Abstract
This paper describes an approach to rank the efficient decision making units (DMUs) based on a single DMU, referred as virtual DMU. The virtual DMU is created in such a way that its inputs and outputs are the averages of the corresponding inputs and outputs of all the DMUs. It is shown that this DMU is always inefficient compared to the efficient DMUs in the set if there exists at least one inefficient DMU. The work in this paper proposes to rank efficient DMUs based on the influence of efficient DMUs on the efficiency of the virtual DMU. This paper also establishes some of the properties of the virtual DMU. Our proposed method of ranking is compared with the existing methods. This approach of ranking produces stable efficient DMUs in the higher order of the ranks. This method is simple and robust compared to existing methods.
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References
Charnes A., Cooper W.W., Rhodes E.: Measuring the efficiency of decision making units. Eur J Oper Res, 2(4), 429–444 (1978)
Banker R.D., Charnes A., Cooper W.W.: Some models for estimating technical and scale inefficiencies in data envelopment analysis. Manag Sci, 30(9), 1078–1092 (1984)
Adler N., Friedman L., Sinuany-Stern Z.: Review of ranking methods in the data envelopment analysis context. Eur J Oper Res, 140, 249–265 (2002)
Jahanshaloo G.R., Junior H.V., Lofti F.H., Akbarian D.: A new DEA ranking system based on changing the reference set. Eur J Oper Res, 181(1), 331–337 (2007)
Sexton T.R., Silkman R.H., Hogon AJ.: Data Envelopment Analysis. Critique and extensions”, In: Silkman, R.H., (Ed), Measuring efficiency: An assessment of DEA. San Francisco: Jossey-Boss, CA, 73–105 (1986)
Doyle J., Green R.: Efficiency and cross-efficiency in DEA: Derivatives, Meanings and Uses. J Oper Res Soc, 45(5), 567–578 (1994)
Anderson P., Peterson N.C.: A procedure for ranking efficient units in data envelopment analysis. Manag Sci, 39, 1261–1264 (1993)
Seiford L.M., Zhu J.: Infeasibility of super efficiency data envelopment analysis models. INFOR 37(2), 174–187 (1999)
Hibrki N., Sueyoshi T.: DEA sensitivity analysis by changing a reference set: Regional contribution to Japanese industrial development. Omega27, 139–153 (1999)
Liang L., Wu J., Cook D.D., Zhu J.: Alternative secondary goals in DEA cross-efficiency evaluation. Int J Product Eco, 113, 1025–1030 (2008)
Thrall R.M.: Duality, classification and slacks in data envelopment Analysis. Ann Oper Res, 66, 109–138 (1996)
Wang Y.M., Yang J.B.: Measuring the performances of decision-making units using interval efficiencies. J Comput Appl Math, 198, 253–267 (2007)
Cooper W.W., Seiford L.M., Tone K.: Data Envelopment Analysis — A Comprehensive Text with Models, Applications, References and DEA- Solver Software, Kluwer Academic Publishers (1999)
Adler N., Revah A.: Presenting DEA graphically. Omega, 36, 715–729 (2008)
Zhu, J.: Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities. Eur J Oper Res, 111, 50–61 (1998)
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Shetty, U., Pakkala, T.P.M. Ranking efficient DMUs based on single virtual inefficient DMU in DEA. OPSEARCH 47, 50–72 (2010). https://doi.org/10.1007/s12597-010-0004-3
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DOI: https://doi.org/10.1007/s12597-010-0004-3