Inverse Cost Efficiency Data Envelopment Analysis with a Network Structure in the Presence of Fuzzy Data

Authors

https://doi.org/10.48314/anowa.v2i2.78

Abstract

The petrochemical industry is one of the most influential sectors in the economies of oil-producing countries, particularly Iran, as well as the global economy. To make informed managerial decisions in this field, managers must not only evaluate the past performance of organizations and identify sources of inefficiency, but also consider existing operational constraints. Subsequently, strategic objectives should be established in accordance with the macro-level policies of the industry, enabling organizations to compete effectively in the global market and move toward sustainable future development. Data Envelopment Analysis (DEA) is a powerful retrospective performance evaluation tool, whereas Inverse Data Envelopment Analysis (Inverse DEA) is a forward-looking approach capable of estimating the required input or output values while preserving efficiency. The integration of these two powerful methodologies enables managers to develop flexible and informed plans for future decision-making. Furthermore, data encountered in real-world applications are often characterized by uncertainty and imprecision; therefore, it is essential to extend conventional network DEA models to accommodate fuzzy data in order to obtain more realistic and reliable results. This study proposes a novel fuzzy arithmetic-based inverse Network Data Envelopment Analysis (NDEA) model that estimates the required input values while maintaining both the overall process efficiency and cost efficiency at constant levels. Meanwhile, output values are adjusted according to managerial preferences and organizational objectives. The proposed model is applied to a manufacturing workshop in the oil and petrochemical industry, and the results demonstrate its high effectiveness and practical applicability.

Keywords:

Two-stage network data envelopment analysis, Inverse data envelopment analysis, Cost efficiency, Fuzzy data

References

  1. [1] Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the royal statistical society series a: Statistics in society, 120(3), 253–281. https://doi.org/10.2307/2343100
  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] Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078–1092. https://doi.org/10.1287/mnsc.30.9.1078
  4. [4] Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
  5. [5] Wang, Y. M., Luo, Y., & Liang, L. (2009). Fuzzy data envelopment analysis based upon fuzzy arithmetic with an application to performance assessment of manufacturing enterprises. Expert systems with applications, 36(3), 5205–5211. https://doi.org/10.1016/j.eswa.2008.06.102
  6. [6] Kachouei, M., Ebrahimnejad, A., & Bagherzadeh-Valami, H. (2020). A common-weights approach for efficiency evaluation in fuzzy data envelopment analysis with undesirable outputs: Application in banking industry. Journal of intelligent fuzzy systems, 39(5), 7705–7722. https://doi.org/10.3233/JIFS-201022
  7. [7] Majdi, M., Ebrahimnejad, A., & Azizi, A. (2023). Common-weights fuzzy dea model in the presence of undesirable outputs with ideal and anti-ideal points: Development and prospects. Complex intelligent systems, 9(6), 6223–6240. https://doi.org/10.1007/s40747-023-01030-6%0A%0A
  8. [8] Saeedi Aval Noughabi, F., Malekmohammadi, N., Hosseinzadeh Lotfi, F., & Razavyan, S. (2022). Efficiency decomposition in two-stage network in data envelopment analysis with undesirable intermediate measures and fuzzy input and output. Fuzzy information and engineering, 14(2), 123–142. https://doi.org/10.1080/16168658.2022.2121153
  9. [9] Saeedi Aval Noughabia, F., Malekmohammadi, N., Hosseinzadeh Lotfi, F., & Razavyan, S. (2023). Efficiency decomposition in three-stage network with fuzzy desirable and undesirable output and fuzzy input in data envelopment analysis. International journal of intelligent computing and cybernetics, 16(4), 665–696. https://doi.org/10.1108/IJICC-12-2022-0306
  10. [10] Wei, Q., Zhang, J., & Zhang, X. (2000). An inverse dea model for inputs/outputs estimate. European journal of operational research, 121(1), 151–163. https://doi.org/10.1016/S0377-2217(99)00007-7
  11. [11] Yan, H., Wei, Q., & Hao, G. (2002). DEA models for resource reallocation and production input/output estimation. European journal of operational research, 136(1), 19–31. https://doi.org/10.1016/S0377-2217(01)00046-7
  12. [12] Jahanshahloo, G. R., Hosseinzadeh, F., Shoja, N., Sanei, M., & Tohidi, G. (2005). Sensitivity and stability analysis in DEA. Applied mathematics and computation, 169(2), 897–904. https://doi.org/10.1016/j.amc.2004.09.092
  13. [13] Jahanshahloo, G. R., Hadi-Vencheh, A. H., Foroughi, A. A., & Matin, R. K. (2004). Inputs/outputs estimation in DEA when some factors are undesirable. Applied mathematics and computation, 156(1), 19–32. https://doi.org/10.1016/S0096-3003(03)00814-2
  14. [14] Hadi-Vencheh, A., & Foroughi, A. A. (2006). A generalized dea model for inputs/outputs estimation. Mathematical and computer modelling, 43(5–6), 447–457. https://doi.org/10.1016/j.mcm.2005.08.005
  15. [15] Shiri Daryani, Z., & Razavyan, S. (2021). Input estimation in two-stage systems with undesirable outputs based on cost efficiency. International journal of data envelopment analysis, 9(4), 89–102. https://doi.org/10.30495/ijdea.2022.68962.1179
  16. [16] Shiri Daryani, Z., Tohidi, G., Daneshian, B., Razavyan, S., & Hosseinzadeh Lotfi, F. (2021). Inverse DEA in two-stage systems based on allocative efficiency. Journal of intelligent fuzzy systems, 40(1), 591–603. https://doi.org/10.3233/JIFS-200386
  17. [17] Kao, C., & Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in taiwan. European journal of operational research, 185(1), 418–429. https://doi.org/10.1016/j.ejor.2006.11.041
  18. [18] Zimmermann, H. J. (2011). Fuzzy set theory and its applications. Springer Science Business Media. https://www.amazon.com/Fuzzy-Set-Theory_and-Its-Applications/dp/0792374355

Downloads

Published

2026-06-29

Issue

Vol. 2 No. 2 (2026): Annals of Optimization With Applications (ANOWA)

Section

Articles

License

Copyright (c) 2026 Annals of Optimization With Applications

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Hamidi , M. ., & Malekmohammadi, N. . (2026). Inverse Cost Efficiency Data Envelopment Analysis with a Network Structure in the Presence of Fuzzy Data. Annals of Optimization With Applications, 2(2), 153-170. https://doi.org/10.48314/anowa.v2i2.78