Resource Allocation in Data Envelopment Analysis on Fuzzy inputs and outputs

Subject Areas : تحقیق در عملیات

Esmat  Noroozi ¹ (Department of Mathematics, East Tehran Branch, Islamic Azad University, Tehran, Iran)
Hamid  SHarafi ² (Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)

Received: 2022-02-15 Accepted : 2022-11-30 Published : 2023-07-23

Keywords: نظریه فازی, واحد تصمیم‌گیری, تحلیل پوششی داده‌ها, کارایی, تخصیص,

Abstract :

Abstract: Data envelopment analysis technique is used to evaluate the relative efficiency of a set of decision-making units that have been studied in different fields. One of the important issues in data envelopment analysis is sensitivity analysis. Many articles have been presented in this field by researchers, sometimes managers are concentrating on issues that would be critical to allocate a fixed cost to decision-making units. Since in real problems the primary data are not precise but interval, ordinal, and qualitative therefore this study have been discussed this issue and present a model for assigning a fuzzy fixed cost to decision-making units. Moreover, the inputs and outputs of all units are assumed to be fuzzy and the allocation of new costs should be such that the highest number of inefficient units become efficient. At the end, this model has been utilized in two numerical examples and the results have been presented.

References:

[1] Allahviranloo. T, HosseinzadehLotfi. F, Firozja. AM,"Fuzzy Efficiency Measure with Fuzzy Production Possibility Set". Applications and Applied Mathematics; 2(2): (2007), 152–66.

 

[2] Allahviranloo. T, Hosseinzadeh Lotfi.F,. Kiasary. M. Kh,. Kiani. N. A, Alizadeh L,"Solvingfully fuzzy linear programming problem by ranking function"; Applied MathematicalSciences, Vol. 2, ,( 2008),  pp. 19-32.

 

[3] Bellman.R.E, Zadeh. L.A; "Decision making in a fuzzy environment", Management Science, Vol. 17, (1970), pp. 141-164.

 

[4] Banker. R D, Charnes.A, and Cooper. W W, "Some model for estimating technical and scale inefficiencies in data envelopment analysis", Manage. Sci.30, (1984), 1078-1092.

 

[5] Charnes.A, Cooper .W W, Rhodes .E, "Measuring the efficiency of decision making units". European Journal of Operational Research 2 (6), (1978), 429–444.

 

[6] Dehghan. M, Hashemi. B, Ghatee. M, "Computational methods for solving fully fuzzylinear ystems"; Applied Mathematics and Computation, Vol. 179, (2006), pp. 328-343.

 

[7] HosseinzadehLotfi.F,Jahanshahloo. GR, Alimardani. M, A New approach forefficiency measures by fuzzy linear programming and application in insurance, .Applied Mathematics and Computation160 ,(2006), 719–724.

 

[8] HosseinzadehLotfi.F,Jahanshahloo. GR, Allahviranloo. T, Noroozi. E, Hosseinzadeh Lotfi. A. AEquitable Allocation of Shared Costs on Fuzzy Environment, International Mathematical Forum, 2, no. 65, (2007), 3199 – 3210.

 

[9] HosseinzadehLotfi. F, Allahviranloo .T, Jondabeh. M.A, Alizadeh, L,"Solving a full fuzzylinear programming using lexicography method and fuzzy approximate solution"; Applied Mathematical Modelling, Vol. 33,( 2009), pp. 3151-3156.

 

[10] HosseinzadehLotfi. F, Noora. A.A, Jahanshahloo. GR, Gerami. J, Mozaffari. M.R, Centralized resource allocation for enhanced Russell models. Journal of Computational and Applied Mathematics 235, (2010), 1-10.

 

[11] Jahanshahloo. GR, Amirteimoori. A.R , Kordrostami. S, Detarmining an equitable allocation of new inputs and new output in DEA, Journal of the Operations Research Society of Japan 46 (1) , ( 2003), 66–73.

 

[12] Jahanshahloo. GR, Shoja. N , Sanei, .M , An alternative approach for equitable allocation of shared costs by using DEA. Applied Mathematics and Computation, 153, (2004), 267–274.

 

[13] Jahanshahloo. GR, Hosseinzadeh Lotfi.F , Shoja. N , Tohidi. G , Razavyan. S, A one-model approach to classification and sensitivity analysis in DEA. Applied Mathematics and Computation, 169, (2005), 887-896.

 

[14] HosseinzadehLotfi.F,Jahanshahloo. GR, Moradi. M, A DEA approach for fair allocation of common revenue. Applied Mathematics and Computation 160 (2005), 719–724.

 

[15] Kumar. A, Kaur. J ,Singh. P ,"Fuzzy optimal solution of fully fuzzy linearprogramming problems with inequality constraints"; International Journal ofMathematical and Computer Sciences, 61 ,(2010),  pp. 37-41.

 

[16] Kumar. A, Kaur. J, Singh. P ,"A new method for solving fully fuzzy linear programming problems"; Applied Mathematical Modelling, Vol. 35 ,(2011), pp. 817-823.

 

[17].Kazemi. A, Alimi. A, "A fully fuzzy approach to data envelopment analysis", Journal of mathematics and computer science 11,( 2014), 238-245.

 

[18] Momeni. M. .Hosseinzadeh .M, "A new method for solving fully fuzzy linearprogramming problems using fuzzy ranking concept", Journal of Management Research in Iran, Vol. 16, (2013), pp. 171-188.

 

[19] Sharafi. H, Hosseinzadeh Lotfi. F, Jahanshahloo. G.R, Rostamy-Malkhalifeh. M, Soltanifar. M, Razipour-Ghalehjough. S," Ranking Decision Making Units in the Presence of Fuzzy Data Using Cross Efficiency Method", Iranian Data Envelopment Analysis Society, May, (2018), 9-11.

 

[20] Steuer. R. E,"Multiple criteria optimization: Theory, computation, and application", New York: Wiley, (1986).

 

[21]Tanaka. H, Okuda. T, Asai. K,"On fuzzy mathematical programming", J.Cybernet,3, (1963), 37-46.

 

[22] Wen. M, Li H., Fuzzy data envelopment analysis (DEA): Model and ranking method, Journal of Computational and Applied Mathematics, 223 (2009) 872-878.

 

[23] Zadeh. L.A," Optimality and non-scalar valued performance criteria", IEEE Transactions on Automatic Control AC-8, (1963), 59–60

 

[24] Zadeh. L.A,"Fuzzy sets".Information and Control 8, (1965), 338–353.

 

[25] Zadeh. L.A," Fuzzy algorithms". Info.andCtl. 12, (1968), 94–102.

 

[26] Zadeh. L.A, RE Bellman" Decision-making in a fuzzy environment" Management science 17 (4), B-141-B-164, (1970). 10935.

 

[27] Zadeh. L.A," The concept of a linguistic variable and its applications to approximate reasoning". Part I Information Sciences, vol. 8, ,(1975), pp. 199–249; Part II Information Sciences, vol. 8, pp. 301–357; Part III Information Sciences, vol. 9,(1975) pp. 43–80.

 

[28] Zadeh. L.A," Fuzzy sets as a basis for a theory of possibility", Fuzzy Sets and Systems, 1,(1978), 3-28.

 

[29] Zimmermann H.G,"Description and optimization of fuzzy system", Internet J. general system, 2, (1967), 209-215.