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

Abstract :

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.

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