SAW Calculator

The weighted sum model (WSM), also called weighted linear combination (WLC) or simple additive weighting (SAW), is the best known and simplest multi-criteria decision analysis (MCDA) method for evaluating several alternatives in terms of decision criteria.

The best alternative is the one that yields the maximum total performance normalized value.

New here? Try it with example data

Fill every step with “Choosing a laptop” and see a result in one click.

Step 1: Alternatives

Enter at least three alternatives

Alternatives

Step 2: Criteria

Insert criteria

No.	Name	Type	Weight	Qualitative	Actions
1		Benefit
2		Benefit

Step 3: Performance Matrix

Complete previous steps

How SAW works

SAW (Simple Additive Weighting), also called the weighted sum model, scores every alternative as the weighted sum of its normalized values. It is the simplest multi-criteria method and the easiest to explain to other people.

Step by step

Rescale the criteria weights so they sum to 1.
Normalize each criterion column so that values become comparable: divide by the column maximum for benefit criteria, and divide the column minimum by the value for cost criteria. The best alternative on every criterion gets 1.
Multiply each normalized value by the weight of its criterion.
Add the weighted values of each alternative to get its total score.
Rank alternatives by total score, highest first.

Formulas

Normalization for a benefit criterion

\[r_{ij} = \frac{x_{ij}}{\max_i x_{ij}}\]

Normalization for a cost criterion

\[r_{ij} = \frac{\min_i x_{ij}}{x_{ij}}\]

Total score

\[S_i = \sum_{j} w_j \, r_{ij}\]

Worked example

With the laptop data above, the normalized values and total scores are as follows.

Example data: choosing a laptop
Alternative	Price (EUR) (cost, weight 3)	Performance score (benefit, weight 3)	Battery (hours) (benefit, weight 2)	Weight (kg) (cost, weight 2)
Brisk 15	900	6	9	1.8
Cirrus Pro	1500	9	10	1.6
Aurora 14	1200	8	12	1.3
Delta Air	1050	7	15	1.2

SAW normalized values and total scores
Alternative	Price	Performance	Battery	Weight	Total score	Rank
Brisk 15	1.000	0.667	0.600	0.667	0.753	4
Cirrus Pro	0.600	1.000	0.667	0.750	0.763	3
Aurora 14	0.750	0.889	0.800	0.923	0.836	2
Delta Air	0.857	0.778	1.000	1.000	0.890	1

Delta Air wins with a score of 0.890: it has the best battery life and lowest weight, and it is competitive on price and performance. Brisk 15 is the cheapest, but its low performance and battery life leave it last.

Use the "Load example" button at the top of this page to fill in this data and run it yourself.

Frequently asked questions

How does SAW compare criteria with different units?

Normalization turns every value into a unit-free number up to 1, so euros, hours and kilograms can be added together after weighting.

Are the weights percentages?

Weights are relative importance: enter any positive numbers and the calculator rescales them so they sum to 1. Weights of 3, 3, 2 and 2 are the same as 30%, 30%, 20% and 20%.

When is SAW a poor choice?

SAW is compensatory: a very good value on one criterion can cancel out a very poor value on another. If a minimum level on some criterion is non-negotiable, shortlist with ELECTRE first or apply that requirement before scoring.

What is the difference between SAW and WPM?

SAW adds weighted values, WPM multiplies value ratios raised to the weights. WPM penalizes a very low value on one criterion more strongly than SAW does.

How many alternatives and criteria can I use?

You need 3 to 7 alternatives and 2 to 7 criteria, and every performance value must be greater than zero.