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A new method for ranking decision making units using common set of weights: A developed criterion
Department of Mathematics, Faculty of Sciences, University of Qom, Alghadir Bld., Postal code:3716146611, Qom, Iran |
In this paper we have developed a new model by altering Liu and Peng's approach [
References:
[1] |
N. Adler, L. Friedman and Z. Sinuany-Stern,
Review of ranking methods in the data envelopment analysis context, Eur J Oper Res, 140 (2002), 249-265.
doi: 10.1016/S0377-2217(02)00068-1. |
[2] |
N. Aghayi, M. Tavana and M. A. Raayatpanah,
Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty, Eur J. Ind Eng, 10 (2016), 385-405.
doi: 10.1504/EJIE.2016.076386. |
[3] |
A. Aldamak and S. Zolfaghari,
Review of efficiency ranking methods in data envelopment analysis, Meas, 106 (2017), 161-172.
doi: 10.1016/j.measurement.2017.04.028. |
[4] |
R. D. Banker, A. Charnes and W. W. Cooper,
Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage Sci, 30 (1984), 1031-1142.
doi: 10.1287/mnsc.30.9.1078. |
[5] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of DMUs, Eur J Oper Res, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
[6] |
C. I. Chiang, M. J. Hwang and Y. H. Liu,
Determining a common set of weights in a DEA problem using a separation vector, Math and Comput Model, 54 (2002), 2464-2470.
doi: 10.1016/j.mcm.2011.06.002. |
[7] |
C. I. Chiang and G. H. Tzeng,
A new efficiency measure for DEA: Efficiency achievement measure established on fuzzy multiple objectives programming, J Manage, 17 (2000), 369-388.
|
[8] |
W. D. Cook, Y. Roll and A. Kazakov,
A DEA model for measuring the relative efficiency of highway maintenance patrols, Inform Syst Oper Res, 28 (1990), 113-124.
|
[9] |
D. K. Despotis,
Improving the discriminating power of DEA: Focus on globally efficient units, J Oper Res Soc, 53 (2002), 314-323.
doi: 10.1057/palgrave.jors.2601253. |
[10] |
J. A. Ganley and S. A. Cubbin, Public Sector Efficiency Measurement: Applications of Data Envelopment Analysis, North-Holland, Amsterdam, 1992. |
[11] |
A. Hatami Marbini, M. Tavana, P. J. Agrell, F. Hosseinzadeh Lotfi and Z. Ghelej Beigi,
A common-weights DEA model for centralized resource reduction and target setting, Comput Ind Eng, 79 (2015), 195-203.
|
[12] |
F. Hosseinzadeh Lotfi, M. Rostamy-Malkhlifeh, G. R. Jahanshahloo, Z. Moghaddas, M. Khodabakhshi and M. Vaez-Ghasemi, A review of ranking models in data envelopment analysis, J Appl Math., 2013 (2013), Article ID: 492421, 20 pages. |
[13] |
C. K. Hu, F. B. Liu and C. F. Hu,
Efficiency measures in fuzzy data envelopment analysis with common weights, J Ind Manage Opt, 13 (2017), 237-249.
doi: 10.3934/jimo.2016014. |
[14] |
C. L. Hwang and A. S. M. Masud, Multiple Objective Decision Making: Methods and Applications, Springer, Berlin, 1979. |
[15] |
G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Khanmohammadi, M. Kazemimanesh and V. Rezaie,
Ranking of units by positive ideal DMU with common weights, Expert Syst Appl, 37 (2010), 7483-7488.
doi: 10.1016/j.eswa.2010.04.011. |
[16] |
C. Kao and H. Hung,
Data envelopment analysis with common weights: The comprise solution approach, J Oper Res Soc, 56 (2005), 1196-1203.
doi: 10.1057/palgrave.jors.2601924. |
[17] |
M. N. Kritikos,
A full ranking methodology in data envelopment analysis based on a set of dummy decision making units, Expert Systems with Applications: An International Journal, 77 (2017), 211-225.
doi: 10.1016/j.eswa.2017.01.042. |
[18] |
F. Li, J. Song, A. Dolgui and L. Liang,
Using common weights and efficiency invariance principles for resource allocation and target setting, International J Prod Res, 55 (2017), 4982-4997.
doi: 10.1080/00207543.2017.1287450. |
[19] |
R. Lin, Z. Chen and Z. Li,
A new approach for allocating fixed costs among decision making units, J Ind Manag Optim, 12 (2016), 211-228.
doi: 10.3934/jimo.2016.12.211. |
[20] |
F. H. F. Liu and H. H. Peng,
Ranking of units on the DEA frontier with common weights, Comput Oper Res, 35 (2008), 1624-1637.
doi: 10.1016/j.cor.2006.09.006. |
[21] |
S. Mehrabian, G. R. Jahanshahloo, M. R. Alirezaei and G. R. Amin,
An assurance interval of the non-archimedean epsilon in DEA models, Eur J Oper Res, 48 (2000), 189-350.
doi: 10.1287/opre.48.2.344.12381. |
[22] |
J. X. Nan and D. F. Li,
Linear programming technique for solving interval-valued constraint matrix games, J Ind Manag Optim Optimization, 10 (2014), 1059-1070.
doi: 10.3934/jimo.2014.10.1059. |
[23] |
J. Pourmahmoud and Z. Zeynali,
A nonlinear model for common weights set identification in network Data Envelopment Analysis, Int J Ind Math, 38 (2016), 87-98.
|
[24] |
A. Rahman, S. Lee and T. C. Chung,
Accurate multi-criteria decision making methodology for recommending machine learning algorithm, J Expert Syst Appl: An International Journal archive, 71 (2017), 257-278.
|
[25] |
S. Ramazani-Tarkhorani, M. Khodabakhshi, S. Mehrabian and F. Nuri-Bahmani,
Ranking decision-making units using common weights in DEA, Appl Math Model, 38 (2014), 3890-3896.
doi: 10.1016/j.apm.2013.08.029. |
[26] |
Y. Roll, W. D. Cook and B. Golany,
Controlling factor weighs in data envelopment analysis, IIE Trans, 23 (1991), 2-9.
|
[27] |
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), 623-637.
doi: 10.3934/jimo.2012.8.623. |
[28] |
M. Salahi, N. Torabi and A. Amiri,
An optimistic robust optimization approach to common set of weights in DEA, Meas, 93 (2016), 67-73.
doi: 10.1016/j.measurement.2016.06.049. |
[29] |
G. H. Shirdel, S. Ramezani-Tarkhorani and Z. Jafari,
tA Method for Evaluating the Performance of Decision Making Units with Imprecise Data Using Common Set of Weights, Int J Appl Comput Math, 3 (2017), 411-423.
doi: 10.1007/s40819-016-0152-0. |
[30] |
J. Sun, J. Wu and D. Guo,
Performance ranking of units considering ideal and anti-ideal DMU with common weights, Appl Math Model, 37 (2013), 6301-6310.
doi: 10.1016/j.apm.2013.01.010. |
[31] |
K. Tone,
On returns to scale under weight restrictions in data envelopment analysis, J Prod Anal, 16 (2001), 31-47.
|
[32] |
Y. M. Wang, Y. Luo and Y. X. Lan,
Common weights for fully ranking decision making units by regression analysis, Expert Syst Appl, 38 (2011), 9122-9128.
doi: 10.1016/j.eswa.2011.01.004. |
show all references
References:
[1] |
N. Adler, L. Friedman and Z. Sinuany-Stern,
Review of ranking methods in the data envelopment analysis context, Eur J Oper Res, 140 (2002), 249-265.
doi: 10.1016/S0377-2217(02)00068-1. |
[2] |
N. Aghayi, M. Tavana and M. A. Raayatpanah,
Robust efficiency measurement with common set of weights under varying degrees of conservatism and data uncertainty, Eur J. Ind Eng, 10 (2016), 385-405.
doi: 10.1504/EJIE.2016.076386. |
[3] |
A. Aldamak and S. Zolfaghari,
Review of efficiency ranking methods in data envelopment analysis, Meas, 106 (2017), 161-172.
doi: 10.1016/j.measurement.2017.04.028. |
[4] |
R. D. Banker, A. Charnes and W. W. Cooper,
Some models for estimating technical and scale inefficiencies in data envelopment analysis, Manage Sci, 30 (1984), 1031-1142.
doi: 10.1287/mnsc.30.9.1078. |
[5] |
A. Charnes, W. W. Cooper and E. Rhodes,
Measuring the efficiency of DMUs, Eur J Oper Res, 2 (1978), 429-444.
doi: 10.1016/0377-2217(78)90138-8. |
[6] |
C. I. Chiang, M. J. Hwang and Y. H. Liu,
Determining a common set of weights in a DEA problem using a separation vector, Math and Comput Model, 54 (2002), 2464-2470.
doi: 10.1016/j.mcm.2011.06.002. |
[7] |
C. I. Chiang and G. H. Tzeng,
A new efficiency measure for DEA: Efficiency achievement measure established on fuzzy multiple objectives programming, J Manage, 17 (2000), 369-388.
|
[8] |
W. D. Cook, Y. Roll and A. Kazakov,
A DEA model for measuring the relative efficiency of highway maintenance patrols, Inform Syst Oper Res, 28 (1990), 113-124.
|
[9] |
D. K. Despotis,
Improving the discriminating power of DEA: Focus on globally efficient units, J Oper Res Soc, 53 (2002), 314-323.
doi: 10.1057/palgrave.jors.2601253. |
[10] |
J. A. Ganley and S. A. Cubbin, Public Sector Efficiency Measurement: Applications of Data Envelopment Analysis, North-Holland, Amsterdam, 1992. |
[11] |
A. Hatami Marbini, M. Tavana, P. J. Agrell, F. Hosseinzadeh Lotfi and Z. Ghelej Beigi,
A common-weights DEA model for centralized resource reduction and target setting, Comput Ind Eng, 79 (2015), 195-203.
|
[12] |
F. Hosseinzadeh Lotfi, M. Rostamy-Malkhlifeh, G. R. Jahanshahloo, Z. Moghaddas, M. Khodabakhshi and M. Vaez-Ghasemi, A review of ranking models in data envelopment analysis, J Appl Math., 2013 (2013), Article ID: 492421, 20 pages. |
[13] |
C. K. Hu, F. B. Liu and C. F. Hu,
Efficiency measures in fuzzy data envelopment analysis with common weights, J Ind Manage Opt, 13 (2017), 237-249.
doi: 10.3934/jimo.2016014. |
[14] |
C. L. Hwang and A. S. M. Masud, Multiple Objective Decision Making: Methods and Applications, Springer, Berlin, 1979. |
[15] |
G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Khanmohammadi, M. Kazemimanesh and V. Rezaie,
Ranking of units by positive ideal DMU with common weights, Expert Syst Appl, 37 (2010), 7483-7488.
doi: 10.1016/j.eswa.2010.04.011. |
[16] |
C. Kao and H. Hung,
Data envelopment analysis with common weights: The comprise solution approach, J Oper Res Soc, 56 (2005), 1196-1203.
doi: 10.1057/palgrave.jors.2601924. |
[17] |
M. N. Kritikos,
A full ranking methodology in data envelopment analysis based on a set of dummy decision making units, Expert Systems with Applications: An International Journal, 77 (2017), 211-225.
doi: 10.1016/j.eswa.2017.01.042. |
[18] |
F. Li, J. Song, A. Dolgui and L. Liang,
Using common weights and efficiency invariance principles for resource allocation and target setting, International J Prod Res, 55 (2017), 4982-4997.
doi: 10.1080/00207543.2017.1287450. |
[19] |
R. Lin, Z. Chen and Z. Li,
A new approach for allocating fixed costs among decision making units, J Ind Manag Optim, 12 (2016), 211-228.
doi: 10.3934/jimo.2016.12.211. |
[20] |
F. H. F. Liu and H. H. Peng,
Ranking of units on the DEA frontier with common weights, Comput Oper Res, 35 (2008), 1624-1637.
doi: 10.1016/j.cor.2006.09.006. |
[21] |
S. Mehrabian, G. R. Jahanshahloo, M. R. Alirezaei and G. R. Amin,
An assurance interval of the non-archimedean epsilon in DEA models, Eur J Oper Res, 48 (2000), 189-350.
doi: 10.1287/opre.48.2.344.12381. |
[22] |
J. X. Nan and D. F. Li,
Linear programming technique for solving interval-valued constraint matrix games, J Ind Manag Optim Optimization, 10 (2014), 1059-1070.
doi: 10.3934/jimo.2014.10.1059. |
[23] |
J. Pourmahmoud and Z. Zeynali,
A nonlinear model for common weights set identification in network Data Envelopment Analysis, Int J Ind Math, 38 (2016), 87-98.
|
[24] |
A. Rahman, S. Lee and T. C. Chung,
Accurate multi-criteria decision making methodology for recommending machine learning algorithm, J Expert Syst Appl: An International Journal archive, 71 (2017), 257-278.
|
[25] |
S. Ramazani-Tarkhorani, M. Khodabakhshi, S. Mehrabian and F. Nuri-Bahmani,
Ranking decision-making units using common weights in DEA, Appl Math Model, 38 (2014), 3890-3896.
doi: 10.1016/j.apm.2013.08.029. |
[26] |
Y. Roll, W. D. Cook and B. Golany,
Controlling factor weighs in data envelopment analysis, IIE Trans, 23 (1991), 2-9.
|
[27] |
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), 623-637.
doi: 10.3934/jimo.2012.8.623. |
[28] |
M. Salahi, N. Torabi and A. Amiri,
An optimistic robust optimization approach to common set of weights in DEA, Meas, 93 (2016), 67-73.
doi: 10.1016/j.measurement.2016.06.049. |
[29] |
G. H. Shirdel, S. Ramezani-Tarkhorani and Z. Jafari,
tA Method for Evaluating the Performance of Decision Making Units with Imprecise Data Using Common Set of Weights, Int J Appl Comput Math, 3 (2017), 411-423.
doi: 10.1007/s40819-016-0152-0. |
[30] |
J. Sun, J. Wu and D. Guo,
Performance ranking of units considering ideal and anti-ideal DMU with common weights, Appl Math Model, 37 (2013), 6301-6310.
doi: 10.1016/j.apm.2013.01.010. |
[31] |
K. Tone,
On returns to scale under weight restrictions in data envelopment analysis, J Prod Anal, 16 (2001), 31-47.
|
[32] |
Y. M. Wang, Y. Luo and Y. X. Lan,
Common weights for fully ranking decision making units by regression analysis, Expert Syst Appl, 38 (2011), 9122-9128.
doi: 10.1016/j.eswa.2011.01.004. |






| | | | | | |
| 995 | 6205 | 1375 | 2629 | 4127 | 1678 |
| 917 | 5898 | 1379 | 2047 | 3721 | 1277 |
| 3178 | 10049 | 3615 | 3511 | 2706 | 2051 |
| 813 | 5833 | 1124 | 1730 | 2176 | 1538 |
| 1236 | 8639 | 2486 | 4990 | 5220 | 2042 |
| 1146 | 7610 | 1600 | 3589 | 3517 | 1856 |
| 705 | 5600 | 1557 | 3623 | 2352 | 2060 |
| 2871 | 11524 | 2880 | 2452 | 1755 | 1664 |
| 1098 | 8998 | 1730 | 2823 | 4412 | 2334 |
| 2032 | 9383 | 2421 | 4454 | 5386 | 2080 |
| 1414 | 10468 | 2140 | 3649 | 5735 | 2691 |
| 1967 | 11260 | 2759 | 3178 | 6079 | 2804 |
| 1851 | 9880 | 2335 | 4570 | 5893 | 2495 |
| 3100 | 15649 | 5487 | 2940 | 5248 | 3692 |
| 5016 | 18010 | 4008 | 3567 | 7800 | 4852 |
| 1924 | 12682 | 2490 | 2975 | 6040 | 3396 |
| | | | | | |
| 995 | 6205 | 1375 | 2629 | 4127 | 1678 |
| 917 | 5898 | 1379 | 2047 | 3721 | 1277 |
| 3178 | 10049 | 3615 | 3511 | 2706 | 2051 |
| 813 | 5833 | 1124 | 1730 | 2176 | 1538 |
| 1236 | 8639 | 2486 | 4990 | 5220 | 2042 |
| 1146 | 7610 | 1600 | 3589 | 3517 | 1856 |
| 705 | 5600 | 1557 | 3623 | 2352 | 2060 |
| 2871 | 11524 | 2880 | 2452 | 1755 | 1664 |
| 1098 | 8998 | 1730 | 2823 | 4412 | 2334 |
| 2032 | 9383 | 2421 | 4454 | 5386 | 2080 |
| 1414 | 10468 | 2140 | 3649 | 5735 | 2691 |
| 1967 | 11260 | 2759 | 3178 | 6079 | 2804 |
| 1851 | 9880 | 2335 | 4570 | 5893 | 2495 |
| 3100 | 15649 | 5487 | 2940 | 5248 | 3692 |
| 5016 | 18010 | 4008 | 3567 | 7800 | 4852 |
| 1924 | 12682 | 2490 | 2975 | 6040 | 3396 |
| | | | | | |
Our method | 0.000001 | 0.181081 | 0.000001 | 0.124392 | 0.116466 | 0.578059 |
Liu and Peng's method [20] | 0.000001 | 0.000001 | 0.000001 | 7.50E-07 | 8.70E- 07 | 0.000004 |
| | | | | | |
Our method | 0.000001 | 0.181081 | 0.000001 | 0.124392 | 0.116466 | 0.578059 |
Liu and Peng's method [20] | 0.000001 | 0.000001 | 0.000001 | 7.50E-07 | 8.70E- 07 | 0.000004 |
| CWA-Efficiency | CCR-Efficiency | |
1 | 1 | 1 | |
| 0.885761 | 0.877007 | 1 |
| 0.665101 | 0.55716 | 0.690363 |
| 0.89857 | 0.911488 | 1 |
| 0.818436 | 0.807723 | 1 |
| 0.812557 | 0.823997 | 0.881091 |
| 1 | 1 | 1 |
| 0.48762 | 0.440469 | 0.555791 |
| 0.940676 | 0.968986 | 1 |
| 0.812047 | 0.774854 | 0.863042 |
| 0.94638 | 0.963253 | 0.996068 |
| 0.956693 | 0.920591 | 1 |
| 0.90288 | 0.884299 | 0.915511 |
| 0.858084 | 0.75116 | 1 |
| 0.960084 | 0.867478 | 1 |
| 1 | 1 | 1 |
| CWA-Efficiency | CCR-Efficiency | |
1 | 1 | 1 | |
| 0.885761 | 0.877007 | 1 |
| 0.665101 | 0.55716 | 0.690363 |
| 0.89857 | 0.911488 | 1 |
| 0.818436 | 0.807723 | 1 |
| 0.812557 | 0.823997 | 0.881091 |
| 1 | 1 | 1 |
| 0.48762 | 0.440469 | 0.555791 |
| 0.940676 | 0.968986 | 1 |
| 0.812047 | 0.774854 | 0.863042 |
| 0.94638 | 0.963253 | 0.996068 |
| 0.956693 | 0.920591 | 1 |
| 0.90288 | 0.884299 | 0.915511 |
| 0.858084 | 0.75116 | 1 |
| 0.960084 | 0.867478 | 1 |
| 1 | 1 | 1 |
Our method | Liu and Peng's method [20] | The ratio |
0.871556 | 0.846779 | 1.02926 |
Our method | Liu and Peng's method [20] | The ratio |
0.871556 | 0.846779 | 1.02926 |
| Our method: Input-oriented approach | Our method: Output-oriented approach | CWA-ranking | CCR |
| 1 | 3 | 2 | 1 |
| 10 | 10 | 9 | 1 |
| 15 | 15 | 15 | 6 |
| 9 | 9 | 7 | 1 |
| 12 | 12 | 12 | 1 |
| 13 | 13 | 11 | 4 |
| 2 | 2 | 3 | 1 |
| 16 | 16 | 16 | 7 |
| 7 | 7 | 4 | 1 |
| 14 | 14 | 13 | 5 |
| 6 | 6 | 5 | 2 |
| 5 | 5 | 6 | 1 |
| 8 | 8 | 8 | 3 |
| 11 | 11 | 14 | 1 |
| 4 | 4 | 10 | 1 |
| 3 | 1 | 1 | 1 |
| Our method: Input-oriented approach | Our method: Output-oriented approach | CWA-ranking | CCR |
| 1 | 3 | 2 | 1 |
| 10 | 10 | 9 | 1 |
| 15 | 15 | 15 | 6 |
| 9 | 9 | 7 | 1 |
| 12 | 12 | 12 | 1 |
| 13 | 13 | 11 | 4 |
| 2 | 2 | 3 | 1 |
| 16 | 16 | 16 | 7 |
| 7 | 7 | 4 | 1 |
| 14 | 14 | 13 | 5 |
| 6 | 6 | 5 | 2 |
| 5 | 5 | 6 | 1 |
| 8 | 8 | 8 | 3 |
| 11 | 11 | 14 | 1 |
| 4 | 4 | 10 | 1 |
| 3 | 1 | 1 | 1 |
Size of the sample | Our method | CWA-Efficiencies | The ratio |
6 | 0.916128 | 0.906961 | 1.010107 |
12 | 0.539086 | 0.539082 | 1.000006 |
25 | 0.689937 | 0.148176 | 4.656189 |
50 | 0.550724 | 0.553320 | 0.995309 |
100 | 0.639243 | 0.471678 | 1.355254 |
200 | 0.582310 | 0.580711 | 1.002753 |
Size of the sample | Our method | CWA-Efficiencies | The ratio |
6 | 0.916128 | 0.906961 | 1.010107 |
12 | 0.539086 | 0.539082 | 1.000006 |
25 | 0.689937 | 0.148176 | 4.656189 |
50 | 0.550724 | 0.553320 | 0.995309 |
100 | 0.639243 | 0.471678 | 1.355254 |
200 | 0.582310 | 0.580711 | 1.002753 |
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