A new multi-component DEA approach using common set of weights methodology and imprecise data: an application to public sector banks in India with undesirable and shared resources
Owing to the importance of internal structure of decision making units (DMUs) and data uncertainties in real situations, the present paper focuses on multi-component data envelopment analysis (MC-DEA) approach with imprecise data. The undesirable outputs and shared resources are also incorporated in the production process of multi-component DMUs to validate real problems. The interval efficiencies of DMUs and their components in MC-DEA are often challenging with imprecise data. In many practical situations, different set of weights may be resulted into valid efficiency intervals for DMUs but invalid interval efficiencies for their components. Therefore, the present study proposes a new common set of weights methodology, based on interval arithmetic and unified production frontier, to determine unique weights for measuring these interval efficiencies. It is a two-level mathematical programming approach that preserves linearity of DEA and exhibits stronger discrimination power among the DMUs as compared to some existing approaches. Theoretically, the aggregate efficiency interval of each DMU lies between the components’ interval efficiencies. Further, the proposed approach is also applied to banks in India for proving its acceptability in practical applications. The performance of each bank is investigated in terms of two components: general business and bancassurance business for the years 2011–2013. The present study emphasized expanding pattern of bancassurance business in current market scenario with more percentage increase as contrasted to general business.
KeywordsMulti-component DEA Undesirable outputs Shared resources Imprecise data Interval efficiency Bank performance
The authors are thankful to the editor and anonymous reviewers for their constructive comments and suggestions that helped us in improving the paper significantly.
- Ashrafi, & Jaafar, A. B. (2011). Efficiency measurement of series and parallel production systems with interval data by data envelopment analysis. Australian Journal of Basic and Applied Sciences, 5(11), 1435–1443.Google Scholar
- Cook, W. D., & Roll, Y. (1993). Partial efficiencies in data envelopment analysis. Socio-Economic Planning Sciences, 37(3), 171–179.Google Scholar
- Cook, W. D., Roll, Y., & Kazakov, A. (1990). A DEA model for measuring the relative efficiency of highway maintenance patrols. INFOR, 28(2), 113–124.Google Scholar
- Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software (2nd ed.). New York: Springer.Google Scholar
- Emrouznejad, A., & Cabanda, E. (2015). Introduction to data envelopment analysis and its applications. In A. L. Osman, A. L. Anouze & A. Emrouznejad (Eds.), Handbook of research on strategic performance management and measurement using data envelopment analysis, (pp. 235–255). IGI Global.Google Scholar
- Eslami, G. R., Mehralizadeh, M., & Jahanshahloo, G. R. (2009). Efficiency measurement of multi-component decision making units using data envelopment analysis. Applied Mathematical Sciences, 3(52), 2575–2594.Google Scholar
- Hosseinzadeh Lotfi, F., & Vaez-Ghasemi, M. (2013). Multi-component efficiency with shared resources in commercial banks. International Journal of Applied Operational Research, 3(4), 93–104.Google Scholar
- Jelodar, M. F., Shoja, N., Sanei, M., & Abri, A. G. (2009). Efficiency measurement of multiple components units in data envelopment analysis using common set of weights. International Journal of Industrial Mathematics, 1(2), 183–195.Google Scholar
- Noora, A. A., Hosseinzadeh Lotfi, F., & Payan, A. (2011). Measuring the relative efficiency in multi-component decision making units and its application to bank branches. Journal of Mathematical Extension, 5(2), 101–119.Google Scholar
- Pourmahmoud, J., & Zeynali, Z. (2016). A nonlinear model for common weights set identification in network data envelopment analysis. International Journal of Industrial Mathematics, 8(1), 87–98.Google Scholar
- Ramli, N. A., & Munisamy, S. (2013). Modeling undesirable factors in efficiency measurement using data envelopment analysis: A review. Journal of Sustainability Science and Management, 8(1), 126–135.Google Scholar
- Rezaie, V., Ahmad, T., Awang, S. R., Khanmohammadi, M., & Maan, N. (2014). Ranking DMUs by calculating the interval efficiency with a common set of weights in DEA. Journal of Applied Mathematics, Article ID 346763, 9.Google Scholar
- RBI. (2012). Reserve Bank of India: Statistical tables relating to banks in India, 2011–2012. Available from http://rbidocs.rbi.org.in/rdocs/Publications/PDFs/00STB071112FLS.pdf.
- RBI. (2013a). Reserve Bank of India: Statistical tables relating to Banks in India, 2012–2013. Available from http://rbidocs.rbi.org.in/rdocs/Publications/PDFs/0STR191113FL.pdf.
- RBI. (2013b). Reserve Bank of India: Master circular—prudential norms on income recognition, asset classification and provisioning pertaining to advances, 2013. Available from http://rbidocs.rbi.org.in/rdocs/notification/PDFs/62MCIRAC290613.pdf.