A Modified Model to Find the Most Efficient Decision-Making Unit

Authors

  • Abbas Ghomashi Department of Mathematics‎, Ker.C., Islamic Azad‎ ‎University, ‎Kermanshah, ‎Iran.
  • Masoumeh Abbasi * Department of Mathematics‎, Ker.C., Islamic Azad‎ ‎University, ‎Kermanshah, ‎Iran.
  • Saeid Shahghobadi Department of Mathematics‎, Ker.C., Islamic Azad‎ ‎University, ‎Kermanshah, ‎Iran.

https://doi.org/10.48314/anowa.v1i4.60

Abstract

The use of Data-Envelopment Analysis (DEA) to determine the most efficient Decision Making Unit (DMU) has drawn attention in the literature. For some applications of DEA, decision-makers may only want to identify the most efficient DMU rather than determining the efficiencies of all possible DMUs. In this study, we present an modified model based on model in Özsoy et al. [1], A simplistic approach without epsilon to choose the most efficient unit in DEA. Expert systems with applications, 2021. 168: p. 114472] to identify the most efficient DMU. The proposed model with low complexity respect to model in [1] find only one DMU with an efficiency score greater than one, while all others receive scores strictly less than one. This structure enhances the model’s ability to fully rank all units. To demonstrate its effectiveness and compare it with two well-known models, the proposed model is applied to two real-world examples from the literature. The results show the appropriate performance of the proposed model in identifying the most efficient units and full ranking of the units.

Keywords:

Data envelopment analysis, Most efficient decision making unit, Mixed integer linear programming, Ranking

References

  1. [1] Özsoy, V. S., Örkcü, H. H., & Örkcü, M. (2021). A simplistic approach without epsilon to choose the most efficient unit in data envelopment analysis. Expert systems with applications, 168, 114472. https://doi.org/10.1016/j.eswa.2020.114472
  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] Karsak, E. E., & Ahiska, S. S. (2005). Practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection. International journal of production research, 43(8), 1537-1554. https://doi.org/10.1080/13528160412331326478
  4. [4] Amin, G. R., Toloo, M., & Sohrabi, B. (2006). An improved MCDM DEA model for technology selection. International journal of production research, 44(13), 2681-2686. https://doi.org/10.1080/00207540500472754
  5. [5] Amin, G. R., & Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & industrial engineering, 52(1), 71-77. https://doi.org/10.1016/j.cie.2006.10.003
  6. [6] Toloo, M., & Nalchigar, S. (2011). On ranking discovered rules of data mining by data envelopment analysis: Some new models with applications. In New fundamental technologies in data mining, (pp. 425–446). IntechOpen. https://B2n.ir/tz6046
  7. [7] Amin, G. R. (2009). Comments on finding the most efficient DMUs in DEA: An improved integrated model. Computers & industrial engineering, 56(4), 1701-1702. https://doi.org/10.1016/j.cie.2008.07.014
  8. [8] Toloo, M., Sohrabi, B., & Nalchigar, S. (2009). A new method for ranking discovered rules from data mining by DEA. Expert systems with applications, 36(4), 8503-8508. https://doi.org/10.1016/j.eswa.2008.10.038
  9. [9] Toloo, M., & Nalchigar, S. (2009). A new integrated DEA model for finding most BCC-efficient DMU. Applied mathematical modelling, 33(1), 597-604. https://doi.org/10.1016/j.apm.2008.02.001
  10. [10] Foroughi, A. A. (2011). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers & industrial engineering, 60(4), 550-554. https://doi.org/10.1016/j.cie.2010.12.012
  11. [11] Wang, Y. M., & Jiang, P. (2012). Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis. Computers & industrial engineering, 62(2), 546-553. https://doi.org/10.1016/j.cie.2011.11.003
  12. [12] Toloo, M. (2013). The most efficient unit without explicit inputs: An extended MILP-DEA model. Measurement, 46(9), 3628-3634. https://doi.org/10.1016/j.measurement.2013.06.030
  13. [13] Toloo, M. (2014). An epsilon-free approach for finding the most efficient unit in DEA. Applied mathematical modelling, 38(13), 3182-3192. https://doi.org/10.1016/j.apm.2013.11.028
  14. [14] Toloo, M. (2014). Selecting and full ranking suppliers with imprecise data: A new DEA method. The international journal of advanced manufacturing technology, 74(5), 1141-1148. https://doi.org/10.1007/s00170-014-6035-9
  15. [15] Toloo, M. (2015). Alternative minimax model for finding the most efficient unit in data envelopment analysis. Computers & industrial engineering, 81, 186-194. https://doi.org/10.1016/j.cie.2014.12.032
  16. [16] Lam, K. F. (2015). In the determination of the most efficient decision making unit in data envelopment analysis. Computers & industrial engineering, 79, 76-84. https://doi.org/10.1016/j.cie.2014.10.027
  17. [17] Salahi, M., & Toloo, M. (2017). In the determination of the most efficient decision making unit in data envelopment analysis: A comment. Computers & industrial engineering, 104, 216-218. https://doi.org/10.1016/j.cie.2016.12.032
  18. [18] Toloo, M. (2016). A cost efficiency approach for strategic vendor selection problem under certain input prices assumption. Measurement, 85, 175-183. https://doi.org/10.1016/j.measurement.2016.02.010
  19. [19] Toloo, M., & Ertay, T. (2014). The most cost efficient automotive vendor with price uncertainty: A new DEA approach. Measurement, 52, 135-144. https://doi.org/10.1016/j.measurement.2014.03.002
  20. [20] Toloo, M., & Salahi, M. (2018). A powerful discriminative approach for selecting the most efficient unit in DEA. Computers & industrial engineering, 115, 269-277. https://doi.org/10.1016/j.cie.2017.11.011
  21. [21] Ebrahimi, B., Fischer, S., & Milovancevic, M. (2024). An improved mixed-integer DEA approach to determine the most efficient unit. Optimality, 1(2), 224-231. https://doi.org/10.22105/opt.v1i2.59
  22. [22] Noori, Z., Rezai, H. Z., Davoodi, A., & Kordrostami, S. (2024). The relationship between extreme efficient and most efficient unit (s) in data envelopment analysis. Journal of mathematical extension, 18(8), 1–18. https://doi.org/10.30495/JME.2024.3025
  23. [23] Sueyoshi, T. (1999). DEA non-parametric ranking test and index measurement: Slack-adjusted DEA and an application to Japanese agriculture cooperatives. Omega, 27(3), 315-326. https://doi.org/10.1016/S0305-0483(98)00057-7
  24. [24] Ertay, T., Ruan, D., & Tuzkaya, U. R. (2006). Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems. Information sciences, 176(3), 237-262. https://doi.org/10.1016/j.ins.2004.12.001

Downloads

Published

2025-12-08

Issue

Vol. 1 No. 4 (2025): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

Ghomashi, A. ., Abbasi, M. ., & Shahghobadi, S. . (2025). A Modified Model to Find the Most Efficient Decision-Making Unit. Annals of Optimization With Applications, 1(4), 234-240. https://doi.org/10.48314/anowa.v1i4.60

Similar Articles

11-17 of 17

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