DEA

DEA Cross-Efficiency: peer appraisal using cross-evaluation matrix

Sexton, T. R., Silkman, R. H., Hogan, A. J. · 1986

Overview

DEA extension: cross-evaluation with peer appraisal averaging. Output typically efficiency (higher value = preferred).

Strengths

•Method-specific: DEA extension: cross-evaluation with peer appraisal averaging

Limitations

•Assumes: Clear input and output criteria distinction
•Assumes: All DMUs in same industry/context

Method assistant

Grounded explanations: it explains the method, it does not compute.

Assumptions to verify

•Clear input and output criteria distinction
•All DMUs in same industry/context

When not to use

•Mixed input/output direction confusion
•Small sample (m < 3·(inputs+outputs))

Edge cases

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

Common pitfalls

•Hatalı: 'DEA-CROSSEFF bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Clear input and output criteria distinction
•Hatalı: 'DEA-CROSSEFF bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All DMUs in same industry/context
•Hatalı: DEA-CROSSEFF'yi 'Mixed input/output direction confusion' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
•Hatalı: DEA-CROSSEFF'yi 'Small sample (m < 3·(inputs+outputs))' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Identify inputs and outputs per DMU; same as CCR. Formül: X\in\mathbb{R}^{p\times m},\ Y\in\mathbb{R}^{q\times m} Anchor: Sexton 1986, p.74 Sec.2
2.Adım 2 (F2): Step 2: Solve CCR LP per DMU_o to obtain own efficiency θ*_o and weights. Formül: \max \dfrac{\mathbf{u}_{o}^{T} Y_{o}}{\mathbf{v}_{o}^{T} X_{o}} \ \text{s.t.}\ \dfrac{\mathbf{u}_{o}^{T} Y_{j}}{\mathbf{v}_{o}^{T} X_{j}}\le 1 Anchor: Sexton 1986, p.75 Eq.(1)
3.Adım 3 (F3): Step 3: Cross-efficiency E_oj = (u_o^T Y_j)/(v_o^T X_j) using DMU_o's weights on DMU_j. Formül: E_{oj} = \dfrac{\mathbf{u}_{o}^{T} Y_{j}}{\mathbf{v}_{o}^{T} X_{j}} Anchor: Sexton 1986, p.76 Eq.(2)
4.Adım 4 (F4): Step 4: Average cross-efficiency ē_j = (1/m) Σ_o E_oj; descending ranking. Formül: \bar{e}_{j} = \dfrac{1}{m} \sum_{o=1}^{m} E_{oj} Anchor: Sexton 1986, p.76 Eq.(3)

How to cite

Sexton, T. R.; Silkman, R. H.; Hogan, A. J. (1986). Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation. https://doi.org/10.1002/ev.1441

BibTeX RIS APA (.txt)DOI ↗

Common pitfalls

•Hatalı: 'DEA-CROSSEFF bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Clear input and output criteria distinction

•Hatalı: 'DEA-CROSSEFF bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All DMUs in same industry/context

•Hatalı: DEA-CROSSEFF'yi 'Mixed input/output direction confusion' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

•Hatalı: DEA-CROSSEFF'yi 'Small sample (m < 3·(inputs+outputs))' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1.Adım 1 (F1): Step 1: Identify inputs and outputs per DMU; same as CCR. Formül: X\in\mathbb{R}^{p\times m},\ Y\in\mathbb{R}^{q\times m} Anchor: Sexton 1986, p.74 Sec.2

2.Adım 2 (F2): Step 2: Solve CCR LP per DMU_o to obtain own efficiency θ*_o and weights. Formül: \max \dfrac{\mathbf{u}_{o}^{T} Y_{o}}{\mathbf{v}_{o}^{T} X_{o}} \ \text{s.t.}\ \dfrac{\mathbf{u}_{o}^{T} Y_{j}}{\mathbf{v}_{o}^{T} X_{j}}\le 1 Anchor: Sexton 1986, p.75 Eq.(1)

3.Adım 3 (F3): Step 3: Cross-efficiency E_oj = (u_o^T Y_j)/(v_o^T X_j) using DMU_o's weights on DMU_j. Formül: E_{oj} = \dfrac{\mathbf{u}_{o}^{T} Y_{j}}{\mathbf{v}_{o}^{T} X_{j}} Anchor: Sexton 1986, p.76 Eq.(2)

4.Adım 4 (F4): Step 4: Average cross-efficiency ē_j = (1/m) Σ_o E_oj; descending ranking. Formül: \bar{e}_{j} = \dfrac{1}{m} \sum_{o=1}^{m} E_{oj} Anchor: Sexton 1986, p.76 Eq.(3)