A structure for classifying and characterizing efficiency and inefficiency in Data Envelopment Analysis

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 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 and, in addition, sources and amounts of inefficiency are estimated for each input and each output for every DMU. Earlier theory is extended so that DEA can deal with zero inputs and outputs and zero virtual multipliers (shadow prices). This is accomplished by partitioning DMUs into six classes via primal and dual representation theorems by means of which restrictions to positive observed values for all inputs and outputs are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts. Three of the six classes are scale inefficient and two of the three scale efficient classes are also technically (zero waste) efficient.The refereeing process of this paper was handled through R. Banker. This paper was prepared as part of the research supported by National Science Foundation grant SES-8722504 and by the IC² Institute of The University of Texas and was initially submitted in May 1985.