Modifying the interconnecting activities through an adjusted dynamic DEA model: a slacks-based measure approach

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran.

2 Department of Industrial Management, Faculty of Economic and Management, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

10.22105/jarie.2020.229872.1163

Abstract

A new approach to the dynamic Data Envelopment Analysis (DEA) referred to as the adjusted dynamic DEA, is proposed in this study. Adjusted dynamic DEA optimizes the production activity of DMUs by introducing adjustment variables to modify the interconnecting activities between consecutive terms, solving conflicts that arise between terms and between management and shareholders. The non-oriented Slack Based Model (SBM) is used as a base model and is extended to the adjusted dynamic framework, where adjustment variables are introduced. And also, in this paper, an attempt has been made to consider ratio data and extend traditional ratio DEA models to dynamic DEA-R model. In order to examine the applicability of the proposed method, the model is applied to evaluate the efficiency of ten branches of an Iranian bank during three consecutive terms. The adjusted dynamic SBM model under Variable Return to Scale (VRS) is solved and reference units for each inefficient DMU are identified. In addition, the slacks and adjustment variables are analyzed and further suggestions about the efficient conditions to the management are provided.

Keywords

Main Subjects


[1]     Emrouznejad, A., Parker, B. R., & Tavares, G. (2008). Evaluation of research in efficiency and productivity: a survey and analysis of the first 30 years of scholarly literature in DEA. Socio-economic planning sciences, 42(3), 151–7.
[2]     Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444.
[3]     Banker, R.D. Charnes, A., & Cooper, A. A. (1984). Models for estimation of technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078–1092.
[4]     Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European journal of operational research, 130(3), 498–509.
[5]     Zorriyeh habib, M. & Maghbouli, M. (2014). Identifying the best university educational departments using data envelopment analysis. Journal of applied research on industrial engineering, 1(1), 28-34.
[6]     Aliheidari bioki, T.  & Khademi Zare, T. (2014). Adaptive DEA for clustering of credit clients. Journal of applied research on industrial engineering, 1(1), 35-49.
[7]     Ebrahimzadeh Shermeh, H., Alavidoost, M. H., & Darvishinia. R. (2018). Evaluating the efficiency of power companies using data envelopment analysis based on SBM models: a case study in power industry of Iran. Journal of applied research on industrial engineering, 5(4), 286–295.
[8]     Färe, R. & Grosskopf, S. (1996). Intertemporal production frontiers: with dynamic DEA. Norwell: Kluwer.
[9]   Bogetoft, P., F¨are, R., Grosskopf, S., Hayes, K., & Taylor, L. (2008). Network DEA: some applications and illustrations, DEA symposium 2008 (pp. 5-12). Seikei University, Japan.
[10] Färe, R., & Grosskopf, S. (1997). Intertemporal production frontiers: with dynamic DEA. Journal of the operational research society, 48(6), 656-656.
[11] Nemoto, J., & Goto, M. (1999). Dynamic data envelopment analysis modeling intertemporal behavior of a firm in the presence of productive inefficiencies. Economic letters, 64(1), 51–6.
[12] Sueyoshi, T., & Sekitani, K. (2005). Returns to scale in dynamic DEA.  European journal of operational research, 161(2), 536–44.
[13] Park, K. S., & Park K. (2009). Measurement of multi period aggregative efficiency. European journal of operational research, 193(2), 567–80.
[14] Chang, H., Choy, H. L., Cooper, W.W., & Ruefli, T.W. (2009). Using malmquist indexes to measure changes in the productivity and efficiency of US accounting firms before and after the Sarbanes, Oxley Act. Omega, 37(5), 951–60.
[15] Sengupta, k. (1999). A dynamic efficiency model using data envelopment analysis. International journal of production economics, 62(3), 209-218.
[16] Tone, K. & Tsutsui, M. (2010). Dynamic DEA: A slacks-based measure approach. Omega, 38(3), 145-156.
[17] Thanassoulis, E. (2005). Introduction to the theory and application of data envelopment analysis: a foundation text with integrated software. Kluwer Academic Publishers.
[18] Hollingsworth, B., & Smith, P. C. (2003). The use of ratios in data envelopment analysis. Applied economics letters, 10(11), 733–735.
[19] Despic, O., Despic, M., & Paradi, J. C. (2007). DEA-R: Ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications. Journal of productivity analysis, 28(1-2), 33–46.
[20] Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Using the DEA-R model in the hospital industry to study the pseudo-inefficiency problem. Expert systems with applications, 38(3), 2172–2176.
[21] Wei, C. K., Chen, L. C., Li, R. K., & Tsai, C. H. (2011). Exploration of efficiency under estimation of CCR model: Based on medical sectors with DEA-R model. Expert systems with applications, 38(4), 3155–3160.
[22] Emrouznejad, A., & Amin, G. R. (2009). DEA models for ratio data: Convexity consideration. Applied mathematical modelling, 33(1), 486–498.
[23] Khoshnevis, P., & Teirlinck, P. (2018). Performance evaluation of R&D active firms. Socio-economic planning sciences, 61(1), 16–28.
[24] Olesen, O. B., Petersen, N. C., & Podinovski, V. V. (2015). Efficiency analysis with ratio measures. European journal of operational research, 245(2), 446–462.
[25] Gidion, D. K., Hong, J., Adams, M. Z. A., & Khoveyni, M. (2019). Network DEA models for assessing urban water utility efficiency. Utilities policy, 57, 48–58.
[26] Mozaffari, M.R., Kamyab, P., Jablonsky, J., & Gerami. J. (2014). Cost and revenue efficiency in DEA-R models. Computers & industrial engineering, 78, 188–194.
[27] Mozaffari. M. R., Gerami, J., & Jablonsky. J. (2014). Relationship between DEA models without explicit inputs and DEA-R models. Central European journal of operations research, 22(1), 1–12.
[28] Tone, K., & Tsutsui, M. (2014). Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42(1), 124-131.
[29]  Cooper, W.W., Seiford, L.M., & Tone, K. (2007). Data envelopment analysis: a comprehensive text with models, applications, references and DEA-solver software. Springer.