The set of efficient units from which an inefficient unit’s inefficiency has been determined. Originally, the term was used to denote the set of all units in the analysis (i.e. the field) and the set of efficient units was known as a reference subset, a term still used by some.

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, additional restrictions on weights may be used.

Bessent et al (1988) coined this term (later simply known as unenveloped units) to refer to those inefficient units that are not fully enveloped by the efficiency frontier. To be fully enveloped in the CCR model, an inefficient DMU needs to have (m+n) -1 reference units where m+n denotes the number of factors. Unenveloped units can be identified from the results of the ratio models as those units with non-zero values in any of their input or output slacks. [Bessent A, Bessent W, Clark T and Elam J (1988) ‘Efficiency frontier determination by constrained facet analysis’, Operations Research, 36, pp 785-706.]

Any unit that is part of a reference set

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.

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 M and Seil ord L (1993), ‘On the use of ordinal data in data envelopment analysis’, J. of the Opi. Res. Soc., 44, pp 133-140.]

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.

If a DMU is rated efficient and more or less equal importance has been given to each of its factors, it is said to exhibit well-rounded performance.

Generally taken to mean an odd unit with an input-output mix that significantly differs from the rest of the units. This can be due to a measurement error, or as a result of the outlier having different operating practices. Outliers that are efficient can introduce bias into the analysis. See Epstein and Henderson (1989). [Epstein M K and Henderson J C (1989) ‘Data envelopment analysis for managerial control and diagnosis’, Decision Sciences, 20, pp 90-119.]

The so-called ‘size’ of the DMU, it may be associated with either the inputs or the outputs, depending on the situation.