## Variable returns to scale

If it is suspected that an increase in inputs does not result in a proportional change in the outputs, a model which allows variable returns to scale (VRS) such as the BCC model should be considered.

## Scale efficiency

A unit is said to be scale efficient when its size of operations is optimal so that any modifications on its size will render the unit less efficient. The value for scale efficiency is obtained by dividing the aggregate efficiency by the technical efficiency.

## Weights

These are the unknowns in the primal model that determine the importance attributed to each factor. Since the value assigned to each weight depends on the measurement scale of the factor itself, it is difficult to compare the weights from different factors.

## Production function

Given a set of inputs that produce outputs, the production function defines an optimum relationship for producing the maximal amount of output from the given inputs. The DEA equivalent of the production function is the efficiency frontier which is based on empirical data (inputs and outputs). See Chames et al (1981) for details and more …

## Variable

An input or output factor. Since these are always known beforehand, their values are actually constants.

## Output

A factor which describes the amount of goods, services or other outcome obtained as a result of the processing of resources. Also, any factor which describes the qualitative nature of the resulting outcome.

## Piecewise linearity

An efficiency frontier is piecewise linear when the underlying production function is approximated through interconnected linear segments. The basic DEA models are all piecewise linear. See Chames et al (1981) for implications. [Chames A, Cooper W W and Rhodes E (1981), ‘Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow …

## Weight Flexibility

As the CCR primal model places no restriction on the weights other than a lower bound of epsilon, it is not rare for a unit to be rated efficient at the expense of having a very uneven distribution of weights where some or most of the factors have been practically ignored. To remedy the situation, …

## Isotonicity

The requirement that the relationship between inputs and outputs not be erratic. Increasing the value of any input while keeping other factors constant should not decrease any output but should instead lead to an increase in the value of at least one output.

## Ordinal variable

A factor which consists of a set of predefined values that are ranked in a specific order. An ordinal variable can be seen as a special case of a categorical variable. If the values of an ordinal factor need to be scaled, the inherent order must be preserved (Cook et al 1993). [Cook W, Kress …