Advertisement

Improving the discrimination power with a new multi-criteria data envelopment model

  • Aneirson Francisco da SilvaEmail author
  • Fernando Augusto S. Marins
  • Erica Ximenes Dias
Original Research
  • 115 Downloads

Abstract

Data envelopment analysis (DEA) allows evaluation of the relative efficiencies of similar entities, known as decision making units (DMUs), which consume the same types of resources and offer similar types of products. It is known that under certain circumstances, when the number of DMUs does not meet the DEA Golden Rule, that is, this number is not sufficiently large compared to the total number of inputs and outputs, traditional DEA models often yield solutions that identify too many DMUs as efficient. In fact, this weak discrimination power and unrealistic weight distribution presented by DEA models remain a major challenge, leading to the development of models to improve this performance, such as: multiple criteria data envelopment analysis (MCDEA), bi-objective multiple criteria data envelopment analysis, goal programming approaches to solve weighted goal programming (WGP–MCDEA) and extended–MCDEA. This paper proposes a new MCDEA model which is based on goal programming, with and without super efficiency concepts, and presents test results that show its advantages over the above cited models. A set of problems from the literature and real-world applications are used in these tests. The results show that the new MCDEA model provides better discrimination of DMUs in all tested problems, and provides a weight dispersion that is statistically equal to that obtained by other MCDEA models. An additional feature of the proposed model is that it allows the identification of the input and output variables that are most important to the problem, to make it easier for the decision maker to improve the efficiency of the DMUs involved. This is very useful in practice, because in general, the available resources are scarce, so it is a further advantage of the proposed MCDEA model over the others tested.

Keywords

Data envelopment analysis Multiple criteria data envelopment analysis Discrimination power Weight dispersion Real-world applications 

Notes

Acknowledgements

This study was partially supported by the National Council for Scientific and Technological Development (CNPq-302730/2018-4; CNPq-303350/2018-0), and the São Paulo State Research Foundation (FAPESP-2018/06858-0; FAPESP-2018/14433-0).

References

  1. Adler, N., Friedman, L., & Sinuany-Stern, Z. (2002). Review of ranking methods in the data envelopment analysis context. European Journal of Operational Research, 140, 249–265.CrossRefGoogle Scholar
  2. Al-Shammari, M. (1999). A multi-criteria data envelopment analysis model for measuring the productive efficiency of hospitals. International Journal of Operations and Production Management, 19, 879–891.CrossRefGoogle Scholar
  3. Amin, G. R., & Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 1, 71–77.CrossRefGoogle Scholar
  4. Andersen, P., & Petersen, N. C. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, 1261–1264.CrossRefGoogle Scholar
  5. Anderson, T. R., Hollingsworth, K., & Inman, L. (2002). The fixed weighting nature of a cross-evaluation model. Journal of Productivity Analysis, 250, 21–35.Google Scholar
  6. Bal, H., Örkcü, H. H., & Celebioglu, S. (2008). A new method based on the dispersion of weights in data envelopment analysis. Computers & Industrial Engineering, 54, 502–512.CrossRefGoogle Scholar
  7. Bal, H., Örkcü, H. H., & Çelebioglu, S. (2010). Improving the discrimination power and weights dispersion in the data envelopment analysis. Computers and Operations Research, 37, 99–107.CrossRefGoogle Scholar
  8. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30, 1078–1092.CrossRefGoogle Scholar
  9. Banker, R. D., Charnes, A., Cooper, W. W., Swarts, J., & Thomas, D. A. (1989). An introduction to data envelopment analysis with some of its models and their uses. Research in Governmental and Non-profit Accounting, 5, 125–163.Google Scholar
  10. Bertrand, J. W. M., & Fransoo, J. C. (2002). Operations management research methodologies using quantitative modeling. International Journal of Operations and Production Management, 22, 241–264.CrossRefGoogle Scholar
  11. Carvalho, C. S. D. (2016). Inserting of the non-motorized transports in the urban planning in cities of the Metropolitan Region of the Paraíba Valley and North Coast. Doctoral thesis, Ph.D. thesis, São Paulo State University (In Portuguese), São Paulo.Google Scholar
  12. Charnes, A., & Cooper, W. W. (1962). Programming with linear fractional functional. Naval Research Logistics Quarterly, 9, 181–185.CrossRefGoogle Scholar
  13. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.CrossRefGoogle Scholar
  14. Cook, W. D., & Seiford, L. M. (2009). Data envelopment analysis (DEA)–thirty years on. European Journal of Operational Research, 92, 1–17.CrossRefGoogle Scholar
  15. Cooper, W. W., Seiford, L. M., & Tone, K. (2006). Introduction to data envelopment analysis and its uses: With DEA-solver software and references (1st ed.). New York: Springer.Google Scholar
  16. Da Silveira, J., De Mello, J., & Meza, L. (2012). Brazilian airlines efficiency evaluation using a data envelopment analysis (DEA) and multiobjective linear programming hybrid model. Ingeniare, 20(3), 331–342.Google Scholar
  17. De Andrade, R. M., Lee, S., Lee, P. T.-W., Kwon, O. K., & Chung, H. M. (2019). Port efficiency incorporating service measurement variables by the bio-MCDEA: Brazilian case. Sustainability, 11, 4340.CrossRefGoogle Scholar
  18. De Mello, J., Clímaco, J., & Meza, L. (2009). Efficiency evaluation of a small number of DMUs: An approach based on li and reeves’s model. Pesquisa Operacional, 29(1), 97–110.CrossRefGoogle Scholar
  19. Dimitrov, S., & Sutton, W. (2010). Promoting symmetric weight selection in data envelopment analysis: A penalty function approach. European Journal of Operational Research, 200, 281–288.CrossRefGoogle Scholar
  20. Ghasemi, M. R., Ignatius, J., & Emrouznejad, A. (2014). A bi-objective weighted model for improving the discrimination power in MCDEA. European Journal of Operational Research, 233, 640–650.CrossRefGoogle Scholar
  21. Hatami-Marbini, A., & Toloo, M. (2017). An extended multiple criteria data envelopment analysis model. Expert Systems with Applications, 73, 201–209.CrossRefGoogle Scholar
  22. Hillier, F. S., & Lieberman, (2014). Introduction to operations research (10th ed.). New York: The McGraw-Hill Companies Inc.Google Scholar
  23. Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G., & Razavyan, S. (2005). Undesirable inputs and outputs in DEA models. Applied Mathematics and Computation, 166, 917–925.CrossRefGoogle Scholar
  24. Kordrostami, S., & Mirmousavi, A. (2013). A new method for improving the discrimination power and weights dispersion in the data envelopment analysis. Journal of Mathematical Extension, 7, 49–65.Google Scholar
  25. Li, X.-B., & Reeves, G. R. A. (1999). Multiple criteria approach to data envelopment analysis. European Journal of Operational Research, 115, 507–517.CrossRefGoogle Scholar
  26. Li, Y., Abtahi, A.-R., & Seyedan, M. (2019). Supply chain performance evaluation using fuzzy network data envelopment analysis: A case study in automotive industry. Annals of Operations Research, 275, 461–484.CrossRefGoogle Scholar
  27. Lin, R., & Liu, Y. (2019). Super-efficiency based on the directional distance function in the presence of negative data. Omega, 85, 26–34.CrossRefGoogle Scholar
  28. Moheb-Alizadeh, H., & Handfield, R. (2018). An integrated chance-constrained stochastic model for efficient and sustainable supplier selection and order allocation. International Journal of Production Research, 56, 6890–6916.CrossRefGoogle Scholar
  29. Moheb-Alizadeh, H., Rasouli, S., & Tavakkoli-Moghaddam, R. (2011). The use of multi-criteria data envelopment analysis (MCDEA) for location-allocation problems in a fuzzy environment. International Journal of Production Research, 38, 5687–5695.Google Scholar
  30. Nallusamy, S. (2016). Enhancement of productivity and efficiency of cnc machines in a small scale industry using total productive maintenance. International Journal of Engineering Research in Africa, 25, 119–126.CrossRefGoogle Scholar
  31. Nordstokke, D. W., & Zumbo, B. D. (2010). A new nonparametric levene test for equal variances. Psicológica, 31, 401–430.Google Scholar
  32. Omrani, H., Adabi, F., & Adabi, N. (2017). Designing an efficient supply chain network with uncertain data: A robust optimization–data envelopment analysis approach. Journal of the Operational Research Society, 68, 816–828.CrossRefGoogle Scholar
  33. Örkcü, H. H., & Bal, H. (2011). Goal programming approaches for data envelopment analysis cross efficiency evaluation. Applied Mathematics and Computation, 218, 346–356.CrossRefGoogle Scholar
  34. Pereira, D. S., Brandão, L. C., & De Mello, J. C. C. B. S. (2019). Efficiency assessment of central Airports in Brazil. Revista Investigacion Operacional, 40, 432–440.Google Scholar
  35. Rani, R., Ismail, W., & Nordin, W. (2015). Pemilihan gabungan produk menggunakan simulasi berkomputer dan analisis penyampulan data. Jurnal Teknologi, 75(1), 83–90.Google Scholar
  36. Razipour-GhalehJough, S., Lotfi, F. H., Jahanshahloo, G., Rostamy-malkhalifeh, M., & Sharafi, H. (2019). Finding closest target for bank branches in the presence of weight restrictions using data envelopment analysis. Annals of Operations Research, 1, 1–33.Google Scholar
  37. Rubem, A. P. S., Soares de Mello, J. C. C. B., & Meza, L. A. (2017). A goal programming approach to solve the multiple criteria DEA model. European Journal of Operational Research, 260, 134–139.CrossRefGoogle Scholar
  38. San Cristóbal, J. M. (2011). A multi criteria data envelopment analysis model to evaluate the efficiency of the renewable energy technologies. Renewable Energy, 36, 2742–2746.CrossRefGoogle Scholar
  39. Sheikhalishahi, M. (2014). An integrated simulation-data envelopment analysis approach for maintenance activities planning. International Journal of Computer Integrated Manufacturing, 27, 858–868.CrossRefGoogle Scholar
  40. Sheikhalishahi, M., Azadeh, A., Firoozi, M., & Khalili, S. (2013). An integrated multi-criteria Taguchi computer simulation-DEA approach for optimum maintenance policy and planning by incorporating learning effects. International Journal of Production Research, 51, 5374–5385.CrossRefGoogle Scholar
  41. Silva, A. F., Marins, F. A. S., Dias, E. X., & Tamura, P. M. (2017). Bi-objective multiple criteria data envelopment analysis combined with the overall equipment effectiveness: An application in an automotive company. Journal of Cleaner Production, 157, 278–288.CrossRefGoogle Scholar
  42. Vakili, J., Amirmoshiri, H., Shiraz, R. K., & Fukuyama, H. (2019). A modified distance friction minimization approach in data envelopment analysis. Annals of Operations Research, 1, 1–16.Google Scholar
  43. Verma, M., Mukherjee, V., & Yadav, V. (2016). Greenfield distribution network expansion strategy with hierarchical GA and MCDEA under uncertainty. International Journal of Electrical Power & Energy Systems, 79, 245–252.Google Scholar
  44. Verma, M. K., Yadav, V. K., Mukherjee, V., & Ghosh, S. (2019). A multi-criteria approach for distribution network expansion through pooled MCDEA and Shannon entropy. International Journal of Emerging Electric Power System, 1, 0043.Google Scholar
  45. Yadav, V. K., Singh, K., & Gupta, S. (2019). Market-oriented transmission expansion planning using non-linear programming and multi-criteria data envelopment analysis. Sustainable Energy, Grids and Networks, 19, 100234.CrossRefGoogle Scholar
  46. Zaim, S., Bayyurt, N., Turkyilmaz, A., Solakoglu, N., & Zaim, H. (2007). Measuring and evaluating efficiency of hospitals through total quality management: A multi-criteria data envelopment analysis model. Journal of Transnational Management, 12(4), 77–97.CrossRefGoogle Scholar
  47. Zhao, M.-H., Cheng, C.-T., Chau, K.-W., & Li, G. (2006). Multiple criteria data envelopment analysis for full ranking units associated to environment impact assessmention. International Journal of Environment and Pollution, 28, 448–464.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of ProductionSão Paulo State UniversitySão PauloBrazil

Personalised recommendations