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

Pejman Peykani (), Roya Soltani, Cristina Tanasescu, Seyed Ehsan Shojaie and Alireza Jandaghian
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Pejman Peykani: Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran 1991633357, Iran
Roya Soltani: Department of Industrial Engineering, Faculty of Engineering, Khatam University, Tehran 1991633357, Iran
Cristina Tanasescu: Faculty of Economic Sciences, Lucian Blaga University of Sibiu, 550324 Sibiu, Romania
Seyed Ehsan Shojaie: Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran
Alireza Jandaghian: Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran 1417935840, Iran

Mathematics, 2025, vol. 13, issue 11, 1-27

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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