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Free disposal hull efficiency scores of units with network structures

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  • Tavakoli, Ibrahim M.
  • Mostafaee, Amin

Abstract

Data Envelopment Analysis (DEA) is a nonparametric method for measuring the performance of a set of decision making units (DMUs). Recently, applications of DEA have attracted particular interest of scholars in circumstances in which two-stage or network structures are involved. This paper is the first systematic attempt to extend the network DEA models to a class of non-convex technologies, i.e., Free Disposal Hull (FDH). The models are provided in both cases of the same and the different optimal peers in both stages. Some closed form formulae are provided to calculate the overall and stage efficiency scores under different RTS assumptions, without solving any mathematical programming problem. Also, the formulations are adapted to include the situations in which some of the data are missing. Furthermore, it is proved that the provided models project the inefficient DMUs onto the efficient frontier. Finally, the case of Bank Keshavarzi Iran is used to validate the reasonableness and acceptability of the proposed approach in FDH models.

Suggested Citation

  • Tavakoli, Ibrahim M. & Mostafaee, Amin, 2019. "Free disposal hull efficiency scores of units with network structures," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1027-1036.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:3:p:1027-1036
    DOI: 10.1016/j.ejor.2019.03.023
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    1. Kao, Chiang, 2009. "Efficiency decomposition in network data envelopment analysis: A relational model," European Journal of Operational Research, Elsevier, vol. 192(3), pages 949-962, February.
    2. Kerstens, Kristiaan & Vanden Eeckaut, Philippe, 1999. "Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit," European Journal of Operational Research, Elsevier, vol. 113(1), pages 206-214, February.
    3. Rolf Färe & Shawna Grosskopf & Gerald Whittaker, 2014. "Network DEA II," International Series in Operations Research & Management Science, in: Wade D. Cook & Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 0, pages 307-327, Springer.
    4. Leleu, Herve, 2006. "A linear programming framework for free disposal hull technologies and cost functions: Primal and dual models," European Journal of Operational Research, Elsevier, vol. 168(2), pages 340-344, January.
    5. Walter Briec & Kristiaan Kerstens & Philippe Venden Eeckaut, 2004. "Non-convex Technologies and Cost Functions: Definitions, Duality and Nonparametric Tests of Convexity," Journal of Economics, Springer, vol. 81(2), pages 155-192, February.
    6. Yu, Ming-Miin & Lin, Erwin T.J., 2008. "Efficiency and effectiveness in railway performance using a multi-activity network DEA model," Omega, Elsevier, vol. 36(6), pages 1005-1017, December.
    7. Soleimani-damaneh, M. & Jahanshahloo, G.R. & Reshadi, M., 2006. "On the estimation of returns-to-scale in FDH models," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1055-1059, October.
    8. Henry Tulkens, 2006. "On FDH Efficiency Analysis: Some Methodological Issues and Applications to Retail Banking, Courts and Urban Transit," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 311-342, Springer.
    9. Walter Briec & Kristiaan Kerstens, 2006. "Input, output and graph technical efficiency measures on non-convex FDH models with various scaling laws: An integrated approach based upon implicit enumeration algorithms," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 135-166, June.
    10. Tone, Kaoru & Tsutsui, Miki, 2009. "Network DEA: A slacks-based measure approach," European Journal of Operational Research, Elsevier, vol. 197(1), pages 243-252, August.
    11. Thomas Sexton & Herbert Lewis, 2003. "Two-Stage DEA: An Application to Major League Baseball," Journal of Productivity Analysis, Springer, vol. 19(2), pages 227-249, April.
    12. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    13. 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.
    14. Kao, Chiang & Hwang, Shiuh-Nan, 2008. "Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan," European Journal of Operational Research, Elsevier, vol. 185(1), pages 418-429, February.
    15. Adler, Nicole & Liebert, Vanessa & Yazhemsky, Ekaterina, 2013. "Benchmarking airports from a managerial perspective," Omega, Elsevier, vol. 41(2), pages 442-458.
    16. Soleimani-damaneh, M. & Mostafaee, A., 2009. "Stability of the classification of returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1223-1228, August.
    17. Kristiaan Kerstens & Ignace Van De Woestyne, 2014. "Solution Methods For Nonconvex Free Disposal Hull Models: A Review And Some Critical Comments," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-13.
    18. Dominique Deprins & Léopold Simar & Henry Tulkens, 2006. "Measuring Labor-Efficiency in Post Offices," Springer Books, in: Parkash Chander & Jacques Drèze & C. Knox Lovell & Jack Mintz (ed.), Public goods, environmental externalities and fiscal competition, chapter 0, pages 285-309, Springer.
    19. Zhu, Joe, 2000. "Multi-factor performance measure model with an application to Fortune 500 companies," European Journal of Operational Research, Elsevier, vol. 123(1), pages 105-124, May.
    20. Chiang Kao, 2017. "Network Data Envelopment Analysis," International Series in Operations Research and Management Science, Springer, number 978-3-319-31718-2, July-Dece.
    21. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    22. Lawrence M. Seiford & Joe Zhu, 1999. "Profitability and Marketability of the Top 55 U.S. Commercial Banks," Management Science, INFORMS, vol. 45(9), pages 1270-1288, September.
    23. J S Liu & W-M Lu, 2012. "Network-based method for ranking of efficient units in two-stage DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(8), pages 1153-1164, August.
    24. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 151-157, September.
    25. Kao, Chiang, 2009. "Efficiency measurement for parallel production systems," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1107-1112, August.
    26. Du, Juan & Liang, Liang & Chen, Yao & Cook, Wade D. & Zhu, Joe, 2011. "A bargaining game model for measuring performance of two-stage network structures," European Journal of Operational Research, Elsevier, vol. 210(2), pages 390-397, April.
    27. Chen, Yao & Cook, Wade D. & Zhu, Joe, 2010. "Deriving the DEA frontier for two-stage processes," European Journal of Operational Research, Elsevier, vol. 202(1), pages 138-142, April.
    28. Podinovski, V. V., 2004. "On the linearisation of reference technologies for testing returns to scale in FDH models," European Journal of Operational Research, Elsevier, vol. 152(3), pages 800-802, February.
    29. Chen, Yao & Cook, Wade D. & Li, Ning & Zhu, Joe, 2009. "Additive efficiency decomposition in two-stage DEA," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1170-1176, August.
    30. Zha, Yong & Liang, Liang, 2010. "Two-stage cooperation model with input freely distributed among the stages," European Journal of Operational Research, Elsevier, vol. 205(2), pages 332-338, September.
    31. Tone, Kaoru & Tsutsui, Miki, 2010. "Dynamic DEA: A slacks-based measure approach," Omega, Elsevier, vol. 38(3-4), pages 145-156, June.
    32. Laurens Cherchye & Timo Kuosmanen & Thierry Post, 2000. "What Is the Economic Meaning of FDH? A Reply to Thrall," Journal of Productivity Analysis, Springer, vol. 13(3), pages 263-267, May.
    33. Liang Liang & Wade D. Cook & Joe Zhu, 2008. "DEA models for two‐stage processes: Game approach and efficiency decomposition," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 643-653, October.
    34. Yao Chen & Liang Liang & Feng Yang, 2006. "A DEA game model approach to supply chain efficiency," Annals of Operations Research, Springer, vol. 145(1), pages 5-13, July.
    35. Kao, Chiang, 2014. "Efficiency decomposition for general multi-stage systems in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 232(1), pages 117-124.
    36. William W. Cooper & Lawrence M. Seiford & Kaoru Tone, 2007. "Data Envelopment Analysis," Springer Books, Springer, edition 0, number 978-0-387-45283-8, October.
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    2. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    3. Walter Briec & Kristiaan Kerstens & Ignace Van de Woestyne, 2022. "Nonconvexity in Production and Cost Functions: An Exploratory and Selective Review," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 18, pages 721-754, Springer.
    4. Qu, Jingjing & Wang, Baohui & Liu, Xiaohong, 2022. "A modified super-efficiency network data envelopment analysis: Assessing regional sustainability performance in China," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    5. M.V. Leonov, 2021. "Review of Modern Approaches for Assessing the Effectiveness of Banking," Journal of Applied Economic Research, Graduate School of Economics and Management, Ural Federal University, vol. 20(2), pages 294-326.

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