Data envelopment analysis

Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers. It is used to empirically measure productive efficiency of decision making units (DMUs). Although DEA has a strong link to production theory in economics, the tool is also used for benchmarking in operations management, where a set of measures is selected to benchmark the performance of manufacturing and service operations. In benchmarking, the efficient DMUs, as defined by DEA, may not necessarily form a “production frontier”, but rather lead to a “best-practice frontier” (Cook, Tone and Zhu, 2014). DEA is referred to as 'balanced benchmarking' by Sherman and Zhu (2013). Data envelopment analysis (DEA) is a nonparametric method in operations research and economics for the estimation of production frontiers. It is used to empirically measure productive efficiency of decision making units (DMUs). Although DEA has a strong link to production theory in economics, the tool is also used for benchmarking in operations management, where a set of measures is selected to benchmark the performance of manufacturing and service operations. In benchmarking, the efficient DMUs, as defined by DEA, may not necessarily form a “production frontier”, but rather lead to a “best-practice frontier” (Cook, Tone and Zhu, 2014). DEA is referred to as 'balanced benchmarking' by Sherman and Zhu (2013). Non-parametric approaches have the benefit of not assuming a particular functional form/shape for the frontier, however they do not provide a general relationship (equation) relating output and input. There are also parametric approaches which are used for the estimation of production frontiers (see Lovell & Schmidt 1988 for an early survey). These require that the shape of the frontier be guessed beforehand by specifying a particular function relating output to input. The relative strengths from each of these approaches can be combined in a hybrid method (Tofallis, 2001,) where the frontier units are identified by DEA, then fitted to a smooth surface. This allows a best-practice relationship between multiple outputs and multiple inputs to be estimated. 'The framework has been adapted from multi-input, multi-output production functions and applied in many industries. DEA develops a function whose form is determined by the most efficient producers. This method differs from the Ordinary Least Squares (OLS) statistical technique that bases comparisons relative to an average producer. Like Stochastic Frontier Analysis (SFA), DEA identifies a 'frontier' which are characterized as an extreme point method that assumes that if a firm can produce a certain level of output utilizing specific input levels, another firm of equal scale should be capable of doing the same. The most efficient producers can form a 'composite producer', allowing the computation of an efficient solution for every level of input or output. Where there is no actual corresponding firm, 'virtual producers' are identified to make comparisons' (Berg 2010). Attempts to synthesize DEA and SFA, improving upon their drawbacks, were also made in the literature, via proposing various versions of non-parametric SFA and Stochastic DEA. In microeconomic production theory, a firm's input and output combinations are depicted using a production function. Using such a function, one can show the maximum output which can be achieved with any possible combination of inputs, that is, one can construct a production technology frontier (Sieford & Thrall 1990). Building on the ideas of Farrell (1957), the seminal work 'Measuring the efficiency of decision making units' by Charnes, Cooper & Rhodes (1978) applies linear programming to estimate an empirical production technology frontier for the first time. In Germany, the procedure was used earlier to estimate the marginal productivity of R&D and other factors of production (Brockhoff 1970). Since then, there have been a large number of books and journal articles written on DEA or applying DEA on various sets of problems.