Interval data without sign restrictions in DEA

Adel Hatami-Marbini, Ali Emrouznejad*, Per J. Agrella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Conventional DEA models assume deterministic, precise and non-negative data for input and output observations. However, real applications may be characterized by observations that are given in form of intervals and include negative numbers. For instance, the consumption of electricity in decentralized energy resources may be either negative or positive, depending on the heat consumption. Likewise, the heat losses in distribution networks may be within a certain range, depending on e.g. external temperature and real-time outtake. Complementing earlier work separately addressing the two problems; interval data and negative data; we propose a comprehensive evaluation process for measuring the relative efficiencies of a set of DMUs in DEA. In our general formulation, the intervals may contain upper or lower bounds with different signs. The proposed method determines upper and lower bounds for the technical efficiency through the limits of the intervals after decomposition. Based on the interval scores, DMUs are then classified into three classes, namely, the strictly efficient, weakly efficient and inefficient. An intuitive ranking approach is presented for the respective classes. The approach is demonstrated through an application to the evaluation of bank branches.

Original languageEnglish
Pages (from-to)2028-2036
Number of pages9
JournalApplied Mathematical Modelling
Issue number7-8
Early online date26 Oct 2013
Publication statusPublished - 1 Apr 2014


  • data envelopment analysis
  • interval data
  • negative data in DEA
  • semi-oriented radial measure


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