ROV (Range of Value Method)

ROV is a ranking method for when you hold a decision table filled with numbers and want the alternatives placed in a single order. The method computes two separate scores for every alternative. The weighted performance on benefit criteria ("higher is better") forms the best-case score; the weighted performance on cost criteria ("lower is better," read after normalisation in the same "goodness" direction) forms the worst-case score. The average of these two gives the final score. It was proposed by Yakowitz, Lane and Szidarovszky in 1993. Its name, Range of Value, comes from this idea: the method finds a midpoint between the most optimistic and the most pessimistic ends of value. It does not generate weights, it takes them from outside.

Behind ROV lies an idea: derive an alternative's value not from a single calculation but from two extremes. The normalised scores on benefit criteria represent the "optimistic" side, and the normalised scores on cost criteria represent the "pessimistic" side. The method sums each side separately with its own weights, then averages the two. The logic is this: reach a middle assessment of an alternative by looking at both its "good" side and its "obligation" side.

Its philosophical consequence belongs to the same family as TOPSIS and SAW: ROV is compensatory, a weakness on one criterion can be closed by strength on another, and the final score is a weighted derivative of every criterion. It differs from TOPSIS in this respect: ROV does not measure distance to two hypothetical alternatives (ideal/anti-ideal). Instead, it divides criteria directly into two groups (benefit/cost), computes each group's own weighted sum separately, and averages the two. Structurally it is closer to OCRA and SAW.

The method proceeds through four steps.

First, scale equalisation. The method places every criterion between 0 and 1 using its own smallest and largest value: for a benefit criterion, the smallest value becomes 0 and the largest becomes 1; for a cost criterion, this direction is reversed, so the largest (worst) value becomes 0 and the smallest (best) value becomes 1. All columns become readable in the same direction ("high is good") as a result.

Second, the best-case score. The method multiplies the equalised benefit criteria by their own weights and sums them; this is a weighted summary of the alternative's performance on the benefit criteria.

Third, the worst-case score. The method multiplies the equalised cost criteria (already reversed in direction and read as "goodness") by their own weights and sums them.

Fourth, averaging the two sides. The method takes the average of the best-case and worst-case scores; this average is the alternative's final score. The method ranks alternatives from the highest score to the lowest.

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

The final score states the average of an alternative's weighted performance on benefit and cost criteria, and nothing more. A score of 0.325 does not mean "32.5 per cent good" or an absolute level of achievement, it is only a relative position within this particular alternative set. It cannot be compared with a score from a different analysis, because the normalisation's reference points (each criterion's own smallest/largest value) are built in every analysis from that analysis's own alternatives.

Thus instead of writing:

"ROV found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative with the highest score is this one; the score summarises the weighted average performance on benefit and cost criteria"

Classical ROV works with crisp data: a single number in every cell. Alongside the base method, DecisionMind holds two extensions (FUZZY-ROV, P-ROV); three ROV members exist in total. You need alternatives in rows, criteria in columns, a number in every cell with no gaps; direction information for every criterion; and criterion weights that sum to 1. ROV does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably, with no upper limit on the number of alternatives. If a criterion column is constant (carries the same value for every alternative), that column's normalisation denominator becomes zero and the calculation is undefined; that column should either be removed or the data reviewed.

ROV is a suitable choice if your criteria are numerical, the table is fully filled, and you accept that a weakness on one criterion may be closed by strength on another; it is used in areas close to TOPSIS's territory (supplier, material, equipment selection).

Where it should not be used follows from its philosophy: where you will not compromise on a criterion. In addition, if a criterion column is constant (the same value for everyone), ROV cannot compute that criterion; the criterion should either be removed or measured differently.

Numerical table, compensation accepted, optimistic–pessimistic average logic fits → ROV

Same idea, but distance to two hypothetical reference points is wanted → TOPSIS

Not "the best" but "the compromise limiting the greatest regret" → VIKOR

No compromise allowed 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)

ROV's strength is its simplicity: the method normalises with min–max, computes the best-case and worst-case scores separately, and then averages them. Its computational burden is small and can be followed by hand on the table. The method looks at benefit and cost criteria from two separate viewpoints (optimistic/pessimistic); this frees the decision from depending on a single reference point (such as an ideal point) alone and offers the decision-maker a two-sided reading.

Its limitations stem from this same simplicity. First, it carries a full-compensation assumption like TOPSIS; a serious weakness on one criterion can be papered over by others. Second, min–max normalisation depends on the alternative set; an alternative added or removed afterwards shifts every column's smallest/largest reference and can also change the scores of the existing alternatives. Third, normalisation remains undefined for a constant criterion column. Fourth, the quality of the weights lies outside the method itself; a flawless calculation built on poor weights still produces a poor ranking. Fifth, its comparative and critical literature is not as extensive as TOPSIS's; application examples are more limited in number (Mitra, 2021).

The most common mistake is marking criterion direction wrongly; if a cost criterion is marked "higher is better," the best-case and worst-case calculations swap places and the ranking reverses. A second mistake is assigning weights equally without justification. A third mistake is adding an alternative once the analysis is finished and being surprised that the normalisation references shift; the candidate set must be fixed from the outset. A fourth mistake is reading the final score as a percentage or an absolute measure of achievement and comparing scores across different analyses. A fifth mistake is feeding a constant criterion column into the calculation unnoticed and ending up with an undefined result.

The governing principle is this:

A ROV score is a consistent summary of the directions, weights and alternative set you supplied; if any input is contested, the score is contested too, and the report must show this.