BCC

Introduced by Banker, Chames and Cooper (1984), this model measures technical efficiency as the convexity constraint ensures that the composite unit is of similar scale size as the unit being measured. The resulting efficiency is always at least equal to the one given by the CCR model, and those DMUs with the lowest input or highest output levels are rated efficient. Unlike the CCR model, the BCC model allows for variable returns to scale.

Productivity

For a single input-output case, the ratio of a unit’s output to its input. Productivity varies according to changes that occur in the production technology, the efficiency of the production process (which can be measured through DEA) and the production environment (Lovell 1993). [Lovel C A K (1993), ‘Productive frontiers and productive efficiency’, in: Fried H, Knox C A K and Schmidt S (editors) The measurement of productive efficiency: techniques and applications, Oxford University Press.]

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.

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.

Projected point

Refers to an inefficient DMU’s composite unit to emphasise that geometrically it involves the projection of the inefficient DMU onto the efficiency frontier (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.]

Virtual input(output)

Virtual input is obtained for each input by taking the product of the input’s value and its corresponding optimal weight as given by the solution to the primal model. Virtual outputs are obtained analogously. A virtual input or output describes the importance attached to the given factor. The virtual inputs always add up to the maximum efficiency score (ie 1) for the unit being analysed, while the sum of the virtual outputs will equal that unit’s efficiency.

Most productive scale size (MPSS)

MPSS is a unit (point) on the efficiency frontier that maximises the average productivity for its given input-output mix and after which decreasing returns to scale set in. See Banker & Kemerer (1989) on how to compute the MPSS. [Banker R and Kemerer C (1989) ‘Scale economies in new software development’, IEEE Trans. On Softw. Eng.., 15, pp 1199-1205.]

Radial measure

Both ratio models rely on a radial or proportional measure as a DMU’s efficiency score depends on its proportional distance to the efficiency frontier

Virtual multipliers

Another name for weights

Multiplier form

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.