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Performance Evaluation in Stochastic Environments Using Mean-Variance Data Envelopment Analysis

Department of Finance and Investment, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands
gtpost{at}few.eur.nl

Traditional Data Envelope Analysis (DEA) neglects uncertainty for the input-output variables by treating the observations as if they were the true input-output variables to select reference units for efficiency estimation and performance benchmarking. In stochastic environments, the traditional framework may include stochastically dominated reference units and exclude stochastically undominated ones. To incorporate uncertainty for the input-output variables in DEA, we propose a mean-variance framework derived from the theory of stochastic dominance. From that framework an extension to the traditional model is derived that prevents the selection of stochastically dominated reference units. In addition, within the mean-variance approach, variance restrictions can be specified that reduce the uncertainty for the performance of the evaluated unit relative to its reference unit.

Subject classifications: Utility theory: DEA, stochastic dominance, mean-variance analysis; Effectiveness/Performance: DEA, stochastic dominance, mean-variance analysis.
History: Received June 1997; revision received January 1998; revision received August 1998; revision received March 1999; accepted November 1999.

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