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Manuscript ID : 536808 Visit : 120 Page: 73 - 86

Article Type: Original Research

A Data Envelopment Analysis Model with Interval Data Using TOPSIS Technique

Subject Areas : Industrial Management

Hossein Azizi 1 , Alireza Amirteimoori 2 , Sohrab Kordrostami 3

1 - Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.
2 - Department of Applied Mathematics, Rasht Branch, Islamic Azad University, Rasht, Iran
3 - Department of Applied Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Received: 2016-11-13 Accepted : 2017-11-22 Published : 2017-12-24

Keywords:

Abstract :

Data envelopment analysis (DEA) is a methodology for assessing the performances of a group of decision-making units (DMUs) that utilize multiple inputs to produce multiple outputs. This paper introduces two virtual DMUs called ideal DMU and anti-ideal DMU into the interval DEA. The resultant interval DEA models are, respectively, referred to as the interval DEA with ideal and anti-ideal DMUs. One evaluates DMUs from the viewpoint of the optimistic efficiency, while the other evaluates them from the perspective of the pessimistic efficiency. The two distinctive interval efficiencies are combined to form a comprehensive index called the relative closeness to the ideal DMU just like the well-known technique for order preference by similarity to ideal solution approach in multiple attribute decision making. The relative closeness index is then used as the evidence of overall assessment of each DMU, based on which an overall ranking for all the DMUs can be obtained. We also present an example on evaluating the performance of twenty bank branches which shows that the proposed interval DEA approach is a simple, efficient, and practical method for performance measurement in real-life situations.

References:


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  20. Stewart, Theodor J. (1996). Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis. Journal of the Operational Research Society, 47(5), 654-665. doi: 10.1057/jors.1996.77
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  21. Wang, Ying-Ming, Greatbanks, Richard, & Yang, Jian-Bo. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153(3), 347-370. doi: http://dx.doi.org/10.1016/j.fss.2004.12.011
    22.
  22. Wang, Ying-Ming, & Luo, Ying. (2006). DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 173(2), 902-915. doi: http://dx.doi.org/10.1016/j.amc.2005.04.023
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  23. Wang, Ying-Ming, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using interval efficiencies. Journal of Computational and Applied Mathematics, 198(1), 253-267. doi: http://dx.doi.org/10.1016/j.cam.2005.12.025
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  24. Zhu, Joe. (2003). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research, 144(3), 513-529. doi: 10.1016/S0377-2217(01)00392-7
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  25. Zhu, Joe. (2004). Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company. Operations Research, 52(2), 323-329. doi: 10.1287/opre.1030.0072
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_||_

  1. Azizi, Hossein, & Ganjeh Ajirlu, Hassan. (2011). Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data. Applied Mathematical Modelling, 35(9), 4149-4156. doi: http://dx.doi.org/10.1016/j.apm.2011.02.038
    2.
  2. Belton, Valerie, & Vickers, Stephen P. (1993). Demystifying DEA — A Visual Interactive Approach Based on Multiple Criteria Analysis. Journal of the Operational Research Society, 44(9), 883-896. doi: 10.1057/jors.1993.157
    3.
  3. Bouyssou, D. (1999). Using DEA as a tool for MCDM: some remarks. Journal of the Operational Research Society, 50(9), 974-978.
    4.
  4. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2(6), 429-444. doi: http://dx.doi.org/10.1016/0377-2217(78)90138-8
    5.
  5. Cook, Wade D., Kress, Moshe, & Seiford, Lawrence M. (1993). On the Use of Ordinal Data in Data Envelopment Analysis. Journal of the Operational Research Society, 44(2), 133-140.
    6.
  6. Cook, Wade D., Kress, Moshe, & Seiford, Lawrence M. (1996). Data Envelopment Analysis in the Presence of Both Quantitative and Qualitative Factors. J Oper Res Soc, 47(7), 945-953.
    7.
  7. Cooper, W. W., Park, K. S., & Yu, G. (2001a). IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units). Journal of the Operational Research Society, 52(2), 176-181. doi: 10.1057/palgrave.jors.2601070
    8.
  8. Cooper, W. W., Park, K. S., & Yu, G. (2001b). An Illustrative Application of Idea (Imprecise Data Envelopment Analysis) to a Korean Mobile Telecommunication Company. Operations Research, 49(6), 807-820. doi: 10.1287/opre.49.6.807.10022
    9.
  9. Cooper, William W., Park, Kyung Sam, & Yu, Gang. (1999). IDEA and AR-IDEA: Models for Dealing with Imprecise Data in DEA. Management Science, 45(4), 597-607. doi: 10.1287/mnsc.45.4.597
    10.
  10. Despotis, Dimitris K., & Smirlis, Yiannis G. (2002). Data envelopment analysis with imprecise data. European Journal of Operational Research, 140(1), 24-36. doi: http://dx.doi.org/10.1016/S0377-2217(01)00200-4
    11.
  11. Entani, Tomoe, Maeda, Yutaka, & Tanaka, Hideo. (2002). Dual models of interval DEA and its extension to interval data. European Journal of Operational Research, 136(1), 32-45. doi: https://doi.org/10.1016/S0377-2217(01)00055-8
    12.
  12. Hwang, Ching-Lai, & Yoon, Kwangsun. (1981). Multiple attribute decision making: methods and applications: a state-of-the-art survey. Berlin; New York: Springer-Verlag.
    13.
  13. Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Rostamy Malkhalifeh, M., & Ahadzadeh Namin, M. (2009). A generalized model for data envelopment analysis with interval data. Applied Mathematical Modelling, 33(7), 3237-3244. doi: 10.1016/j.apm.2008.10.030
    14.
  14. Kao, Chiang, & Liu, Shiang-Tai. (2000a). Data Envelopment Analysis with Missing Data: An Application to University Libraries in Taiwan. The Journal of the Operational Research Society, 51(8), 897-905. doi: 10.2307/254045
    15.
  15. Kao, Chiang, & Liu, Shiang-Tai. (2000b). Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets and Systems, 113(3), 427-437. doi: http://dx.doi.org/10.1016/S0165-0114(98)00137-7
    16.
  16. Kim, Soung-Hie, Park, Choong-Gyoo, & Park, Kyung-Sam. (1999). An application of data envelopment analysis in telephone officesevaluation with partial data. Computers & Operations Research, 26(1), 59-72. doi: http://dx.doi.org/10.1016/S0305-0548(98)00041-0
    17.
  17. Park, K. S. (2004). Simplification of the transformations and redundancy of assurance regions in IDEA (imprecise DEA). Journal of the Operational Research Society, 55(12), 1363-1366. doi: 10.1057/palgrave.jors.2601824
    18.
  18. Park, Kyung Sam, & Kim, Soung Hie. (1997). Tools for interactive multiattribute decisionmaking with incompletely identified information. European Journal of Operational Research, 98(1), 111-123. doi: http://dx.doi.org/10.1016/0377-2217(95)00121-2
    19.
  19. Sage, A. P., & White, C. C. (1984). ARIADNE: A knowledge-based interactive system for planning and decision support. Systems, Man and Cybernetics, IEEE Transactions on, SMC-14(1), 35-47. doi: 10.1109/TSMC.1984.6313267
    20.
  20. Stewart, Theodor J. (1996). Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis. Journal of the Operational Research Society, 47(5), 654-665. doi: 10.1057/jors.1996.77
    21.
  21. Wang, Ying-Ming, Greatbanks, Richard, & Yang, Jian-Bo. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153(3), 347-370. doi: http://dx.doi.org/10.1016/j.fss.2004.12.011
    22.
  22. Wang, Ying-Ming, & Luo, Ying. (2006). DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 173(2), 902-915. doi: http://dx.doi.org/10.1016/j.amc.2005.04.023
    23.
  23. Wang, Ying-Ming, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using interval efficiencies. Journal of Computational and Applied Mathematics, 198(1), 253-267. doi: http://dx.doi.org/10.1016/j.cam.2005.12.025
    24.
  24. Zhu, Joe. (2003). Imprecise data envelopment analysis (IDEA): A review and improvement with an application. European Journal of Operational Research, 144(3), 513-529. doi: 10.1016/S0377-2217(01)00392-7
    25.
  25. Zhu, Joe. (2004). Imprecise DEA via Standard Linear DEA Models with a Revisit to a Korean Mobile Telecommunication Company. Operations Research, 52(2), 323-329. doi: 10.1287/opre.1030.0072
    26.

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