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

الموضوعات :

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

تاريخ الإرسال : 12 الأربعاء , رمضان, 1435 تاريخ التأكيد : 03 السبت , ذو الحجة, 1435 تاريخ الإصدار : 05 الإثنين , ذو الحجة, 1435

الکلمات المفتاحية: Data envelopment analysis (DEA), Malmquist Index, Circularity, Returns to scale (VRS), Negative data, Cost efficiency,

ملخص المقالة :

In some data envelopment analysis (DEA) applications, some inputs of DMUshave negative values with positive cost. This paper generalizes the global cost Malmquistproductivity index to compare the productivity of dierent DMUs with negative inputs inany two periods of times under variable returns to scale (VRS) technology, and then thegeneralized index is decomposed to several components. The obtained components are computed using the nonparametric linear programming models, known as DEA. To illustrate thegeneralized index and its components, a numerical example at three successive periods oftime is given.

المصادر:

[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.