Document Type : Original Article
MA, Vali-e-Asr University of Rafsanjan.
Assistant Professor, Vali-e-Asr University of Rafsanjan.
Associate Professor, Vali-e-Asr University of Rafsanjan.
Early models of data envelopment analysis are not suitable for evaluating two-stage structures due to the black box view and lack of attention to internal processes. In these structures, Deriving the efficiency frontier and fairly determining the optimal value of variables is the most important challenge. In many existing two-stage models, the efficiency frontier is not plotted or the optimal value of intermediate variables is determined by one of two steps. This leads to incorrect calculation of the efficiency of the next stage and the total efficiency. In fact, in these models, poor performance of one stage leads to reduced efficiency of the other stage. In this study, by keeping the intermediate variables constant at the current level and with an input-output oriented approach, radial and non-radial models were developed on a constant and variable returns to scale in terms of efficiency. Using mathematical relations, the validity of the models was proved and shown that in the proposed models, the performance of the units in steps is compared with a unit on the efficiency frontier, and the models make the whole structure efficient by bringing the steps to the efficiency frontier. The proposed models were used in an applied study to evaluate the sustainability of nine supply chains of tomato producers. Their performance results were expressed by four models as well as the optimal value of inefficient unit variables in each of these models.
- An, Q., Chen, H., Xiong, B., Wu, J., Liang, L. (2017). Target intermediate products setting in a two-stage system with fairness concern. Omega, 73,49–59.
- Avkiran, N., Mccrystal, A. (2014). Dynamic network range-adjusted measure vs. dynamic network slacks-based measure. Journal of the Operations Research Society of japan, 57(1), 1-14.
- Badiezadeh, T., Farzipoor, R. & Samavati, T. (2017). Assessing sustainability of supply chains by double frontier network DEA: A big data approach, Computers and Operations Research, 98, 284-290.
- Charnes, A., Cooper, W.W. & Rhodes, E. (1978). Measuring the efficiency of decision making units; European Journal of Operational Research, 2, 429-444.
- Chen, Y., Cook, W. D., Kao, C. & Zhu, J. (2013). Network DEA Pitfalls: Divisional Efficiency and Frontier Projection under general network structures, European Journal of Operational Research,226, 507-515.
- Chen, Y., Cook, W. D., Li, N., & Zhu, J. (2009). Additive efficiency decomposition in two-stage DEA. European Journal of Operational Reaearch, 196, 1170-1176.
- Cook, W. D., Zhu, J., Bi, G. B., & Yang, F. (2010). Network DEA: Additive efficiency decomposition. European Journal of Operational Research, 207, 1122-1129.
- Cook, W. D., Liang, L. & Zhu, J. (2010). Measuring performance of two-stage network structures by DEA: A review and future perspective. Omega, 38, 423-430.
- Farrell, M. J. (1957). The Measurement of Productive Efficiency. Journal of Royal Statistical Society, 120(3), 81-115.
- Flegl, M., Bandala, C., Juarez, I., Matus, E. (2022). Analysis of production and investment efficiency in the Mexican food industry: Application of two-stage DEA. Czech Journal of Food Sciences, 40, 109-117.
- Fukuyama, H., & Weber, W.L. (2010). A slacks-based inefficiency measure for a two stage system with bad outputs. Omega, 38, 398-409.
- Gharib, A., Azar, A., Moghbel, A., Dehghan, M. (2019).Designing Organizational Innovation Measuring Model with Dynamic Network DEA (Case Study: Iranian First Level Universities). The journal of Industrial Management Perspective, 9(33), 9-29. (In Persian)
- Guan, J. & Chen, K. (2012). Modeling the relative efficiency of national innovation systems. Research Policy, 41, 102-115.
- Halkos, G., Argyropoulou, G. (2021). Modeling energy and air pollution health damaging: a two-stage DEA approach. Air Quality, Atmosphere & Health, 14, 1221-1231.
- Halkos, G.E., Tzeremes, N.G., & Kourtzidis, S. A. (2014). A unified classification of two-stage DEA models. Surveys in Operations Research and Management Science, 19(1), 1-16.
- Hassanzadeh, A. & Mostafaee, A. (2019). Measuring the efficiency of network structures: Link control approach. Computers & Industrial Engineering, 128, 437-446.
- Kahi, V. S., Yousefi, S., Shabanpour, H.,& Farzipoor, R. (2017). How to evaluate sustainability of supply chains? A dynamic network DEA approach. Industrial Management & Data Systems,117, 9, 1866-1869.
- Kao, C. (2009). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192, 949-962.
- Kao, C. (2014a). Efficiency decomposition for general multi-stage systems in data envelopment analysis. European Journal of Operational Research, 232, 117-124.
- Kao, C. (2014b). Network data envelopment analysis: A review. European Journal of Operational Research, 239(1), 1-16.
- Kao, C. (2016). Efficiency decomposition and aggregation in network data envelopment analysis. European Journal of Operational Research, 231, 1-9.
- Kao, C. (2018). A classification of slacks-based efficiency measures in network data envelopment analysis with an analysis of the properties possessed. European Journal of Operational Research, 270 (3), 1109-1121.
- 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, 418-429.
- Kao, C., & Hwang, S. N. (2010). Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems, 48, 437-446.
- Kao, C., & Hwang, S. N. (2011). Decomposition of technical and scale efficiencies in two-stage production systems. European Journal of Operational Research, 211, 515–519.
- Koronakos, G. (2019). A Taxonomy and Review of the Network Data Envelopment Analysis Literature. Machine Learing Paradigms, Learning and Analytics in Intelligent Systems, 1, 255-311.
- Li, H., Xiong, J., Xie, J., Zhou Z. & Zhang, J. (2019). A Unified Approach to Efficiency Decomposition for a Two-Stage Network DEA Model with Application of Performance Evaluation in Banks and Sustainable Product Design. Sustainability, 11, 4401.
- Moghaddas, Z., Tosarkani, B. M. & Yousefi, S. (2022). A Developmed Data Envelopment Analysis Model for Efficient Sustainable Supply Chain Network Design. Sustainability, 14(1), 262. https://doi.org/10.3390/su14010262.
- Moutinho, V. & Madaleno, M. (2021). A Two-stage DEA Model to Evaluate the Technical Eco-Efficiency Indicator in the EU Countries. International Journal of Environmental Research and Public Health, 18, 3038.
- Soleymani-Damaneh, R., Momeni, M., Mostafaei, A. & Rostami, M. (2017). Developing of a Dynamic Network Data Envelopment Analysis Model for Performance Evaluating Banking Sector. The journal of Industrial Management Perspective, 7(1), 67-89. (In Persian)
- Su, Y. & Sun, W. (2018). Sustainability evaluation of the supply chain with undesired outputs and dual-role factors based on double frontier network DEA. Soft Computing, 22, 5525-5533.
- Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operational Research, 197, 243-252.
- Tone, T., & Tsutsui, M. (2014). Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42, 124-131.
- Torabandeh, M. A., Dorri, B., Motameni, A., & Rabieh, M. (2021). Comparative-fuzzy Analysis of National Innovation Capability Based on Results of Dynamic Network DEA Model. The journal of Industrial Management Perspective, 11(42), 207-246. (In Persian)
- Tsai, M. C., Cheng, C. H., Nguyen, V. T., &Tsai, M. I. (2020). The Theoretical Relationship between the CCR Model and the Two-Stage DEA Model with an Application in the Efficiency Analysis of the Financial Industry. Symmetry, 12 (5) ,712. https://doi.org/10.3390/sym12050712.
- Tsaples, G., Papathanasiou, J., Georgiou, A.,& Samaras, N. (2019). Assessing Multidimensional Sustainability of European Countries with a Novel Two-Stage DEA. Decision Support Systems, 348, 111-122.
- Wang, M., Chen, Y. & Zhou, Z. (2020). A Novel Stochastic Two-Stage DEA Model for Evaluating Industrial Production and Waste Gas Treatment Systems. Sustainability, 12, 2316.
- Wang, M., Huang, Y. & Li, D. (2021). Assessing the performance of industrial water resource utilization systems in China based on a tw0-stage DEA approach with game cross efficiency. Journal of Cleaner Production, 312, 127722.
- Wen, Y., Hu, J., An, Q. & Ang, S. (2022). Cooperative performance evaluation among homogeneous parallel decision making units with coalition structures. Computers & Industrial Engineering, 168, https://doi.org/10.1016/j.cie.2022. 10810.
- Wu, J., Xu, G., Zhu, Q., Zhang, C. (2021). Two-stage DEA models with fairness concern: Modelling and computational aspects. Omega, 105, 102521.
- Zha, Y., Wang, J., Liang, N.,& Zhou, C. (2016). Utility-based two-stage models with fairness concern. Cent Eur J Oper Res, 24(4), 877–900.
- Zhang, J., Wu, Q., &Zhou, Z. (2019). A two-stage DEA model for resource allocation in industrial pollution treatment and its application in China, Journal of Cleaner Production, 228, 29-39.
- Zhang, L., Zhao, L. & Zha, Y. (2021). Efficiency evaluation of Chinese regional industrial systems using a dynamic two-stage DEA approach. Socio-Economic Planning Sciences, 77, 101-131.
- Zhao, T., Xie, J., Chen, Y. & Liang, L. (2021). Coordination efficiency in two-stage network DEA: application to a supplier-manufacture sustainable supply chain. International Journal of Logistics Research and Applications, 25(3), 1-22.
- Zhu, Q., Li, F., Wu, J., & Sun, J. (2020). Cross-efficiency evaluation in data envelopment analysis based on the perspective of fairness utility. Computer Industrial Engineering, 151, https://doi.org/10.1016/j.cie.2020.106926.