Finding the Best Performance in Non-Parametric Efficiency Analysis Techniques

Subject Areas : تحقیق در عملیات

Mohsen Mirzaei Chalakei ¹ , Atefeh Masoumzadeh ²

1 - Department of Applied Mathematics, Astaneh Ashrafieh Branch, Islamic Azad University, Astaneh Ashrafieh, Iran
2 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

Received: 2023-02-28 Accepted : 2024-03-07 Published : 2025-06-11

Keywords: Data Envelopment Analysis, Efficiency, Input/Output, Ranking, Optimally-efficient,

Abstract :

In classic data envelopment analysis (DEA) models, the best performance is the fully efficient state, which is represented by the number one, and we know from experience that more than one unit will have this efficient state. One of the most recent studies and an interesting topic of research is the distinction between the performance of fully efficient decision-making units (DMUs). Several authors studied the problem of finding an optimally efficient DMU from different perspectives. However, as far as we are aware, there is no clear description or definition of an optimal DMU. As a result, in various studies, different units are introduced as the unit with the highest efficiency. In this paper, we present a new definition for an optimally efficient DMU. For this purpose, a comparison scale was defined for each DMU, and by using this scale, a ranking method for DMUs was obtained. The application of the conducted research was verified by numerical examples.

References:

1. Ahadzadeh Namin, M., Khamseh. E., Ranking Efficient DMUs in Two-stage Network DEA with Common Weights method. Journal of New Researches in Mathematics 3 (11) (2017) 5-18.
2. Amin G.R., Comments on finding the most efficient DMUs in DEA: An improved integrated mode, Computers and Industrial Engineering, 56 (4) (2009) 1701–1702.
3. Amin G.R., Toloo M., Finding the most efficient DMUs in DEA: An improved integrated model, Computers and Industrial Engineering, 52 (2) (2007) 71–77.
4. Andersen P., Petersen N. C., A procedure for ranking efficient units in data envelopment analysis, Management Science, 39 (1993) 1261-1264.
5. Banker R. D., Chang H., The super-efficiency procedure for outlier identification, not for ranking efficient units. European Journal of Operational Research 175(2006) 1311-1320
6. Banker R.D., Charnes A., Cooper W.W., Some models for estimating technical and scale inefficiency in data envelopment analysis, Management Science, 30 (1984)1078–1092.
7. Bodaghi, Z., Ahadzadeh Namin, M., Shahverdiani, S., Analysis of Common Weighting Method in Data Envelopment Analysis Based on Customer Satisfaction of Companies Active in Tehran Stock Exchange. Financial Engineering and Portfolio Management 10 (38) (2019) 19-41.
8. Charnes A., Cooper W.W., Rhodes E., Measuring the efficiency of decision-making units, European Journal of Operational Research. 2 (1978) 429–444.
9. Ertay T., Ruan D., Tuzkaya U.R., Integrating data envelopment analysis and analytic hierarchy for the facility layout design in manufacturing systems, Information Sciences, 176 (2006) 237–262.
10. Fernandez-Castro A., Smith P., Towards a general non-parametric model of corporate performance, Omega, 22 (1994) 237-249.
11. Foroughi A. A., A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60 (2011) 550–554.
12. Foroughi A. A., A note on ‘‘A new method for ranking discovered rules from data mining by DEA and a full ranking approach’’. Expert Systems with Applications, 38 (2011) 12913–12916.
13. Ghorban Shiroudi, H., & Hosseinzadeh Lotfi, F. A model for finding the most efficient DMU in DEA. International Journal of Applied Operational Research, 8(1) (2018) 47-55.‎
14. Karsak, E. E., & Ahiska, S. S. Practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection. International Journal of Production Research, 43(8) (2005) 1537-1554.
15. Karsak, E. E., & Ahiska, S. S. Improved common weight MCDM model for technology selection. International Journal of Production Research, 46(24) (2008) 6933-6944.
16. Majdi, M., Ebrahimnejad, A. & Azizi, A. Common-weights fuzzy DEA model in the presence of undesirable outputs with ideal and anti-ideal points: development and prospects. Complex & Intelligent Systems, (2023).
17. Mohammadi, S., Mirdehghan, S. M., & Jahanshahloo, G. Finding the most preferred decision-making unit in data envelopment analysis. Advances in Operations Research, (2016) 1-8.http://dx.doi.org/10.1155/2016/7171467
18. Noori, Z., Zhiani Rezai, H., Davoodi, A., & Kordrostami, S. Finding the most efficient DMU in DEA‎: A model-free procedure. Control and Optimization in Applied Mathematics, 7(1) (2022) 15-29.
19. Pourhabib Yekta, A., Kordrostami, S., Amirteimoori, A., Kazemi Matin, R., Data envelopment analysis with common weights: the weight restriction approach. Mathematical Sciences, 12 (2018) 197–203.
20. Toloo M., Nalchigar S., A new integrated DEA model for finding most BCC-efficient DMU, Applied Mathematical Modelling, 33 (2009) 597–604.
21. Toloo M., On finding the most BCC-efficient DMU: A new integrated MIP–DEA model, Applied Mathematical Modelling, 36 (2012) 5515–5520.
22. Toloo, M., & Tavana, M. A novel method for selecting a single efficient unit in data envelopment analysis without explicit inputs/outputs. Annals of Operations Research, 253(1) (2017) 657-681.
23. Toloo, M., Nalchigar, S., & Sohrabi, B. Selecting most efficient information system projects in presence of user subjective opinions: a DEA approach. Central European Journal of Operations Research, 26(4) (2018) 1027-1051.
24. Vakili, J. Finding the most efficient decision making unit in data envelopment Analysis. Journal of New Researches in Mathematics, 2(8) (2017) 37-44.
25. Wang Y. M., Jiang P., Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis, Computers & Industrial Engineering, 62(2) (2012), 546-553.