WASPAS (Weighted Aggregated Sum Product Assessment)

WASPAS is a ranking method that orders alternatives into a single sequence once you already hold a decision table. Its output is a combined score for every alternative and the rank that score produces. Zavadskas, Turskis, Antuchevičienė and Zakarevičius proposed it in 2012 by combining two well-established methods that otherwise operate differently: the Weighted Sum Model (WSM) and the Weighted Product Model (WPM). It does not generate weights; weights are supplied from outside. It is a plain, quick method to compute, applied frequently in manufacturing, supplier selection and construction-engineering decisions.

WASPAS starts from the observation that two old aggregation methods, each usable on its own, have weaknesses that complement one another. The Weighted Sum Model (WSM) multiplies each criterion's normalised value by its weight and sums the products. It is simple, but a very low value on one criterion can be comfortably offset by a high value on another; sometimes too comfortably to be realistic. The Weighted Product Model (WPM), by contrast, multiplies the normalised values raised to the power of their weights. This lets a very low value on one criterion pull the whole product down; it is, in other words, more punishing towards weaknesses than the sum. But used alone it tends to exaggerate small differences.

WASPAS blends these two logics with a coefficient, λ (lambda): the combined score is the WSM score multiplied by λ plus the WPM score multiplied by (1−λ). At λ=1, WASPAS reduces to pure WSM; at λ=0, to pure WPM; at λ=0.5, the two logics are combined with equal weight. This construction carries a philosophical consequence: WASPAS is a compromise for decision-makers who want "the ease of the sum together with the discipline of the product"; it is neither as fully compensatory as WSM nor as harshly punishing as WPM. λ leaves the balance between the two in the decision-maker's hands.

The method proceeds through four steps.

First, scale equalisation. For a "higher is better" criterion, every value is divided by the largest value in that column; for a "lower is better" criterion, the smallest value in the column is divided by every value. Every column is thereby scaled between 0 and 1, with the best value always coming out at 1.

Second, the weighted-sum component. The method multiplies each equalised column by the criterion's weight and sums them; this is the classical score of the Weighted Sum Model (WSM).

Third, the weighted-product component. The method raises each equalised value to the power of the criterion's weight and multiplies these across all criteria; this is the classical score of the Weighted Product Model (WPM). If the equalised value on any criterion is zero, this product becomes zero. A single very weak criterion can wipe out the product component entirely.

Fourth, the combined score and the rank. The method weights the WSM score by λ and the WPM score by (1−λ) and sums them; DecisionMind assumes λ=0.5 if no value is specified. The method ranks the alternatives by this combined 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 combined score shows how good an alternative is relative to the other alternatives in this particular analysis, blended from WSM and WPM at a given λ; on its own it does not mean "per cent good" or "probability." The score's magnitude depends on the λ chosen; a different λ can give the same table a different ranking, particularly where WSM and WPM alone suggest different orders. The report should therefore show which λ was used and whether the ranking is sensitive to λ; if WSM and WPM alone already give the same ranking, this is a sign that the result is robust regardless of the choice of λ.

Thus instead of writing:

"WASPAS shows A1 as the best alternative"

the report should read:

"With the chosen λ=0.5 and these weights, A1 has the highest combined score; the WSM and WPM components separately give the same ranking, so this result is comparatively robust to the choice of λ"

WASPAS works with crisp data: a single number per cell, in a table containing no zero or negative values (the product component becomes undefined at a zero or negative value). You need alternatives in rows, criteria in columns, a positive number in every cell; direction information for every criterion; weights that sum to 1; and a λ value between 0 and 1 (DecisionMind assumes 0.5 if none is specified). It does not produce weights, it asks for them; they can come from sources such as AHP, BWM, CRITIC or Entropy. DecisionMind holds eighteen WASPAS members alongside the base method. A minimum of two alternatives and two criteria is required, and three to twelve criteria work comfortably.

WASPAS is a sound choice if your criteria can be measured numerically, the table is completely filled, all values are positive, and your decision matches the intuition of "wanting a bit of both the sum's ease and the product's discipline." Its typical territory includes manufacturing-technology selection, supplier assessment and comparing construction or engineering alternatives.

It should not be used in the following situations: where the data contains a zero or negative value (the product component becomes undefined; the data must first be transformed, or another method chosen), where you leave λ at 0.5 without justification and never test it (this is a serious shortcoming wherever WSM and WPM separately suggest different rankings), and where no compromise at all can be made on one criterion (WASPAS is compensatory and unsuited to a case that calls for elimination logic).

A balanced blend of sum and product is wanted → WASPAS

A plain, fully compensatory aggregation alone is sufficient → SAW or TOPSIS

Weaknesses should be penalised severely → WPM alone (λ=0)

No compromise allowed on one criterion, sub-threshold alternatives must be eliminated → elimination first, then ranking

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

WASPAS's greatest strength is that it combines two well-established methods (WSM and WPM) within a single framework and lets λ move between them; this gives the decision-maker a concrete control point for the question "how compensatory, how punishing do I want to be." Second, its computational burden is small; unlike TOPSIS or PROMETHEE, it constructs no hypothetical reference point or pairwise comparison, computing the two aggregation formulas directly. Third, being able to report the WSM and WPM components separately makes visible how independent the result is from the choice of λ, that is, whether the two components agree on the ranking. Fourth, a substantial applied literature has accumulated for manufacturing and engineering decision problems (Chakraborty and Zavadskas, 2014).

Its limitations stem from the same structure. First, the choice of λ can directly affect the result; where the WSM and WPM components suggest different rankings, the value at which λ is fixed is a critical decision, and it remains arbitrary unless justified (Baykasoğlu and Gölcük, 2019). Second, the product component is undefined at zero or negative values; if the data allows these, pre-processing is required. Third, the form of normalisation (dividing by the largest or the smallest value) affects the result; different normalisation choices can give different rankings (Mardani, Nilashi, Zakuan, Loganathan, Soheilirad, Saman and Ibrahim, 2017). Fourth, the method treats criteria as independent; where criteria influence one another, weight is implicitly counted twice.

The most common mistake is leaving λ at the default of 0.5 without ever testing it, and never looking at what the WSM and WPM components say separately; if the two components suggest different rankings, this is a sign that the combined score is fragile. A second mistake is trying to compute the product component when the data contains a zero or negative value; this gives an undefined or misleading result. A third is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," the normalisation is reversed. A fourth is reading the combined score as a percentage or a probability and comparing scores from different analyses. A fifth is adding an alternative once the analysis is finished and being surprised that the normalisation (based on the largest or smallest value) changes.

The governing principle is this:

The combined score is a product of the chosen λ, the form of normalisation and the weights; if the WSM and WPM components do not agree on the ranking, the report must show this disagreement clearly, along with the justification for the choice of λ.