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An interactive MOLP method for solving output-oriented DEA problems with undesirable factors
1. | Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr 47651-61964, Iran |
2. | Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, United States, Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany |
3. | Department of Mathematics, University of Mazandaran, Babolsar 47416-95447, Iran |
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R. Allen, A. Athanassopoulis, R. G. Dyson and E. Thanassoulis, Weights restrictions and value judgements in data envelopment analysis: Evolution, development and future directions,, Annals of Operations Research, 73 (1997), 13. Google Scholar |
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A. Amirteimoori and S. Kordrostami, An alternative clustering approach: a DEA-based procedure,, Optimization: A Journal of Mathematical Programming and Operations Research, 62 (2013), 227.
doi: 10.1080/02331934.2011.585466. |
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J. Aparicio, J. L. Ruiz and I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA,, Journal of Productivity Analysis, 28 (2007), 209.
doi: 10.1007/s11123-007-0039-5. |
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M. Asmild, J. C. Paradi, D. N. Reese and F. Tam, Measuring overall efficiency and effectiveness using DEA,, European Journal of Operational Research, 178 (2007), 305.
doi: 10.1016/j.ejor.2006.01.014. |
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R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis,, Management Science, 30 (1984), 1078.
doi: 10.1287/mnsc.30.9.1078. |
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C. P. Barros, S. Managi and R. Matousek, The technical efficiency of Japanese banks: Non radial directional performance measurement with undesirable output,, Omega, 40 (2012), 1.
doi: 10.1016/j.omega.2011.02.005. |
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G. Bi, J. Ding, Y. Luo and L. Liang, Resource allocation and target setting for parallel production system based on DEA,, Applied Mathematical Modelling, 35 (2011), 4270.
doi: 10.1016/j.apm.2011.02.048. |
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R. Benayoun, J. Montgolfier, J. Tergny and O. Laritchev, Linear programming with multiple objective functions: Step method (STEM),, Mathematical Programming, 1 (1971), 366.
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A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units,, European Journal of Operational Research, 2 (1978), 429.
doi: 10.1016/0377-2217(78)90138-8. |
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A. Charnes, W. W. Cooper, Z. M. Huang and D. B. Sun, Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks,, Journal of Econometrics, 46 (1990), 73.
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A. Ebrahimnejad, A new link between output-oriented BCC model with fuzzy data in the present of undesirable outputs and MOLP,, Fuzzy Information and Engineering, 3 (2011), 113.
doi: 10.1007/s12543-011-0070-0. |
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A. Ebrahimnejad, R. Shahverdi, F. Rezai Balf and M. Hatefi, Finding target units in FDH model by least-distance measure model,, Measurement, 49 (2013), 619.
|
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A. Ebrahimnejad, M. Tavana, F. Hosseinzadeh Lotfi, R. Shahverdi and M. Yousefpour, A three-stage data envelopment analysis model with application to banking industry,, Measurement, 49 (2014), 308.
doi: 10.1016/j.measurement.2013.11.043. |
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A. Ebrahimnejad and M. Tavana, An interactive MOLP method for identifying target units in Output-Oriented DEA models: The NATO enlargement problem,, Measurement, 52 (2014), 124.
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M. A. Hinojosa and A. M. Mármol, Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences,, Omega, 39 (2011), 159.
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F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, A. Ebrahimnejad, M. Soltanifar and S. M. Manosourzadeh, Target setting in the general combined-oriented CCR model using an interactive MOLP method,, Journal of Computational and Applied Mathematics, 234 (2010), 1.
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F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, M. Soltanifar, A. Ebrahimnejad and S. M. Manosourzadeh, Relationship between MOLP and DEA based on output-orientated CCR dual model,, Expert Systems with Applications, 37 (2010), 4331.
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doi: 10.1057/jors.2011.77. |
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Z. S. Hua, Y. W. Bian and L. Liang, Eco-efficiency analysis of paper mills along the Huai River: An extended DEA approach,, Omega, 35 (2007), 578.
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A. Jess, H. Th. Jongen, L. Neralic and O. Stein, A semi-infinite programming model in data envelopment analysis,, European Journal of Operational Research, 49 (2001), 369.
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P. J. Korhonen and M. Luptacik, Eco-efficiency analysis of power plants: an extension of data envelopment analysis,, European Journal of Operational Research, 154 (2004), 437.
doi: 10.1016/S0377-2217(03)00180-2. |
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P. Korhonen, S. Stenfors and M. Syrjänen, Multiple objective approach as an alternative to radial projection in DEA,, Journal of Productivity Analysis, 20 (2003), 305. Google Scholar |
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S. Kumar Mandal and S. Madheswaran, Environmental efficiency of the Indian cement industry: An interstate analysis,, Energy Policy, 38 (2010), 1108. Google Scholar |
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M. Mahdiloo, A. Noorizadeh and R. Farzipoor Saen, Developing a new data envelopment analysis model for customer value analysis,, Journal of Industrial and Management Optimization, 7 (2011), 531.
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R. Riccardi, G. Oggioni and R. Toninelli, Efficiency analysis of world cement industry in presence of undesirable output: Application of data envelopment analysis and directional distance function,, Energy Policy, 44 (2012), 140.
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show all references
References:
[1] |
R. Allen, A. Athanassopoulis, R. G. Dyson and E. Thanassoulis, Weights restrictions and value judgements in data envelopment analysis: Evolution, development and future directions,, Annals of Operations Research, 73 (1997), 13. Google Scholar |
[2] |
A. Amirteimoori and S. Kordrostami, An alternative clustering approach: a DEA-based procedure,, Optimization: A Journal of Mathematical Programming and Operations Research, 62 (2013), 227.
doi: 10.1080/02331934.2011.585466. |
[3] |
J. Aparicio, J. L. Ruiz and I. Sirvent, Closest targets and minimum distance to the Pareto-efficient frontier in DEA,, Journal of Productivity Analysis, 28 (2007), 209.
doi: 10.1007/s11123-007-0039-5. |
[4] |
M. Asmild, J. C. Paradi, D. N. Reese and F. Tam, Measuring overall efficiency and effectiveness using DEA,, European Journal of Operational Research, 178 (2007), 305.
doi: 10.1016/j.ejor.2006.01.014. |
[5] |
R. D. Banker, A. Charnes and W. W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis,, Management Science, 30 (1984), 1078.
doi: 10.1287/mnsc.30.9.1078. |
[6] |
C. P. Barros, S. Managi and R. Matousek, The technical efficiency of Japanese banks: Non radial directional performance measurement with undesirable output,, Omega, 40 (2012), 1.
doi: 10.1016/j.omega.2011.02.005. |
[7] |
G. Bi, J. Ding, Y. Luo and L. Liang, Resource allocation and target setting for parallel production system based on DEA,, Applied Mathematical Modelling, 35 (2011), 4270.
doi: 10.1016/j.apm.2011.02.048. |
[8] |
R. Benayoun, J. Montgolfier, J. Tergny and O. Laritchev, Linear programming with multiple objective functions: Step method (STEM),, Mathematical Programming, 1 (1971), 366.
doi: 10.1007/BF01584098. |
[9] |
A. Charnes, W. W. Cooper and E. Rhodes, Measuring the efficiency of decision making units,, European Journal of Operational Research, 2 (1978), 429.
doi: 10.1016/0377-2217(78)90138-8. |
[10] |
A. Charnes, W. W. Cooper, Z. M. Huang and D. B. Sun, Polyhedral cone-ratio DEA models with an illustrative application to large commercial banks,, Journal of Econometrics, 46 (1990), 73.
doi: 10.1016/0304-4076(90)90048-X. |
[11] |
R. G. Dyson and E. Thannassoulis, Reducing weight flexibility in data envelopment analysis,, Journal of Operational Research Society, 39 (1988), 563.
doi: 10.2307/2582861. |
[12] |
A. Ebrahimnejad, A new link between output-oriented BCC model with fuzzy data in the present of undesirable outputs and MOLP,, Fuzzy Information and Engineering, 3 (2011), 113.
doi: 10.1007/s12543-011-0070-0. |
[13] |
A. Ebrahimnejad, R. Shahverdi, F. Rezai Balf and M. Hatefi, Finding target units in FDH model by least-distance measure model,, Measurement, 49 (2013), 619.
|
[14] |
A. Ebrahimnejad, M. Tavana, F. Hosseinzadeh Lotfi, R. Shahverdi and M. Yousefpour, A three-stage data envelopment analysis model with application to banking industry,, Measurement, 49 (2014), 308.
doi: 10.1016/j.measurement.2013.11.043. |
[15] |
A. Ebrahimnejad and M. Tavana, An interactive MOLP method for identifying target units in Output-Oriented DEA models: The NATO enlargement problem,, Measurement, 52 (2014), 124.
doi: 10.1016/j.measurement.2014.03.016. |
[16] |
M. Ehrgott, Multicriteria Optimization,, $2^{nd}$ edition, (2005). Google Scholar |
[17] |
R. Fare and S. Grosskopf, Modelling undesirable factors in efficiency evaluation: Comment,, European Journal of Operational Research, 157 (2004), 242.
doi: 10.1016/S0377-2217(03)00191-7. |
[18] |
R. Fare, S. Grosskopf, C. A. K. Lovell and C. Pasurka, Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach,, The Review of Economics and Statistics, 71 (1989), 90.
doi: 10.2307/1928055. |
[19] |
R. Fare, S. Grosskopf and C. Pasurka, Accounting for air pollution emissions in measures of state manufacturing productivity growth,, Journal of Regional Science, 41 (2001), 381.
doi: 10.1111/0022-4146.00223. |
[20] |
A. M. Geoffrion, J. S. Dyer and A. Feinberg, An interactive approach for multi-criterion optimization with an application to the operation of an academic department, Part I,, Management Science, 19 (1972), 357. Google Scholar |
[21] |
B. Golany, An interactive MOLP procedure for the extension of DEA to effectiveness analysis,, Journal of the Operational Research Society, 39 (1988), 725.
doi: 10.2307/2583767. |
[22] |
M. A. Hinojosa and A. M. Mármol, Axial solutions for multiple objective linear problems. An application to target setting in DEA models with preferences,, Omega, 39 (2011), 159.
doi: 10.1016/j.omega.2010.06.001. |
[23] |
F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, A. Ebrahimnejad, M. Soltanifar and S. M. Manosourzadeh, Target setting in the general combined-oriented CCR model using an interactive MOLP method,, Journal of Computational and Applied Mathematics, 234 (2010), 1.
doi: 10.1016/j.cam.2009.11.045. |
[24] |
F. Hosseinzadeh Lotfi, G. R. Jahanshaloo, M. Soltanifar, A. Ebrahimnejad and S. M. Manosourzadeh, Relationship between MOLP and DEA based on output-orientated CCR dual model,, Expert Systems with Applications, 37 (2010), 4331.
doi: 10.1016/j.eswa.2009.11.066. |
[25] |
H. H. Hu, Q. Qi and C. H. Yang, Evaluation of China's regional hospital efficiency: DEA approach with undesirable output,, Journal of the Operational Research Society, 63 (2011), 715.
doi: 10.1057/jors.2011.77. |
[26] |
Z. S. Hua, Y. W. Bian and L. Liang, Eco-efficiency analysis of paper mills along the Huai River: An extended DEA approach,, Omega, 35 (2007), 578.
doi: 10.1016/j.omega.2005.11.001. |
[27] |
X. Huang, D. Hu and Z. Zhou, Measuring efficiency in Chinese commercial banks using a DEA model with undesirable output,, International Journal of Information and Decision Sciences, 5 (2013), 140.
doi: 10.1504/IJIDS.2013.053801. |
[28] |
S. Jain, K. P. Triantis and S. Liu, Manufacturing performance measurement and target setting: A data envelopment analysis approach,, European Journal of Operational Research, 214 (2011), 616.
doi: 10.1016/j.ejor.2011.05.028. |
[29] |
A. Jess, H. Th. Jongen, L. Neralic and O. Stein, A semi-infinite programming model in data envelopment analysis,, European Journal of Operational Research, 49 (2001), 369.
doi: 10.1080/02331930108844538. |
[30] |
P. J. Korhonen and M. Luptacik, Eco-efficiency analysis of power plants: an extension of data envelopment analysis,, European Journal of Operational Research, 154 (2004), 437.
doi: 10.1016/S0377-2217(03)00180-2. |
[31] |
P. Korhonen, S. Stenfors and M. Syrjänen, Multiple objective approach as an alternative to radial projection in DEA,, Journal of Productivity Analysis, 20 (2003), 305. Google Scholar |
[32] |
S. Kumar Mandal and S. Madheswaran, Environmental efficiency of the Indian cement industry: An interstate analysis,, Energy Policy, 38 (2010), 1108. Google Scholar |
[33] |
H. F. Lewis and T. R. Sexton, Data envelopment analysis with reverse inputs and outputs,, Journal of Productivity Analysis, 21 (2004), 113.
doi: 10.1023/B:PROD.0000016868.69586.b4. |
[34] |
Y. Liu and U. R. Sumaila, Estimating pollution abatement costs of salmon aquaculture: A joint production approach,, Land Economics, 86 (2010), 569. Google Scholar |
[35] |
C. A. K. Lovell, J. T. Pastor and J. A. Turner, Measuring macroeconomic performance in the OECD: A comparison of European and non-European countries,, European Journal of Operational Research, 87 (1995), 507. Google Scholar |
[36] |
S. Lozano and E. Gutierrez, Efficiency analysis and target setting of Spanish airports,, Netw. Spat. Econ., 11 (2011), 139.
doi: 10.1007/s11067-008-9096-1. |
[37] |
W. M. Lu and S. F. Lo, A closer look at the economic-environmental disparities for regional development in China,, European Journal of Operational Research, 183 (2007), 882.
doi: 10.1016/j.ejor.2006.10.027. |
[38] |
M. Mahdiloo, A. Noorizadeh and R. Farzipoor Saen, Developing a new data envelopment analysis model for customer value analysis,, Journal of Industrial and Management Optimization, 7 (2011), 531.
doi: 10.3934/jimo.2011.7.531. |
[39] |
N. Malekmohammadi, F. Hosseinzadeh Lotfi and A. B. Jaafar, Target setting in data envelopment analysis using MOLP,, Applied Mathematical Modelling, 35 (2011), 328.
doi: 10.1016/j.apm.2010.06.007. |
[40] |
H. Nakayama and Y. Sawaragi, Satisficing trade-off method for multiobjective programming. An interactive decision analysis,, in Lecture notes in economics and mathematical systems (eds. M. Grauer and A.P. Wierzbicki), 229 (1984), 113.
doi: 10.1007/978-3-662-00184-4_13. |
[41] |
F. Pedraja-Chaparro, J. Salinas-Jimenez and P. Smith, On the role of weight restrictions in data envelopment analysis,, Journal of Productivity Analysis, 8 (1997), 215. Google Scholar |
[42] |
V. V. Podinovski, Suitability and redundancy of non-homogeneous weight restrictions for measuring the relative efficiency in DEA,, European Journal of Operational Research, 154 (2004), 380.
doi: 10.1016/S0377-2217(03)00176-0. |
[43] |
S. Reinhard, C. A. K. Lovell and G. Thijssen, Environmental efficiency with multiple environmentally detrimental variables; estimated with SFA and DEA,, European Journal of Operational Research, 121 (2000), 287.
doi: 10.1016/S0377-2217(99)00218-0. |
[44] |
S. Reinhard and G. Thijssen, Nitrogen efficiency of Dutch dairy farms: A shadow cost system approach,, European Review of Agricultural Economics, 27 (2000), 167.
doi: 10.1093/erae/27.2.167. |
[45] |
R. Riccardi, G. Oggioni and R. Toninelli, Efficiency analysis of world cement industry in presence of undesirable output: Application of data envelopment analysis and directional distance function,, Energy Policy, 44 (2012), 140.
doi: 10.1016/j.enpol.2012.01.030. |
[46] |
S. Saati, A. Hatami-Marbini, P. J. Agrell and M. Tavana, A common set of weight approach using an ideal decision making unit in data envelopment analysis,, Journal of Industrial and Management Optimization, 8 (2012), 623.
doi: 10.3934/jimo.2012.8.623. |
[47] |
M. Seiford and J. Zhu, Modeling undesirable factors in efficiency evaluation,, European Journal of Operational Research, 142 (2002), 16.
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