SAW - Simple Additive Weighting

Overview

S_i ∈ [0,1] after linear-max normalisation (assuming all positive values). Higher S_i means better overall performance. SAW is fully compensatory - a very high value on one criterion can offset a low value on another.

Output

utility, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Alternative selection, Supplier evaluation

How it works

1. 1

   Linear max-normalisation per criterion direction.

   $$r_{ij}=\{\begin{array}{ll}{x}_{ij}/{\max }_i{x}_{ij}& j\in J^{+}\\ {\min }_i{x}_{ij}/x_{ij}& j\in J^{-}\end{array}$$

   MacCrimmon 1968, p.27

2. 2

   Weighted sum S_i = Σ w_j r_ij and descending ranking.

   $$S_i=\sum _{j=1}^n{w}_j{r}_{ij}$$

   MacCrimmon 1968, p.28 Eq.(2)

Look elsewhere when

Assumptions to verify

• Criteria preferences are independent (no synergistic interactions)
• Compensation is acceptable: high score on one criterion can offset low on another
• Decision matrix is complete (no missing values)

Edge cases and pitfalls

• Full compensability: SAW allows perfect scores on some criteria to completely mask poor performance on others - check individual criterion scores if compensation is a concern.

• Scale sensitivity: without normalisation, criteria with larger raw values dominate - always normalise.

Works with

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