DEA

DEA: Data Envelopment Analysis (CCR model) for efficiency-based ranking

Charnes, A., Cooper, W. W., Rhodes, E. · 1978

Overview

Non-parametric efficiency frontier (CCR model). Output typically efficiency (higher value = preferred).

Strengths

•Method-specific: Non-parametric efficiency frontier (CCR model)

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

•tier DMUs (θ*=1) and inefficient ones (θ*<1).
•tier members tie at top.

Common pitfalls

•Hatalı: 'DEA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Clear input and output criteria distinction
•Hatalı: 'DEA bu varsayımı kontrol etmeden uygulamak'. Doğrusu: All DMUs in same industry/context
•Hatalı: DEA'yi 'Mixed input/output direction confusion' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
•Hatalı: DEA'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 X (cost) and outputs Y (benefit) per DMU. Formül: X\in\mathbb{R}^{p\times m},\ Y\in\mathbb{R}^{q\times m},\ p=\#\text{inputs},\ q=\#\text{outputs} Anchor: CCR 1978, p.430 Sec.2
2.Adım 2 (F2): Step 2: Solve CCR LP per DMU_o: max u^TY_o / v^TX_o s.t. u^TY_j / v^TX_j ≤ 1 ∀j. Formül: \max \dfrac{\mathbf{u}^{T} Y_{o}}{\mathbf{v}^{T} X_{o}} \ \text{s.t.}\ \dfrac{\mathbf{u}^{T} Y_{j}}{\mathbf{v}^{T} X_{j}} \le 1,\ \mathbf{u},\mathbf{v}\ge 0 Anchor: CCR 1978, p.430 Eq.(1)
3.Adım 3 (F3): Step 3: Identify efficient frontier DMUs (θ*=1) and inefficient ones (θ*<1). Formül: \mathcal{F} = \{j: \theta^{*}_{j}=1\} Anchor: CCR 1978, p.431
4.Adım 4 (F4): Step 4: Rank DMUs by efficiency θ* descending; frontier members tie at top. Formül: \text{rank}(j) \propto -\theta^{*}_{j} Anchor: CCR 1978, p.431

How to cite

Charnes, A.; Cooper, W. W.; Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research. https://doi.org/10.1016/0377-2217(78)90138-8

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Common pitfalls

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

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

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

•Hatalı: DEA'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 X (cost) and outputs Y (benefit) per DMU. Formül: X\in\mathbb{R}^{p\times m},\ Y\in\mathbb{R}^{q\times m},\ p=\#\text{inputs},\ q=\#\text{outputs} Anchor: CCR 1978, p.430 Sec.2

2.Adım 2 (F2): Step 2: Solve CCR LP per DMU_o: max u^TY_o / v^TX_o s.t. u^TY_j / v^TX_j ≤ 1 ∀j. Formül: \max \dfrac{\mathbf{u}^{T} Y_{o}}{\mathbf{v}^{T} X_{o}} \ \text{s.t.}\ \dfrac{\mathbf{u}^{T} Y_{j}}{\mathbf{v}^{T} X_{j}} \le 1,\ \mathbf{u},\mathbf{v}\ge 0 Anchor: CCR 1978, p.430 Eq.(1)

3.Adım 3 (F3): Step 3: Identify efficient frontier DMUs (θ*=1) and inefficient ones (θ*<1). Formül: \mathcal{F} = \{j: \theta^{*}_{j}=1\} Anchor: CCR 1978, p.431

4.Adım 4 (F4): Step 4: Rank DMUs by efficiency θ* descending; frontier members tie at top. Formül: \text{rank}(j) \propto -\theta^{*}_{j} Anchor: CCR 1978, p.431