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Mathematics
Volume 13
Issue 11
10.3390/math13111727
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty

by
Pejman Peykani
1,*,
Roya Soltani
1,
Cristina Tanasescu
2,
Seyed Ehsan Shojaie
3 and
Alireza Jandaghian
4
1
Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran 1991633357, Iran
2
Faculty of Economic Sciences, Lucian Blaga University of Sibiu, 550324 Sibiu, Romania
3
Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran
4
Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran 1417935840, Iran
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1727; https://doi.org/10.3390/math13111727
Submission received: 25 March 2025 / Revised: 20 May 2025 / Accepted: 21 May 2025 / Published: 23 May 2025
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-criteria Decision-Making Methods)
Versions Notes

Abstract

The purpose of this study is to propose a novel approach for measuring productivity changes in decision-making units (DMUs) over time and evaluating the performance of each DMU under uncertainty in terms of progress, regression, and stagnation. To achieve this, the Malmquist productivity index (MPI) and the data envelopment analysis (DEA) models are extended, and a new productivity index capable of handling uncertain data are introduced through a robust optimization approach. Robust optimization is recognized as one of the most applicable and effective methods in uncertain programming. The implementation and calculation of the proposed index are demonstrated using data from 15 actively traded stocks in the petroleum products industry on the Tehran stock exchange over two consecutive years. The results reveal that a significant number of stocks exhibit an unfavorable trend, marked by a decline in productivity. The findings highlight the efficacy and effectiveness of the proposed robust Malmquist productivity index (RMPI) in measuring and identifying productivity trends for each stock under data uncertainty.
Keywords: Malmquist productivity index (MPI); data envelopment analysis (DEA); data uncertainty; robust optimization; stock market Malmquist productivity index (MPI); data envelopment analysis (DEA); data uncertainty; robust optimization; stock market

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MDPI and ACS Style

Peykani, P.; Soltani, R.; Tanasescu, C.; Shojaie, S.E.; Jandaghian, A. The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty. Mathematics 2025, 13, 1727. https://doi.org/10.3390/math13111727

AMA Style

Peykani P, Soltani R, Tanasescu C, Shojaie SE, Jandaghian A. The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty. Mathematics. 2025; 13(11):1727. https://doi.org/10.3390/math13111727

Chicago/Turabian Style

Peykani, Pejman, Roya Soltani, Cristina Tanasescu, Seyed Ehsan Shojaie, and Alireza Jandaghian. 2025. "The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty" Mathematics 13, no. 11: 1727. https://doi.org/10.3390/math13111727

APA Style

Peykani, P., Soltani, R., Tanasescu, C., Shojaie, S. E., & Jandaghian, A. (2025). The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty. Mathematics, 13(11), 1727. https://doi.org/10.3390/math13111727

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