[ronin123]

The Data Envelopment Analysis (DEA) is a linear programming procedure for a frontier analysis of inputs and outputs. The DEA assigns a score of 1 to a unit only when comparisons with other relevant units do not provide evidence of inefficiency in the use of any input or output. The DEA assigns an efficiency score less than one to (relatively) inefficient units. A score of less than one means that a linear combination of other units from the sample could produce the same vector of outputs when using a smaller vector of inputs. The score reflects the radial distance from the estimated production frontier to the Decision Making Unit (DMU) under consideration.

There are a number of equivalent formulations for DEA. The most direct formulation of the exposition i given above is as follows:
• Let Xi be the vector of inputs into DMU i. Let Yi be the corresponding vector of outputs. Let X0 be the inputs into a DMU for which we want to determine its efficiency and any Y0 be the outputs
• We would like to find the best combination that dominates DMUs

The measure of efficiency for DMU0 is given by the following fractional program:

Min 
s.t.  i Xi ≤ X0
 i Yi ≥ Y0
Where i is the weight given to DMUi in its efforts to dominate DMU 0 and  is the efficiency of DMU 0. In general, we should include DMU 0 on the left hand side of the equations. Then, the optimal  cannot possibly be more than 1. When we solve this linear program, we get a number of things.

1. The efficiency of DMU 0 (), with =1 meaning that the unit is efficient.
2. The unit’s “comparables” (those DMU with nonzero )
3. The “goal” inputs (the differences between X0 and  i Xi)
4. Alternatively, we can keep inputs fixed and get goal outputs (1/i Yi)

Firms like LoanMax of rod aycox fame have always adhered to goal based outputs with minimum inputs. This is one major reason as to why this firm is able to post profits even during these times of recession.