RAM (Root Assessment Method)

RAM is a ranking method for arranging alternatives into a single order once you already hold a numerical decision table. Its output is a score for every alternative and a descending rank based on that score. Sotoudeh-Anvari proposed it in 2023 for use in sustainability assessments. Its name comes from the word "root," because the final score is computed through an exponential-root expression: benefit acts as the base, cost as the exponential power.

RAM's underlying idea is to treat benefit and cost not within the same sum but in separate roles, as a number's base and exponent. The larger an alternative's total contribution on the benefit criteria, the larger the base of the calculation grows; the larger its total contribution on the cost criteria, the larger the exponent's denominator grows, which shrinks the exponent. A fixed value of "2" is added to both sides; this is a safety margin that keeps both the base and the exponent's denominator from falling to zero.

This structure carries a philosophical consequence: RAM, too, is compensatory, in that a high benefit can offset a high cost. But unlike TOPSIS's Euclidean distance or PROBID's graded ideal, RAM combines the effect of benefit and cost through a multiplicative-exponential structure rather than an additive one. This can mean that a large increase in cost shrinks the score more sharply than proportionally; this non-linear structure sets the method apart from linear summation methods such as SAW or WPM.

The method proceeds through four steps.

First, sum normalisation. Every criterion column is divided by its own total: each value in the column is divided by the sum of all values in that column. This step is direction-blind, whether the criterion is benefit or cost, and is applied identically to every column.

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

Third, separating the benefit and cost totals. In the weighted table, the columns belonging to benefit criteria are summed together to give each alternative a "benefit total"; the columns belonging to cost criteria are summed separately to give a "cost total."

Fourth, the RAM score. Every alternative's score is found by raising the benefit total, added to two, to a power equal to the reciprocal of the cost total, added to two: a high cost total shrinks the exponent and pulls the score down, while a high benefit total grows the base and pulls the score up. Alternatives are then ranked by this score from highest to lowest.

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

The RAM score is a number that combines an alternative's total contribution on the benefit and cost criteria; it always comes out slightly above 2, because both the base and the exponent of the calculation start from the fixed value "2." The magnitude of the score carries no meaning on its own; it only determines the order within this particular alternative set. It cannot be compared with a RAM score from a different analysis, because sum normalisation is built, in every analysis, from that analysis's own alternatives.

A small score gap between two alternatives can be more fragile than it looks, because of the exponential structure; a small change in the cost total shifts the exponent, and this affects the score in a non-linear way.

Thus instead of writing:

"RAM found the most sustainable alternative"

the report should read:

"With these weights and this alternative set, the alternative with the highest RAM score is this one; the magnitude of the score cannot be interpreted on its own, only the rank is meaningful"

RAM works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, a positive number in every cell, direction information for every criterion (benefit or cost), and criterion weights summing to 1. RAM does not produce weights, it asks for them from outside. DecisionMind currently holds no extension of this method; it runs in its base crisp form, though the literature has defined an extension for a neutrosophic setting (Sotoudeh-Anvari, 2025).

Because the normalisation step is direction-blind, reversing cost columns beforehand (taking 1/x, say) is wrong; the method makes the direction distinction in the third step, by separating the benefit and cost totals.

RAM is a suitable choice when your criteria can be measured numerically, the table is fully populated, and you accept compensation. The method was proposed specifically for sustainability and environmental-impact assessments; it can also be used in decisions with a clear benefit-cost trade-off, such as supplier and process selection.

It should not be used where the decision-maker finds the exponential structure hard to interpret, or where no compromise at all is acceptable on one criterion. RAM's score is not a directly interpretable percentage or distance; where the decision-maker needs an explanation beyond "the highest score wins," a more intuitive method (TOPSIS, SAW) may be preferable.

Numerical table, a clear benefit-cost trade-off, compensation accepted → RAM

Intuitive explainability of the score takes priority → TOPSIS, SAW

No compromise allowed on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Weights are needed rather than a ranking → AHP, BWM, SWARA (subjective) · Entropy, CRITIC (objective)

RAM's greatest strength is that, rather than mixing benefit and cost into a single sum, it accumulates them separately and combines them only in the final step; this makes it easy to trace, at intermediate steps, how each group of criteria affects the result. Its calculation stays simple: sum normalisation, weighting, separation, and a single exponential formula. Sotoudeh-Anvari's (2023) original paper tested the method in sustainability applications and showed it produces rankings close to TOPSIS's.

RAM's most contested point is the non-linear behaviour of the exponential formula; this structure can be exposed to rank reversal in some datasets, differently from TOPSIS (Amjad and Stoklasa, 2025, systematically examined these properties after RAM's publication). Second, the score's starting point at the constant "2" makes the score hard to interpret on its own (what a value of 1.47 means, say); the score is meaningful only for ranking. Third, the method is relatively new, proposed in 2023; it does not yet carry as broad a body of independent application and critique as TOPSIS or AHP.

The most common mistake is reversing cost columns before normalisation (taking 1/x, say); RAM's sum normalisation is direction-blind, and the direction distinction is made in the third step, by separating the benefit and cost totals. Reversing beforehand applies the direction distinction twice and corrupts the result. A second mistake is directly comparing a RAM score with TOPSIS's closeness score or another method's score; the two methods' score scales are entirely different. A third is assigning equal weights without justification. A fourth is assuming, because of the exponential structure, that a small score gap between two alternatives is as "small" as it would be in a linear method; in RAM, a small cost difference can shift the exponent and affect the score disproportionately.

The governing principle is this:

A RAM result is a consistent summary of the directions, weights and alternative set you supplied; a small change in the cost total can affect the score disproportionately because of the exponential structure, and the report must show this sensitivity.