Kybernetika 53 no. 2, 244-262, 2017

Evaluation of decision-making units based on the weight-optimized DEA model

Jiasen Sun, Rui Yang, Xiang Ji and Jie WuDOI: 10.14736/kyb-2017-2-0244

Abstract:

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.

Keywords:

efficiency, data envelopment analysis (DEA), weight-optimized model, cross evaluation

Classification:

90B50

paper.pdf

References:

  1. T. R. Anderson, K. Hollingsworth and L. Inman: The fixed weighting nature of a cross-evaluation model. J. Productivity Anal. 17 (2002), 3, 249-255.   DOI:10.1023/a:1015012121760
  2. P. Andersen and N. C. Petersen: A procedure for ranking efficient units in data envelopment analysis. Management Sci. 39 (1993), 10, 1261-1264.   DOI:10.1287/mnsc.39.10.1261
  3. R. D. Banker, A. Charnes and W. W. Cooper: 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
  4. M. L. Bougnol and J. H. Dulá: Anchor points in DEA. Europ. J. Oper. Res. 192 (2009), 2, 668-676.   DOI:10.1016/j.ejor.2007.10.034
  5. A. Boussofiane, R. G. Dyson and E. Thanassoulis: Applied data envelopment analysis. Europ. J. Oper. Res. 52 (1991), 1, 1-15.   DOI:10.1016/0377-2217(91)90331-o
  6. A. Charnes, W. W. Cooper and E. Rhodes: Measuring the efficiency of decision making units. Europ. J. Oper. Res. 2 (1978), 6, 429-444.   DOI:10.1016/0377-2217(78)90138-8
  7. C. M. Chen, M. A. Delmas and M. B. Lieberman: 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. W. D. Cook and K. Bala: 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. W. D. Cook and L. M. Seiford: Data envelopment analysis (DEA) - Thirty years on. Europ. J. Oper. Res. 192 (2009), 1, 1-17.   DOI:10.1016/j.ejor.2008.01.032
  10. W. D. Cook, K. Tone and J. Zhu: Data envelopment analysis: Prior to choosing a model. Omega 44 (2014), 1-4.   DOI:10.1016/j.omega.2013.09.004
  11. W. D. Cook and J. Zhu: DEA Cobb-Douglas frontier and cross-efficiency. J. Oper. Res. Soc. 65 (2013), 2, 265-268.   DOI:10.1057/jors.2013.13
  12. W. D. Cook and J. Zhu: DEA Cross Efficiency. In Data Envelopment Analysis. Springer US 2015.   DOI:10.1007/978-1-4899-7553-9_2
  13. W. W. Cooper, L. M. Seiford and K. Tone: 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
  14. W. W. Cooper, L. M. Seiford and J. Zhu: Data envelopment analysis. In Handbook on data envelopment analysis. Springer US 2004.   DOI:10.1007/1-4020-7798-x_1
  15. Q. Cui and Y. Li: 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. D. K. Despotis: 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
  17. J. R. Doyle and R. H. Green: 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
  18. J. R. Doyle and R. H. Green: Cross-evaluation in DEA: improving discrimination among DMUs. Infor 33 (1995), 3, 205-222.   DOI:10.1080/03155986.1995.11732281
  19. A. Emrouznejad, B. R. Parker and G. Tavares: 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
  20. M. Falagario, F. Sciancalepore, N. Costantino and R. Pietroforte: 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
  21. R. H. Green, J. R. Doyle and W. D. Cook: 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
  22. G. R. Jahanshahloo, F. H. Lotfi, Y. Jafari and R. Maddahi: 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
  23. X. Ji, J. Sun, Y. Wang and Q. Yuan: 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. X. Ji, J. Wu and Q. Zhu: 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. M. Khouja: 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. L. Liang, J. Wu, W. D. Cook and J. Zhu: 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. L. Liang, J. Wu, W. D. Cook and J. Zhu: The DEA game cross-efficiency model and its Nash equilibrium. Oper. Res. 56 (2008), 5, 1278-1288.   DOI:10.1287/opre.1070.0487
  28. L. Liang, F. Yang, W. D. Cook and J. Zhu: DEA models for supply chain efficiency evaluation. Ann. Oper. Res. 145 (2006), 1, 35-49.   DOI:10.1007/s10479-006-0026-7
  29. S. Lim: 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. S. Lim and J. Zhu: DEA cross-efficiency evaluation under variable returns to scale. J. Oper. Res. Soc. 66 (2014), 3, 476-487.   DOI:10.1057/jors.2014.13
  31. S. Lim and J. Zhu: DEA Cross Efficiency Under Variable Returns to Scale. In Data Envelopment Analysis. Springer US 2015.   CrossRef
  32. R. Maddahi, G.J. ZhuR. Jahanshahloo, F. Hosseinzadeh Lotfi and A. Ebrahimnejad: 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
  33. N. Ramón, J.J. ZhuL. Ruiz and I. Sirvent: 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
  34. N. Ramón, J. L. Ruiz and I. Sirvent: 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. N. Ramón, J. L. Ruiz and I. Sirvent: 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. T. R. Sexton, R. H. Silkman and A. J. Hogan: Data envelopment analysis: Critique and extensions. New Directions for Program Evaluation 1986 (1986), 32, 73-105.   DOI:10.1002/ev.1441
  37. J. Sun, Y. Miao, J. Wu, L. Cui and R. Zhong: Improved interval DEA models with common weight. Kybernetika 50 (2014), 5, 774-785.   DOI:10.14736/kyb-2014-5-0774
  38. J. Sun, J. Wu and D. Guo: 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
  39. J. Sun, J. Wu, L. Liang, R. Y. Zhong and G. Q. Huang: 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. S. Sun: Assessing computer numerical control machines using data envelopment analysis. Int. J. Product. Res. 40 (2002), 9, 2011-2039.   DOI:10.1080/00207540210123634
  41. K. Tone: 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
  42. Y. .M. Wang and K. S. Chin: 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. Y. M. Wang and K. S. Chin: 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. Y. M. Wang, K. S. Chin and P. Jiang: Weight determination in the cross-efficiency evaluation. Computers Industr. Engrg. 61 (2011), 3, 497-502.   DOI:10.1016/j.cie.2011.04.004
  45. Y. M. Wang, K. S. Chin and Y. Luo: 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. Y. M. Wang and Y. Luo: 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
  47. J. Wu, L. Liang and Y. Chen: DEA game cross-efficiency approach to Olympic rankings. Omega 37 (2009), 4, 909-918.   DOI:10.1016/j.omega.2008.07.001
  48. J. Wu, L. Liang and F. Yang: 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. J. Wu, J. Sun and L. Liang: 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. J. Wu, J. Sun, Y. Zha and L. Liang: 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. P. Zhou, B. Wang and K. L. Poh: 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