A DEA model formulation involving the concept of a composite unit. The term ‘envelopment’ stresses the fact that a composite unit is a combination of efficient units enveloping an inefficient unit.

While in the strictest sense all factors depend on their environment, an input or output factor that purposefully attempts to make up for the inherent differences in the DMIJs being analysed is generally referred to as an environmental factor. The larger the field, the more probable that some units have intrinsic advantages over others. Environmental inputs typically take the age and the nature of its resources (je educational level of the staff) into account, while environmental outputs usually focus on the quality, rather than the quantity, of the outputs.

A very small positive constant (generally taken to be 1.0E-6) whose purpose in the primal model, Epsilon prevents any factor from being abused as a free commodity and avoid a unit being falsely classified as efficient. In the dual model, epsilon’s role is to make sure that the minimisation of the intensity factor, takes precedence over the maximisation of the sum of the slacks. The value of epsilon may cause computational inaccuracies, a solution is provided in 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.

An input or output that is beyond the control of the DMU manager. A fast-food restaurant may have an input such as years of operations, that it cannot control and hence the unit cannot improve its efficiency by reducing that input.

In higher dimensions, the segments forming the efficiency frontier are known as facets.

Refers to the degree of similarity between the units in the field. Only units that bear some similarities in their operational goals should be included in the same field, otherwise the results may be biased.

A DMU is said to operate at increasing returns to scale (IRS) if a proportionate increase in all of its inputs results in a greater than proportionate increase in its outputs. If for a given unit the sum of its dual weights in the dual model turns out to be less than 1, then that unit can be said to operate at IRS, assuming it is technically efficient.

Any factor used as a resource by the DMU for producing something of value.

A term used in conjunction with the ratio models to indicate that an inefficient unit is made efficient through the proportional reduction of its inputs while its outputs proportions are held constant. While the CCR model yields the same efficiencies regardless of whether it is input or output-oriented, this is not so with the BCC model.

The proportions in which a unit’s input/output values are combined.