CODAS (Combinative Distance-Based Assessment)

CODAS is a ranking method that orders alternatives into a single sequence once you hold a decision table filled with numbers. Its output is an assessment score for every alternative; this score can be positive or negative. Alternatives are ranked by this score. The method uses a distance measure, as TOPSIS does, but unlike TOPSIS it looks at only a single "worst" reference point. It uses two different types of distance in sequence rather than a single one. It does not generate weights, it takes them from outside. Keshavarz Ghorabaee, Zavadskas, Turskis and Antucheviciene proposed the method in 2016. It has been applied in areas such as supplier selection, market-segment assessment and production planning.

The idea behind CODAS is to look at how far alternatives sit from the worst possible one. But the method tests this with two different distance measures rather than one. It first calculates straight-line, Euclidean, distance; this is the classical geometric distance TOPSIS also uses. Two alternatives' Euclidean distances can come out very close to one another, meaning the difference between them falls below a set threshold. In that case a second measure is brought in to separate them. This measure is city-block distance, the sum of horizontal and vertical differences.

This is what distinguishes TOPSIS from CODAS. TOPSIS looks at both the ideal and the anti-ideal and uses a single type of distance. CODAS looks only at the anti-ideal, that is the negative-ideal, but uses two different distance types in sequence, one acting as referee for the other.

This idea carries a philosophical consequence. CODAS is also compensatory, but it carries an additional mechanism for telling apart rival alternatives that come out very close together. If two alternatives sit at almost the same straight-line, Euclidean, distance, the city-block distance reveals which of them has the more "uneven" profile across criteria. The reason is this: city-block distance sums the difference on each criterion separately, so it can punish a single large deviation differently from several small ones.

The threshold value (τ) is a parameter that determines the switch between these two measures. The user should set this value according to the scale of the data. DecisionMind fixes this threshold at 0.02 for classical CODAS and states this in the report.

The method proceeds through six steps.

First, linear normalisation. For a benefit criterion, the method divides each cell by the column's largest value; for a cost criterion, it divides the column's smallest value by each cell. Every column becomes unit-free as a result.

Second, weighting. The method multiplies each normalised column by the criterion's weight.

Third, the negative-ideal point. In the weighted table, the method builds a hypothetical "worst alternative" from each criterion's worst, that is smallest, value. CODAS uses only this single reference. It does not, unlike TOPSIS, also build a "best," that is ideal, reference.

Fourth, two distances. The method calculates every real alternative's straight-line (Euclidean) distance and horizontal-plus-vertical (city-block) distance to this negative-ideal. Every alternative carries both these distance values.

Fifth, pairwise comparison. The method compares alternatives against one another two at a time. It first looks at the difference between their Euclidean distances. If this difference exceeds a set threshold, the comparison is settled directly by that difference. If the difference is smaller than the threshold, meaning the two alternatives are practically equal in a straight line, the difference between their city-block distances is brought in and settles the comparison instead.

Sixth, the assessment score. The method sums each alternative's pairwise-comparison results against every other alternative; this total can be positive or negative. Alternatives are 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 assessment score states how well an alternative is positioned, relative to the negative-ideal, against the other alternatives in this set. It says nothing more. A negative score does not mean "poor" or "unsuccessful." It only shows that this alternative fell behind the others in the pairwise comparisons. The scores form a relative scale around zero, not an absolute measure of quality. A score of 0.39 does not mean "39 per cent good." This score cannot be compared with a CODAS score from a different analysis. The reason is this: the negative-ideal is built afresh, in every analysis, from that analysis's own alternatives.

If the score gap between two alternatives is small, the report should state separately where this gap comes from: whether it comes from the Euclidean distance, or from the city-block distance the threshold has brought into play. Changing the threshold value (τ) can reverse the direction of these small gaps.

For this reason:

"CODAS found the best alternative with certainty"

should be written as:

"With these weights, this threshold value and this alternative set, the alternative furthest from the worst reference is this one; the ranking is sensitive to the weight on these criteria and to the threshold value"

Classical CODAS works with crisp data: one number in every cell. If your data is uncertain by expert judgement, given as a range, or contradictory across experts, what needs to change is the data type, not the method. CODAS has fuzzy, grey, intuitionistic and other extensions. DecisionMind holds eighteen CODAS members alongside the base method.

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; criterion weights that sum to 1; and a threshold value (τ). CODAS does not produce weights, it asks for them. The threshold value should be set according to the scale of the data. A very small threshold brings the city-block distance into play in almost every comparison. A very large threshold never lets the city-block distance be used at all; CODAS then effectively reduces to Euclidean distance alone. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

CODAS is a suitable choice if your criteria can be measured numerically, your table has no gaps, and there is a chance that some alternatives sit too close together to be told apart by straight-line distance alone. In that case a second distance measure sharpens the discrimination. Its typical territory is supplier and market-segment evaluation, production processes and technology selection.

The case where it should not be used follows from the method's own philosophy. If you will not compromise on one criterion, CODAS will not prevent this, because it is compensatory. If you have no justification for how to set the threshold value (τ) and your data scale is unusual, for example made up of very small or very large numbers, do not trust CODAS without first testing how the default threshold affects the result. Where criteria are strongly linked to one another, that link needs handling first.

A numerical table, a second distance measure wanted to tell close rivals apart → CODAS

Same goal, but the data is fuzzy / grey / intuitionistic → the relevant CODAS extension

Looking at both the ideal and the anti-ideal with a single distance type is enough → TOPSIS

No compromise on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking; or elimination-based methods

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

CODAS's chief advantage is that it carries a second distance measure for telling apart alternatives that come out very close together. This gives it a discriminating power not found in methods that rely on Euclidean distance alone. Using two different distance types together also takes into account, indirectly, how balanced an alternative is across criteria: this balance shows whether an alternative's deviations are spread out or concentrated in a single criterion. The computational burden is small, and the method has been applied in areas such as supplier selection and market-segment evaluation (Keshavarz Ghorabaee et al., 2016; Keshavarz Ghorabaee et al., 2017).

Its limitations stem from the same structure. First, the method assumes full compensation, so a weakness on one criterion can be papered over by strength on others. Second, like other distance-based ranking methods, CODAS is open to rank reversal; because the negative-ideal point is built from the alternatives themselves, an alternative added to or removed from the set shifts this reference (Aires and Ferreira, 2018). Third, the threshold value (τ) is a parameter set by the user from outside the method. If how this value was chosen is not justified, the result can look arbitrary. Fourth, the method assumes criteria are independent of one another. Fifth, the quality of the weights lies outside the method itself.

The most common mistake is marking criterion direction wrongly. This builds the negative-ideal point incorrectly and reverses the ranking. A second mistake is interpreting a negative assessment score as a "failed alternative." In fact this score only shows the alternative's relative standing within this set. A third mistake is leaving the threshold value (τ) at its default without ever questioning it; the user then never tests whether the ranking of two close alternatives is sensitive to this threshold. A fourth mistake is adding an alternative once the analysis is finished; this addition changes the negative-ideal, and hence every score, though the user often fails to notice. A fifth mistake is choosing a compensatory method for a situation where one criterion can never be traded away.

The governing principle is this:

A CODAS result is a summary of the alternatives' relative standing, tested with two different distance measures, against this set's own negative-ideal point. This standing changes as the threshold value and the alternative set change, and the report must show this.