WPM - Weighted Product Model

Overview

P(A_i) > 0 (all entries strictly positive). Higher P means better overall performance. WPM is non-compensatory across criteria in the sense that a zero on any criterion yields a zero total - it penalises extreme weakness more harshly than SAW.

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

   Direction-aware normalisation (cost criteria inverted).

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

   Miller-Starr 1969, Ch.2

2. 2

   Weighted product P_i = Π r_ij^{w_j} and descending ranking.

   $$P_i=\prod _{j=1}^n(r_{ij}{)}^{w_j}$$

   Miller-Starr 1969, Ch.2 Eq.(3)

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

• Zero or negative criterion values: WPM is undefined - always verify E-2.

• Scale dependency: unlike SAW, WPM scores change if raw values are rescaled - results are not invariant to linear transformations.

Works with

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