A bi-objective weighted model for improving the discrimination power in MCDEA.

*(English)*Zbl 1339.90297Summary: Lack of discrimination power and poor weight dispersion remain major issues in Data Envelopment Analysis (DEA). Since the initial multiple criteria DEA (MCDEA) model developed in the late 1990s, only goal programming approaches; that is, the GPDEA-CCR and GPDEA-BCC were introduced for solving the said problems in a multi-objective framework. We found GPDEA models to be invalid and demonstrate that our proposed bi-objective multiple criteria DEA (BiO-MCDEA) outperforms the GPDEA models in the aspects of discrimination power and weight dispersion, as well as requiring less computational codes. An application of energy dependency among 25 European Union member countries is further used to describe the efficacy of our approach.

##### MSC:

90C29 | Multi-objective and goal programming |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

##### Keywords:

multi-criteria data envelopment analysis; goal programming; discrimination power; weight dispersion; multi-objective programming; energy policy
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\textit{M. R. Ghasemi} et al., Eur. J. Oper. Res. 233, No. 3, 640--650 (2014; Zbl 1339.90297)

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##### References:

[1] | Amin, G. R.; Emrouznejad, A.; Rezaei, S., Some clarifications on the DEA clustering approach, European Journal of Operational Research, 215, 498-501, (2011) |

[2] | Andersen, P.; Petersen, N. C., A procedure for ranking efficient units in data envelopment analysis, Management Science, 39, 1261-1264, (1993) · Zbl 0800.90096 |

[3] | Anderson, T. R.; Hollingsworth, K.; Inman, L., The fixed weighting nature of a cross-evaluation model, Journal of productivity analysis, 17, 249-255, (2002) |

[4] | Angiz, M. Z.; Sajedi, M. A., Improving cross-efficiency evaluation using fuzzy concepts, World Applied Sciences Journal, 16, 1352-1359, (2012) |

[5] | Bal, H.; Örkcü, H. H.; Çelebioglu, S., Improving the discrimination power and weights dispersion in the data envelopment analysis, Computers & Operations Research, 37, 99-107, (2010) · Zbl 1171.90418 |

[6] | Bal, H.; Örkcü, H. H.; Çelebioğlu, S., A new method based on the dispersion of weights in data envelopment analysis, Computers & Industrial Engineering, 54, 502-512, (2008) |

[7] | Banker, R. D.; Charnes, A.; Cooper, W. W., Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1078-1092, (1984) · Zbl 0552.90055 |

[8] | Banker, R. D.; Zheng, Z.; Natarajan, R., DEA-based hypothesis tests for comparing two groups of decision making units, European Journal of Operational Research, 206, 231-238, (2010) · Zbl 1188.90120 |

[9] | Cao, Y., & Kong, F. (2010). A combined evaluation model based on the cone ratio DEA model. In 2010 International conference on Computer and Communication Technologies in Agriculture Engineering (CCTAE) (Vol. 3, pp. 168-171). Chengdu, China. |

[10] | Charnes, A.; Cooper, W. W.; Huang, Z. M.; Sun, D. B., Polyhedral cone-ratio models with an illustrative application to large commercial banks, Journal of Econometrics, 46, 73-91, (1990) · Zbl 0712.90015 |

[11] | Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429-444, (1978) · Zbl 0416.90080 |

[12] | Chen, Y., Measuring super-efficiency in DEA in the presence of infeasibility, European Journal of Operational Research, 161, 447-468, (2005) |

[13] | Chen, Y.; Du, J.; Huo, J., Super-efficiency based on a modified directional distance function, Omega, 41, 621-625, (2013) |

[14] | Chen, Y.-W.; Larbani, M.; Chang, Y.-P., Multiobjective data envelopment analysis, Journal of the Operational Research Society, 60, 1556-1566, (2009) · Zbl 1171.90515 |

[15] | Chen, Y.; Liang, L., Super-efficiency DEA in the presence of infeasibility: one model approach, European Journal of Operational Research, 213, 359-360, (2011) · Zbl 1247.90167 |

[16] | Cohon, J. L., Multiobjective programming and planning, (1987), Academic Press New York · Zbl 0462.90054 |

[17] | Cook, W. D.; Liang, L.; Zha, Y.; Zhu, J., A modified super-efficiency DEA model for infeasibility, The Journal of the Operational Research Society, 60, 276-281, (2009) · Zbl 1168.90502 |

[18] | Cook, W. D.; Zhu, J., DEA cobb-Douglas frontier and cross-efficiency, Journal of the Operational Research Society, 64, 1-4, (2013) |

[19] | Dimitris, P. M., Multiobjective programming methods in the reserve selection problem, European Journal of Operational Research, 150, 640-652, (2003) · Zbl 1033.90052 |

[20] | Doyle, J. R.; Green, R. H., Cross-evaluation in DEA: improving discrimination among dmus, INFOR, 33, 205-222, (1995) · Zbl 0832.90002 |

[21] | Dyson, R. G.; Thanassoulis, E., Reducing weight flexibility in data envelopment analysis, Journal of the Operational Research Society, 39, 563-576, (1988) |

[22] | Emrouznejad, A.; Amin, G. R.; Thanassoulis, E.; Anouze, A. L., On the boundedness of the SORM DEA models with negative data, European Journal of Operational Research, 206, 265-268, (2010) · Zbl 1188.90122 |

[23] | Emrouznejad, A.; Anouze, A. L.; Thanassoulis, E., A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA, European Journal of Operational Research, 200, 297-304, (2010) · Zbl 1183.90230 |

[24] | Emrouznejad, A.; De Witte, K., COOPER-framework: A unified process for non-parametric projects, European Journal of Operational Research, 207, 1573-1586, (2010) |

[25] | Emrouznejad, A.; Parker, B. R.; Tavares, G., 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, 42, 151-157, (2008) |

[26] | Foroughi, A. A., A note on “A new method for ranking discovered rules from data mining by DEA”, and a full ranking approach, Expert Systems with Applications, 38, 12913-12916, (2011) |

[27] | Golany, B.; Storbeck, J. E., A data envelopment analysis of the operational efficiency of bank branche, Interfaces, 29, 14-26, (1999) |

[28] | Green, R. H.; Doyle, J. R.; Cook, W. D., Preference voting and project ranking using DEA and cross-evaluation, European Journal of Operational Research, 90, 461-472, (1996) · Zbl 0911.90009 |

[29] | Hatami-Marbini, A.; Emrouznejad, A.; Tavana, M., A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making, European Journal of Operational Research, 214, 457-472, (2011) · Zbl 1219.90199 |

[30] | Ignizio, J. P., Goal programming and extensions, (1976), Lexington Books Lexington |

[31] | Khalili, M.; Camanho, A. S.; Portela, M. C.A. S.; Alirezaee, M. R., The measurement of relative efficiency using data envelopment analysis with assurance regions that link inputs and outputs, European Journal of Operational Research, 203, 761-770, (2010) · Zbl 1177.90216 |

[32] | Lee, S. M., Goal programming for decision analysis, (1972), Auerback Philadelphia |

[33] | Lee, H.-S.; Chu, C.-W.; Zhu, J., Super-efficiency DEA in the presence of infeasibility, European Journal of Operational Research, 212, 141-147, (2011) · Zbl 1237.90115 |

[34] | Lee, H.-S.; Zhu, J., Super-efficiency infeasibility and zero data in DEA, European Journal of Operational Research, 216, 429-433, (2012) · Zbl 1237.90116 |

[35] | Lim, T.-S.; Loh, W.-Y., A comparison of tests of equality of variances, Computational Statistics & Data Analysis, 22, 287-301, (1996) · Zbl 0900.62101 |

[36] | Li, X.-B.; Reeves, G. R., A multiple criteria approach to data envelopment analysis, European Journal of Operational Research, 115, 507-517, (1999) · Zbl 0953.91022 |

[37] | Mann, H. B.; Whitney, D. R., On a test of whether one of two random variables is stochastically larger than the other, Annals of Mathematical Statistics, 18, 1, 50-60, (1947) · Zbl 0041.26103 |

[38] | Mecit, E. D.; Alp, I., A new proposed model of restricted data envelopment analysis by correlation coefficients, Applied Mathematical Modelling, 37, 3407-3425, (2013) · Zbl 1351.90121 |

[39] | Nordstokke, D. W.; Zumbo, B. D., A new nonparametric levene test for equal variances, Psicológica, 31, 401-430, (2010) |

[40] | Sarrico, C. S.; Dyson, R. G., Restricting virtual weights in data envelopment analysis, European Journal of Operational Research, 159, 17-34, (2004) · Zbl 1067.90086 |

[41] | Sexton, T. R.; Silkman, R. H.; Hogan, A. J., The methodology of data envelopment analysis, (Silkman, R. H., Measuring efficiency: An assessment of data envelopment analysis, (1986), Jossey-Bass San Fransisco), 7-29 |

[42] | Soleimani-damaneh, M.; Jahanshahloo, G. R.; Foroughi, A. A., A comment on “measuring super-efficiency in DEA in the presence of infeasibility, European Journal of Operational Research, 170, 323-325, (2006) · Zbl 1134.90428 |

[43] | Sueyoshi, T.; Goto, M., Environmental assessment by DEA radial measurement: US coal-fired power plants in ISO (independent system operator) and RTO (regional transmission organization), Energy Economics, 34, 663-676, (2012) |

[44] | Thanassoulis, E.; Allen, R., Simulating weights restrictions in data envelopment analysis by means of unobserved dmus, Management Science, 44, 586-594, (1998) · Zbl 1003.90511 |

[45] | Thompson, R. G.; Langemeier, L. N.; Lee, C. T.; Thrall, R. M., The role of multiplier bounds in efficiency analysis with application to kansas farming, Journal of Econometrics, 46, 93-108, (1990) |

[46] | Thompson, R. G.; Singleton, F. D.; Thrall, R. M.; Smith, B. A., Comparative site evaluations for locating a high-energy physics lab in Texas, INTERFACES, 16, 35-49, (1986) |

[47] | Wang, Y.-M.; Chin, K.-S., A neutral DEA model for cross-efficiency evaluation and its extension, Expert Systems with Applications, 37, 3666-3675, (2010) |

[48] | Wang, Y.-M.; Chin, K.-S., The use of OWA operator weights for cross-efficiency aggregation, Omega, 39, 493-503, (2011) |

[49] | Ward, P.; Storbeck, J.; Mangum, S.; Byrnes, P., An analysis of staffing efficiency in US manufacturing: 1983 and 1989, Annals of Operations Research, 73, 67-89, (1997) · Zbl 0891.90120 |

[50] | Zimmerman, D. W., Two separate effects of variance heterogeneity on the validity and power of significance tests of location, Statistical Methodology, 3, 351-374, (2006) · Zbl 1248.62075 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.