WSM (Weighted Sum Model)

WSM is a method for when you hold a decision table filled with numbers and want to collapse the alternatives into a single score and rank them. Its output is a score for each alternative and the ranking that follows from it. It does not sort alternatives into groups, and it does not produce weights, taking them from outside. Fishburn proposed it in 1967, and it is also known as Simple Additive Weighting (SAW). It is the first method taught in multi-criteria decision-analysis textbooks, because its logic maps directly onto the everyday intuition of "weighing up the pros and cons."

The idea behind WSM is the assumption that benefits are directly additive. High performance on one criterion offsets low performance on another by an amount equal to the gap multiplied by the weight, and this rate of compensation is constant throughout. Unlike TOPSIS, it does not measure distance to a reference point (an ideal or anti-ideal); it multiplies performance values directly by their weights and sums them.

This idea carries a philosophical consequence: WSM is fully compensatory, and moreover its compensation is linear. If you can accept that "each unit of gain on one criterion always offsets a loss on another by the same proportion," WSM is the right place to be. Where the trade-off rate between criteria is not constant, for instance where an extremely low performance cannot be offset by anything, the method's philosophy clashes with the decision's own.

The method proceeds in two steps.

First, direction-sensitive normalisation. Where criteria are in different units (TL, days, points), they cannot be summed directly. WSM scales each criterion between 0 and 1 using its own smallest and largest values: for a "higher is better" criterion, the largest value maps to 1; for a "lower is better" criterion, the smallest value maps to 1. Where the criteria are already in the same unit and all "higher is better," this step can be skipped and the raw values used directly; the classical textbook example does exactly that.

Second, the weighted sum. WSM multiplies each alternative's normalised (or raw) criterion values by the criterion's weight and sums them. A high score is good; alternatives are ranked from highest to lowest on this score.

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

The WSM score states the total an alternative accumulates under these weights; nothing more. A high score does not mean "perfect," only that this alternative delivers the greatest total return within this set of alternatives and these weights. If the criteria are not normalised, the score's unit depends on the criteria's units and cannot be interpreted on its own; if they are normalised, the score is a unit-free quantity between 0 and 1.

A small score gap between two alternatives does not signal a robust ranking but one sensitive to the weights. Because of WSM's linear, fully compensatory structure, a large weakness on one criterion can easily be papered over by moderate strength on others.

Thus instead of writing:

"WSM found the best alternative"

the report should read:

"With these weights, the alternative with the highest total score is this one; if the score gap is small, the ranking is sensitive to the weights"

Classical WSM works with crisp data: a single number per cell. Criteria should be in the same unit where possible, or normalised; summing different units without normalising is, in Triantaphyllou's (2000) phrase, like "adding apples to pears." DecisionMind holds only the base WSM, with no extension.

You need alternatives in rows, criteria in columns, one number per cell, and no empty cells; direction information ("higher is better" or "lower is better") for every criterion; and criterion weights that sum to 1. WSM does not produce weights, it asks for them. A minimum of two alternatives and one criterion is required; three to ten criteria work comfortably. There is no upper limit on the number of alternatives.

WSM is a sound choice if your criteria can be measured in the same or a compatible unit, your table has no gaps, you want a fast and transparent calculation, and you accept full compensation. Its typical fields are supplier evaluation, personnel selection and site selection.

It should not be used where criteria are in different units and have not been normalised, or where no compromise is acceptable on one criterion. If you do not want an alternative below a safety threshold to come out ahead simply because it is cheap, WSM will not stop that; you must screen out anything below the threshold first, then rank what remains with WSM.

Criteria in the same unit, compensation accepted, a fast and transparent calculation → WSM

Criteria in different units, positioning relative to an ideal/anti-ideal point 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)

WSM's greatest strength is its simplicity. Its calculation can be followed by hand, and explaining it to anyone needs no special training; a decision-maker understands the result from the sentence "we summed each criterion's weighted contribution." Its computational burden is small, and it runs at the same speed as the number of alternatives and criteria grows. This transparency is why WSM is still the first method taught in textbooks, and why it is often reached for as a fast first-round evaluation in practice.

Its limitations stem from that same simplicity. First, there is a risk of dimensional inconsistency: if criteria are in different units and are not normalised, the sum becomes meaningless (Triantaphyllou, 2000). Second, there is the assumption of full and linear compensation: a serious weakness on one criterion is always closed by moderate strength on another, at a fixed rate that never changes. Third, Triantaphyllou and Mann's (1989) "decision-making paradox" finding has shown that different simple-summation-based methods, WSM included, can give different rankings for the same decision table. Fourth, large-scale comparative studies have found that WSM's ranking can diverge from other methods' depending on the structure of the alternatives and criteria (Zanakis et al., 1998).

The most common mistake is summing criteria in different units directly, without normalising; this lets a criterion with large numbers dominate one with small numbers in the calculation. A second mistake is using weights without adjusting them to sum to 1; weights that do not sum to 1 make the scores' magnitude meaningless. A third mistake is choosing WSM when full compensation is not wanted; it allows an alternative below a critical threshold to come out ahead through strength on other criteria. A fourth mistake is reporting a small score gap as a definite superiority.

The governing principle is this:

A WSM score is a direct sum of the weights and normalisation decision you supplied; if the criteria are not compatible in scale, the sum is not reliable either.