Chance-constrained cost efficiency in data envelopment analysis model with random inputs and outputs

  • Rashed Khanjani Shiraz
  • Adel Hatami-Marbini
  • Ali Emrouznejad
  • Hirofumi Fukuyama
Original Paper


Data envelopment analysis (DEA) is a well-known non-parametric technique primarily used to estimate radial efficiency under a set of mild assumptions regarding the production possibility set and the production function. The technical efficiency measure can be complemented with a consistent radial metrics for cost, revenue and profit efficiency in DEA, but only for the setting with known input and output prices. In many real applications of performance measurement, such as the evaluation of utilities, banks and supply chain operations, the input and/or output data are often stochastic and linked to exogenous random variables. It is known from standard results in stochastic programming that rankings of stochastic functions are biased if expected values are used for key parameters. In this paper, we propose economic efficiency measures for stochastic data with known input and output prices. We transform the stochastic economic efficiency models into a deterministic equivalent non-linear form that can be simplified to a deterministic programming with quadratic constraints. An application for a cost minimizing planning problem of a state government in the US is presented to illustrate the applicability of the proposed framework.


Data envelopment analysis Weight restrictions Random input–output Cost efficiency Quadratic programming 


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Copyright information

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

Authors and Affiliations

  • Rashed Khanjani Shiraz
    • 1
  • Adel Hatami-Marbini
    • 2
  • Ali Emrouznejad
    • 3
  • Hirofumi Fukuyama
    • 4
  1. 1.School of Mathematical ScienceUniversity of TabrizTabrizIran
  2. 2.Department of Strategic Management and Marketing, Leicester Business SchoolDe Montfort UniversityLeicesterUK
  3. 3.Operations and Information Management Group, Aston Business SchoolAston UniversityBirminghamUK
  4. 4.Faculty of CommerceFukuoka UniversityFukuoka CityJapan

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