Document Type : Research Paper


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Applied Mathematics, Yadegar-e-Imam Khomeini (RAH) Shahre Rey Branch, Islamic Azad University, Tehran, Iran.


Network DEA models deal with measurements of relative efficiency of Decision-Making Units (DMUs) when the insight of their internal structures is available. In network models, sub-processes are connected by links or intermediate products. Links have the dual role of output from one division or sub-process and input to another one. Therefore, improving the efficiency score of one division by increasing its output may reduce the score of another division because of increasing its input. To address this conflict, in the present paper we proposed a new approach in Slack-Based Measure (SBM) framework which provides deeper insights regarding the sources of inefficiency. The proposed approach is a two-phase procedure in which Phase-I determine the role of intermediate measures by solving a linear program and partitions the intermediate measures into three groups of “input type”, “output type” and “fixed-flows” and Phase-II measures the scores of the DMUs under evaluation. Providing a classification for intermediate products and account their excesses or shortfalls in efficiency calculation while the continuity of link flows between subunits are kept, are the advantages of the proposed approach.


Main Subjects

[1]    Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444.
[2]    Färe, R. (1991). Measuring Farrell efficiency for a firm with intermediate inputs. Academia economic papers, 19(2), 329–340.
[3]    Färe, R., Grosskopf, S. (2000). Network DEA. Socio-economic planning sciences, 34(1), 35–49.
[4]    Yong, Z. H. A., Liang, L., & Xu, C. (2008). Two-stage BCC model for cooperative efficiency evaluation using a geometric mean method. Systems engineering-theory & practice, 28(10), 53–58.
[5]    Kao, C., & Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan. European journal of operational research, 185(1), 418–429.
[6]     Liang, L., Cook, W. D., & Zhu, J. (2008). DEA models for two-stage processes: Game approach and efficiency decomposition. Naval research logistics (NRL), 55(7), 643–653.
[7]     Sexton, T. R., & Lewis, H. F. (2003). Two-stage DEA: An application to major league baseball. Journal of productivity analysis, 19, 227–249.
[8]     Lewis, H. F., & Sexton, T. R. (2004). Network DEA: efficiency analysis of organizations with complex internal structure. Computers & operations research, 31(9), 1365–1410.
[9]     Lewis, H. F., Mallikarjun, S., & Sexton, T. R. (2013). Unoriented two-stage DEA: The case of the oscillating intermediate products. European journal of operational research, 229(2), 529–539.
[10]  Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management science, 30(9), 1078–1092.
[11]  Tone, K. (2001). A slacks-based measure of efficiency in data envelopment analysis. European journal of operational research, 130(3), 498–509.
[12]  Pastor, J. T., Ruiz, J. L., & Sirvent, I. (1999). An enhanced DEA Russell graph efficiency measure. European journal of operational research, 115(3), 596–607.
[13]  Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European journal of operational research, 197(1), 243–252.
[14]   Fukuyama, H., & Weber, W. L. (2010). A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega, 38(5), 398–409.
[15] Paradi, J. C., Rouatt, S., & Zhu, H. (2011). Two-stage evaluation of bank branch efficiency using data envelopment analysis. Omega, 39(1), 99–109.
[16]  Lozano, S. (2015). Alternative SBM model for network DEA. Computers & industrial engineering, 82, 33–40.
[17]  Shamsijamkhaneh, A., Hadjimolana, S. M., Rahmani Parchicolaie, B., & Hosseinzadehlotfi, F. (2018). Incorporation of inefficiency associated with link flows in efficiency measurement in network DEA. Mathematical problems in engineering, 2018, 1–12.
[18] Kord, A., Payan, A., & Saati, S. (2022). Network DEA Models with stochastic data to assess the sustainability performance of agricultural practices: an application for Sistan and Baluchestan Province in Iran. Journal of mathematics, 2022, 1–19.
[19]  Abdali, E., Moradipour, K., Asadi-Rahmati, S., & Fallah, M. (2022). Efficiency evaluation in hybrid two-stage network DEA with non-discretionary inputs and shared discretionary inputs. International journal of computer mathematics: computer systems theory, 7(1), 33–41.
[20]  Pereira, M. A., Dinis, D. C., Ferreira, D. C., Figueira, J. R., & Marques, R. C. (2022). A network data envelopment analysis to estimate nations’ efficiency in the fight against SARS-CoV-2. Expert systems with applications, 210, 118362.
[21]  Md Hamzah, N., Yu, M. M., & See, K. F. (2021). Assessing the efficiency of Malaysia health system in COVID-19 prevention and treatment response. Health care management science, 24, 273–285.
[22]  Mariano, E., Torres, B., Almeida, M., Ferraz, D., Rebelatto, D., & de Mello, J. C. S. (2021). Brazilian states in the context of COVID-19 pandemic: an index proposition using Network Data Envelopment Analysis. IEEE latin america transactions, 19(6), 917–924.
[23]  Zhang, R., Wei, Q., Li, A., & Chen, S. (2022). A new intermediate network data envelopment analysis model for evaluating China’s sustainability. Journal of cleaner production, 356, 131845.
[24]  Roudabr, N., Najafi, S. E., Moghaddas, Z., Movahedi Sobhani, F., & others. (2022). Overall efficiency of four-stage structure with undesirable outputs: a new SBM network DEA model. Complexity, 2022.
[25]  Zhu, Q., Aparicio, J., Li, F., Wu, J., & Kou, G. (2022). Determining closest targets on the extended facet production possibility set in data envelopment analysis: modeling and computational aspects. European journal of operational research, 296(3), 927–939.
[26]  Yang, F., Wang, D., Zhao, L., & Wei, F. (2021). Efficiency evaluation for regional industrial water use and wastewater treatment systems in China: a dynamic interactive network slacks-based measure model. Journal of environmental management, 279, 111721.
[27]  Li, H., Zhu, X., & Chen, J. (2020). Total factor waste gas treatment efficiency of China’s iron and steel enterprises and its influencing factors: An empirical analysis based on the four-stage SBM-DEA model. Ecological indicators, 119, 106812.
[28]  Liang, L., Yang, F., Cook, W. D., & Zhu, J. (2006). DEA models for supply chain efficiency evaluation. Annals of operations research, 145, 35–49.