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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 824316, 15 pages
Research Article

Malmquist Productivity Index by Extended VIKOR Method Using Interval Numbers

1Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran 1151863411, Iran
2Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran

Received 19 May 2013; Revised 27 July 2013; Accepted 7 August 2013

Academic Editor: Patricia J. Y. Wong

Copyright © 2013 Mohammad Fallah 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.


The VIKOR method was developed for multicriteria optimization of complex systems. It determines the compromise ranking list and the compromise solution obtained with the given weights. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. Here, the VIKOR method is used for two times and . In order to calculate the progress or regression via Malmquist productivity index, the positive and negative ideals at times and are calculated first. Then we introduce the multi-criteria ranking index based on the particular measure of “closeness” to the ideal solution and calculate the separation of each alternative from the ideal solution at times and . Then we use the Malmquist productivity index to calculate the progress or regression of all alternatives. In this paper, productivity of alternatives available in decision matrix with interval numbers and their improvement or deterioration is researched. To achieve this practical goal, use of extended VIKOR is made to calculate Malmquist productivity index for multicriteria decision-making (MCDM) problem with interval numbers, and by applying Malmquist productivity index, productivity rate of growth for alternatives is calculated. Finally, a numerical example illustrates and clarifies the main results developed in this paper.