| Title:
|
Evaluation of decision-making units based on the weight-optimized DEA model (English) |
| Author:
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Sun, Jiasen |
| Author:
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Yang, Rui |
| Author:
|
Ji, Xiang |
| Author:
|
Wu, Jie |
| Language:
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English |
| Journal:
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Kybernetika |
| ISSN:
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0023-5954 (print) |
| ISSN:
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1805-949X (online) |
| Volume:
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53 |
| Issue:
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2 |
| Year:
|
2017 |
| Pages:
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244-262 |
| Summary lang:
|
English |
| . |
| Category:
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math |
| . |
| Summary:
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Data envelopment analysis (DEA) is a methodology for measuring best relative efficiencies of a group of peer decision-making units (DMUs) that take multiple inputs to produce multiple outputs. However, the traditional DEA model only aims to maximize the efficiency of the DMU under evaluation. This usually leads to very small weights (even zero weights) being assigned to some inputs or outputs. Correspondingly, these inputs or outputs have little or even no contribution to efficiency, which is unfair and irrational. The purpose of this paper is to address this problem. Two new weight-optimized models are proposed based upon the perspective of cross evaluation. Using the results of an Advanced Manufacturing Technology (AMT) example, it is found that all AMTs are fully sorted. The decision maker can easily choose the best AMT. In addition, unreasonable weights of AMTs are effectively avoided. (English) |
| Keyword:
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data envelopment analysis (DEA) |
| Keyword:
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efficiency |
| Keyword:
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weight-optimized model |
| Keyword:
|
cross evaluation |
| MSC:
|
90B50 |
| idZBL:
|
Zbl 06770167 |
| idMR:
|
MR3661351 |
| DOI:
|
10.14736/kyb-2017-2-0244 |
| . |
| Date available:
|
2017-06-25T17:57:46Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146804 |
| . |
| Reference:
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[1] Anderson, T. R., Hollingsworth, K., Inman, L.: The fixed weighting nature of a cross-evaluation model..J. Productivity Anal. 17 (2002), 3, 249-255. 10.1023/a:1015012121760 |
| Reference:
|
[2] Andersen, P., Petersen, N. C.: A procedure for ranking efficient units in data envelopment analysis..Management Sci. 39 (1993), 10, 1261-1264. Zbl 0800.90096, 10.1287/mnsc.39.10.1261 |
| Reference:
|
[3] Banker, R. D., Charnes, A., Cooper, W. W.: Some models for estimating technical and scale inefficiencies in data envelopment analysis..Management Sci. 30 (1984), 9, 1078-1092. Zbl 0552.90055, 10.1287/mnsc.30.9.1078 |
| Reference:
|
[4] Bougnol, M. L., Dulá, J. H.: Anchor points in DEA..Europ. J. Oper. Res. 192 (2009), 2, 668-676. Zbl 1157.90435, MR 2454796, 10.1016/j.ejor.2007.10.034 |
| Reference:
|
[5] Boussofiane, A., Dyson, R. G., Thanassoulis, E.: Applied data envelopment analysis..Europ. J. Oper. Res. 52 (1991), 1, 1-15. 10.1016/0377-2217(91)90331-o |
| Reference:
|
[6] Charnes, A., Cooper, W. W., Rhodes, E.: Measuring the efficiency of decision making units..Europ. J. Oper. Res. 2 (1978), 6, 429-444. Zbl 0425.90086, MR 0525905, 10.1016/0377-2217(78)90138-8 |
| Reference:
|
[7] Chen, C. M., Delmas, M. A., Lieberman, M. B.: Production frontier methodologies and efficiency as a performance measure in strategic management research..Strategic Management J. 36 (2015), 1, 19-36. 10.1002/smj.2199 |
| Reference:
|
[8] Cook, W. D., Bala, K.: Performance measurement and classification data in DEA: input-oriented model..Omega 35 (2007), 1, 39-52. 10.1016/j.omega.2005.02.002 |
| Reference:
|
[9] Cook, W. D., Seiford, L. M.: Data envelopment analysis (DEA) - Thirty years on..Europ. J. Oper. Res. 192 (2009), 1, 1-17. Zbl 1180.90151, MR 2458453, 10.1016/j.ejor.2008.01.032 |
| Reference:
|
[10] Cook, W. D., Tone, K., Zhu, J.: Data envelopment analysis: Prior to choosing a model..Omega 44 (2014), 1-4. 10.1016/j.omega.2013.09.004 |
| Reference:
|
[11] Cook, W. D., Zhu, J.: DEA Cobb-Douglas frontier and cross-efficiency..J. Oper. Res. Soc. 65 (2013), 2, 265-268. 10.1057/jors.2013.13 |
| Reference:
|
[12] Cook, W. D., Zhu, J.: DEA Cross Efficiency. In Data Envelopment Analysis..Springer US 2015. MR 3362964, 10.1007/978-1-4899-7553-9_2 |
| Reference:
|
[13] Cooper, W. W., Seiford, L. M., Tone, K.: Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software..Springer-Verlag US, 2007. Zbl 1111.90001, 10.1007/978-0-387-45283-8 |
| Reference:
|
[14] Cooper, W. W., Seiford, L. M., Zhu, J.: Data envelopment analysis. In Handbook on data envelopment analysis..Springer US 2004. MR 2077628, 10.1007/1-4020-7798-x_1 |
| Reference:
|
[15] Cui, Q., Li, Y.: Evaluating energy efficiency for airlines: An application of VFB-DEA..J. Air Transport Management 44 (2015), 34-41. 10.1016/j.jairtraman.2015.02.008 |
| Reference:
|
[16] Despotis, D. K.: Improving the discriminating power of DEA: focus on globally efficient units..J. Oper. Res. Soc. 53 (2002), 3, 314-323. Zbl 1103.90350, 10.1057/palgrave/jors/2601253 |
| Reference:
|
[17] Doyle, J. R., Green, R. H.: Efficiency and cross-efficiency in DEA: Derivations, meanings and uses..J. Oper. Res. Soc. 45 (1994), 5, 567-578. Zbl 0807.90016, 10.1038/sj/jors/0450509 |
| Reference:
|
[18] Doyle, J. R., Green, R. H.: Cross-evaluation in DEA: improving discrimination among DMUs..Infor 33 (1995), 3, 205-222. Zbl 0832.90002, 10.1080/03155986.1995.11732281 |
| Reference:
|
[19] 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 Sci. 42 (2008), 3, 151-157. MR 2593179, 10.1016/j.seps.2007.07.002 |
| Reference:
|
[20] Falagario, M., Sciancalepore, F., Costantino, N., Pietroforte, R.: Using a DEA-cross efficiency approach in public procurement tenders..Europ. J. Oper. Res. 218 (2012), 2, 523-529. Zbl 1244.90156, MR 2874471, 10.1016/j.ejor.2011.10.031 |
| Reference:
|
[21] Green, R. H., Doyle, J. R., Cook, W. D.: Preference voting and project ranking using DEA and cross-evaluation..Europ. J. Oper. Res. 90 (1996), 3, 461-472. Zbl 0911.90009, 10.1016/0377-2217(95)00039-9 |
| Reference:
|
[22] Jahanshahloo, G. R., Lotfi, F. H., Jafari, Y., Maddahi, R.: Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation..Appl. Math. Modelling 35 (2011), 1, 544-549. Zbl 1202.90249, MR 2677963, 10.1016/j.apm.2010.07.020 |
| Reference:
|
[23] Ji, X., Sun, J., Wang, Y., Yuan, Q.: Allocation of emission permits in large data sets: a robust multi-criteria approach..J. Cleaner Product. 142 (2017), 894-906. 10.1016/j.jclepro.2016.02.117 |
| Reference:
|
[24] Ji, X., Wu, J., Zhu, Q.: Eco-design of transportation in sustainable supply chain management: A DEA-like method..Transport. Res. Part D: Transport and Environment 48 (2016), 451-459. 10.1016/j.trd.2015.08.007 |
| Reference:
|
[25] Khouja, M.: The use of data envelopment analysis for technology selection..Computers Industr. Engrg. 28 (1995), 1, 123-132. 10.1016/0360-8352(94)00032-i |
| Reference:
|
[26] Liang, L., Wu, J., Cook, W. D., Zhu, J.: Alternative secondary goals in DEA cross-efficiency evaluation..Int. J. Product. Econom. 113 (2008), 2, 1025-1030. 10.1016/j.ijpe.2007.12.006 |
| Reference:
|
[27] Liang, L., Wu, J., Cook, W. D., Zhu, J.: The DEA game cross-efficiency model and its Nash equilibrium..Oper. Res. 56 (2008), 5, 1278-1288. Zbl 1167.91330, MR 2468913, 10.1287/opre.1070.0487 |
| Reference:
|
[28] Liang, L., Yang, F., Cook, W. D., Zhu, J.: DEA models for supply chain efficiency evaluation..Ann. Oper. Res. 145 (2006), 1, 35-49. Zbl 1106.90045, MR 2258637, 10.1007/s10479-006-0026-7 |
| Reference:
|
[29] Lim, S.: Minimax and maximin formulations of cross-efficiency in DEA..Computers Industr. Engrg. 62 (2002), 3, 726-731. 10.1016/j.cie.2011.11.010 |
| Reference:
|
[30] Lim, S., Zhu, J.: DEA cross-efficiency evaluation under variable returns to scale..J. Oper. Res. Soc. 66 (2014), 3, 476-487. MR 3362965, 10.1057/jors.2014.13 |
| Reference:
|
[31] Lim, S., Zhu, J.: DEA Cross Efficiency Under Variable Returns to Scale. In Data Envelopment Analysis..Springer US 2015. MR 3362965 |
| Reference:
|
[32] Maddahi, R., Jahanshahloo, G.J. ZhuR., Lotfi, F. Hosseinzadeh, Ebrahimnejad, A.: Optimising proportional weights as a secondary goal in DEA cross-efficiency evaluation..Int. J. Oper. Res. 19 (2014), 2, 234-245. MR 3242695, 10.1504/ijor.2014.058953 |
| Reference:
|
[33] Ramón, N., Ruiz, J.J. ZhuL., Sirvent, I.: A multiplier bound approach to assess relative efficiency in DEA without slacks..Europ. J. Oper. Res. 203 (2010), 1, 261-269. Zbl 1176.90313, 10.1016/j.ejor.2009.07.009 |
| Reference:
|
[34] Ramón, N., Ruiz, J. L., Sirvent, I.: On the choice of weights profiles in cross-efficiency evaluations..Europ. J. Oper. Res. 207 (2010), 3, 1564-1572. 10.1016/j.ejor.2010.07.022 |
| Reference:
|
[35] Ramón, N., Ruiz, J. L., Sirvent, I.: Reducing differences between profiles of weights: A "peer-restricted" cross-efficiency evaluation..Omega 39 (2011), 6, 634-641. 10.1016/j.omega.2011.01.004 |
| Reference:
|
[36] Sexton, T. R., Silkman, R. H., Hogan, A. J.: Data envelopment analysis: Critique and extensions..New Directions for Program Evaluation 1986 (1986), 32, 73-105. 10.1002/ev.1441 |
| Reference:
|
[37] Sun, J., Miao, Y., Wu, J., Cui, L., Zhong, R.: Improved interval DEA models with common weight..Kybernetika 50 (2014), 5, 774-785. Zbl 1308.90078, MR 3301860, 10.14736/kyb-2014-5-0774 |
| Reference:
|
[38] Sun, J., Wu, J., Guo, D.: Performance ranking of units considering ideal and anti-ideal DMU with common weights..Appl. Math. Modelling 37 (2013), 9, 6301-6310. MR 3039010, 10.1016/j.apm.2013.01.010 |
| Reference:
|
[39] Sun, J., Wu, J., Liang, L., Zhong, R. Y., Huang, G. Q.: Allocation of emission permits using DEA: centralised and individual points of view..Int. J. Product. Res. 52 (2014), 2, 419-435. 10.1080/00207543.2013.829592 |
| Reference:
|
[40] Sun, S.: Assessing computer numerical control machines using data envelopment analysis..Int. J. Product. Res. 40 (2002), 9, 2011-2039. Zbl 1048.90509, 10.1080/00207540210123634 |
| Reference:
|
[41] Tone, K.: A slacks-based measure of efficiency in data envelopment analysis..Europ. J. Oper. Res. 130 (2001), 3, 498-509. Zbl 0990.90523, MR 1816667, 10.1016/s0377-2217(99)00407-5 |
| Reference:
|
[42] Wang, Y. .M., Chin, K. S.: Some alternative models for DEA cross-efficiency evaluation..Int. J. Product. Econom. 128 (2010), 1, 332-338. 10.1016/j.ijpe.2010.07.032 |
| Reference:
|
[43] Wang, Y. M., Chin, K. S.: A neutral DEA model for cross-efficiency evaluation and its extension..Expert Systems Appl. 37 (2010), 5, 3666-3675. 10.1016/j.eswa.2009.10.024 |
| Reference:
|
[44] Wang, Y. M., Chin, K. S., Jiang, P.: Weight determination in the cross-efficiency evaluation..Computers Industr. Engrg. 61 (2011), 3, 497-502. 10.1016/j.cie.2011.04.004 |
| Reference:
|
[45] Wang, Y. M., Chin, K. S., Luo, Y.: Cross-efficiency evaluation based on ideal and anti-ideal decision making units..Expert Systems Appl. 38 (2011), 8, 10312-10319. 10.1016/j.eswa.2011.02.116 |
| Reference:
|
[46] Wang, Y. M., Luo, Y.: DEA efficiency assessment using ideal and anti-ideal decision making units..Appl. Math. Comput. 173 (2006), 2, 902-915. Zbl 1112.90355, MR 2207985, 10.1016/j.amc.2005.04.023 |
| Reference:
|
[47] Wu, J., Liang, L., Chen, Y.: DEA game cross-efficiency approach to Olympic rankings..Omega 37 (2009), 4, 909-918. 10.1016/j.omega.2008.07.001 |
| Reference:
|
[48] Wu, J., Liang, L., Yang, F.: Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game..Expert Systems Appl. 36 (2009), 1, 872-876. 10.1016/j.eswa.2007.10.006 |
| Reference:
|
[49] Wu, J., Sun, J., Liang, L.: Cross efficiency evaluation method based on weight-balanced data envelopment analysis model..Computers Industr. Engrg. 63 (2012), 2, 513-519. 10.1016/j.cie.2012.04.017 |
| Reference:
|
[50] Wu, J., Sun, J., Zha, Y., Liang, L.: Ranking approach of cross-efficiency based on improved TOPSIS technique..J. Systems Engrg. Electron. 22 (2011), 4, 604-608. 10.3969/j.issn.1004-4132.2011.04.008 |
| Reference:
|
[51] Zhou, P., Wang, B., Poh, K. L.: A survey of data envelopment analysis in energy and environmental studies..Europ. J. Oper. Res. 189 (2008), 1, 1-18. MR 2397682, 10.1016/j.ejor.2007.04.042 |
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