A Structure for Classifying and Characterizing Efficiencies and Inefficiencies in Data Envelopment Analysis

Abstract
DEA (Data Envelopment Analysis) attempts to identify sources and estimate amounts of inefficiencies contained in the outputs and inputs generated by managed entities called DMUs (= Decision Making Units). Explicit formulation of underlying functional relations with specified parametric forms relating inputs to outputs is not required. An overall (scalar) measure of efficiency is also obtained for each DMU from the observed magnitudes of its multiple inputs and outputs without requiring use of a priori weights or relative value assumptions. A partition of DMUs into six classes is established via primal and dual representation theorems and three classification theorems which do not depend on non-archimedian analysis. Earlier theory is extended to explain the consequences of zero inputs and outputs and to utilize zero virtual multipliers (shadow prices). Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (= zero waste) efficient. Keywords: dual linear programs; multicriterion efficiency analysis.

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