A ranking method for DMUs with interval data based on dea cross-efficiency evaluation and TOPSIS

Abstract

The traditional data envelopment analysis (DEA) model can evaluate the relative efficiencies of a set of decision making units (DMUs) with exact values of inputs and outputs, but it cannot handle imprecise data. Imprecise data, for example, can be expressed in the form of the interval data or mixtures of interval data and ordinal data. In this study, a cross-efficiency method is introduced into the DEA model to calculate the interval of cross-efficiency values, based on which a new TOPSIS method is proposed to rank the DMUs. Two examples are presented to illustrate and validate the proposed method.

Keywords

Data envelopment analysis (DEA) / cross-efficiency / TOPSIS

References

[1] Amiri M, Zandieh M, Vahdani B, Soltani R, Roshanaei V. An integrated eigenvector-DEA-TOPSIS methodology for portfolio risk evaluation in the FOREX spot market. Expert Systems with Applications, 2010, 37(1): 509-516.

[2] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. European Journal of Operational Research, 1978, 2(6): 429-444.

[3] Chen Y, Li KW, Xu HY, Liu SF. A DEA-TOPSIS method for multiple criteria decision analysis in emergency management. Journal of Systems Science and Systems Engineering, 2009, 18(4): 489-507.

[4] Despotis DK. Improving the discriminating power of DEA: focus on globally efficient units. Journal of the Operational Research Society, 2002, 53(3): 314-323.

[5] Despotis DK, Smirlis YG. Data envelopment analysis with imprecise data. European Journal of Operational Research, 2002, 140(1): 24-36.

[6] Doyle J, Green R. Efficiency and cross-efficiency in DEA: derivations, meanings and uses. Journal of the Operations Research Society, 1994, 45(5): 567-578.

[7] Gu H, Song BF. Study on effectiveness evaluation of weapon systems based on grey relational analysis and TOPSIS. Journal of Systems Engineering and Electronics, 2009, 20(1): 106-111.

[8] Hwang CL, Yoon K. Multi-objective Decision Making Methods and Application. A State-of-the-art Study, 1981, New York: Springer-Verlag.

[9] Jahanshahloo GR, Hosseinzadeh Lotfi F, Moradi M. Sensitivity and stability analysis in DEA with interval data. Applied Mathematical Modeling, 2004, 156(2): 463-477.

[10] Jahanshahloo GR, Khodabakhshi M, Hosseinzadeh Lotfi F, Moazami goudarz MR. A cross-efficiency model based on super-efficiency for ranking units through TOPSIS approach and its extension to interval case. Mathematical and Computer Modelling, 2011, 53(9–10): 1946-1955.

[11] Liang L, Wu J, Cook WD, Zhu J. Alternative secondary goals in DEA cross-efficiency evaluation. International Journal of Production Economics, 2008, 113(2): 1025-1030.

[12] Mirhedayatian SM, Vahdat SE, Jelodar MJ, Saen RF. Welding process selection for repairing nodular cast iron engine block by integrated fuzzy data envelopment analysis and TOPSIS approaches. Materials and Design, 2013, 43: 272-282.

[13] Sexton TR, Silkman RH, Hogan AJ. Silkman RH. Data envelopment analysis: critique and extensions. Measuring Efficiency: An Assessment of Data Envelopment Analysis, 1986, San Francisco, CA: Jossey-Bass

[14] Tao LL, Chen Y, Liu XD, Wang X. An integrated multiple criteria decision making model applying axiomatic fuzzy set theory. Applied Mathematical Modelling, 2012, 36(10): 5046-5058.

[15] Tian M, He YY, Liu SF. Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis. Journal of Systems Engineering and Electronics, 2010, 21(3): 416-422.

[16] Wang YM, Chin KS. A neutral DEA model for cross-efficiency evaluation and its extension. Expert Systems with Applications, 2010, 37(5): 3666-3675.

[17] Wang YM, Greatbanks R, Yang JB. Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 2005, 153(3): 347-370.

[18] Wang YM, Luo Y. DEA efficiency assessment using ideal and anti-ideal decision making units. Applied Mathematics and Computation, 2006, 173(2): 902-915.

[19] Wu D. A note on DEA efficiency assessment using ideal point: an improvement of Wang and Luo’s model. Applied Mathematics and Computation, 2006, 183(2): 819-830.

[20] Yang JB. Multi-objective decision-making methods and applications, 1996, Changsha: Hunan Press 140