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Data envelopment analysis and big data

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  • Khezrimotlagh, Dariush
  • Zhu, Joe
  • Cook, Wade D.
  • Toloo, Mehdi

Abstract

In the traditional data envelopment analysis (DEA) approach for a set of n Decision Making Units (DMUs), a standard DEA model is solved n times, one for each DMU. As the number of DMUs increases, the running-time to solve the standard model sharply rises. In this study, a new framework is proposed to significantly decrease the required DEA calculation time in comparison with the existing methodologies when a large set of DMUs (e.g., 20,000 DMUs or more) is present. The framework includes five steps: (i) selecting a subsample of DMUs using a proposed algorithm, (ii) finding the best-practice DMUs in the selected subsample, (iii) finding the exterior DMUs to the hull of the selected subsample, (iv) identifying the set of all efficient DMUs, and (v) measuring the performance scores of DMUs as those arising from the traditional DEA approach. The variable returns to scale technology is assumed and several simulation experiments are designed to estimate the running-time for applying the proposed method for big data. The obtained results in this study point out that the running-time is decreased up to 99.9% in comparison with the existing techniques. In addition, we illustrate the essential computation time for applying the proposed method as a function of the number of DMUs (cardinality), number of inputs and outputs (dimension), and the proportion of efficient DMUs (density). The methods are also compared on a real data set consisting of 30,099 electric power plants in the United States from 1996 to 2016.

Suggested Citation

  • Khezrimotlagh, Dariush & Zhu, Joe & Cook, Wade D. & Toloo, Mehdi, 2019. "Data envelopment analysis and big data," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1047-1054.
    • Handle: RePEc:eee:ejores:v:274:y:2019:i:3:p:1047-1054
    DOI: 10.1016/j.ejor.2018.10.044
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    References listed on IDEAS

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    1. Richard Barr & Matthew Durchholz, 1997. "Parallel and hierarchical decomposition approaches for solving large-scale Data Envelopment Analysis models," Annals of Operations Research, Springer, vol. 73(0), pages 339-372, October.
    2. Wen-Chih Chen & Sheng-Yung Lai, 2017. "Determining radial efficiency with a large data set by solving small-size linear programs," Annals of Operations Research, Springer, vol. 250(1), pages 147-166, March.
    3. Dula, J. H. & Helgason, R. V., 1996. "A new procedure for identifying the frame of the convex hull of a finite collection of points in multidimensional space," European Journal of Operational Research, Elsevier, vol. 92(2), pages 352-367, July.
    4. J.H. Dulá & R.M. Thrall, 2001. "A Computational Framework for Accelerating DEA," Journal of Productivity Analysis, Springer, vol. 16(1), pages 63-78, July.
    5. J. H. Dulá & R. V. Helgason & N. Venugopal, 1998. "An Algorithm for Identifying the Frame of a Pointed Finite Conical Hull," INFORMS Journal on Computing, INFORMS, vol. 10(3), pages 323-330, August.
    6. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    7. Ali, Agha Iqbal, 1993. "Streamlined computation for data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 64(1), pages 61-67, January.
    8. Seiford, Lawrence M. & Zhu, Joe, 2005. "A response to comments on modeling undesirable factors in efficiency evaluation," European Journal of Operational Research, Elsevier, vol. 161(2), pages 579-581, March.
    9. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, November.
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    9. Ya Chen & Mike Tsionas & Valentin Zelenyuk, 2020. "LASSO DEA for small and big data," CEPA Working Papers Series WP022020, School of Economics, University of Queensland, Australia.
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    13. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    14. Chen, Ya & Tsionas, Mike G. & Zelenyuk, Valentin, 2021. "LASSO+DEA for small and big wide data," Omega, Elsevier, vol. 102(C).
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    17. Khezrimotlagh, Dariush & Cook, Wade D. & Zhu, Joe, 2020. "A nonparametric framework to detect outliers in estimating production frontiers," European Journal of Operational Research, Elsevier, vol. 286(1), pages 375-388.
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