A generalized cost Malmquist index to compare the productivities of units with negative data in DEA

Subject Areas : Calculus of variations and optimal control; optimization

G. Tohidi ¹ , S. Razavyan ² , S. Tohidnia ³

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Islamic Azad University, South Tehran Branch, Tehran, Iran
3 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran

Received: 2014-07-09 Accepted : 2014-09-27 Published : 2014-09-29

Keywords:

References:

[1] D. W. Caves, L. R. Christensen and W. E. Diewert, The economic theory of index numbers and the measurement of input, output and productivity, Econometrica, 50, (1982) 1393-1414.

 

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

 

[3] A. Emrouznejad, A. L. Anouze and E. Thanassoulis, A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA, European Journal of Operational Research, 200, (2010) 297-304.

 

[4] R. Fare, S. Grosskopf, M. Norris and Z. Zhang, Productivity growth, technical progress and efficiency changes in industrialized countries, American Economic Review, 84, (1994) 66-83.

 

[5] N. Maniadakis and E. Thanassoulis, A cost Malmquist productivity index, European Journal of Operational Research, 154, (2004) 396-409.

 

[6] M. C. A. S. Portela, E. Thanassoulis and G. P. M. Simpson, Negative data in DEA: A directional distance approach applied to bank branches, Journal of the Operational Research Society, 55, (2004) 1111-1121.

 

[7] M. C. A. S. Portela and E. Thanassoulis, A circular Malmquist-type index for measuring productivity, Aston Working Paper RP08-02., Aston University Birmingham B47ET, UK, (2008).

 

[8] M. C. A. S. Portela and E. Thanassoulis, Malmquist-type indices in the presence of negative data: An application to bank branches, Journal of banking & Finance, 34, (2010) 1472-1483.

 

[9] J. A. Sharp, W. Meng and W. Liu, A modied slacks-based measure model for data envelopment analysis with natural negative outputs and inputs, Journal of the Operational Research Society, 58, (2007) 1672-1677.

 

[10] G. Tohidi, S. Razavyan and S. Tohidnia, A global cost Malmquist productivity index using data envelopment analysis, Journal of the Operational Research Society, 63 (2012) 72-78.

 

[11] G. Tohidi, S. Razavyan and S. Tohidnia, A prot Malmquist productivity index, Journal of Industrial En-

gineering International, 6, No. 10, (2010) 23-30.

 

[12] G. Tohidi, S. Razavyan, A circular global prot Malmquist productivity index in data Envelopment analysis,

Applied Mathematical Modelling, 37, (2013) 216-227.

 

[13] G. Tohidi, S. Razavyan and S. Tohidnia, Prot Malmquist index and its global form in the presence of the

negative data in DEA, Journal of Applied Mathematics, doi.org/10.1155/2014/276092.