Radial Models for Classifying Flexible Measures in Two-Stage Network DEA-RA

Authors

https://doi.org/10.22105/raise.v1i3.60

Abstract

In conventional Data Envelopment Analysis (DEA) models it has been assumed that each measure status is considered input or output. However, a performance measure in some cases can have input role for some DMUs and output role for others and is known as flexible measure. In this paper new radial FNDEA-R models are proposed in the presence of flexible measures based on the ratio of input components to output components or vice versa in the input and output orientation under constant returns to scale in general two-stage network. In our proposed models, flexible measures are determined as input or output to improve performance to maximize the relative efficiency of the DMU under evaluation. The FNDEA-R models versus FNDEA models prevent efficiency underestimation and pseudo inefficiency issues. The status of one flexible measure in the input-oriented and output-oriented FNDEA-R models may have different conclusions. The radial FNDEA and FNDEA-R models have units-invariant. A numerical example is used to illustrate the procedures.

Keywords:

Data envelopment analysis, Flexible measures, Ratio analysis, Radial models, General two-stage network

References

  1. [1] Cook, W. D., & Zhu, J. (2007). Classifying inputs and outputs in data envelopment analysis. European journal of operational research, 180(2), 692–699. https://doi.org/10.1016/j.ejor.2006.03.048

  2. [2] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444. https://doi.org/10.1016/0377-2217(78)90138-8

  3. [3] Amirteimoori, A., & Emrouznejad, A. (2011). Flexible measures in production process: A DEA-based approach. RAIRO-operations research, 45(1), 63–74. https://doi.org/10.1051/ro/2011103

  4. [4] Toloo, M. (2009). On classifying inputs and outputs in DEA: A revised model. European journal of operational research, 198(1), 358–360. https://doi.org/10.1016/j.ejor.2008.08.017

  5. [5] Kordrostami, S., & Noveiri, M. J. S. (2012). Evaluating the efficiency of decision making units in the presence of flexible and negative data. Indian journal of science and technology, 5(12), 3776–3782. https://sciresol.s3.us-east-2.amazonaws.com/IJST/Articles/2012/Issue-12/Article14.pdf

  6. [6] Tohidi, G., & Matroud, F. (2017). A new non-oriented model for classifying flexible measures in DEA. Journal of the operational research society, 68(9), 1019–1029. https://doi.org/10.1057/s41274-017-0207-6

  7. [7] Tavana, M., Izadikhah, M., Toloo, M., & Roostaee, R. (2021). A new non-radial directional distance model for data envelopment analysis problems with negative and flexible measures. Omega, 102, 102355. https://doi.org/10.1016/j.omega.2020.102355

  8. [8] Jahani Sayyad Noveiri, M., Kordrostami, S., & Lozano, S. (2024). Assessing sustainability indicators using inverse integer-valued data envelopment analysis with undesirable outputs. Environment, development and sustainability, 1–30. https://doi.org/10.1007/s10668-024-05043-0

  9. [9] Monfared, S. N. H., Lotfi, F. H., Mozaffari, M. R., & Malkhalifeh, M. R. (2021). Radial models for classifying flexible measures in two-stage network dea. Progress in intelligent decision science: proceeding of ids 2020 (pp. 483–500). Springer Nature. https://doi.org/10.1007/978-3-030-66501-2_38

  10. [10] Hosseini Monfared, S. N., Mozaffari, M. R., & Rostami-Malkhslifrh, M. (2022). Classifying flexible measures in two-stage network DEA. International journal of industrial mathematics, 14(3), p305. https://B2n.ir/xy7511

  11. [11] Hatami-Marbini, A., & Toloo, M. (2019). Data envelopment analysis models with ratio data: A revisit. Computers & industrial engineering, 133, 331–338. https://doi.org/10.1016/j.cie.2019.04.041

  12. [12] Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: Convexity consideration. Applied mathematical modelling, 33(1), 486–498. https://doi.org/10.1016/j.apm.2007.11.018

  13. [13] Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2015). Efficiency analysis with ratio measures. European journal of operational research, 245(2), 446–462. https://doi.org/10.1016/j.ejor.2015.03.013

  14. [14] Despić, O., Despić, M., & Paradi, J. C. (2007). DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of productivity analysis, 28(1), 33–44. https://doi.org/10.1007/s11123-007-0050-x

  15. [15] Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). A study of developing an input-oriented ratio-based comparative efficiency model. Expert systems with applications, 38(3), 2473–2477. https://doi.org/10.1016/j.eswa.2010.08.036

  16. [16] Mozaffari, M. R., Gerami, J., & Jablonsky, J. (2014). Relationship between DEA models without explicit inputs and DEA-R models. Central european journal of operations research, 22, 1–12. https://doi.org/10.1007/s10100-012-0273-4

  17. [17] Mozaffari, M. R., Kamyab, P., Jablonsky, J., & Gerami, J. (2014). Cost and revenue efficiency in DEA-R models. Computers & industrial engineering, 78, 188–194. https://doi.org/10.1016/j.cie.2014.10.001

  18. [18] Gerami, J., Mozaffari, M. R., & Wanke, P. F. (2020). A multi-criteria ratio-based approach for two-stage data envelopment analysis. Expert systems with applications, 158, 113508. https://doi.org/10.1016/j.eswa.2020.113508

  19. [19] Gerami, J., Mozaffari, M. R., Wanke, P. F., & Correa, H. (2022). A novel slacks-based model for efficiency and super-efficiency in DEA-R. Operational research, 22(10), 1–38. https://doi.org/10.1007/s12351-021-00679-6

  20. [20] Ghiyasi, M., Soltanifar, M., & Sharafi, H. (2022). A novel inverse DEA-R model with application in hospital efficiency. Socio-economic planning sciences, 84, 101427. https://doi.org/10.1016/j.seps.2022.101427

Published

2024-09-26

How to Cite

Radial Models for Classifying Flexible Measures in Two-Stage Network DEA-RA. (2024). Research Annals of Industrial and Systems Engineering, 1(3), 192-204. https://doi.org/10.22105/raise.v1i3.60

Similar Articles

1-10 of 24

You may also start an advanced similarity search for this article.