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Journal of Applied Mathematics
Volume 2014, Article ID 276092, 8 pages
Research Article

Profit Malmquist Index and Its Global Form in the Presence of the Negative Data in DEA

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

Received 8 January 2014; Accepted 7 August 2014; Published 31 August 2014

Academic Editor: Farhad Hosseinzadeh Lotfi

Copyright © 2014 Ghasem Tohidi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper first introduces the allocative and profit efficiency in the presence of the negative data and then presents a new circular index to measure the productivity change of decision making units (DMUs) for the case that the dataset contains the inputs and/or outputs with the negative values in data envelopment analysis (DEA). The proposed index is decomposed into four components in the two stages. The range directional model (RDM) and the proposed efficiencies are used to compute the proposed index and its components. The interpretations of the components are presented. Finally, a numerical example is organized to illustrate the proposed index and its components at three successive periods of time.