Annals of Operations Research

, Volume 259, Issue 1–2, pp 351–388 | Cite as

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

  • Jolly Puri
  • Shiv Prasad Yadav
  • Harish Garg


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.


Multi-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.


  1. Amin, G. R., & Toloo, M. (2007). Finding the most efficient DMUs in DEA: An improved integrated model. Computers & Industrial Engineering, 52, 71–77.CrossRefGoogle Scholar
  2. Amirteimoori, A., & Kordrostami, S. (2005). Multi-component efficiency measurement with imprecise data. Applied Mathatics and Computation, 162, 1265–1277.CrossRefGoogle Scholar
  3. 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
  4. Azar, A., Mahmoudabadi, M. Z., & Emrouznejad, A. (2016). A new fuzzy additive model for determining the common set of weights in data envelopment analysis. Journal of Intelligent & Fuzzy Systems, 30, 61–69.CrossRefGoogle Scholar
  5. Azizi, H. (2014). A note on ”Supplier selection by the new AR-IDEA model”. International Journal of Advanced Manufacturing Technology, 71, 711–716.CrossRefGoogle Scholar
  6. Bi, G., Ding, J., Luo, Y., & Liang, L. (2011). Resource allocation and target setting for parallel production system based on DEA. Applied Mathematical Modelling, 35, 4270–4280.CrossRefGoogle Scholar
  7. Castelli, L., Pesenti, R., & Ukovich, W. (2010). A classification of DEA models when the internal structure of the decision making units is considered. Annals of Operations Research, 173, 207–235.CrossRefGoogle Scholar
  8. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European Journal of Operational Research, 2, 429–444.CrossRefGoogle Scholar
  9. Chen, Y., Du, J., Sherman, H. D., & Zhu, J. (2010). DEA model with shared resources and efficiency decomposition. European Journal of Operational Research, 207, 339–349.CrossRefGoogle Scholar
  10. Cook, W. D., Hababou, M., & Tuenter, H. J. H. (2000). Multicomponent efficiency measurement and shared inputs in DEA: An application to sales and service performance in bank branches. Journal of Productivity Analysis, 14(3), 209–224.CrossRefGoogle Scholar
  11. Cook, W. D., & Roll, Y. (1993). Partial efficiencies in data envelopment analysis. Socio-Economic Planning Sciences, 37(3), 171–179.Google Scholar
  12. 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
  13. Cook, W. D., Zhu, J., Bi, G. B., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European Journal of Operational Research, 207, 1122–1129.CrossRefGoogle Scholar
  14. Cooper, W. W., Park, K. S., & Yu, G. (1999). IDEA and AR-IDEA: Models for dealing with imprecise data in DEA. Management Science, 45, 597–607.CrossRefGoogle Scholar
  15. 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
  16. Emrouznejad, A., & Tavana, M. (2014). Performance measurement with fuzzy data envelopment analysis. Berlin: Springer.CrossRefGoogle Scholar
  17. Emrouznejad, A. (2014). Advances in data envelopment analysis. Annals of Operations Reseach, 214(1), 1–4.CrossRefGoogle Scholar
  18. 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
  19. 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
  20. Färe, R., Grabowski, R., Grosskopf, S., & Kraft, S. (1997). Efficiency of a fixed but allocatable input: A non-parametric approach. Economics Letters, 56, 187–193.CrossRefGoogle Scholar
  21. Färe, R., & Grosskopf, S. (1996). Productivity and intermediate products: A frontier approach. Economics Letters, 50(1), 65–70.CrossRefGoogle Scholar
  22. 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
  23. Imanirad, R., Cook, W. D., & Zhu, J. (2013). Partial input to output impacts in DEA: Production considerations and resource sharing among business subunits. Naval Reserach Logistics, 60(3), 190–207.CrossRefGoogle Scholar
  24. Jahanshahloo, G. R., Amirteimoori, A. R., & Kordrostami, S. (2004a). Multi-component performance, progress and regress measurement and shared inputs and outputs in DEA for panel data: An application in commercial bank branches. Applied Mathatics and Computation, 151, 1–16.CrossRefGoogle Scholar
  25. Jahanshahloo, G. R., Amirteimoori, A. R., & Kordrostami, S. (2004b). Measuring the multi-component efficiency with shared inputs and outputs in data envelopment analysis. Applied Mathatics and Computation, 155, 283–293.CrossRefGoogle Scholar
  26. Jahanshahloo, G. R., Memariani, A., Hosseinzadeh Lotfi, F., & Rezaei, H. Z. (2005). A note on some DEA models and finding efficiency and complete ranking using common set of weights. Applied Mathematics and Computation, 166, 265–281.CrossRefGoogle Scholar
  27. 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
  28. Kao, C. (2009a). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192, 949–962.CrossRefGoogle Scholar
  29. Kao, C. (2009b). Efficiency measurement for parallel production systems. European Journal of Operational Research, 196, 1107–1112.CrossRefGoogle Scholar
  30. Kao, C. (2012). Efficiency decomposition for parallel production systems. Journal of the Operational Research Society, 63, 64–71.CrossRefGoogle Scholar
  31. Kao, C. (2014a). Efficiency decomposition for general multi-stage systems in data envelopment analysis. European Journal of Operational Research, 232, 117–124.CrossRefGoogle Scholar
  32. Kao, C. (2014b). Network data envelopment analysis: A review. European Journal of Operational Research, 239, 1–16.CrossRefGoogle Scholar
  33. Khalili-Damghani, K., Tavana, M., & Haji-Saami, E. (2015). A data envelopment analysis model with interval data and undesirable output for combined cycle power plant performance assessment. Expert Systems with Applications, 42, 760–773.CrossRefGoogle Scholar
  34. Kordrostami, S., & Amirteimoori, A. (2005). Un-desirable factors in multi-component performance measurement. Applied Mathematics and Computation, 171, 721–729.CrossRefGoogle Scholar
  35. Korhonen, P. J., & Luptacik, M. (2004). Eco-efficiency analysis of power plants: An extension of data envelopment analysis. European Journal of Operational Research, 154, 437–446.CrossRefGoogle Scholar
  36. Lewis, H. F., & Sexton, T. R. (2004). Network DEA: Efficiency analysis of organizations with complex internal structure. Computers & Operations Research, 31, 1365–1410.CrossRefGoogle Scholar
  37. Liang, L., Li, Y., & Li, S. (2009). Increasing the discriminatory power of DEA in the presence of the undesirable outputs and large dimensionality of data sets with PCA. Expert Systems with Applications, 36, 5895–5899.CrossRefGoogle Scholar
  38. Liu, W. B., Meng, W., Li, X. X., & Zhang, D. Q. (2010). DEA models with undesirable inputs and outputs. Annals of Operations Research, 173(1), 177–194.CrossRefGoogle Scholar
  39. Liu, F. H. F., & Peng, H. H. (2008). Ranking of units on the DEA frontier with common weights. Computers & Operations Research, 35, 1624–1637.CrossRefGoogle Scholar
  40. 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
  41. Omrani, H. (2013). Common weights data envelopment analysis with uncertain data: A robust optimization approach. Computers & Industrial Engineering, 66(4), 1163–1170.CrossRefGoogle Scholar
  42. 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
  43. Puri, J., & Yadav, S. P. (2013a). Performance evaluation of public and private sector banks in India using DEA. International Journal of Operational Research, 18(1), 91–121.CrossRefGoogle Scholar
  44. Puri, J., & Yadav, S. P. (2013b). A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector. Expert Systems with Applications, 40, 1437–1450.CrossRefGoogle Scholar
  45. Puri, J., & Yadav, S. P. (2014). A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India. Expert Systems with Applications, 41, 6419–6432.CrossRefGoogle Scholar
  46. 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
  47. Ramón, N., Ruiz, J. L., & Sirvent, I. (2012). Common sets of weights as summaries of DEA profiles of weights: With an application to the ranking of professional tennis players. Expert Systems with Applications, 39, 4882–4889.CrossRefGoogle Scholar
  48. 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
  49. Roll, Y., Cook, W. D., & Golany, B. (1991). Controlling factor weights in data envelopment analysis. IIE Transactions, 23(1), 2–9.CrossRefGoogle Scholar
  50. RBI. (2012). Reserve Bank of India: Statistical tables relating to banks in India, 2011–2012. Available from
  51. RBI. (2013a). Reserve Bank of India: Statistical tables relating to Banks in India, 2012–2013. Available from
  52. RBI. (2013b). Reserve Bank of India: Master circular—prudential norms on income recognition, asset classification and provisioning pertaining to advances, 2013. Available from
  53. Scheel, H. (2001). Undesiarable outputs in efficiency valuations. European Journal of Operational Research, 132(2), 400–410.CrossRefGoogle Scholar
  54. Seiford, L., & Zhu, J. (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142(1), 16–20.CrossRefGoogle Scholar
  55. Toloo, M., Emrouznejad, A., & Moreno, P. (2015). A linear relational DEA model to evaluate two-stage processes with shared inputs. Computational and Applied Mathematics, 34, 1–17.CrossRefGoogle Scholar
  56. Tyagi, P., Yadav, S. P., & Singh, S. P. (2009). Relative performance of academic departments using DEA with senstivity analysis. Evaluation and Program Planning, 32(2), 168–177.CrossRefGoogle Scholar
  57. Wang, Y. M., Greatbanks, R., & Yang, J. B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy Sets and Systems, 153, 347–370.CrossRefGoogle Scholar
  58. Wu, J., Zhu, Q., Chu, J., & Liang, L. (2015). Two-stage network structures with undesirable intermediate outputs reused: A DEA based approach. Computational Economics, 46, 455–477.CrossRefGoogle Scholar
  59. Yang, Y., Ma, B., & Koike, M. (2000). Efficiency-measuring DEA model for production system with k independent subsystems. Journal of the Operations Research Society of Japan, 43, 343–354.CrossRefGoogle Scholar
  60. Zhou, G., Chung, W., & Zhang, Y. (2014). Measuring energy efficiency performance of China’s transport sector: A data envelopment analysis approach. Expert Systems with Applications, 41, 709–722.CrossRefGoogle Scholar
  61. Zhu, J. (2003). Imprecise data envelopment analysis (IDEA): A review and improvemet with an application. European Journal of Operational Research, 144, 513–529.CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.School of MathematicsThapar UniversityPatialaIndia
  2. 2.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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