In simple terms, the DEA approach is a data envelopment analysis. The formal development of DEA is attributed to Edwardo Rhode (1978). DEA is a nonparametric (i.e., nonstatistical) or mathematical programming approach for considering optimum solutions relative to individual units (e.g., firms) rather than assuming, as in optimized regression, that a solution applies to each decision making unit (DMU). DEA has been widely applied to problems in which answers about optimum input levels, their characteristics, and output levels were desired. A comprehensive discussion and introduction to DEA may be found in Charnes et al. (1995) and Fare et al. (1985;1994); similarly, an exhaustive discussion of intertemporal production frontiers with dynamic DEA is available in Fare and Grosskopf (1996).
There are two primary orientations of the DEA approach to assess technical and economic efficiency, capacity, capacity utilization, capital utilization, and input utilization: input- and output-oriented. The input based measure considers how inputs may be reduced relative to a desired output level. The output-based measure indicates how output could be expanded given the input levels. There is also a non-orienting DEA measure in which the frontier output and various concepts of technical and economic efficiency may be determined without being conditional on input or output levels being held constant.
There is an on-going debate among researchers about the applicability and usefulness of the DEA approach vs. the stochastic frontier approach. The DEA is purely deterministic and thus cannot accommodate the stochastic nature of fisheries. The criticism of being nonstochastic can be easily overcome through the use of bootstrapping DEA. The DEA approach relative to the frontier approach easily permits an assessment of a multiple input, multiple output technology. It also does not have the problem of zero-valued outputs or inputs which are typical of many multi-species fisheries (e.g., some vessels or trips harvest only a few of many species and thus have zero-valued output for some species). Neither the stochastic frontier nor the dual-based approaches can easily accommodate the zero-valued dependent variable problem. Even in the absence of zero valued-outputs, the stochastic frontier approach cannot easily handle multiple outputs. Canonical ridge regression as used by Vinod permits estimation of a primal with multiple outputs but does not address the zero valued output. The stochastic frontier also requires the assumption of some underlying functional form and thus offers the possibility for specification error.
The DEA approach also recognizes or can accommodate both discretionary and nondiscretionary inputs and outputs. It also can facilitate temporal analysis using what is called a Windows technique (Charnes et al., 1994). Technical change as well as network or dynamic assessments can easily be accommodated with DEA (Fare and Grosskopf, 1996). DEA may also accommodate the determination of capacity and capacity output subject to different levels of bycatch or combinations of multiple outputs (e.g., determination of efficiency, capacity, or capacity utilization when one or more outputs are constrained to zero); it is only necessary to impose constraints in terms of nondiscretionary and weak disposability of inputs or outputs.
A recognized limitation of using the DEA to assess technical efficiency is that recommendations for decreasing input usage or expanding output levels are in terms of scalar valued ratios which are held constant (i.e., recommendations are in terms of fixed proportions). This limitation, however, is partially mitigated by considering changes in terms of slack variables. In this case, it is possible to determine decreases in inputs or increases in outputs relative to the slack variables; changes are not restricted to constancy of the input or output mixes. Another option to avoid the problem of constant mix ratios is to consider either an economic cost approach or an economic revenue approach. With the economic DEA approaches, prices on inputs or on outputs are all that are required. Changes to achieve technically and allocatively efficient levels are determined and are not restricted to constant input or output mixes.
A simple approach, when the data contains observations on only the physical quantities of inputs and outputs, for determining productive capacity and capacity utilization for a plant is presented in Fare et al. (1994). The Fare et al. approach may be modified to reflect cost minimization or revenue maximization. The simple approach commences with the determination of an output-oriented measure of technical efficiency; constant or variable returns to scale and weak or strong disposability may be imposed; we designate this measure as F0. To determine capacity output, the conventional output-oriented approach is modified such that input constraints are specified as equalities rather than inequalities. We may call this Fio. The ratio, F0/Fio, is called the plant capacity utilization measure (Fare et al. 1994). The measure is consistent with the economic notion of capacity but modified to allow for multiple outputs and multiple fixed or quasi-fixed factors.