DATA ENVELOPMENT ANALYSIS

About Data Envelopment

Analysis (DEA):

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DEA

has become very important tool for quantitative analysis to check and evaluate

the performance of one, two or multiple firms and to understand how the efficiencies

of the firm can be improved with reference to the benchmark firms. This

approach can be applied to extensive variety of activities with respect to the

current requirement. Gradually DEA utilization is increasing in the current

market as it aids in meeting the todays demand.

Data

Envelopment Analysis (DEA) an extensive and useful technique was originally

developed by Rhodes and Charnes_Cooper in 1978 to majorly do the evaluation of public

sector organizations and NGOs. DEA has been utilized to improve the efficiency

to optimize the resources majorly in services which may not be easy to

calculate even based on the experience. Majority of service providers can take

advantage from this power technique and improve efficiency and productivity. More

people start using this it will help the research assistant to identify the

“benefits” and “banes” of this tool and may highlight the limitations, if any.

Research

on DEA and its fetched result will help to identify the areas where this tool

may not be effective as desired. DEA approach is not user-friendly or handy for

managers to understand and implement the technique. This is one of the bottlenecks

which is preventing DEA from entering the business. Aim is to focus on how this tool helps in

evaluating efficiency, to identify the areas to advance productivity, understand

limitations of DEA, and how to make use of this tool. This will assist applicators

to evaluate the importance of using it in services domain.

DEA

can be of help in the situations where a comparative performance of dissimilar

components is to be linked and assessed, like,

Ø To

check for inconsistency or inefficiency in the operations.

Ø DEA

can deal with intricate relation between multiple inputs and multiple outputs.

Ø

DEA techniques are associated

to linear programming concepts.

Efficiency

Measurement

To

calculate the efficiency of the various service units and demonstrate the same

is very critical and at the same time biggest concern on which technique to be

adopted. E.g. How to optimize the staff in big departmental stores, how to

aptly distribute the number of doctors/nurses on daily basis in hospital, how

to fix the no. of branches of banks in particular region etc.

Efficiency = Output / Input

This

formula though looks simple becomes complicated based on the number of outputs

and inputs given in the specified problem. If output is higher than the input

it suggests that efficiency is very high. Once the system/ unit reaches its

optimum efficiency level i.e. output /input ratio cannot be increased further,

it becomes evident that certain new method or technology needs to be adopted to

establish new benchmarks.

Technical and Scale Efficiency

For

example, in effectiveness of Portable charger, we might measure it as charging

rate i.e hours per full charge. We can define

the efficiency of “Charger” with the ideal chargers rate of charge. Let us take

that Full charge of I-phone 5S taken by Charger is 2 hours, however as

committed is 2.5 hours. We can say that charger is operating at 80% efficiency (2/2.5

Hours). To give the optimize results; charger shall perform at 125% (2.5/2

Hours) from its current level. This would reduce the time taken. Further, after

this efficiency is achieved for higher benchmarks, technology of charger needs

to be improved. It is to be ensured that charger of similar kinds are compared

to establish the realistic results.

Price Efficiency

If

A choose to use the cannon copier which generates 1000 B&W printout per

cartridge and cost of cartridge is INR 5000. Thus resulting cost is 5 rupees

per printout. B chooses to opt for HP printer which generates 1000 B& W

printouts per cartridge and the cost of cartridge is INR 4500 which derives the

price to 4.5 rupees per printout. A is less efficient than B but it is not due

to efficiency of copier but because of Price efficiency of HP cartridge.

Relative efficiency

measurement

In

this DMU has to be valued as 100% efficient after referring all the presented

confirmations, only in case if enactments of all presented DMUs cannot show /

increase the efficiency either by changing the inputs or outputs.

The

measurement of relative efficiency is used where there are numerous possible

insufficient inputs and outputs. A common measure for relative efficiency is,

Efficiency = Weighted sum

of Outputs

Weighted sum of inputs

Which

introducing the usual notation can be written as

Efficiency

of Unit = U1Y1j + U2Y2j +….

V1X1j + V2X2j +……

U1

= Weight of Output i

Y1j=

Amount of Output 1 from unit j

V1

= Wright given to input 1

X1j=

Amount of input 1 to unit j

(Efficiency usually lie in

the range 0,1).

E.g.

Input

Output

Student

Hours of Study for

DS

marks out of 100

Marks per Hour of

Study

Relative efficiency

A

6

80

13.333

78.4%

B

7

74

10.571

62.2%

C

5

85

17.000

100.0%

D

4

65

16.250

95.6%

DEA

process

Output/

Efficiency of the system can be evaluated by two approaches.

v Partial

efficiency measures

v Total

factor efficiency measures

Partial

efficiency approach does not account all the output and input factors, whereas,

total factor effectiveness approach is designed to consider all the data

outputs and inputs.

To

contemplate the available data, a technique is must with ability to address and

account the mentioned critical areas.

v To

arrive at single ratio with multiple outputs and multiple inputs.

v How

to prioritize or to understand the criticality of one attribute with respect to

others.

v Addressing

the challenge of varied variables and constraints?

SINGLE

INPUT AND SINGLE OUTPUT

If

we refer to the single output to single input case let us understand one simple

example. Cricket Tournament has 6 Teams which are T1 to T6

The

number of Bowlers and wicket taken are observed for further evaluation of

performance. First line is the number of bowlers who bowled for the team and

second line is the number of wickets taken by the total number of bowlers in

the respective team. The last line of the below mentioned table reflects “Wickets

taken per bowler” measure of efficiency or effectiveness of a Bowler.

Cricket Team

T1

T2

T3

T4

T5

T6

Bowlers

2

3

3

5

6

5

Wickets

1

3

1

3

3

2

Wickets/Bowler

0.5

1

0.33

0.6

0.5

0.4

_____ Frontier line ______

Regression line

By

this we are able to see that T2( 1) is the most efficient team in terms of

bowling and T3(0.33) is the team least

efficient . Highest slope is achieved by the Frontier line and it is

also known as “efficient frontier” It is necessary/must that this line should

touch at least one point and all other points should either be below or above

this line and thus it is known as envelopment .

Regression

line passes from the (0,0) and is usually determined by statistical approach

and it goes from the centre of all the plotted points such that residual value

is always zero.. Frontier line highlights the performance of the team T2. DEA helps

to point out the benchmark for others to move towards improvements.

We

can assess the effectiveness of other teams relative to T2 and can organize

them in order by referring the output:

0<= Wickets/Bowler of others<= 1 Wickets/Bowler of B 1=T2>T4>T5=T1>T6>T3=0.33

Thus

Team T3 has the worst efficiency i.e. 0.33 *100% =33% of T2 efficiency

TWO

INPUTS AND ONE OUTPUT CASE

Let

us look at two inputs and single output case and its handling, table shows the

performance of 9 teams each having two inputs and one output. Input x1 is the

number of bowlers, Input X2 the wickets and Output Y1 number of wins However, number

of wins has been normalized to 1 .

Cricket Team

T1

T2

T3

T4

T5

T6

T7

T8

Bowlers(Input

X1)

4

7

8

4

2

5

6

5

Wickets(Input

X2)

3

3

1

2

4

2

4

2.5

Wins (

Output) Y1

1

1

1

1

1

1

1

1

Bowlers/Win

4

7

8

4

2

5

6

5

wickets/win

3

3

1

2

4

2

4

2.5

T1

T3

T4

T5

____ Efficient Frontier

With

efficiency in mind it is but obvious that the team which utilizes less inputs

to get the same output is more efficient compared to others. Thus the Frontier

line drawn which shows all points(teams)

lying above needs to be more efficient No team mentioned on the frontier line can get better its input values with no decline

of the other. We call this region the production possibility set.

The

effectiveness of teams not coinciding on frontier line can be calculated by the

frontier point. For illustration, T1 is unproductive. To calculate its ineffectiveness

let OT1, the line from Origin (0, 0) to T1, cross the frontier line at B, Then,

the effectiveness of T1 will be formulated by OB/ OT1

This

way the inadequacy of T1 is to be evaluated by a arrangement of T4 and T5

because the point B is on the line linking these two points. T4 and T5 are

called the position set for T1. This set for an unproductive team may differ.

For

example, T1 can be successfully enhanced by progress to B because these are the

coordinates of P, the point on the efficient frontier that we beforehand recognized

with the line segment OT1. However, any point on this segment may be used to

improve the efficiency of Team T1. M is achieved by reducing X1 (Bowlers) and N

is achieved by dipping Input X2 Wickets

N

B

M

ONE

INPUT AND TWO OUTPUTS CASE

Tbl

below mentions the number of Bold per bowler and LBW per bowler for 6 teams. To

get a frontier for this scenario, outputs are divided by the inputs (Bowlers).

Bowlers are normalized to one for calculation effectiveness. The proficient

frontier will have the line connecting T2, T5 and T6.

Team

T1

T2

T3

T4

T5

T6

Bowler

X

1

1

1

1

1

1

Bold

Y1

1

2

3

4

4

6

LBW

Y2

5

7

4

3

6

2

Bold/Bowler

1

2

3

4

4

6

LBW/Bowler

5

7

4

3

6

2

The

production set is the region enclosed by the axis and the frontier line. Team

T1, T3 and T4 are unproductive and their effectiveness can be calculated by

referring to the frontier lines.

Efficiency

of T1 can be improved by changing the outputs and keeping the input normalized.

FIXED

AND VARIABLE WEIGHTS

The

cases used to this point have been very narrow in the number of inputs and

outputs used. Idea is to build up methods that ensure that it is feasible to treat

such applications with no load on the executer to solve this with undue scrutiny

or working out and with no large numbers of suppositions.

think,

for example, the condition is which

records actions planned to serve up as a basis for evaluating the relation

efficiency of 12 teams in terms of two inputs, number of bowlers and number of batsmen, and two outputs acknowledged

as number of wins in Test and One day

Team

T1

T2

T3

T4

T5

T6

T7

T8

T9

T10

T11

T12

Bowler

X1

5

4

6

6

4

5

4

7

4

5

4

6

Batsmen

X2

8

6

7

8

8

7

7

6

7

6

7

5

Test Win

Y1

4

5

7

5

4

2

4

6

5

3

6

4

One day Win

Y2

6

7

3

4

6

3

2

1

3

5

4

2

CCR

is calculated by forming the equation for all the teams as per the criteria and

to calculate the efficiency using the solver.

Eg.

U1 is for output 1 and U2 is output 2. V1 is for input 1 and V2 is for input 2

Efficiency

is output/ Input within the range 0,1. For team T1

0<= 4U1 +6U2/ 5V1 +8 V2<=1 0<= 4U1 +6U2 <=5V1 +8 V2 4U1 +6U2 - 5V1 -8 V2 <=0 ----- (1) Similarly, all 11 equations are created. Input is normalized and fixed to any value . Solving this with solver gives the CCR T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 CCR 0.69 1.00 1.00 0.68 0.86 0.37 0.67 1.00 1.00 0.71 1.00 0.81 DEA, by difference or exclusively, uses variable weights. In meticulous way, the weights are derived using solver directly from the Excel. Moreover, the weights are selected in modes that assign a best set of weights to each team. The term "best" is referred here to denote that the ensuing input-to output ratio for each team is maximized relative to all other teams. The row labelled CCR in above mentioned table shows results calculated from DEA using "CCR model". Furthermore, this "best ratio" result is obtained under the following conditions: (1) All data derived are nonnegative (2) The consequential ratio must lie between the range0,1 (3) These weights for the target entity (=team) are useful to all. 69% for Team T1 means that it is 31% inefficient. That is, in comparison to the team lying on the efficient frontier, it is achievable to recognize a technical inefficiency of 31%—and other possible inefficiencies.