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Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach

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  • Alcaraz, Javier
  • Anton-Sanchez, Laura
  • Aparicio, Juan
  • Monge, Juan F.
  • Ramón, Nuria

Abstract

The measurement of technical efficiency is a topic of great interest. Since the beginning, many researchers have developed new approaches to gauge technical efficiency, mainly in the non-parametric area of Data Envelopment Analysis (DEA). However, the first measures in DEA, the well-known radial models, only accounted for radial inefficiency, which motivated the introduction in the literature of the so-called Global Efficiency Measures (GEMs); non-oriented and non-radial in nature. Two famous GEMs are the Russell Graph Measure and the Enhanced Russell Graph Measure, also known as the Slacks-Based Measure. These approaches aggregate input and output specific efficiencies through the arithmetic mean, which may not be the most appropriate aggregator function when input and output efficiency ratios are considered, as will be shown. In this paper, in contrast, we propose aggregating input and output specific inefficiencies by applying the geometric average, which will allow us to define new multiplicative versions of the Russell Graph Measures. We also prove some theoretical results and introduce an iterative algorithm, based upon Second Order Cone Programming, to solve the new models. Finally, the implementation of the introduced approaches is empirically illustrated through a data set taken from the literature.

Suggested Citation

  • Alcaraz, Javier & Anton-Sanchez, Laura & Aparicio, Juan & Monge, Juan F. & Ramón, Nuria, 2021. "Russell Graph efficiency measures in Data Envelopment Analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 292(2), pages 663-674.
    • Handle: RePEc:eee:ejores:v:292:y:2021:i:2:p:663-674
    DOI: 10.1016/j.ejor.2020.11.001
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    1. Guo, Chuanyin & Wei, Fajie & Chen, Yao, 2017. "A note on second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 263(2), pages 733-735.
    2. R. Russell & William Schworm, 2009. "Axiomatic foundations of efficiency measurement on data-generated technologies," Journal of Productivity Analysis, Springer, vol. 31(2), pages 77-86, April.
    3. Leopold Simar & Valentin Zelenyuk, 2006. "On Testing Equality of Distributions of Technical Efficiency Scores," Econometric Reviews, Taylor & Francis Journals, vol. 25(4), pages 497-522.
    4. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    5. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264.
    6. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    7. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The weighted additive distance function," European Journal of Operational Research, Elsevier, vol. 254(1), pages 338-346.
    8. Fare, Rolf & Knox Lovell, C. A., 1978. "Measuring the technical efficiency of production," Journal of Economic Theory, Elsevier, vol. 19(1), pages 150-162, October.
    9. Juan Aparicio & José Ruiz & Inmaculada Sirvent, 2007. "Closest targets and minimum distance to the Pareto-efficient frontier in DEA," Journal of Productivity Analysis, Springer, vol. 28(3), pages 209-218, December.
    10. Aparicio, Juan & Cordero, Jose M. & Pastor, Jesus T., 2017. "The determination of the least distance to the strongly efficient frontier in Data Envelopment Analysis oriented models: Modelling and computational aspects," Omega, Elsevier, vol. 71(C), pages 1-10.
    11. Pastor, J. T. & Ruiz, J. L. & Sirvent, I., 1999. "An enhanced DEA Russell graph efficiency measure," European Journal of Operational Research, Elsevier, vol. 115(3), pages 596-607, June.
    12. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    13. William Cooper & Kyung Park & Jesus Pastor, 1999. "RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models, and Relations to Other Models and Measures in DEA," Journal of Productivity Analysis, Springer, vol. 11(1), pages 5-42, February.
    14. Chen, Kun & Zhu, Joe, 2020. "Additive slacks-based measure: Computational strategy and extension to network DEA," Omega, Elsevier, vol. 91(C).
    15. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    16. Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    17. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Computational strategy for Russell measure in DEA: Second-order cone programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 459-471, July.
    18. Chen, Kun & Zhu, Joe, 2017. "Second order cone programming approach to two-stage network data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 262(1), pages 231-238.
    19. R. Robert Russell & William Schworm, 2018. "Technological inefficiency indexes: a binary taxonomy and a generic theorem," Journal of Productivity Analysis, Springer, vol. 49(1), pages 17-23, February.
    20. Hasannasab, Maryam & Margaritis, Dimitris & Roshdi, Israfil & Rouse, Paul, 2019. "Hyperbolic efficiency measurement: A conic programming approach," European Journal of Operational Research, Elsevier, vol. 278(2), pages 401-409.
    21. 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.
    22. Aparicio, Juan & Mahlberg, Bernhard & Pastor, Jesus T. & Sahoo, Biresh K., 2014. "Decomposing technical inefficiency using the principle of least action," European Journal of Operational Research, Elsevier, vol. 239(3), pages 776-785.
    23. Fare, Rolf, et al, 1989. "Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 90-98, February.
    24. Chen, Zhongfei & Matousek, Roman & Wanke, Peter, 2018. "Chinese bank efficiency during the global financial crisis: A combined approach using satisficing DEA and Support Vector Machines☆," The North American Journal of Economics and Finance, Elsevier, vol. 43(C), pages 71-86.
    25. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    26. Tone, Kaoru, 2001. "A slacks-based measure of efficiency in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 130(3), pages 498-509, May.
    27. Renato A. Villano & Carolyn-Dung T. T. Tran, 2018. "Performance of private higher education institutions in Vietnam: evidence using DEA-based bootstrap directional distance approach with quasi-fixed inputs," Applied Economics, Taylor & Francis Journals, vol. 50(55), pages 5966-5978, November.
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    2. Naghavi, Mostafa & Roshdi, Israfil & Arjomandi, Amir & Margaritis, Dimitris, 2023. "Some comments on Russell graph efficiency measures in data envelopment analysis: The multiplicative approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 494-497.
    3. Alcaraz, Javier & Aparicio, Juan & Monge, Juan Fco & Ramón, Nuria, 2022. "Weight profiles in cross-efficiency evaluation based on hypervolume maximization," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    4. Aparicio, Juan & Monge, Juan F., 2022. "The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality," European Journal of Operational Research, Elsevier, vol. 302(2), pages 621-632.
    5. Sekitani, Kazuyuki & Zhao, Yu, 2023. "Least-distance approach for efficiency analysis: A framework for nonlinear DEA models," European Journal of Operational Research, Elsevier, vol. 306(3), pages 1296-1310.

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