Data Envelopment Analysis in Three-Stage Network Structure with Slack Based Measure (SBM)

  • Qaiser Farooq Dar Department of International Trade, Incheon National University, South Korea
  • Young Hyo Ahn Incheon National University, South Korea
  • Gulbadin Farooq Dar Pondicherry University, India
  • Jin Hee Ma Incheon National University, South Korea
Keywords: Network Data envelopment analysis, Decision-Making Units, Three-stage structure, Efficiency, Slacks-based measure.

Abstract

Data envelopment analysis (DEA) is a non-parametric technique for measuring and analyzing the relative efficiency of the Decision-Making Unit (DMU) having multiple homogeneous types of inputs and outputs. Traditional DEA treats DMU as black boxes and calculates their efficiencies by considering their initial inputs and final outputs. But the overall efficiency of DMU is directly depended upon the performances of intermediate processes of operations. In many situations, DMUs have a three-stage network structure. Against the aforesaid backdrop, this paper introduces a non-oriented and non-radial the slacks-based measure (SBM) of efficiency framework for the three-stage network production process. In the proposed model we have considered both series and parallel relationship between the inputs and outputs of different independent and dependent stages. Additionally, this research is aimed at measuring the Indian banking efficiency by using the three-stage network DEA model.

Author Biography

Qaiser Farooq Dar, Department of International Trade, Incheon National University, South Korea
Qaiser Farooq DarPostdoc Fellow

References

Ashrafi, A., Jaafar, A. B., Lee, L. S., and Bakar, M. A. , Measure of Efficiency in Two-Stage Data Envelopment Analysis,

International Journal of Mathematical Analysis, vol. 5, no. 29, pp. 1435–1444, 2011.

Avkiran, N. K. , Opening the black box of efficiency analysis: An illustration with UAE banks, Omega, vol. 37, no. 4, pp. 930–941, 2009.

Banker, R. D., Charnes, A., and Cooper, W. W. , Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management science, vol. 30, no. 9, pp. 1078–1092, 1984.

Bhattacharyya, A., Lovell, C. K., and Sahay, P., The impact of liberalization on the productive efficiency of Indian commercial banks, European Journal of operational research, vol. 98, no. 2, pp. 332–345, 197.

Bi, G., Feng, C., Ding, J., and Khan, M. R., Estimating relative efficiency of DMU: Pareto principle and Monte Carlo oriented

DEA approach, INFOR: Information Systems and Operational Research, vol. 50, no. 1, pp. 44–57, 2012.

Pournader, M., Kach, A., Hajiagha, S. H. R., and Emrouznejad, A., Investigating the impact of behavioral factors on supply

network efficiency: insights from banking???s corporate bond networks, Annals of Operations Research, vol. 254, no, 1-2

pp. 277-3021, 2017.

Charnes, A., and Cooper, W. W., Preface to topics in data envelopment analysis, Annals of Operations research, vol. 2, no. 1, pp. 59–94, 1984.

Tone, K., and Tsutsui, M., Network DEA: A slacks-based measure approach, European journal of operational research,

vol. 197, no. 1, pp. 243–252, 2009.

Wanke, P., Barros, C. P., and Emrouznejad, A., Assessing productive efficiency of banks using integrated Fuzzy-DEA and

bootstrapping: A case of Mozambican banks, European Journal of Operational Research, vol. 249, no. 1, pp. 378-389, 2016.

Charnes, A., Cooper, W. W., and Rhodes, E., Measuring the efficiency of decision making units, European journal of

operational research, vol. 2, no. 6, pp. 429–444, 1978.

Charnes, A., Cooper, W. W., Golany, B., Seiford, L., and Stutz, J., Foundations of data envelopment analysis for ParetoKoopmans efficient empirical production functions, Journal of econometrics, vol. 30, no. 1, pp. 91–107, 1985.

Chen, Y., Cook, W. D., and Zhu, J., Deriving the DEA frontier for two-stage processes, European Journal of Operational

Research, vol. 202, no. 1, pp. 138–142, 2010.

Chen, L. F., Hsiao, C. H., and Tsai, C. F., Three-stage-DEA model selections and managerial decision, African Journal of

Business Management, vol. 4, no. 14, pp. 3122–3133, 2010.

Chen, Y., Cook, W. D., Li, N., and Zhu, J., Additive efficiency decomposition in two-stage DEA, European Journal of

Operational Research, vol. 196, no. 3, pp. 1170–1176, 2009.

Wanke, P., Barros, C. P., and Emrouznejad, A., A comparison between stochastic DEA and fuzzy DEA approaches: revisiting efficiency in Angolan banks, RAIRO-Operations Research, vol. 52, no. 1, pp. 285-303, 2018.

Charnes, Abraham, and William W. Cooper., Programming with linear fractional functionals, Naval Research logistics

quarterly, vol. 9, no. 3–4, pp. 181–186, 1962.

Emrouznejad, A., Tavana, M., Lotfi, F. H., Shahverdi, R., and Yousefpour, M., A three-stage data envelopment analysis model with application to banking industry, Measurement, vol. 49, pp. 308–1319, 2014.

Emrouznejad, A., and Yang, G. L., A survey and analysis of the first 40 years of scholarly literature in DEA: 1978-2016,

Socio-Economic Planning Sciences, vol. 61, pp. 4–8, 2018.

Fare, R., Grabowski, R., Grosskopf, S., and Kraft, S., Efficiency of a fixed but allocatable input: A non-parametric approach, Economics Letters, vol. 56, no. 2, pp. 187–193, 1997.

Kao, C., Efficiency measurement for parallel production systems, European Journal of Operational Research, vol. 196, no. 3, pp. 1107–1112, 2009.

Kao, C., Efficiency decomposition for general multi-stage systems in data envelopment analysis, European Journal of

Operational Research, vol. 231, no. 1, pp. 117–124, 2014.

Khalili-Damghani, K., Tavana, M., Santos-Arteaga, F. J., and Mohtasham, S., A dynamic multi-stage data envelopment

analysis model with application to energy consumption in the cotton industry, nergy Economics, vol. 51, pp. 320–328, 2015.

Koopmans, T. C., Activity analysis of production and allocation, New York: Wiley, No. 13, 1951.

Lewis, H. F., and Sexton, T. R., Network DEA: efficiency analysis of organizations with complex internal structure, Computers and Operations Research, vol. 31, no. 9, pp. 1365–1410, 2004.

Liu, H. H., Chen, T. Y., Chiu, Y. H., and Kuo, F. H., A comparison of three-stage DEA and artificial neural network on the

operational efficiency of semi-conductor firms in Taiwan, vol. 00, no. 00, pp. 00–00, 2013.

Lotfi, F. H., Eshlaghy, A. T., Saleh, H., Nikoomaram, H., and Seyedhoseini, S. M., A new two-stage data envelopment

analysis (DEA) model for evaluating the branch performance of banks, African Journal of Business Management, vol. 6, no.24, pp. 7220–7230, 2012.

Dar, Qaiser Farooq, Young-Hyo Ahn, and Gulbadin Farooq Dar, The Impact of International Trade on Central Bank Efficiency: An Application of DEA and Tobit Regression Analysis, Statistics, Optimization & Information Computing, vol. 9, no. 1, pp. 223–240, 2021.

Pasiouras, F., International evidence on the impact of regulations and supervision on banks, technical efficiency: an application of two-stage data envelopment analysis, Review of Quantitative Finance and Accounting, vol. 30, no. 2, pp. 187–1223, 2008.

Prieto, A. M., and Zofio, J. L. , Network DEA efficiency in input-output models: With an application to OECD countries,

European Journal of Operational Research, vol. 178, no. 1, pp. 292–304, 2007.

Dar, Q. F., Padi, T. R., and Tali, A. M., Decision support system through data envelopment analysis & stochastic frontier analysis, International Journal of modern mathematical sciences, vol. 15, no. 1, pp. 1-13, 2017.

Dar, Q. F., Padi, T. R., and Tali, A. M., Mixed input and output orientations of data envelopment analysis with linear fractional programming and least distance measures, Statistics, Optimization & Information Computing, vol. 4, no. 4, pp. 326-341, 2016.

Dar, Q. F., Pad, T. R., Tali, A. M., Hamid, Y., and Danish, F., Data Envelopment Analysis with Sensitive Analysis and Superefficiency in Indian Banking Sector, International Journal of Data Envelopment Analysis, vol. 5, no. 2, pp. 1193-1206, 2017.

R. Fare, Measuring Farrell efficiency for a firm with intermediate inputs, Academia Economic Papers, vol. 19, no. 2, pp. 329–340, 1991.

R. Fare, S. Grosskopf, Intertemporal Production Frontiers: With Dynamic DEA, Kluwer Academic Publishers, Boston, 1996.

R. Fare, S. Grosskopf, Network DEA, Socio-Economic Planning Sciences, vol. 34, pp. 35–49, 2000.

Saha, A., and Ravisankar, T. S., Rating of Indian commercial banks: a DEA approach, European Journal of Operational

Research, vol. 124, no. 1, pp. 187–203, 2000.

Sahoo, B. K., and Tone, K., Decomposing capacity utilization in data envelopment analysis: An application to banks in India, European Journal of Operational Research, vol. 195, no. 2, pp. 575–594, 2009.

Sathye, M., Efficiency of banks in a developing economy: The case of India, European Journal of Operational Research,

vol. 148, no. 3, pp. 662–671, 2003.

Seljak, J., and Kvas, A., Three-stage data envelopment analysis as a tool for nurse leader performance appraisals, SAGE Open, vol. 5, no. 1, 2158244015577666, 2015.

Sexton, T. R., and Lewis, H. F., Two-stage DEA: An application to major league baseball, Journal of Productivity Analysis,

vol. 19, no. (2-3), pp. 227–249, 2003.

Sharma, M. J., and Yu, S. J., Multi-Stage data envelopment analysis congestion model, Operational Research, vol. 13, no. 3, pp. 399–413, 2013.

Tali, A. M., Padi, T. R., and Dar, Q. F., Slack-based Measures of Efficiency in Two-stage Process: An Approach Based on Data Envelopment Analysis with Double Frontiers, International Journal of Latest Trends in Finance and Economic Sciences,

vol. 6, no. 3, pp. 1194–1204, 2017.

Dar, Qaiser Farooq, Ahn Young-Hyo, and Gulbadin Farooq Dar, Evaluation and investigation: the determinants of central

banking efficiency, RAIRO–Operations Research, vol. 55, no. 2, 2021.

Tone, K. , A slacks-based measure of efficiency in data envelopment analysis, European journal of operational research, vol. 130, no. 3, pp. 498–509, 2001.

Wang, C. H., Lu, Y. H., Huang, C. W., and Lee, J. Y., R and D, productivity, and market value: An empirical study from

high-technology firms, Omega, vol. 41, no. 1, pp. 143–155, 2013.

Muhammad, Arif, Tirupathi Rao, and Qaiser Farooq, DEA Window Analysis with slack-based measure of Efficiency in Indian Cement Industry, Statistics, Optimization & Information Computing, vol. 6, no. 2, pp. 143–155, 2013.

Published
2022-03-23
How to Cite
Dar, Q. F., Young Hyo Ahn, Gulbadin Farooq Dar, & Jin Hee Ma. (2022). Data Envelopment Analysis in Three-Stage Network Structure with Slack Based Measure (SBM). Statistics, Optimization & Information Computing, 10(2), 643-657. https://doi.org/10.19139/soic-2310-5070-840
Section
Research Articles