Central European Journal of Operations Research

, Volume 26, Issue 4, pp 909–932 | Cite as

Efficiency analysis in two-stage structures using fuzzy data envelopment analysis

  • Adel Hatami-Marbini
  • Saber Saati
  • Seyed Mojtaba SajadiEmail author
Original Paper


Two-stage data envelopment analysis (TsDEA) models evaluate the performance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management. Contrary to conventional DEA models as a black-box structure, TsDEA provides further insight into sources of inefficiencies and a more informative basis for performance evaluation. In addition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system efficiency. We present the fuzzy input and output-oriented TsDEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are fuzzy. To this end, we propose a possibilistic programming problem and then convert it into a deterministic interval programming problem using the α-level based method. The proposed method preserves the link between two stages in the sense that the total efficiency of the system is equal to the product of the efficiencies derived from two stages. In addition to the study of technical efficiency, this research includes two further contributions to the ancillary literature; firstly, we minutely discuss the efficiency decompositions to indicate the sources of inefficiency and secondly, we present a method for ranking the efficient units in a fuzzy environment. An empirical illustration is also utilised to show the applicability of the proposed technique.


Data envelopment analysis Efficiency Two-level systems Fuzzy data Ranking 

Mathematics Subject Classification

90C05 94D05 90C70 90C90 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Strategic Management and Marketing, Leicester Business SchoolDe Montfort UniversityLeicesterUK
  2. 2.New Business Department, Faculty of EntrepreneurshipUniversity of TehranTehranIran
  3. 3.Department of Mathematics, Tehran-North BranchIslamic Azad UniversityTehranIran

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