MOOSRA (Multi-Objective Optimization on the basis of Simple Ratio Analysis)

MOOSRA 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 a ratio (benefit/cost) for every alternative and an order from the largest ratio to the smallest. It was proposed by Das, Sarkar and Ray in 2012, and introduced through an application by Sarkar and colleagues in 2015 to the problem of choosing a non-conventional machining method. It takes its weights from outside and produces none of its own.

MOOSRA's idea extends the ratio-system approach of the MOORA family: rather than comparing criteria one by one, it first sums the benefit criteria (the "higher is better" ones) among themselves, then sums the cost criteria (the "lower is better" ones) among themselves, and divides the first total by the second. This offers a direct answer to the question "how much larger is the total benefit gained relative to the total price paid." The larger the ratio, the more advantageously the alternative balances benefit against cost.

This idea has a consequence: MOOSRA is compensatory, because the benefit criteria are summed among themselves and the cost criteria among themselves; a weakness on one benefit criterion can be papered over by another. At the same time, the ratio form can make the result highly sensitive where the cost side is small: as the denominator shrinks, the ratio grows rapidly.

The method proceeds through five steps.

First, scale equalisation. Criteria are in different units. MOOSRA divides every column by its own magnitude: each value in the column is divided by the square root of the sum of the squared values in that column. This is the same vector normalisation TOPSIS also uses; every column becomes unit-free and comparable.

Second, the benefit total. The equalised benefit criteria (the "higher is better" ones) are multiplied by their own weights and summed; this gives the alternative's total weighted strength.

Third, the cost total. The equalised cost criteria (the "lower is better" ones) are multiplied by their own weights and summed; this gives the alternative's total weighted burden.

Fourth, the ratio. The benefit total is divided by the cost total. The larger this ratio, the further ahead the alternative stands.

Fifth, ranking. Alternatives are ranked by their ratios from the largest to the smallest.

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

The ratio shows how many times larger an alternative's total weighted benefit is than its total weighted cost; it is not a percentage or a probability. A ratio greater than 1 does not mean "benefit exceeds cost," because the numerator and denominator are weighted, equalised totals of different criterion groups, not a profit-and-loss ratio measured in real currency. The value cannot be compared with a ratio from a different analysis, because equalisation in every analysis is carried out from that analysis's own data.

The smaller the cost group's total, the more rapidly the ratio grows; this is a known sensitivity of MOOSRA. An alternative whose cost criteria sum to almost zero can be brought disproportionately far ahead. The report should therefore show how sensitive the leading alternative's advantage is to the weight given to the cost group.

Thus instead of writing:

"MOOSRA found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative with the highest benefit-cost ratio is this one; the ratio is sensitive to the weight on the cost criteria"

MOOSRA works with crisp data: one number per cell. DecisionMind currently holds only this crisp version; it has no extension for another data type. You need alternatives in rows, criteria in columns, a table with no empty cells, information for every criterion on whether it is a benefit or a cost, and weights. MOOSRA does not produce weights, it asks for them; the weights need not necessarily sum to 1, because the ratio uses the same weight scale in both numerator and denominator, but how different scales affect the comparison should be explained in the report. A minimum of two alternatives and at least one benefit and one cost criterion are required; if only benefit or only cost criteria are present, the ratio can become undefined.

MOOSRA is a reasonable choice if your criteria are a mix of benefit and cost, are numerical, and the table is complete. Its typical territory includes problems in manufacturing where both performance and cost or environmental dimensions matter together, such as machining-method selection or the choice of material and cutting fluid.

MOOSRA is unsuitable if an alternative's cost criteria sum to close to zero, because the ratio becomes undefined or grows disproportionately. It is also unsuitable where no compromise is acceptable on one criterion, because the benefit and cost groups are each compensatory within themselves.

Mixed benefit and cost criteria, a ratio logic is suitable → MOOSRA

The cost total may come close to zero → TOPSIS, MAIRCA and other distance-based methods

No compromise allowed on one criterion → screening first, then ranking

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

MOOSRA's advantage is its simplicity: the computational burden is small, consisting only of summation, multiplication and division. Because it sums the benefit and cost criteria into two separate totals, it gives a direct, single-figure answer to the question "how much larger is the benefit obtained than the price paid." Applications exist in manufacturing engineering, in problems such as machining-method and material selection where both performance and cost or environmental impact matter together.

Its limitations follow from the ratio structure. First, as the cost group's total approaches zero, the ratio grows disproportionately; this is a known numerical fragility of the method. Second, there is the full-compensation assumption: a weakness on one benefit criterion can be papered over by another. Third, there is some confusion in the literature over MOOSRA's founding source. The method was first defined by Das, Sarkar and Ray (2012), while the 2015 application paper by Sarkar and colleagues is more often cited as the reference that introduced it; which of these two sources counts as the "founding" one should be stated clearly to the reader. Fourth, criteria are taken to be independent, and, like other ratio-based methods, MOOSRA does not yet have as extensive an independent rank-reversal literature as TOPSIS or VIKOR.

The most common mistake is marking a criterion's benefit-or-cost status wrongly; if a cost criterion is placed in the benefit group, both the numerator and denominator of the ratio become distorted.

A second mistake is placing all criteria into a single group, only benefit or only cost, and leaving the other group empty; the ratio then becomes undefined or drops to a fixed value. A third mistake is reading the ratio as a percentage or a degree of certainty; the ratio only ranks this alternative set relative to itself. A fourth mistake is presenting the result without questioning why an alternative whose cost-group total comes out very small has come disproportionately far ahead.

The governing principle is this:

A MOOSRA result is a ratio of the weights you gave to the benefit and cost groups; where the cost total is small, the ratio is especially contestable, and the report must show this.