Finding the Most Efficient Unit in Data Envelopment Analysis
محورهای موضوعی : فصلنامه ریاضی
abbas ghomashi langroudi
1
,
Masomeh abbasi maleksari
2
,
saeid shahghobadi
3
1 - Department of mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
2 - Department of Applied Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
3 - Department of Applied Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran.
کلید واژه: Data envelopment analysis, Most efficient DMU, Mixed integer linear programming, ranking, Common set of weights.,
چکیده مقاله :
In data envelopment analysis, identifying the most efficient decision-making unit (DMU) is crucial for gaining insights into efficient DMUs. Various approaches have been suggested in the literature to determine the most efficient DMU in data envelopment analysis. These approaches aim to develop a model with enhanced discriminatory ability among DMUs. This study introduces a new model based on a common set of weights approach using mixed integer linear programming to select the most efficient DMU. The proposed model ensures that the efficiency score of only one DMU (the most efficient) is strictly greater than one, while the efficiency scores of other DMUs are less than or equal to one. This model demonstrates a strong discriminatory capability, enabling the full ranking of all DMUs with fewer constraints than models that allow complete ranking. To validate the proposed model and compare its performance with recent approaches, two numerical examples from the literature are utilized.
In data envelopment analysis, identifying the most efficient decision-making unit (DMU) is crucial for gaining insights into efficient DMUs. Various approaches have been suggested in the literature to determine the most efficient DMU in data envelopment analysis. These approaches aim to develop a model with enhanced discriminatory ability among DMUs. This study introduces a new model based on a common set of weights approach using mixed integer linear programming to select the most efficient DMU. The proposed model ensures that the efficiency score of only one DMU (the most efficient) is strictly greater than one, while the efficiency scores of other DMUs are less than or equal to one. This model demonstrates a strong discriminatory capability, enabling the full ranking of all DMUs with fewer constraints than models that allow complete ranking. To validate the proposed model and compare its performance with recent approaches, two numerical examples from the literature are utilized.
1. Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European journal of operational research. 1978;2(6):429-44.
2. Dyson RG, Allen R, Camanho AS, Podinovski VV, Sarrico CS, Shale EA. Pitfalls and protocols in DEA. J European Journal of operational research. 2001;132(2):245-59.
3. Doyle J, Green R. Efficiency and cross-efficiency in DEA: Derivations, meanings and uses. Journal of the operational research society. 1994;45(5):567-78.
4. Liang L, Wu J, Cook WD, Zhu J. Alternative secondary goals in DEA cross-efficiency evaluation. International Journal of Production Economics. 2008;113(2):1025-30.
5. Wang Y-M, Chin K-S. Some alternative models for DEA cross-efficiency evaluation. International Journal of Production Economics. 2010;128(1):332-8.
6. Kiaei H. Cross-efficiency evaluation by the use of ideal and anti-ideal virtual DMUs’ assessment in DEA. International Journal of Applied Operational Research-An Open Access Journal. 2016;6(3):69-79.
7. Khodabakhshi M, Aryavash K. The cross-efficiency in the optimistic–pessimistic framework. Operational Research. 2017;17(2):619-32.
8. Hou Q, Wang M, Zhou X. Improved DEA cross efficiency evaluation method based on ideal and anti-ideal points. Discrete Dynamics in Nature Society. 2018;2018.
9. Liu H-h, Song Y-y, Yang G-l. Cross-efficiency evaluation in data envelopment analysis based on prospect theory. J European Journal of Operational Research. 2019;273(1):364-75.
10. Shi H-L, Chen S-Q, Chen L, Wang Y-M. A neutral cross-efficiency evaluation method based on interval reference points in consideration of bounded rational behavior. European Journal of Operational Research. 2021;290(3):1098-110.
11. Andersen P, Petersen NC. A procedure for ranking efficient units in data envelopment analysis. Management science. 1993;39(10):1261-4.
12. Karsak E, Ahiska S. Practical common weight multi-criteria decision-making approach with an improved discriminating power for technology selection. International Journal of Production Research. 2005;43(8):1537-54.
13. Liu F-HF, Peng HH. Ranking of units on the DEA frontier with common weights. Computers operations research. 2008;35(5):1624-37.
14. Zohrehbandian M, Makui A, Alinezhad A. A compromise solution approach for finding common weights in DEA: An improvement to Kao and Hung's approach. Journal of the Operational Research Society. 2010;61(4):604-10.
15. Jahanshahloo GR, Zohrehbandian M, Alinezhad A, Naghneh SA, Abbasian H, Mavi RK. Finding common weights based on the DM's preference information. Journal of the Operational Research Society. 2011;62(10):1796-800.
16. Sun J, Wu J, Guo D. Performance ranking of units considering ideal and anti-ideal DMU with common weights. Applied Mathematical Modelling. 2013;37(9):6301-10.
17. Lotfi FH, Hatami-Marbini A, Agrell PJ, Aghayi N, Gholami K. Allocating fixed resources and setting targets using a common-weights DEA approach. Computers Industrial Engineering. 2013;64(2):631-40.
18. Wang Q, Liu Z, Zhang Y. A novel weighting method for finding common weights in DEA. Asia-Pacific Journal of Operational Research. 2017;34(05):1750027.
19. Contreras I. A review of the literature on DEA models under common set of weights. Journal of Modelling in Management. 2020.
20. Kao C, Hung H. Data envelopment analysis with common weights: the compromise solution approach. Journal of the operational research society. 2005;56(10):1196-203.
21. Dong Y, Chen Y, Li Y. Efficiency ranking with common set of weights based on data envelopment analysis and satisfaction degree. International Journal of Information Decision Sciences. 2014;6(4):354-68.
22. Sueyoshi T. DEA non-parametric ranking test and index measurement: slack-adjusted DEA and an application to Japanese agriculture cooperatives. Omega. 1999;27(3):315-26.
23. Torgersen AM, Førsund FR, Kittelsen SA. Slack-adjusted efficiency measures and ranking of efficient units. Journal of Productivity Analysis. 1996;7(4):379-98.
24. Sinuany-Stern Z, Mehrez A, Barboy A. Academic departments efficiency via DEA. Computers Operations Research. 1994;21(5):543-56.
25. Sinuany-Stern Z, Friedman L. DEA and the discriminant analysis of ratios for ranking units. European Journal of Operational Research. 1998;111(3):470-8.
26. Amin GR, Toloo M, Sohrabi B. An improved MCDM DEA model for technology selection. International Journal of Production Research. 2006;44(13):2681-6.
27. Amin GR, Toloo M. Finding the most efficient DMUs in DEA: An improved integrated model. J Computers Industrial Engineering. 2007;52(1):71-7.
28. Toloo M, Nalchigar S. A new integrated DEA model for finding most BCC-efficient DMU. Applied Mathematical Modelling. 2009;33(1):597-604.
29. Amin GR. Comments on finding the most efficient DMUs in DEA: An improved integrated model. Computers Industrial Engineering. 2009;56(4):1701-2.
30. Toloo M, Sohrabi B, Nalchigar S. A new method for ranking discovered rules from data mining by DEA. Expert Systems with Applications. 2009;36(4):8503-8.
31. Foroughi A. A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. J Computers Industrial Engineering. 2011;60(4):550-4.
32. Wang Y-M, Jiang P. Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis. J Computers Industrial Engineering. 2012;62(2):546-53.
33. Toloo M. The most efficient unit without explicit inputs: An extended MILP-DEA model. Measurement. 2013;46(9):3628-34.
34. Toloo M. An epsilon-free approach for finding the most efficient unit in DEA. Applied Mathematical Modelling. 2014;38(13):3182-92.
35. Toloo M. Selecting and full ranking suppliers with imprecise data: A new DEA method. The International Journal of Advanced Manufacturing Technology. 2014;74(5):1141-8.
36. Toloo M. Alternative minimax model for finding the most efficient unit in data envelopment analysis. Computers Industrial Engineering. 2015;81:186-94.
37. Lam KF. In the determination of the most efficient decision making unit in data envelopment analysis. Computers Industrial Engineering. 2015;79:76-84.
38. Salahi M, Toloo M. In the determination of the most efficient decision making unit in data envelopment analysis: A comment. Computers Industrial Engineering. 2017;104:216-8.
39. Toloo M. A cost efficiency approach for strategic vendor selection problem under certain input prices assumption. Measurement. 2016;85:175-83.
40. Toloo M, Ertay T. The most cost efficient automotive vendor with price uncertainty: A new DEA approach. Measurement. 2014;52:135-44.
41. Toloo M, Salahi M. A powerful discriminative approach for selecting the most efficient unit in DEA. Computers Industrial Engineering. 2018;115:269-77.
42. Özsoy VS, Örkcü HH, Örkcü M. A simplistic approach without epsilon to choose the most efficient unit in data envelopment analysis. Expert Systems with Applications. 2021;168:114472.
43. Cooper WW, Seiford LM, Tone K. Introduction to data envelopment analysis and its uses: with DEA-solver software and references: Springer Science & Business Media; 2006.
44. Amin GR, Toloo M. A polynomial-time algorithm for finding ε in DEA models. Computers operations research. 2004;31(5):803-5.
45. Toloo M, Tichý T. Two alternative approaches for selecting performance measures in data envelopment analysis. Measurement. 2015;65:29-40.
