Group Malmquist Productivity Index, focusing on local and global role of groups: A case study of banking industry

Document Type : Research Paper


School of Mathematics, Iran University of Science and Technology, Tehran, Iran


Evaluating the performance of the groups of decision-making units (DMUs) in an organization and ranking them is very important because the groups are the basic components of organizations. Also, assessing the performance of groups and finding their strengths and weaknesses affect the future decisions of the organization. Most previous research has been done on the Malmquist productivity index of decision-making units to evaluate productivity changes of them. In practical evaluation problems, although decision units are homogeneous in many organizations, in the sense that they produce similar outputs by receiving the same input sources; However, these units are classified into different groups based on management strategies and environmental conditions. In this paper, we want to develop the Malmquist productivity index for a group of DMU’s and examine the productivity changes of groups. We also identify local and global factors that affect changes in group productivity. Finally, to explain the applicability of the proposed index, a case study is presented on the evaluation of bank branches in different regions.


Main Subjects

Abbaspour, M., Hosseinzadeh Lotfi, F., Karbassi, A. R., Roayaei, E., & Nikoomaram, H. (2009). Development of the Group Malmquist Productivity Index on non-discretionary Factors. International Journal of Environmental Research, 3(1), 109-116.
Afsharian, M., Ahn, H., Harms, S. G. (2019), Performance comparison of management groups under centralised management, European Journal of Operational Research, 278, 845-854.
Ang, S., Chen, M., & Yang, F. (2018). Group cross-efficiency evaluation in data envelopment analysis: An application to Taiwan hotels. Computers and Industrial Engineering journal, 125, 190-199.
Aparicio, J., Crespo-Cebada, E., Pedraja-Chaparro, F., Santín, D. (2017). Comparing school ownership performance using a pseudo-panel database: A Malmquist-type index approach. European Journal of Operational Research, 256(2), 533-542.
Aparicioa, J., Ortiza, L., Santínb, D. (2021), Comparing group performance over time through the Luenberger productivity indicator: An application to school ownership in European countries, European Journal of Operational Research, 294(2), 651-672.
Aparicio, J., Santin, D. (2018). A note on measuring group performance over time with pseudopanels. European Journal of Operational Research, 267(1), 227-235.
Bagherzadeh Valami, H. (2009). Group performance evaluation, an application of data envelopment analysis. Journal of Computational and Applied Mathematics, 230, 485-490.
Berg, S. A., Forsund, F. R., Hjalmarsson, L., & Suominen, M. (1993). Banking efficiency in the Nordic countries. Journal of Banking and Finance, 17, 371-388.
Boďa, M., Považanová, M. (2020), Productivity patterns in Europe: adaptation of the Malmquist index to measuring group performance and productivity change over time, Empirica, Springer;Austrian Institute for Economic Research; Austrian Economic Association, 47(4), 949-989.
Camanho, A. S., & Dyson, R. G. (2006). Data envelopment analysis and Malmquist indices for measuring group performance. Journal of Productivity Analysis, 26, 35-49.
Caves, D., Chirstensen, L., & Dievert, W. (1982). The economic theory of index number and the measurement of input, output and productivity. Econometrica, 50(6), 1393-1414.
Charnes, A, Cooper, W. W., & Rhodes, E. (1981). Evaluating program and managerial efficiency: an application of data envelopment analysis to program follow through. Management Science, 27(6), 668-697.
Cook, W. D., & Zhu, J. (2007). Within-group common weights in DEA: An analysis of power plant efficiency. European Journal of Operational Research, 178, 207-216.
Fang, L. (2022), Measuring and decomposing group performance under centralized management, European Journal of Operational Research, 297(3), 1006-1013.
Fare, R., Grosskopf, S., Lindgren, B., & Roose, P. (1992), Productivity change in Swedish analysis pharmacies 1980-1989, a nonparametric Malmquist approach. Journal of Productivity Analysis, 3, 85-102.
Fare, R., Grosskopf, S., Norris, M., & Zhang, A. (1994), Productivity growth, technical progress, and efficiency changes in industrial country. American Economic Review, 84, 66–83.
Forsund, F. R., & Hjalmarsson, L. (1979). Generalized Farrell measures of efficiency: An application to milk processing in Swedish dairy plants. The Economic Journal, 89, 294-315.
Grifell-Tatjé, E., & Lovell, C. (1997). The sources of productivity change in Spanish banking. European Journal of Operational Research, 98, 364-380.
Li, S. K., & Ng, Y. C. (1995). Measuring the productive efficiency of a group of firms. International Advances in Economic Research, 1(4), 377-390.
Maniadakis, N., & Thanassoulis, E. (2004). A cost Malmquist productivity index. European Journal of Operational Research, 154, 396-409.
Mirghaderi, S. A. H., & Sheikh Aboumasoudi, A. (2017). The Ranking of Financial Efficiency of Companies Accepted in Stock Exchange of Tehran between 2013 to 2016 through Financial Ratio Approach and Using DEA. International Journal of Data Envelopment Analysis, 5(3), 1337-1352.
Paradi, J. C., & Zhu, H. (2013). A survey on bank branch efficiency and performance research with data envelopment analysis. Omega, 41, 61-79.
Pastor, J. T., Perez, F. (1997), Quesada, Efficiency analysis in banking firms: an international comparison. European Journal of Operational Research, 98, 395-407.
Payan, A., & Rahmani Parchikolaei, B. (2014). Analysis of Group Performance Using Common Weights. International Journal of Mathematical models and Methods in Applied Sciences, 8, 59-68.
Rezaee, M. J., & Karimdadi, A. (2015). Do Geographical Locations Affect in Hospitals Performance? A Multi-group Data Envelopment Analysis. Journal of Medical Systems, 39, 1-11.
Thanassoulis, E., Khanjani Shiraz, R. & Maniadakis, N. (2015). A Cost Malmquist Productive Index Capturing Group Performance. Journal of Operational Research, 241, 1-32.
Walheer, B. (2018), Cost Malmquist productivity index: an output-specific approach for group comparison, Journal of Productivity Analysis, 49, 79-94.
Ylvinger, S., (2000). Industry performance and structural efficiency measures: Solutions to problems in firm models. European Journal of Operational Research, 121(1), 164- 174.