Showing papers by "William W. Cooper published in 1991"
TL;DR: In this paper, DEA is extended to deal with zero inputs and outputs and zero virtual multipliers (shadow prices) 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 output are eliminated along with positivity conditions imposed on the variables which are usually accomplished by recourse to nonarchimedian concepts.
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 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.
326 citations
TL;DR: In this article, analytic relations between the two representations of cones in polyhedral cone-ratio DEA models are derived, which, for useful classes of cases in which they are simple, can make available the advantages of both for analysis and computation.
Abstract: Analytic relations between the two representations (half-space and finitely generated) of cones in polyhedral cone-ratio DEA models are derived, which, for useful classes of cases in which they are simple, can make available the advantages of both for analysis and computation. We prove that such transfers between the two may be made through, essentially, the inverse of an associated matrix available in the computation and we provide formulae connecting solutions in the two representations.
42 citations