Some models and measures for evaluating performances with DEA: past accomplishments and future prospects

This paper covers some of the past accomplishments of DEA (Data Envelopment Analysis) and some of its future prospects. It starts with the "engineering-science" definitions of efficiency and uses the duality theory of linear programming to show how, in DEA, they can be related to the Pareto-Koopmans definitions used in "welfare economics" as well as in the economic theory of production. Some of the models that have now been developed for implementing these concepts are then described and properties of these models and the associated measures of efficiency are examined for weaknesses and strengths along with measures of distance that may be used to determine their optimal values. Relations between the models are also demonstrated en route to delineating paths for future developments. These include extensions to different objectives such as "satisfactory" versus "full" (or "strong") efficiency. They also include extensions from "efficiency" to "effectiveness" evaluations of performances as well as extensions to evaluate social-economic performances of countries and other entities where "inputs" and "outputs" give way to other categories in which increases and decreases are located in the numerator or denominator of the ratio (=engineering-science) definition of efficiency in a manner analogous to the way output (in the numerator) and input (in the denominator) are usually positioned in the fractional programming form of DEA. Beginnings in each of these extensions are noted and the role of applications in bringing further possibilities to the fore is highlighted.