A joint chance-constrained data envelopment analysis model with random output data

  • Rashed Khanjani Shiraz
  • Madjid TavanaEmail author
  • Hirofumi Fukuyama
Original Paper


Data envelopment analysis (DEA) is a mathematical programming approach for evaluating the technical efficiency performances of a set of comparable decision-making units that transform multiple inputs into multiple outputs. The conventional DEA models are based on crisp input and output data, but real-world problems often involve random output data. The main purpose of the paper is to propose a joint chance-constrained DEA model for analyzing a real-world situation characterized by random outputs and crisp inputs. After developing the model, we carry out the following: First, we obtain an upper bound of this stochastic non-linear model deterministically by applying a piecewise linear approximation algorithm based on second-order cone programming; Second, we obtain a lower bound with use of a piecewise tangent approximation algorithm, which is also based on second-order cone programming; and then we use a numerical example to demonstrate the applicability of the proposed joint chance-constrained DEA framework.


Data envelopment analysis Joint chance-constrained programming Random data Second-order cone programming 



This research is partially supported by the research grant GAČR 19-13946S awarded to Dr. Tavana by the Czech Science Foundation. Dr. Khanjani Shiraz received a grant from the Ministry of science, Research and Technology of the Islamic Republic of Iran in partial support of this research.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of TabrizTabrizIran
  2. 2.Business Systems and Analytics Department, Distinguished Chair of Business Systems and AnalyticsLa Salle UniversityPhiladelphiaUSA
  3. 3.Business Information Systems Department, Faculty of Business Administration and EconomicsUniversity of PaderbornPaderbornGermany
  4. 4.Faculty of CommerceFukuoka UniversityFukuokaJapan
  5. 5.Business Systems and Analytics Department, Distinguished Chair of Business AnalyticsLa Salle UniversityPhiladelphiaUSA

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