Efficiency score in the presence of flexible factors, integer and fuzzy integer data
الموضوعات : مجله بین المللی ریاضیات صنعتی
Zahra Moazenzadeh
1
,
Saber Saati
2
,
reza farzipoor saen
3
,
Reza Kazemi Matin
4
,
sevan sohraiee
5
1 - Mathematics Department, Tehran-North Branch, Islamic Azad University, Tehran, IRAN
2 - Dep. of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, IRAN
3 - Faculty of Business, Sohar University, Sohar, Oman
4 - Dept. of Mathematics, Islamic Azad University, Karaj, IRAN
5 - Dept. of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, IRAN
الکلمات المفتاحية: : Data Envelopment Analysis, Efficiency, Slack-Based Efficiency Measure Model, Flexible Factor, Fuzzy Integer Data, Integer Data.,
ملخص المقالة :
In traditional Data Envelopment Analysis (DEA) approaches, inputs and outputs are usually considered as exact and real values. The relative efficiency of the Decision Making Units (DMUs) is evaluated and it is known that the factors are inputs and/or outputs. However, there are some conditions under which the efficiency of DMUs should be calculated while the data are integer and ambiguous. Therefore, various integer DEA models have been proposed to determine the performance of DMUs when integer data and fuzzy factors are available. In addition, there are cases where the efficiency of DMUs should be determined when integer data and flexible factors are available. Therefore, some integer DEA methods have been proposed to calculate the performance of DMUs and specify the role of flexible measures when some of the data are integer and flexible factors are available. However, there are some situations where there are integer data, fuzzy integer measures and flexible factors. Therefore, this paper sheds light on the nature of the model to determine the efficiency of DMUs when there are integer inputs and/or outputs, flexible factors and fuzzy integer measures, and determines the role of factors with uncertain inputs or outputs. In fact, slacks are addressed and a slack-based efficiency measure (SBM) is defined to compute the performance of DMUs in the presence of flexible factors, integer data and fuzzy integer measures. The proposed approaches are demonstrated and illustrated using an example.
[1] Charnes A, Cooper W.W and Rhodes E 1978 Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 429-444.
[2] Banker R.J, Charnes A, and Cooper W.W 1984 Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science. 30 1078-1092.
[3] Cook W.D and Zhu J 2007 Classifying inputs and outputs in data envelopment analysis, Eur. J. Oper. Res. 180 692-699.
[4] Amirteimoori A, Emrouznejad A and Khoshandam L 2013 Classifying flexible measures in data envelopment analysis: A slack-based measure, Measurement, 46 4100-4107.
[5] Tohidi G and Matroud F 2017 A new non-oriented model for classifying flexible measures in DEA, J. Oper. Res. Society. 68 1019-1029.
[6] Toloo M, Allahyar M and Hanclova J 2018 A non-radial directional distance method on classifying inputs and outputs in DEA: Application to banking industry, Expert Systems with applications 92 495-506.
[7] Kordrostami S, Amirteimoori A and Noveiri M.J.S 2019 Inputs and Outputs Classification in Integer Data Envelopment Analysis. Measurement 139 317-325.
[8] Lozano S and Villa G 2006 Data envelopment analysis of integer inputs and outputs. Comput. Oper. Res. 33 3004-3014.
[9] Kuosmanen T and Matin R.K 2009 Theory of integer data envelopment analysis, Eur. J. Oper. Res. 192 658-667.
[10] Jie T, Yan Q and Xu W 2015 A technical note on “A note on integer radial model in DEA”, Computers & Industrial Engineering, 87 308-310.
[11] Due J, Chen C.M, Chen Y, Cook W.D and Zhu J 2012 Additive super-efficiency in integer data envelopment analysis, Eur. J. Oper. Res. 218 186-192.
[12] Abolghasem S, Toloo M and Amezquita S 2019 Cross-efficiency evaluation in the presence of flexible measures with an application to healthcare systems. Healthcare Manag. Sci. 22 512-513.
[13] Sedighi Hassan Kiyadeh M, Saati S and Kordrostami S 2019 Improvement of models for determination of flexible factor type in data envelopment analysis. Measurement 137 49-57.
[14] Toloo M, Bohlool E and Amin G.H.R 2021 New data envelopment analysis model for classifying flexible measures: the role of non-Archimedean epsilon. Eur. J. Oper. Res, 293(3) 1037-1050.
[15] Salehian M.V, Saati S and Sohraee S 2023 Flexible factors in categorized data for data envelopment analysis.
[16] Zadeh L.A 1965 Fuzzy sets, Inf. Control. 8 338-353.
[17] Kao C and Liu S.T 2000 Fuzzy efficiency measures in data envelopment analysis. Fyzzy Sets and Systems, 113 427-437.
[18] Hatami-Marbini A, Ebrahimnejad A and Lozano S 2017 Fuzzy efficiency measures in data envelopment analysis using lexicographic multiobjective approach, Computers & Industrial Engineering, 105 362-376.
[19] Ebrahimnejad A and Amani N 2021 Fuzzy data envelopment analysis in the presence of undesirable output with ideal points. Complex & Intelligent Systems 7 379-400.
[20] Peykani P, Hosseinzadeh Lotfi F, Sadjadi S.J, Ebrahimnejad A and Mohammadi E 2021 Fuzzy chance-constrained data envelopment analysis: A structured literature review, current trends, and future directions. Fuzzy Optimization and Decision Making, http://doi.org/10.1007/s 10700-021-09364-x.
[21] Saati S, Hatami-Marbini A, Tavana M, Agrell P 2013 A fuzzy data envelopment analysis for clustering operating units with imprecise data. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21 1:29-54.
[22] Hatami-Marbini, Saati S, and Sajadi S.M 2018 Efficiency analysis in two-stage structures using fuzzy data envelopment analysis, Central European Journal of Operations Research. 26 909-932.
[23] Kordrostami S, Farajpour G, Jahani Sayyad Noveiri M 2014 Evaluating the efficiency and classifying the fuzzy data: A DEA based approach, Int. J. Industrial Mathematics (ISSN). 6 No 4 321-327.
[24] Saati S, Imani N 2015 Classifying Flexible factors Using Fuzzy Concept, Journal of New Researches in Mathematics, 1 No 2, 35-46.
[25] Kordrostami S, Amirteimoori A and Noveiri M.J.S 2018 Fuzzy integer data envelopment analysis, RAIRO. Oper. Res. 52 1429-1444.
[26] Mirmozaffari M, Yazdani R, Shadkam E, Khalili S.M, Tavassoli L.S and Boskabadi A 2021 Anovel hybrid parametric and non-parametric optimization model for average technical efficiency assessment in public hospitals during and post-COVID-19 pandemic. Bioengineering, 27 9(1):7.
[27] Mirmozaffari M, Yazdani R, Shadkam E, Tavassoli L.S and Massah R [C] 2021 VCS and CVS: New combined parametric and non-parametric operation research models. Sustainable operations and computers, 1 2:36-56.
[28] Mirmozaffari M, Shadkam E, Khalili S.M, Yazdani M 2021 Developing a novel integrated generalized data envelopment analysis (DEA) to evaluate hospitals providing stroke care services. Bioengineering 10 8(12):207.
[29] Mirmozaffari M, Yazdani R, Shadkam E, Khalili S.M 2022 An integrated artificial intelligence model for efficiency assessment in pharmaceutical companies during the COVID-19 pandemic. Sustainable Operations and Computers, 1 3:156-67.
[30] Mirmozaffari M and Kamal N The application of Data Envelopment Analysis to Emergency Departments and Management of Emergency Conditions: A Narrative Review “Healthcare 11, no. 18:2541. http://doi.org/10.3390/healthcare11182541.
[31] Karsak E.E 2008 Using data envelopment analysis for evaluating flexible manufacturing systems in the presence of imprecise data. The International Journal of Advanced Manufacturing Technology 35: 867-74.
[32] Mirmozaffari M, Yazdani M, Boskabadi A, Ahady Dolatsara H, Kabirifar K, Amiri Golilarz N 2020 A novel machine learning approach combined with optimization models for eco-efficiency evaluation. Applied Science, 28 10(15):5210.
[33] Mirmozaffari M, Shadkam E, Khalili S.M, Kabirifar K, Yazdani R, Asgari Gashteroodkhani T 2021 A novel artificial intelligent approach: Comparison of machine learning tools and algorithms based on optimization DEA Malmquist productivity index for eco-efficiency evaluation. International journal of energy sector management, 12 15(3): 523-50.
[34] Charnes A and Cooper W.W 1962 Programming with linear fractional functionals, Naval. Research Logistics Quarterly, 9 181-186.
[35] Lai Y.J and Hwang C.L 1992 A new approach to some possibilistic linear programming problems. Fuzzy Sets Syst. 49 121-133.
