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Manuscript ID : IMJ-1812-1164 (R2) Visit : 153 Page: 31 - 50

Article Type: Original Research

Evaluating the performances of decision-making units based on the ‎optimistic and pessimistic points of view

Subject Areas : Industrial Management

Hossein Azizi 1 , Maziar Salahi 2

1 - Department of Applied Mathematics, Parsabad Moghan Branch, Islamic Azad University, Parsabad Moghan, Iran.
2 - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Iran

Received: 2018-12-25 Accepted : 2019-05-14 Published : 2019-09-21

Keywords: Data envelopment analysis, ‎Bounded DEA models, Efficiency Interval, Optimistic and pessimistic efficiencies,

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. It ‎measures the performances of the DMUs by maximizing the efficiency of every DMU, ‎respectively, subject to the constraints that none of the efficiencies of the DMUs can be less ‎than one. The efficiencies measured in this way are referred to as optimistic efficiencies or the ‎best relative efficiencies. The way to measure the optimistic efficiencies of the DMUs is ‎referred to as self-evaluation. If a DMU is self-evaluated to have an efficiency score of one, ‎then it is said to be DEA efficient; otherwise, the DMU is said to be non-DEA efficient. ‎There is a comparable approach which uses the concept of inefficiency frontier for ‎determining the worst relative efficiency score that can be assigned to each DMU. DMUs on ‎the inefficiency frontier are specified as DEA-inefficient, and those that do not lie on the ‎inefficient frontier, are declared to be DEA-non-inefficient. In this paper, we argue that both ‎relative efficiencies should be considered simultaneously, and any approach that considers ‎only one of them will be biased. For measuring the overall performance of the DMUs, we ‎propose to integrate both efficiencies in the form of an interval, and we call the proposed ‎DEA models for efficiency measurement the bounded DEA models. In this way, the ‎efficiency interval provides the decision maker with all the possible values of efficiency, ‎which reflect various perspectives.

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  1. Ahmady, Nazanin, Azadi, Majid, Sadeghi, Seyed Amir Hossein, & Farzipoor Saen, Reza. (2013). A novel fuzzy data envelopment analysis model with double frontiers for supplier selection. International Journal of Logistics Research and Applications, 16(2), 87-98. doi: 10.1080/13675567.2013.772957
    2.
  2. Amirteimoori, Alireza. (2007). DEA efficiency analysis: Efficient and anti-efficient frontier. Applied Mathematics and Computation, 186(1), 10-16. doi: https://doi.org/10.1016/j.amc.2006.07.006
    3.
  3. Amirteimoori, Alireza, Kordrostami, Sohrab, & Rezaitabar, Aliakbar. (2006). An improvement to the cost efficiency interval: A DEA-based approach. Applied Mathematics and Computation, 181(1), 775-781. doi: https://doi.org/10.1016/j.amc.2006.02.005
    4.
  4. Azizi, Hossein. (2011). The interval efficiency based on the optimistic and pessimistic points of view. Applied Mathematical Modelling, 35(5), 2384-2393. doi: https://doi.org/10.1016/j.apm.2010.11.055
    5.
  5. Azizi, Hossein, & Ajirlu, Hassan Ganjeh. (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: https://doi.org/10.1016/j.apm.2011.02.038
    6.
  6. Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functionals. Naval Research Logistics Quarterly, 9(3-4), 181-186. doi: 10.1002/nav.3800090303
    7.
  7. 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: https://doi.org/10.1016/0377-2217(78)90138-8
    8.
  8. Chen, Jin-Xiao. (2012). A comment on DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 219(2), 583-591. doi: https://doi.org/10.1016/j.amc.2012.06.046
    9.
  9. Chin, Kwai-Sang, Wang, Ying-Ming, Poon, Gary Ka Kwai, & Yang, Jian-Bo. (2009). Failure mode and effects analysis by data envelopment analysis. Decision Support Systems, 48(1), 246-256. doi: https://doi.org/10.1016/j.dss.2009.08.005
    10.
  10. 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
    11.
  11. Entani, Tomoe, & Tanaka, Hideo. (2006). Improvement of efficiency intervals based on DEA by adjusting inputs and outputs. European Journal of Operational Research, 172(3), 1004-1017. doi: https://doi.org/10.1016/j.ejor.2004.11.010
    12.
  12. Foroughi, Ali Asghar, & Aouni, Belaïd. (2012). Ranking units in DEA based on efficiency intervals and decision-maker's preferences. International Transactions in Operational Research, 19(4), 567-579. doi: 10.1111/j.1475-3995.2011.00834.x
    13.
  13. Hatami-Marbini, Adel, Saati, Saber, & Tavana, Madjid. (2010). An ideal-seeking fuzzy data envelopment analysis framework. Applied Soft Computing, 10(4), 1062-1070. doi: https://doi.org/10.1016/j.asoc.2009.12.031
    14.
  14. Jahanshahloo, G. R., & Afzalinejad, M. (2006). A ranking method based on a full-inefficient frontier. Applied Mathematical Modelling, 30(3), 248-260. doi: https://doi.org/10.1016/j.apm.2005.03.023
    15.
  15. Jahed, Rasul, Amirteimoori, Alireza, & Azizi, Hossein. (2015). Performance measurement of decision-making units under uncertainty conditions: An approach based on double frontier analysis. Measurement, 69, 264-279. doi: https://doi.org/10.1016/j.measurement.2015.03.014
    16.
  16. Liu, Fuh-hwa Franklin, & Chen, Cheng-Li. (2009). The worst-practice DEA model with slack-based measurement. Computers & Industrial Engineering, 57(2), 496-505. doi: https://doi.org/10.1016/j.cie.2007.12.021
    17.
  17. Mirhedayatian, Seyed Mostafa, Vahdat, Seyed Ebrahim, Jafarian Jelodar, Mostafa, & Farzipoor Saen, Reza. (2013). Welding process selection for repairing nodular cast iron engine block by integrated fuzzy data envelopment analysis and TOPSIS approaches. Materials & Design, 43, 272-282. doi: https://doi.org/10.1016/j.matdes.2012.07.010
    18.
  18. Serrano-Cinca, Carlos, MarMoliero, Cecillo, & Chaparro, Fernando. (2004). Spanish savings banks: a view on intangibles. Knowledge Management Research & Practice, 2(2), 103-117. doi: 10.1057/palgrave.kmrp.8500025
    19.
  19. Wang, Ying-Ming, & Chin, Kwai-Sang. (2009). A new approach for the selection of advanced manufacturing technologies: DEA with double frontiers. International Journal of Production Research, 47(23), 6663-6679. doi: 10.1080/00207540802314845
    20.
  20. Wang, Ying-Ming, & Chin, Kwai-Sang. (2011). Fuzzy data envelopment analysis: A fuzzy expected value approach. Expert Systems with Applications, 38(9), 11678-11685. doi: https://doi.org/10.1016/j.eswa.2011.03.049
    21.
  21. Wang, Ying-Ming, Chin, Kwai-Sang, & Yang, Jian-Bo. (2007). Measuring the performances of decision-making units using geometric average efficiency. Journal of the Operational Research Society, 58(7), 929-937. doi: 10.1057/palgrave.jors.2602205
    22.
  22. Wang, Ying-Ming, & Lan, Yi-Xin. (2011). Measuring Malmquist productivity index: A new approach based on double frontiers data envelopment analysis. Mathematical and Computer Modelling, 54(11), 2760-2771. doi: https://doi.org/10.1016/j.mcm.2011.06.064
    23.
  23. Wang, Ying-Ming, & Lan, Yi-Xin. (2013). Estimating most productive scale size with double frontiers data envelopment analysis. Economic Modelling, 33, 182-186. doi: https://doi.org/10.1016/j.econmod.2013.04.021
    24.
  24. 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: https://doi.org/10.1016/j.amc.2005.04.023
    25.
  25. 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: https://doi.org/10.1016/j.cam.2005.12.025
    26.
  26. Wu, Desheng. (2006). A note on DEA efficiency assessment using ideal point: An improvement of Wang and Luo’s model. Applied Mathematics and Computation, 183(2), 819-830. doi: https://doi.org/10.1016/j.amc.2006.06.030
    27.
  27. Xu, Ji Heng, Li, Ling, Liu, Jian Yong, Fu, Cheng Qun, & Zheng, Ji Lin. (2011). Imprecise DEA Model Based on TOPSIS. Applied Mechanics and Materials, 63-64, 723-727. doi: 10.4028/www.scientific.net/AMM.63-64.723
    28.

 

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