Another name for reference set

Short for decision making unit or DMU.

An efficiency frontier is piecewise linear when the underlying production function is approximated through interconnected linear segments. The basic DEA models are all piecewise linear. See Chames et al (1981) for implications. [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.]

Yet another name for the efficiency frontier, this term emphasises the fact that each segment of the frontier represents the trade-off possibilities that can be made between the inputs or outputs of a given DMU on the isoquant segment while keeping the DMU efficient.

The primal model allows the DMU being measured to determine the set of optimal weights for each of its factors (outputs are denoted by y. and inputs by x in the following model) so as to maximise its efficiency. The solution consists of a set of weights (for outputs and y for inputs) chosen so that the efficiency of any other unit with these weights won’t exceed 1, the value at which a unit is relatively efficient. Which model is denoted primal and which dual is arbitrary, some authors prefer to call this model the primal model, as it conveys better the basic idea behind DEA. The convention followed here is the same as that used by the developers in their original paper, Chames et al (1978).

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.