DEA on Relaxed Convexity Assumptions

Peter Bogetoft

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Efficiency Analysis Using DEA Multi-Criteria Decision Making Optimization and Mathematical Programming

Abstract

In a recent paper, Petersen (Petersen, N. C. 1990. Data envelopment analysis on a relaxed set of assumptions. Management Sci. 36 305–314.) proposed to relax the convexity assumptions invoked in traditional Data Envelopment Analysis (DEA). Unfortunately, the new approach is not consistent with the relaxed assumptions. Also, the efficiency evaluations in input and output spaces are based on different technologies assumptions. The aim of this paper is to clarify which assumptions are actually involved and to develop modifications such that the input and output based measures are consistent. In effect, a family of DEA methods based on relaxed convexity assumptions is identified.

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References

1978Measuring the efficiency of decision making units 1984Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis 1984Estimating most productive scale size using data envelopment analysis 2006Measuring Labor-Efficiency in Post Offices 1992Estimation of returns to scale using data envelopment analysis 1993On FDH efficiency analysis: Some methodological issues and applications to retail banking, courts, and urban transit 1990Data Envelopment Analysis on a Relaxed Set of Assumptions 1979SHORT COMMUNICATION: MEASURING EFFICIENCY OF DECISION MAKING UNITS

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