Data Envelopment Analysis

<aside> 💡 A non-parametric mathematical method to find the production frontier.

</aside>

DEA Logic

• Using a DMU’s weights, if it can’t achieve an efficiency of 1, then it is truly efficient.
• Using a DMU’s weight, if an other DMU gets an efficiency of 1, then that other DMU is really good!

Efficiency

$$ \frac{\text{Weighted Output}}{\text{Weighted Input}} $$

For a particular DMU k, the efficiency is:

$$ E_k = \frac{y_{1k}o_{1k}+y_{2k}o_{2k}+..+y_{Mk}o_{Mk}}{x_{1k}o_{1k}+x_{2k}o_{2k}+..+x_{Nk}o_{Nk}} $$

Optimisation Problem

• Each DMU tries to maximize their own efficiency by adjusting the weights assigned to the inputs and the outputs.
• Constraint: No DMU should get efficiency more than 1.

$$ \text{Max } E_k \\ \text{subject to } E_k ≤ 1, k = 1,2,..,k \\ \text{Decision variables: } x_{ik}, y_{jk} ≥ 0, \forall i, \forall j $$