Associated with each DEA model type (eg CCR, BCC) is both a primal and dual formulation. To avoid confusion over which formulation is primal and which dual, the multiplier form is always understood to refer to the formulation involving virtual multipliers (Ali and Seiford 1993). [Ali A and Seiford L (1993), ‘The mathematical programming approach to efficiency analysis’, in: Fried H, Knox C A K and Schmidt S (editors), The measurement of productive efficiency: techniques and applications, Oxford University Press.

The CCR and BCC models both define efficiency as a ratio of weighted outputs over weighted inputs, hence they are often known as ratio models.

The process of developing a set of visual techniques such as graphs and charts through which the DEA results can be better understood.

Same as exogenously fixed factor.

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.]