COBRA (COmprehensive distance Based RAnking)

COBRA is a ranking method that orders alternatives into a single sequence once you hold a decision table filled with numbers. Its output is a comprehensive distance score for every alternative, together with the rank that score produces; the lowest score marks the best alternative. Krstić, Agnusdei, Tadić, Miglietta and Roso proposed it in 2022 to assess how applicable Industry 4.0 technologies are in reverse logistics. The method does not sort alternatives into "acceptable / unacceptable" groups and does not generate criterion weights; weights are supplied from outside.

COBRA's underlying idea is to judge an alternative against four reference points rather than a single one. Classical methods generally look at an ideal (best) and an anti-ideal (worst) point. COBRA adds two further references: the part of the alternative set that sits above the average, and the part that sits below it. An alternative is rewarded not only for being close to the ideal but also for sitting above the average; sitting below the average is separately penalised.

This idea has a consequence: COBRA is compensatory, but unlike TOPSIS it computes distance using both the straight-line (Euclidean) and the city-block (Manhattan) measure together. Even when two alternatives share the same straight-line distance, the way the differences across criteria are distributed, concentrated in one criterion or spread evenly, changes the result. This rests on the view that it is not only the average distance that matters, but how that distance is distributed.

The method proceeds through six steps.

First and second step, scale equalisation. Each criterion column is divided by its own largest value, in the same way regardless of direction. Each column is then multiplied by the criterion's weight. This brings a large-valued criterion (such as price) and a small-valued one (such as a 1–9 score) onto a comparable scale.

Third step, four reference points. In the weighted table, the best value on each criterion (largest for a benefit, smallest for a cost) builds the ideal point, and the worst value builds the anti-ideal point. Each criterion's average is also calculated; this average forms the basis for the "above-average" and "below-average" references.

Fourth step, combined distance. COBRA measures each alternative's distance to the four reference points using a combination of straight-line and city-block distance. This combination accounts not only for the total difference but also for how unevenly the differences are spread across criteria.

Fifth step, above-average and below-average distances. The criteria on which an alternative sits above the average and those on which it sits below are treated separately; only the criteria in the relevant direction enter this calculation.

Sixth step, the comprehensive score. The sum of the distance to the ideal and the above-average distance has the sum of the distance to the anti-ideal and the below-average distance subtracted from it. Alternatives are ranked by this score from lowest to highest; the lowest score marks the best alternative.

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

The comprehensive distance score summarises an alternative's position, relative to the four reference points, within this particular alternative set, and nothing more. The score can be negative or positive and does not sit within a fixed range such as 0–1; it cannot be set against a score from a different analysis, because the reference points are built afresh, in every analysis, from that analysis's own alternatives. The lowest score marks the best alternative; this is the reverse of TOPSIS's rule that the highest score is best, and it must not be confused when reporting.

A small score gap between two alternatives signals not a robust ranking but one sensitive to the weights. The report should therefore show which criterion's weight the ranking is sensitive to. For this reason:

"COBRA found the best alternative"

should be written as:

"With these weights and this alternative set, the lowest comprehensive distance falls on this alternative; the ranking is sensitive to the weight on this criterion"

COBRA works with crisp data: one number per cell. DecisionMind currently holds no extension of this method for another data type; if your data is fuzzy, interval-based or drawn from expert opinion, another family member should be sought.

You need alternatives in rows, criteria in columns, one number per cell and no empty cells; for every criterion, whether more is better or less is better, and weights that sum to 1. COBRA does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

COBRA is a suitable choice if your criteria can be measured numerically, your table has no gaps, and you accept that a weakness on one criterion may be offset by strength on another. The method was proposed specifically for sustainability and circular-economy assessments, but its logic does not depend on the field and it can also be used in general ranking problems such as supplier selection.

If you will not compromise on one criterion, COBRA is not suitable; sub-threshold alternatives should first be screened out and only the remainder ranked. Where criteria are strongly linked to one another, that link needs handling first.

A numerical table, compensation accepted, evaluation against four references → COBRA

Evaluation against the ideal and anti-ideal alone is sufficient → TOPSIS

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

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

COBRA's advantage is that it uses four reference points together, looking not only at closeness to the ideal but also at an alternative's position relative to the average. This makes the difference more visible between an alternative that sits above the average but far from the ideal and one that sits below the average. Using straight-line and city-block distance together also accounts for whether the differences are spread evenly across criteria or concentrated in a single one. Comparative studies have reported that COBRA shows high agreement with other ranking methods.

Its limitations are shared with the TOPSIS family. When the alternative set changes, all four reference points shift with it; an alternative added or removed afterwards can change how the others rank relative to one another (García-Cascales and Lamata, 2012). The assumption of full compensation applies: a serious weakness on one criterion can be papered over by others. Because the method was proposed only in 2022, its literature has not yet been tested as widely as TOPSIS's or VIKOR's; the number of independent applications remains limited. The quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking.

The most common mistake is marking criterion direction wrongly, which reverses the best and worst reference points. A second mistake is mistaking the lowest score for the "worst" one; in COBRA the lowest comprehensive distance marks the best alternative. A third is assigning equal weights without justification. A fourth is adding an alternative once the analysis is finished and being surprised the ranking shifts. A fifth is reading the comprehensive distance score as a percentage and comparing scores from different analyses.

The governing principle is this:

COBRA's comprehensive distance score is a four-reference summary of the directions, weights and alternative set you supplied; if any input is contested, the ranking is contested too.