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## Technical Efficiency Measurement by Data Envelopment Analysis

capital, land, fuel and materials, to produce services. If an agency is not using its inputs in a technically ef- ficient manner, it is possible to increase the quantities of outputs without increasing inputs, or to reduce the inputs being used to produce given quantities of out- puts.

# What is Data Envelopment Analysis?

Data envelopment analysis is a Linear Programming Problem that provides a means of calculating appar- ent efficiency levels within a group of organizations. The efficiency of an organization is calculated relative to the group’s observed best practice.

tions that would minimize costs. An organization that is operating at best practice in engineering terms could still be allocatively inefficient because it is not using inputs in the proportions which minimize its costs, given relative input prices.

Finally, cost efficiency refers to the combination of technical and allocative efficiency. An organization will only be cost efficient if it is both technically and allocatively efficient. Cost efficiency is calculated as the product of the technical and allocative efficiency scores (expressed as a percentage), so an organization can only achieve a 100% score in cost efficiency if it has achieved 100% in both technical and allocative ef- ficiency.

# DEA and Different Efficiency Concepts

Typically using linear programming, DEA measures the efficiency of an organization within a group rel- ative to observed best practice within that group. The organizations can be whole agencies (for exam- ple, state road transport undertaking), separate enti- ties within the agency or disaggregated business units within the separate entities.

These concepts are best depicted graphically, as in Figure 1 which plots different combinations of two in- puts, labor and capital, required to produce a given

output

quantity.

# The

curve

plotting

the

minimum

amounts

of

the

two

inputs

required

to

produce

the

out-

put quantity is known as tier. It is a smooth curve

an isoquant or efficient fron- representing theoretical best

engineering

practice.

# Producers

can

change

input

combinations

given

current

technological

possi-

To discuss DEA in more detail it is necessary to look at the different concepts of efficiency. The most common efficiency concept is technical efficiency: the conver- sion of physical inputs (such as the services of employ- ees and machines) into outputs relative to best prac- tice. In other words, given current technology, there is no wastage of inputs whatsoever in producing the given quantity of output. An organization operating at best practice is said to be 100% technically efficient. If operating below best practice levels, then the organiza- tion’s technical efficiency is expressed as a percentage of best practice. Managerial practices and the scale or size of operations affect technical efficiency, which is based on engineering relationships but not on prices and costs.

Allocative efficiency refers to whether inputs, for a given level of output and set of input prices, are chosen to minimize the cost of production, assuming that the organization being examined is already fully techni- cally efficient. Allocative efficiency is also expressed as a percentage score, with a score of 100% indicating that the organization is using its inputs in the propor-

bilities.

an

organization

is

producing

at

a

point

on

the

isoquant

then

it

is

technically

efficient.

# The

straight

line denoted as the budget the two inputs that have the budget line is given by the

line plots combinations of same cost. The slope of the negative of the ratio of the

capital price to the the origin represent

labor price. Budget lines closer a lower total cost. Thus, the cost

to of

producing

a

given

output

quantity

is

minimized

at

the

point where the budget line At this point both technical are attained.

is tangent to the isoquant. and allocative efficiencies

The point of operation marked A would be techni- cally inefficient because more inputs are used than are needed to produce the level of output designated by the isoquant. Point B is technically efficient but not cost efficient because the same level of output could be produced at less cost at point C. Thus, if an organiza- tion moved from point A to point C its cost efficiency would increase by (OA-OA”)/OA. This would consist of an improvement in technical efficiency measured by the distance (OA-OA’)/OA and an allocative effi-

### Alliance Journal of Business Research

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