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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 607190, 8 pages
Research Article

Modified Malmquist Productivity Index Based on Present Time Value of Money

1Department of Mathematics, Islamic Azad University, Science and Research Branch, P.O. Box 14155/4933, Tehran, Iran
2Department of Electrical, Computer and Biomedical Engineering, Islamic Azad University, Qazvin Branch, P.O. Box 34185/1416, Qazvin, Iran

Received 9 September 2012; Revised 11 December 2012; Accepted 30 December 2012

Academic Editor: Mohammad Khodabakhshi

Copyright © 2013 Farhad Hosseinzadeh Lotfi 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.


Data envelopment analysis (DEA) models can calculate the Malmquist Productivity Index (MPI). Classic Malmquist Productivity Index shows regress and progress of a DMU in different periods with efficiency and technology variations without considering the present value of money. This issue is of major importance since while a currency of in previous year is not equal to that of now this would yield bias results which can affect the correct interpretation. The index developed here is defined in terms of Modified Malmquist Productivity Index model, which can calculate progress and regress by using the factor of present time value of money. The incorporation of present time value of money is also calculated within the framework of data envelopment analysis. This factor is fundamental and should be considered in DEA Malmquist Productivity Index. Moreover, here, differences between presented models are compared to those of previous ones indeed, biased results will be shown in the case study in banks, and problem and solution have been investigated in the literature.