Multi-period data envelopment analysis based on Chebyshev inequality bounds

Seyed Hossein Razavi Hajiagha, Shide Sadat Hashemi, Hannan Amoozad Mahdiraji, Jamshid Azaddel

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)
101 Downloads (Pure)


Data envelopment analysis is a cross-sectional approach to evaluate the relative efficiency of a set of homogeneous units in a single time point; nonetheless, organizational units have been performing continuously over a period of time; hence, their performances are considered within this period. Cumulating inputs and outputs over the time periods provide an unnecessary compensating impact, making the efficiency appraisal unrealistic. To avoid this negative impact of data accumulation, a two-stage approach on the basis of Chebyshev inequality bounds is proposed to find interval efficiency of decision making units (henceforth DMUs). The proposed method is applied in a real case encompassing 115 bank branches over 6 periods of time. This application indicated the significant cautious approach of the proposed method in multi-period data envelopment analysis (hereafter DEA).

Original languageEnglish
Pages (from-to)7759-7767
Number of pages9
JournalExpert Systems with Applications
Issue number21
Early online date9 Jun 2015
Publication statusPublished - 30 Nov 2015
Externally publishedYes

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Expert Systems with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Expert Systems with Applications, Vol. 42, No. 21, (2015) DOI: 10.1016/j.eswa.2015.06.008

© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International


  • Data envelopment analysis
  • Multi-period efficiency
  • Chebyshev inequality bounds
  • Two-stage efficiency approximations


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