WPM: Weighted Product Model

Overview

Multiplicative utility. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Multiplicative utility

Limitations

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

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)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

• •See F.steps and D.parameters for WPM-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'WPM bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: WPM'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: WPM'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Direction-aware normalisation (cost criteria inverted). Formül: r_{ij} = \begin{cases} x_{ij}/\max_{i} x_{ij} & j\in J^{+} \\ \min_{i} x_{ij}/x_{ij} & j\in J^{-} \end{cases} Anchor: Miller-Starr 1969, Ch.2
2. 2.Adım 2 (F2): Step 2: Weighted product P_i = Π r_ij^{w_j} and descending ranking. Formül: P_{i} = \prod_{j=1}^{n} (r_{ij})^{w_{j}} Anchor: Miller-Starr 1969, Ch.2 Eq.(3)

Commonly paired with

• •AHP + WPM (high)
• •BWM + WPM (high)
• •ENTROPY + WPM (high)
• •CRITIC + WPM (high)
• •SWARA + WPM (high)

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