A generalized fuzzy cost efficiency model
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1775-1791.

The concept of cost efficiency has become tremendously popular in data envelopment analysis (DEA) as it serves to assess a decision-making unit (DMU) in terms of producing minimum-cost outputs. A large variety of precise and imprecise models have been put forward to measure cost efficiency for the DMUs which have a role in constructing the production possibility set; yet, there’s not an extensive literature on the cost efficiency (CE) measurement for sample DMUs (SDMUs). In an effort to remedy the shortcomings of current models, herein is introduced a generalized cost efficiency model that is capable of operating in a fuzzy environment-involving different types of fuzzy numbers-while preserving the Farrell’s decomposition of cost efficiency. Moreover, to the best of our knowledge, the present paper is the first to measure cost efficiency by using vectors. Ultimately, a useful example is provided to confirm the applicability of the proposed methods.

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DOI : 10.1051/ro/2019102
Classification : 90C70
Mots-clés : Cost efficiency, sample decision-making unit, fuzzy numbers, $$-cut 
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Aghayi, Nazila; Salehpour, Samira. A generalized fuzzy cost efficiency model. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1775-1791. doi : 10.1051/ro/2019102. http://www.numdam.org/articles/10.1051/ro/2019102/

[1] N. Aghayi, Cost efficiency measurement with fuzzy data in DEA. J. Intell. Fuzzy Syst. 32 (2017) 409–420. | DOI

[2] N. Aghayi and S. Salehpour, Revenue efficiency of fuzzy sample decision making unit. Int. J. Meas. Technol. Instrum. Eng. (IJMTIE) 5 (2015) 14–27.

[3] H. Bagherzadeh Valami, Cost efficiency with triangular fuzzy number input prices: an application of DEA. Chaos Solitons Fractals 42 (2009) 1631–1637. | DOI | MR | Zbl

[4] R.D. Banker, A. Charnes and W.W. Cooper, Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manage. Sci. 30 (1984) 1078–1092. | DOI | Zbl

[5] W.J. Baumol, J.C. Panzar and R.D. Willig, Contestable Markets and the Theory of Industry Structure. Harcourt Brace Jovanovich, New York (1982).

[6] A. Bhattacharya and P. Vasant, Soft-sensing of level of satisfaction in TOC product-mix decision heuristic using robust fuzzy-LP. Eur. J. Oper. Res. 177 (2007) 55–70. | DOI | Zbl

[7] A.S. Camanho and R.G. Dyson, Cost efficiency measurement with price uncertainty: a DEA application to bank branch assessments. Eur. J. Oper. Res. 161 (2007) 432–446. | DOI | Zbl

[8] G. Cesaroni, Industry cost efficiency in data envelopment analysis. Soc.-Econ. Planning Sci. 61 (2017) 37–43. | DOI

[9] G. Cesaroni and D. Giovannola, Average-cost efficiency and optimal scale sizes in non-parametric analysis. Eur. J. Oper. Res. 242 (2015) 121–133. | DOI | MR | Zbl

[10] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444. | DOI | MR | Zbl

[11] P. Dutta, H. Boruah and T. Ali, Fuzzy Arithmetic with and without using α-cut method: a Comparative Study. Int. J. Latest Trends Comput. 2 (2011) 99–107.

[12] A. Emrouznejad, M. Rostamy-Malkhalifeh, A. Hatami-Marbini, M. Tavana and N. Aghayi, An overall profit Malmquist productivity index with fuzzy and interval data. Math. Comput. Modell. 54 (2011) 2827–2838. | DOI | MR | Zbl

[13] A. Emrouznejad, M. Tavana and A. Hatami-Marbini, The state of the art in fuzzy data envelopment analysis. In: Performance Measurement with Fuzzy Data Envelopment Analysis, Springer, Berlin, Heidelberg (2014). | DOI

[14] L. Fang and H. Li, Cost efficiency in data envelopment analysis under the law of one price. Eur. J. Oper. Res. 240 (2015) 488–492. | DOI | MR | Zbl

[15] R. Färe, S. Grosskopf and C.K. Lovell, The Measurement of Efficiency of Production. Kluwer Nijhoff, Boston (1985). | DOI

[16] M.J. Farrell, The measurement of productive efficiency. J. R. Stat. Soc. Ser. A (General) 120 (1957) 253–290. | DOI

[17] O. Hasançebi, Cost efficiency analyses of steel frameworks for economical design of multi-storey buildings. J. Constr. Steel Res. 128 380–396. | DOI

[18] A. Hatami-Marbini, S. Saati and M. Tavana, An ideal-seeking fuzzy data envelopment analysis framework. Appl. Soft Comput. 10 (2010) 1062–1070. | DOI

[19] A. Hatami-Marbini, A. Emrouznejad and M. Tavana, A taxonomy and review of the fuzzy data envelopment analysis literature: two decades in the making. Eur. J. Oper. Res. 214 (2011) 457–472. | DOI | MR | Zbl

[20] G.R. Jahanshahloo, M. Soleimani-Damaneh and A. Mostafaee, A simplified version of the DEA cost efficiency model. Eur. J. Oper. Res. 184 (2008) 814–815. | DOI | Zbl

[21] C. Kao and S.T. Liu, Fuzzy efficiency measures in data envelopment analysis. Fuzzy Sets Syst. 113 (2000) 427–437. | DOI | Zbl

[22] T. Kuosmanen, M. Kortelainen, T. Sipiläinen and L. Cherchye, Firm and industry level profit efficiency analysis using absolute and uniform shadow prices. Eur. J. Oper. Res. 202 (2010) 584–594. | DOI | MR | Zbl

[23] Y.J. Lai and C.L. Hwang, Fuzzy mathematical programming. In: Fuzzy mathematical programming, Springer, Berlin, Heidelberg (1992) 74–186. | DOI

[24] C.C. Lee and T.H. Huang, Cost efficiency and technological gap in Western European banks: a stochastic metafrontier analysis. Int. Rev. Econ. Finance 48 (2017) 161–178. | DOI

[25] Z. Ma and W. Cui, Fuzzy data envelopment analysis approach based on sample decision making units. J. Syst. Eng. Electron. 23 (2012) 399–407. | DOI

[26] Z. Ma and W. Cui, Generalized fuzzy data envelopment analysis methods. Appl. Soft Comput. 19 (2014) 215–225. | DOI

[27] M.R. Mozaffari, P. Kamyab, J. Jablonsky and J. Gerami, Cost and revenue efficiency in DEA-R models. Comput. Ind. Eng. 78 (2014) 188–194. | DOI

[28] R. Mu, Z.X. Ma, W. Cui and Y.M. Wu, Generalized fuzzy sample DEA model and its application in the evaluation of projects. In: Vol. 63 of Applied Mechanics and Materials. Trans Tech Publications (2011) 407–411. | DOI

[29] J. Puig-Junoy, Partitioning input cost efficiency into its allocative and technical components: an empirical DEA application to hospitals. Soc.-Econ. Planning Sci. 34 (2000) 199–218. | DOI

[30] B.K. Sahoo, M. Mehdiloozad and K. Tone, Cost, revenue and profit efficiency measurement in DEA: a directional distance function approach. Eur. J. Oper. Res. 237 (2014) 921–931. | DOI | MR | Zbl

[31] C. Schaffnit, D. Rosen and J.C. Paradi, Best practice analysis of bank branches: an application of DEA in a large Canadian bank. Eur. J. Oper. Res. 98 (1997) 269–289. | DOI | Zbl

[32] T. Sueyoshi, Measuring efficiencies and returns to scale of Nippon Telegraph & Telephone in production and cost analyses. Manage. Sci. 43 (1997) 779–796. | DOI | Zbl

[33] K. Tone, A strange case of the cost and allocative efficiencies in DEA. J. Oper. Res. Soc. 53 (2002) 1225–1231. | DOI | Zbl

[34] K. Tone and M. Tsutsui, Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons. Soc.-Econ. Planning Sci. 41 (2007) 91–106. | DOI

[35] P. Vasant, A. Bhattacharya, B. Sarkar and S.K. Mukherjee, Detection of level of satisfaction and fuzziness patterns for MCDM model with modified flexible S-curve MF. Appl. Soft Comput. 7 (2007) 1044–1054. | DOI

[36] P. Vasant, T. Ganesan and I. Elamvazuthi, Fuzzy linear programming using modified logistic membership function. J. Eng. Appl. Sci. 5 (2010) 239–245.

[37] Q. Wei and H. Yan, A data envelopment analysis (DEA) evaluation method based on sample decision making units. Int. J. Inf. Technol. Decis. Making 9 (2010) 601–624. | DOI | Zbl

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