Data Envelopment Analysis on a Relaxed Set of Assumptions

Abstract

Data Envelopment Analysis is a procedure for evaluation of the relative efficiency of units in a production system. DEA involves construction of composite units as convex combinations of other units' inputs and outputs under various conditions related to returns to scale. The assumption of convexity is inconsistent with increasing returns to scale and not implied by constant or non-increasing returns to scale. An alternative DEA approach which does not invoke the assumption of a convex production possibility set is developed in this paper. It is implemented in two stages. Stage one is concerned with the spanning of isoquants and stage two with an evaluation of the position of an observed input-output combination compared to the isoquants. Both stages involve linear programming techniques solely.data envelopment analysis (DEA), efficiency, production function, nonparametric models

Analyzing Cost-Efficient Production Behavior Under Economies of Scope: A Nonparametric Methodology

“…Both technology properties have often been used in a nonparametric setting. For example, Varian (1984) suggests the assumption of nested input sets, while Petersen (1990) and Bogetoft (1996) suggest the use of convexity in output space. As we will discuss, these minimal assumptions allow for analyzing cost efficient behavior from the raw price and quantity data by exploiting specific features of production processes characterized by economies of scope.…”

Data envelopment analysis: The evolution of the state of the art (1978?1995)

“…Studies comparing the various DEA models (Ahn et al 1988a;Charnes et al 1990d;Epstein and Henderson 1989;Fare et al 1988~;Seiford and Thrall 1990) provided a framework for understanding implicit assumptions and requirements. A Malmquist index (finally published as Fare et al 1994a) had been developed to examine components of producvitity growth, and technical, scale, and allocative efficiency Morey et al 1990;Retzlaff-Roberts 1990) had been compared and contrasted, Nonconvex models had been introduced by Petersen (1990) which enlarged the perspective on basic assumptions of DEA. A number of significant model extensions had been developed including: the capability to handle nondiscretionary variables and/or categorical variables (Banker and Morey 1986a, e); the ability to incorporate judgment (restricing multipliers (Dyson and Thanassoulis 1988;Wong and Beasley 1990), the cone ratio model (Charnes et al 1989e, 199Ob), and assurance regions (Thompson et al 1986(Thompson et al , 1990)); and model ordinal relationships (Golany 1988b;Ali et al 1991).…”

“…Examples of SOA include relaxed nonconvex assumptions (Petersen 1990), various approaches to placing restriction on the possible range of multipliers for incorporating judgment or managerial preference (see earlier references), a more balanced perspective on DEA (Epstein and Henderson 1989;Stolp 1990), and connections with econometrics (Varian 1990). …”

“…However, their unanimous choice for most influential paper was Chames, Cooper, and Rhodes (CCR) (1978b) followed closely by CCR (1981), Banker, Charnes, and Cooper (BCC) (1984) and the ParetoKoopmans foundation and additive model paper (Charnes et al 1985d). Other significant papers include the Banker and Morey (1986a) paper on nondiscretionary variables, a number of references on incorporating judgment (Dyson and Thanassoulis 1988; Charnes et al 1989e, 1990aThompson et al 1986Thompson et al , 1990, references for the Mahnquist (Fare et al 1994a) and window analysis techniques (Charnes et al 1985a), nonconvex models/FDH (Petersen 1990, Tulkens 1993, and a number of papers best characterized as conceptual introductions, overviews, or explanations of DEA (Ali, Lerme, and Seiford 1995;Ali and Seiford 1993b;Fried, Lovell, and Schmidt 1993b;Charnes and Cooper 1985;and Seiford and Thrall 1990). Surprisingly, the DEA bibliography of Seiford received a number of nominations even though it had only been distributed as a working paper.…”

DEA with efficiency classification preserving conditional convexity

“…In the literature on nonparametric production analysis, Hanoch and Rothschild (1972) and Varian (1984) have discussed the possibility of imposing convexity on the input correspondence, which does not necessarily imply convexity of the production set. In the DEA literature, Petersen (1990), Bogetoft (1996), Bogetoft et al (forthcoming), and Post (forthcoming) have further developed the idea of convex input/output correspondences of a nonconvex production set. Furthermore, Vanden Eeckaut (1998, 1999) have presented models that impose monotonicity and CRS, but not convexity.…”