Robust optimization and its duality in data envelopment analysis

Mehdi Toloo*, Emmanuel Kwasi Mensah, Maziar Salahi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Robust Data Envelopment Analysis (RDEA) is a DEA-based conservative approach used for modeling uncertainties in the input and output data of Decision-Making Units (DMUs) to guarantee stable and reliable performance evaluation. The RDEA models proposed in the literature apply robust optimization techniques to the linear and conventional DEA models which lead to the difficulty of obtaining a robust efficient DMU. To overcome this difficulty, this paper tackles uncertainty in DMUs from the original fractional DEA model. We propose a robust fractional DEA (RFDEA) model in both input and output orientation which enables us to overcome the deficiency of existing RDEA models. The linearized models of the fractional DEA are further used to establish duality relations from a pessimistic and optimistic view of the data. We show that the primal worst of the multiplier model is equivalent to the dual best of the envelopment model. Furthermore, we show that the robust efficiency in the input- and output-oriented DEA models are still equivalent in the new approach which is not the case in conventional RDEA models. We finally present a study of the largest airports in Europe to illustrate the efficacy of the proposed models. The proposed RDEA is found to provide an effective management evaluation strategy under uncertain environments.

Original languageEnglish
Article number102583
JournalOmega (United Kingdom)
Publication statusPublished - Apr 2022


  • Data envelopment analysis
  • Duality in Robust DEA
  • European airports
  • Robust DEA
  • Uncertainty in efficiency measurement

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Information Systems and Management

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