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Continuity of DEA Efficiency Measures

Universität Dortmund, Operations Research und Wirtschaftsinformatik, D-44221 Dortmund, Germany
University of Cambridge, Judge Institute of Management, Cambridge CB2 1AG, England
h.scheel{at}wiso.uni-dortmund.de
s.scholtes{at}jims.cam.ac.uk

Data envelopment analysis (DEA) is a methodology that allows, in one way or other, the assignment of efficiency scores to members of a group of decision-making units. We call an efficiency measure "continuous" if small perturbations of the input-output data cause only small changes in the score. Continuity is a desirable property of an efficiency measure, in particular in the presence of measurement tolerances. Continuity is also desirable from a numerical point of view because the scores are computed by linear programming software.

Focusing on convex production possibility sets, we give examples where radial DEA measures fail to be continuous, i.e., they "jump" under small data perturbations. We present necessary and sufficient conditions for continuity in terms of the data and show that these conditions are satisfied for "almost all" data. We also discuss continuity of nonradial measures and identify possible problems of "multistage approaches" to compute mix efficiencies.

Subject classifications: Economics: continuity of DEA efficiency measures; Linear programming: continuity of the value function.
History: Received August 2000; revision received November 2001; accepted December 2001.