Efficiency analysis with ratio measures

Ole Bent Olesen, Niels Chr. Petersen, Victor V. Podinovski

Research output: Contribution to journalJournal articleResearchpeer-review


In applications of data envelopment analysis (DEA) data about some inputs and outputs is often available only in the form of ratios such as averages and percentages. In this paper we provide a positive answer to the long-standing debate as to whether such data could be used in DEA. The problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions, e.g., that the technology is a convex set. Our approach is based on the formulation of new production assumptions that explicitly account for ratio measures. This leads to the estimation of production technologies under variable and constant returns-to-scale assumptions in which both volume and ratio measures are native types of data. The resulting DEA models allow the use of ratio measures "as is", without any transformation or use of the underlying volume measures. This provides theoretical foundations for the use of DEA in applications where important data are reported in the form of ratios.

Original languageEnglish
JournalEuropean Journal of Operational Research
Issue number2
Pages (from-to)446-462
Publication statusPublished - 2015


  • Data envelopment analysis
  • Efficiency
  • Production assumptions
  • Ratio measures
  • Technology


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