Category Archive: Frequently Asked Question


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 …

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Well-rounded performance

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.

Reference set

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.

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 …

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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. …

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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

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.

Technology/Production technology

The operational practices (a combination of the management and engineering knowledge) that determine how a DMU’s inputs are transformed into outputs.

Pareto-efficiency/Pareto-Koopmans efficiency:

Simply stated, a unit is Pareto-efficient when an attempt to improve on any of its inputs or outputs will adversely affect some other inputs or outputs. Formally, Chames et al (1981) consider a DMU to be 100% efficient only when ‘none of its inputs can be decreased without either (i) decreasing some of its outputs, …

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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.

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