Data Envelopment

Analysis

Data Envelopment Analysis (DEA):

o Introduced by Charnes, Cooper and Rhodes (1978)

• http://en.wikipedia.org/wiki/William_W._Cooper

• Father of DEA in particular, but also massive contributions to the field of Management Science in general

o DEA is building on work by Farrell (1957)

o But using linear programming to estimate the efficiency enabled simultaneous consideration of multiple inputs and multiple outputs

• A separate LP problem is run for each of the DMU to measure their respective efficiencies

Since the seminal paper from 1978, some 5000 papers have been published on DEA

o Both theoretical and empirical contributions

o DEA is, however, still not mainstream in economics

• •

DEA models aim to identify efficient and inefficient DMUs

o For the inefficient DMUs:

• Benchmarks and better performing peers are identified

Different DEA models can accommodate different assumptions

o Returns to scale

o Non-discretionary variables o:

•

DEA cont’

DEA can incorporate:

o Multiple inputs and multiple outputs at the same time

o Different metrics for the variables

o Relative prices/weights if desired – but they are not

required

Benchmarking, CBS, 2014 Lecture 2  3



DEA input efficiency

5

4

3

2

1

0

B4

B1

*

B3

B2

012345

Supervisory hours

• A bank has four branches

• Each branch manages a certain number of accounts and uses a certain number of supervisory and trainee hours

Branch

Supervisory hours (Input 1)

Trainee hours (Input 2)

Accounts thousands (Output)

1

2

3

1

2

4

1

1

3

2

2

1

4

1

4

1

Benchmarking, CBS, 2014

• B1 exhibits input inefficiency

• The inefficiency can be eliminated without changing proportions between its inputs and/or outputs

• This is known as technical inefficiency Lecture 2  4

Trainee hours

•

Revised example: Mix (in)efficiency

B1 exhibits inefficiency o It is dominated by B2

• Buttheinefficiencycannotbeeliminatedwithoutchangingthe proportions (or mix) between its inputs and/or outputs

• Thisisknownasmixinefficiency •

B5 exhibits both technical and mix inefficiency

5

4

3

2

1

0

B4

B3

B2 A *

...