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

Overview

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

Output

Efficiency, higher is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Efficiency analysis, benchmarking, productivity measurement

How it works

1. 1

   Identify inputs X (cost) and outputs Y (benefit) per DMU.

   $$X\in {\mathbb{R}}^{p\times m},Y\in {\mathbb{R}}^{q\times m},p=\#\text{inputs},q=\#\text{outputs}$$

   CCR 1978, p.430 Sec.2

2. 2

   Solve CCR LP per DMU_o: max u^TY_o / v^TX_o s.t. u^TY_j / v^TX_j ≤ 1 ∀j.

   $$\max \frac{{\mathbf{u}}^T{Y}_o}{{\mathbf{v}}^T{X}_o}\text{s.t.}\frac{{\mathbf{u}}^T{Y}_j}{{\mathbf{v}}^T{X}_j}\le 1,\mathbf{u},\mathbf{v}\ge 0$$

   CCR 1978, p.430 Eq.(1)

3. 3

   Identify efficient frontier DMUs (θ*=1) and inefficient ones (θ*<1).

   $$\mathcal{F}=\{j:{\theta }_j^{\ast }=1\}$$

   CCR 1978, p.431

4. 4

   Rank DMUs by efficiency θ* descending; frontier members tie at top.

   $$\text{rank}(j)\propto -{\theta }_j^{\ast }$$

   CCR 1978, p.431

Look elsewhere when

Assumptions to verify

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

Edge cases and pitfalls

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

• Applying DEA without verifying this assumption.

  Requirement: Clear input and output criteria distinction

• Applying DEA without verifying this assumption.

  Requirement: All DMUs in same industry/context

• Using DEA when: Mixed input/output direction confusion.

  An alternative method is recommended in this situation.

• Using DEA when: Small sample (m < 3·(inputs+outputs)).

  An alternative method is recommended in this situation.

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