Document Type : Original Article


1 Department of Industrial Management, Allameh Tabatabai University, Tehran, Iran.

2 Department of Management, College of Business, Bryant University, Smithfield, USA.


Purpose: In this study, the grey data envelopment analysis approach and the Malmquist productivity index were used to measure the efficiency and productivity of companies in the Tehran Stock Exchange cement industry.
Methodology: First, we identify the appropriate financial ratios for measuring efficiency. Then, we calculate these ratios for each financial year as grey numbers (intervals). In the next step, these ratios are divided into two groups of input and output variables under research variables. Finally, the efficiency and productivity of the studied companies for the two fiscal years, 2018 and 2019, were determined using CCR and BCC models. Its components have been estimated.
Findings: The results of this study provide a suitable framework for using uncertain information (grey) to replace definite information and thus allow more realistic results to be estimated about the performance of companies.
Findings: The results of this study provide a suitable framework for using uncertain information (grey) to replace definite information and thus allow more realistic results to be estimated about the performance of companies.
Originality/Value: This study uses the Malmquist-Grey Productivity Index to provide a framework for comparing productivity changes over time. This index measures the ratio of the measured efficiencies of a production unit in two different periods.


Alinezhad, A., Mirmozaffari, M. (2018). Malmquist productivity index using two-stage dea model in heart hospitals. Iranian journal of optimization, 10(2), 81-92.
Alvarez, M. A. G. (2004). Market-based land reform: violence, efficiency, and redistribution in rural Colombia. University of Connecticut.
Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science30(9), 1078-1092.
Caves, D. W., Christensen, L. R., & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrical: journal of the econometric society, 50, 1393-1414.
Coelli, T. J., Rao, D. S. P., O'Donnell, C. J., & Battese, G. E. (2005). An introduction to efficiency and productivity analysis. Springer Science & Business Media.
Darvish Motevalli, M., Hosseinzadeh Lotfi, F., Shoja, N., Gholamabri, A. (2019). A new model for calculating the efficiency of existing cement companies with a network structure (an application of data envelopment analysis). Financial engineering and portfolio management, 10(38), 65-93. (in Persian)
De, A., Bandyopadhyay, G., & Chakraborty, B. N. (2011). Application of the factor analysis on the financial ratios and validation of the results by the cluster analysis: an empirical study on the Indian cement industry. Journal of business studies quarterly2(3), 13-31.
Despotis, D. K., & Smirlis, Y. G. (2002). Data envelopment analysis with imprecise data. European journal of operational research140(1), 24-36.
Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1994). Productivity developments in Swedish hospitals: a Malmquist output index approach. In Data envelopment analysis: Theory, methodology, and applications (pp. 253-272). Springer, Dordrecht.
Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. The American economic review, 84(1), 66-83.
Fried, H. O., Lovell, C. K., Schmidt, S. S., & Schmidt, S. S. (2008). The measurement of productive efficiency and productivity growth. Oxford University Press.
Ju-Long, D. (1982). Control problems of grey systems. Systems & control letters1(5), 288-294.
Khajavi, Sh., Salimifard, A. R., & Rabieh, M. (2005). The application of data envelopment analysis (DEA) in determining a portfolio of the most efficient companies accepted at Tehran Stock Exchange. Journal of social sciences and humanities of shiraz university, 22(2), 75-89. (In Persian). URL:
Lee, J. Y., & Kim, D. (2013). Bank performance and its determinants in Korea. Japan and the world economy27, 83-94.
Mahotra, D. K., & Malhotra, R. (2008). Analyzing financial statements using data envelopment analysis. Com, lending rev.23, 25-39.
Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de estadística4(2), 209-242.
Mehrolhassani M, Goudarzi R, Yazdi Feyzabadi V, Pourhosseini S, Darvishi A. (2019). Efficiency and productivity measurement in research sector of iranian medical sciences universities using data envelopment analysis and malmquist index. Iranian journal of epidemiology. 14, 1-11. (in Persian) URL:
Momeni, M. (2008). New topics in operations research. University of Tehran.
Sadaghiani, J. S., Amiri, M., & Kayedpour, F. (2013). Performance measurement of companies of pharmaceutical substances industry in Tehran Stock Exchange with the approach of COLS and DEA. Life science journal10(8), 70-91.
Schmiedel, H. (2004). Performance of international securities markets. Helsinki: Bank of Finland.
Serifsoy, B. (2006). Essays on stock exchange efficiency, business models, and governance (Doctoral dissertation, Dissertation zur Erlangung des Doktorgrades, Johann Wolfgang Goethe-Universität Frankfurt am Main, Wirtschaftswissenschaften, Darmstadt).
Shephard, R. W. (2012). Cost and production functions. Springer Science & Business Media.
Tehrani, R., Mehragan, M. R., & Golkani, M. R. (2012). A model for evaluating financial performance of companies by data envelopment analysis: a case study of 36 corporations affiliated with a private organization. International business research5(8), 8-16.
Worthington, A. C. (1998). The application of mathematical programming techniques to financial statement analysis: Australian gold production and exploration. Australian journal of management23(1), 97-113.
Yang, Y. S. (1998). Data envelopment analysis (DEA) model with interval gray numbers. International journal of information and management sciences9(4), 11-23.
Rahnamay Roodposhti, F., Imeni, M., & Sayadmanesh, S. (2019). BSC application and innovative methods of developed in the management accounting and strategic decisions of performance measurement. Decisions and operations research, 4(3), 246-261. (in Persian) doi: 10.22105/dmor.2020.215116.1135
 Zhu, J. (1996). Robustness of the efficient DMUs in data envelopment analysis. European journal of operational research90(3), 451-460.