Continuity of DEA Efficiency Measures

Abstract

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.

Data envelopment analysis models of investment funds

“…This cannot be done. Scheel and Scholtes (2003) show for the vrs model that, although φ o is continuous almost everywhere, it may have discontinuities on the frontier and at points where x ij = 0. While continuity of efficiency measures is desirable (Russell, 1990), we deliberately allow a discontinuity at y o = 0 because it is unlikely that a rational investor would consider a fund with no risk and negative return to be efficient.…”

Resampling DEA estimates of investment fund performance

“…Then η o = max r=1,...,s η ro is the solution to the output-oriented nirs model. The linear programme has a bounded feasible set and so (see Scheel and Scholtes (2003); Robinson (1977)) each ψ ro is continuous at X and Y . Since the functions max and η ro are p-continuous almost everywhere it follows that φ o = 1/η o is also p-continuous almost everywhere.…”

Assessing the Efficiency of Public Universities through DEA. A Case Study

“…The relationship between the optimal solutions of the CCR and SBM models leads to the following definition of Mix Efficiency [8,38]. Let η * 0 and ρ * 0 be the efficiency scores of the CCR-O (output-oriented CCR) and SBM-O (output-oriented SBM) models of DMU 0 , respectively.…”