed within their groups, and a weakness on one criterion can be papered over by another criterion in the same group. At the same time, the method treats criteria not one by one but as two large groups, benefit and cost. For this reason, the relative weight of criteria within the same group does not appear as clearly separated in the area calculation as it does in TOPSIS; this brings MARA closer to being read as a method that seeks a "balance between groups."

The method proceeds through nine steps; the first three are preparatory, the rest form the area calculation.

First and second step, the matrix and scale equalisation. The decision matrix is built, and every column is then equalised linearly: for a benefit criterion, the value is divided by the column's largest value; for a cost criterion, the column's smallest value is divided by the value.

Third step, weighting. Every equalised value is multiplied by its criterion's weight.

Fourth step, the ideal alternative. The hypothetical ideal alternative is built by taking the largest weighted value on every criterion.

Fifth and sixth step, grouping. The ideal alternative's criteria are split into benefit and cost groups; the same split is made for every real alternative.

Seventh step, group totals. The ideal alternative's benefit-group total and cost-group total, and every real alternative's benefit-group total and cost-group total, are computed separately.

Eighth step, two linear functions. For the ideal alternative and for every real alternative, a linear function defined between 0 and 1 is built from the benefit and cost group totals.

Ninth step, the area difference. The difference between the areas beneath the two functions is computed; the smaller this difference (the closer to the area beneath the ideal), the further ahead the alternative stands. Alternatives are ranked from smallest to largest.

The formulas behind these steps are given on the DecisionMind method page; this card carries no formulas.

The area score is a unitless number showing how far an alternative sits from the ideal alternative; it is not a percentage or a probability. An area close to zero shows the alternative is very close to the ideal; a large area shows a wide gap. The value cannot be compared with an area value from a different analysis, because the ideal alternative is built afresh, in every analysis, from that analysis's own data.

A small area score does not mean "perfect," but "closest to the ideal within this alternative set." A small gap between two alternatives, as in TOPSIS, does not signal a robust ranking but one that is sensitive to the weights.

For this reason, instead of writing:

"MARA found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative closest to the ideal is this one; the ranking is sensitive to the weight of the benefit and cost groups"

MARA works with crisp data: one number per cell. DecisionMind currently carries only this crisp version; it has no extension in another data type. You need alternatives in rows, criteria in columns, a fully populated table with no empty cells, direction information for every criterion, and weights summing to 1. MARA does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

MARA is a suitable choice if your criteria are numerical, your table is fully populated, and you accept that a weakness on one criterion may be offset by strength on another. Its typical territory includes equipment and support-system selection, supplier evaluation, and logistics performance comparison.

MARA is not suitable where a criterion can never be compromised; because the area difference comes from the sum of the benefit and cost groups, a serious weakness on one criterion can be papered over by another criterion in the same group. Where criteria are strongly linked, this link needs handling first.

A numerical table, compensation accepted, the goal is ranking → MARA

Not a benefit-cost balance but a criterion-by-criterion comparison is wanted → TOPSIS, MAIRCA

No compromise allowed on one criterion → screen first, then rank

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

MARA's strength is that it reduces the criteria to two large groups, benefit and cost, and turns the comparison into a geometric area difference; this makes the balance between alternatives explainable visually as well. The computational load is small, and the method continues to work in the same way as the number of alternatives grows. In its source paper, the method was developed and tested on a decision problem with a direct bearing on safety, that of underground mine support systems.

Its limitations stem from its own structure. First, the assumption of full compensation: a serious weakness on one criterion can be papered over by another criterion in the same group (benefit or cost). Second, MARA is a new method, proposed in 2022; it does not yet have as broad an independent body of applied and critical literature as TOPSIS or VIKOR. The rapidly growing number of multi-criteria decision methods, and the difficulty of tracking how independently each new method has been tested beyond its own paper, is discussed in the literature as a general problem (Guitouni and Martel, 1998; Zavadskas, Turskis and Kildienė, 2014). Third, because the method treats criteria in two large groups, benefit and cost, the relative weight of criteria within the same group may not appear as clearly separated in the final step of the area calculation as it does in TOPSIS. Fourth, criteria are treated as independent.

The most common mistake is marking criterion direction wrongly; if a cost criterion is marked as a benefit criterion, the ideal alternative is built incorrectly and the ranking becomes meaningless.

A second mistake is reading the area score as a percentage or a degree of certainty; the score only ranks this alternative set relative to itself. A third mistake is assigning equal weights without justification and presenting this as "neutrality"; in MARA, a change in weights can noticeably affect the ranking. A fourth mistake is choosing a compensatory method for a situation where one criterion can never be compromised.

The governing principle is this:

A MARA result is a summary of the weights you chose and the benefit-cost grouping; if the area difference is small, the ranking is contested, and the report must show this.