The efficiency scores of the DEA ratio models are independent of the units in which the factors are measured. The input and output values can thus be scaled through multiplication by a constant as proven in Chames and Cooper (1985). [Charnes A, Cooper W W (1985) ‘Preface to topics in data envelopment analysis’, in Thompson R G and Thrall R M (editors), The annals of operations research]

Given a set of inputs that produce outputs, the production function defines an optimum relationship for producing the maximal amount of output from the given inputs. The DEA equivalent of the production function is the efficiency frontier which is based on empirical data (inputs and outputs). See Chames et al (1981) for details and more references. [Chames A, Cooper W W and Rhodes E (1981), ‘Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through’, Mgmt. Sci., 6, pp 668-697.]

An input or output factor. Since these are always known beforehand, their values are actually constants.

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.]

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.

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.

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 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.

A measure of a unit’s ability to produce outputs from its set of inputs. Since the efficiency of a given DMU is measured with respect to other DMUs in the field, the obtained efficiency is always relative. From the standpoint of the efficiency frontier, an enveloped unit’s efficiency is related to its radial distance from the frontier.

Efficiency is measured on a scale of 0 to 1, where a value of I indicates the unit is relatively efficient, and a value less than 1 indicates the unit is inefficient. The efficiency score of a unit will vary according to the factors and DMUs included in the analysis. In the early days of DEA, there was some concern as to whether it was justified to rank inefficient units according to their efficiency scores on the grounds that the scores may have been calculated from distinct reference sets.