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DEA cross-efficiency evaluation and ranking method based on interval data

Author

Listed:
  • Yu Yu

    (Nanjing Audit University)

  • Weiwei Zhu

    (Nanjing University of Posts and Telecommunications)

  • Qian Zhang

    (Worcester Polytechnic Institute)

Abstract

Data envelopment analysis (DEA) is an important method of efficiency evaluation. Cross-efficiency evaluation is one of the main aspects of research in the field of DEA that has been applied in various fields. In the traditional cross-efficiency evaluation model, the variable data of decision-making units is exact. Dynamic information is frequently unable to reflect the whole characteristic when determining the exact data. In this study, we select interval data to represent the dynamic information of some variables in the evaluation process. We then build a solution method based on interval efficiency and DEA cross-efficiency. This method retains the reflection of interval data on uncertain variable properties. Finally, the stochastic multi-criteria acceptability analysis 2 (SMAA2) is introduced to solve the whole sequence problem of interval efficiency. We present a case study from a set of 19 reservoir dams suffered from Wenchuan earthquake in Luojiang County, Sichuan Province to demonstrate the applicability of the proposed model.

Suggested Citation

  • Yu Yu & Weiwei Zhu & Qian Zhang, 2019. "DEA cross-efficiency evaluation and ranking method based on interval data," Annals of Operations Research, Springer, vol. 278(1), pages 159-175, July.
    • Handle: RePEc:spr:annopr:v:278:y:2019:i:1:d:10.1007_s10479-017-2669-y
    DOI: 10.1007/s10479-017-2669-y
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    1. Zhu, Joe, 2003. "Imprecise data envelopment analysis (IDEA): A review and improvement with an application," European Journal of Operational Research, Elsevier, vol. 144(3), pages 513-529, February.
    2. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    3. Yang, Feng & Ang, Sheng & Xia, Qiong & Yang, Chenchen, 2012. "Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis," European Journal of Operational Research, Elsevier, vol. 223(2), pages 483-488.
    4. William W. Cooper & Kyung Sam Park & Gang Yu, 2001. "An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 49(6), pages 807-820, December.
    5. Wade D. Cook & Joe Zhu, 2015. "DEA Cross Efficiency," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 2, pages 23-43, Springer.
    6. Han, Yongming & Geng, Zhiqiang & Zhu, Qunxiong & Qu, Yixin, 2015. "Energy efficiency analysis method based on fuzzy DEA cross-model for ethylene production systems in chemical industry," Energy, Elsevier, vol. 83(C), pages 685-695.
    7. Lahdelma, Risto & Hokkanen, Joonas & Salminen, Pekka, 1998. "SMAA - Stochastic multiobjective acceptability analysis," European Journal of Operational Research, Elsevier, vol. 106(1), pages 137-143, April.
    8. Tommi Tervonen, 2014. "JSMAA: open source software for SMAA computations," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(1), pages 69-81.
    9. Risto Lahdelma & Pekka Salminen, 2001. "SMAA-2: Stochastic Multicriteria Acceptability Analysis for Group Decision Making," Operations Research, INFORMS, vol. 49(3), pages 444-454, June.
    10. José L. Ruiz & Inmaculada Sirvent, 2017. "Fuzzy cross-efficiency evaluation: a possibility approach," Fuzzy Optimization and Decision Making, Springer, vol. 16(1), pages 111-126, March.
    11. Yao Chen, 2007. "Imprecise Dea — Envelopment And Multiplier Model Approaches," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 279-291.
    12. William W. Cooper & Kyung Sam Park & Gang Yu, 1999. "IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA," Management Science, INFORMS, vol. 45(4), pages 597-607, April.
    13. Despotis, Dimitris K. & Smirlis, Yiannis G., 2002. "Data envelopment analysis with imprecise data," European Journal of Operational Research, Elsevier, vol. 140(1), pages 24-36, July.
    14. 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.
    15. Adel HATAMI-MARBINI & Per J. AGRELL & Madjid TAVANA & Pegah KHOSHNEVIS, 2017. "A flexible cross-efficiency fuzzy data envelopment analysis model for sustainable sourcing," LIDAM Reprints CORE 2880, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    16. Agha Iqbal Ali & Wade D. Cook & Lawrence M. Seiford, 1991. "Strict vs. Weak Ordinal Relations for Multipliers in Data Envelopment Analysis," Management Science, INFORMS, vol. 37(6), pages 733-738, June.
    17. Editors, 2014. "International Journal of Systems Science," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(12), pages 1-1, December.
    18. Entani, Tomoe & Maeda, Yutaka & Tanaka, Hideo, 2002. "Dual models of interval DEA and its extension to interval data," European Journal of Operational Research, Elsevier, vol. 136(1), pages 32-45, January.
    19. Joe Zhu, 2004. "Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company," Operations Research, INFORMS, vol. 52(2), pages 323-329, April.
    20. Zhu, Joe, 2003. "Efficiency evaluation with strong ordinal input and output measures," European Journal of Operational Research, Elsevier, vol. 146(3), pages 477-485, May.
    21. Liang Liang & Jie Wu & Wade D. Cook & Joe Zhu, 2008. "The DEA Game Cross-Efficiency Model and Its Nash Equilibrium," Operations Research, INFORMS, vol. 56(5), pages 1278-1288, October.
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    Cited by:

    1. Fan Zhang & Nengsheng Luo & Yanfei Li, 2023. "What Type of Energy Structure Improves Eco-Efficiency? A Study Based on Statistical Data of 285 Prefecture-Level Entities in China," Sustainability, MDPI, vol. 15(11), pages 1-26, June.
    2. Bowen Sun & Haibo Wang & Jaime Ortiz & Jun Huang & Can Zhao & Zelang Wang, 2022. "A Decomposed Data Analysis Approach to Assessing City Sustainable Development Performance: A Network DEA Model with a Slack-Based Measure," Sustainability, MDPI, vol. 14(17), pages 1-23, September.
    3. Mostafa Davtalab-Olyaie & Hadis Mahmudi-Baram & Masoud Asgharian, 2023. "Measuring individual efficiency and unit influence in centrally managed systems," Annals of Operations Research, Springer, vol. 321(1), pages 139-164, February.
    4. Borrás, Fernando & Ruiz, José L. & Sirvent, Inmaculada, 2023. "Peer evaluation through cross-efficiency based on reference sets," Omega, Elsevier, vol. 114(C).
    5. Feng Li & Han Wu & Qingyuan Zhu & Liang Liang & Gang Kou, 2021. "Data envelopment analysis cross efficiency evaluation with reciprocal behaviors," Annals of Operations Research, Springer, vol. 302(1), pages 173-210, July.

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