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Keywords:
data envelopment analysis (DEA); efficiency; weight-optimized model; cross evaluation
Summary:
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.
References:
[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. DOI 10.1023/a:1015012121760
[2] Andersen, P., Petersen, N. C.: A procedure for ranking efficient units in data envelopment analysis. Management Sci. 39 (1993), 10, 1261-1264. DOI 10.1287/mnsc.39.10.1261 | Zbl 0800.90096
[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. DOI 10.1287/mnsc.30.9.1078 | Zbl 0552.90055
[4] Bougnol, M. L., Dulá, J. H.: Anchor points in DEA. Europ. J. Oper. Res. 192 (2009), 2, 668-676. DOI 10.1016/j.ejor.2007.10.034 | MR 2454796 | Zbl 1157.90435
[5] Boussofiane, A., Dyson, R. G., Thanassoulis, E.: Applied data envelopment analysis. Europ. J. Oper. Res. 52 (1991), 1, 1-15. DOI 10.1016/0377-2217(91)90331-o
[6] Charnes, A., Cooper, W. W., Rhodes, E.: Measuring the efficiency of decision making units. Europ. J. Oper. Res. 2 (1978), 6, 429-444. DOI 10.1016/0377-2217(78)90138-8 | MR 0525905 | Zbl 0425.90086
[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. DOI 10.1002/smj.2199
[8] Cook, W. D., Bala, K.: Performance measurement and classification data in DEA: input-oriented model. Omega 35 (2007), 1, 39-52. DOI 10.1016/j.omega.2005.02.002
[9] Cook, W. D., Seiford, L. M.: Data envelopment analysis (DEA) - Thirty years on. Europ. J. Oper. Res. 192 (2009), 1, 1-17. DOI 10.1016/j.ejor.2008.01.032 | MR 2458453 | Zbl 1180.90151
[10] Cook, W. D., Tone, K., Zhu, J.: Data envelopment analysis: Prior to choosing a model. Omega 44 (2014), 1-4. DOI 10.1016/j.omega.2013.09.004
[11] Cook, W. D., Zhu, J.: DEA Cobb-Douglas frontier and cross-efficiency. J. Oper. Res. Soc. 65 (2013), 2, 265-268. DOI 10.1057/jors.2013.13
[12] Cook, W. D., Zhu, J.: DEA Cross Efficiency. In Data Envelopment Analysis. Springer US 2015. DOI 10.1007/978-1-4899-7553-9_2 | MR 3362964
[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. DOI 10.1007/978-0-387-45283-8 | Zbl 1111.90001
[14] Cooper, W. W., Seiford, L. M., Zhu, J.: Data envelopment analysis. In Handbook on data envelopment analysis. Springer US 2004. DOI 10.1007/1-4020-7798-x_1 | MR 2077628
[15] Cui, Q., Li, Y.: Evaluating energy efficiency for airlines: An application of VFB-DEA. J. Air Transport Management 44 (2015), 34-41. DOI 10.1016/j.jairtraman.2015.02.008
[16] Despotis, D. K.: Improving the discriminating power of DEA: focus on globally efficient units. J. Oper. Res. Soc. 53 (2002), 3, 314-323. DOI 10.1057/palgrave/jors/2601253 | Zbl 1103.90350
[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. DOI 10.1038/sj/jors/0450509 | Zbl 0807.90016
[18] Doyle, J. R., Green, R. H.: Cross-evaluation in DEA: improving discrimination among DMUs. Infor 33 (1995), 3, 205-222. DOI 10.1080/03155986.1995.11732281 | Zbl 0832.90002
[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. DOI 10.1016/j.seps.2007.07.002 | MR 2593179
[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. DOI 10.1016/j.ejor.2011.10.031 | MR 2874471 | Zbl 1244.90156
[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. DOI 10.1016/0377-2217(95)00039-9 | Zbl 0911.90009
[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. DOI 10.1016/j.apm.2010.07.020 | MR 2677963 | Zbl 1202.90249
[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. DOI 10.1016/j.jclepro.2016.02.117
[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. DOI 10.1016/j.trd.2015.08.007
[25] Khouja, M.: The use of data envelopment analysis for technology selection. Computers Industr. Engrg. 28 (1995), 1, 123-132. DOI 10.1016/0360-8352(94)00032-i
[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. DOI 10.1016/j.ijpe.2007.12.006
[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. DOI 10.1287/opre.1070.0487 | MR 2468913 | Zbl 1167.91330
[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. DOI 10.1007/s10479-006-0026-7 | MR 2258637 | Zbl 1106.90045
[29] Lim, S.: Minimax and maximin formulations of cross-efficiency in DEA. Computers Industr. Engrg. 62 (2002), 3, 726-731. DOI 10.1016/j.cie.2011.11.010
[30] Lim, S., Zhu, J.: DEA cross-efficiency evaluation under variable returns to scale. J. Oper. Res. Soc. 66 (2014), 3, 476-487. DOI 10.1057/jors.2014.13 | MR 3362965
[31] Lim, S., Zhu, J.: DEA Cross Efficiency Under Variable Returns to Scale. In Data Envelopment Analysis. Springer US 2015. MR 3362965
[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. DOI 10.1504/ijor.2014.058953 | MR 3242695
[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. DOI 10.1016/j.ejor.2009.07.009 | Zbl 1176.90313
[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. DOI 10.1016/j.ejor.2010.07.022
[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. DOI 10.1016/j.omega.2011.01.004
[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. DOI 10.1002/ev.1441
[37] Sun, J., Miao, Y., Wu, J., Cui, L., Zhong, R.: Improved interval DEA models with common weight. Kybernetika 50 (2014), 5, 774-785. DOI 10.14736/kyb-2014-5-0774 | MR 3301860 | Zbl 1308.90078
[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. DOI 10.1016/j.apm.2013.01.010 | MR 3039010
[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. DOI 10.1080/00207543.2013.829592
[40] Sun, S.: Assessing computer numerical control machines using data envelopment analysis. Int. J. Product. Res. 40 (2002), 9, 2011-2039. DOI 10.1080/00207540210123634 | Zbl 1048.90509
[41] Tone, K.: A slacks-based measure of efficiency in data envelopment analysis. Europ. J. Oper. Res. 130 (2001), 3, 498-509. DOI 10.1016/s0377-2217(99)00407-5 | MR 1816667 | Zbl 0990.90523
[42] Wang, Y. .M., Chin, K. S.: Some alternative models for DEA cross-efficiency evaluation. Int. J. Product. Econom. 128 (2010), 1, 332-338. DOI 10.1016/j.ijpe.2010.07.032
[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. DOI 10.1016/j.eswa.2009.10.024
[44] Wang, Y. M., Chin, K. S., Jiang, P.: Weight determination in the cross-efficiency evaluation. Computers Industr. Engrg. 61 (2011), 3, 497-502. DOI 10.1016/j.cie.2011.04.004
[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. DOI 10.1016/j.eswa.2011.02.116
[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. DOI 10.1016/j.amc.2005.04.023 | MR 2207985 | Zbl 1112.90355
[47] Wu, J., Liang, L., Chen, Y.: DEA game cross-efficiency approach to Olympic rankings. Omega 37 (2009), 4, 909-918. DOI 10.1016/j.omega.2008.07.001
[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. DOI 10.1016/j.eswa.2007.10.006
[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. DOI 10.1016/j.cie.2012.04.017
[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. DOI 10.3969/j.issn.1004-4132.2011.04.008
[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. DOI 10.1016/j.ejor.2007.04.042 | MR 2397682
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