Novel Approaches for Determining Exogenous Weights in Dynamic Networks DEA

Document Type : Research Paper


1 Department of Industrial Management, Yazd Branch, Islamic Azad University, Yazd, Iran

2 Department of Management, Meybod University, Meybod, Iran


Most analysts believe that the network-based dynamic data envelopment analysis needs to define a set of endogenous/exogenous weights to evaluate the performance scores of stages and periods. Against this background, the general aim of this study is to introduce heuristic novel approaches based on fuzzy interpretive structural modeling along with the historical value of periods to obtain such weights. In this context, a closer look is taken at how to perfect the model established by Kalantary and its shortcomings. The models are initially developed here in both weighted and unweighted forms, in which a company's current performance can be influenced by its past socio-environmental performance. In the next step, heuristic methods for finding weights for stages and periods are described, and depending on the specific conditions of the models, two alternatives are proposed to combine and formulate the calculated weights. This method is then applied to data from a company, Nirou Moharekeh Industrial Group, to demonstrate the capabilities of the proposed models. The results of probing 12 suppliers show the power of the developed models in the differentiation of the decision-making units since there are no two units with the same ranks. In sum, the results can provide rich information for decision-makers. However, analysts must decide which characteristics to prioritize for evaluation purposes to achieve the best results for each situation.


Main Subjects

[1] Balfaqih H, Nopiah ZM, Saibani N, Al-Nory MT. Review of supply chain performance measurement systems: 1998–2015. Comput Ind 2016;82:135–50.
[2] Alimohammadlou M, Khoshsepehr Z. Investigating organizational sustainable development through an integrated method of interval-valued intuitionistic fuzzy AHP and WASPAS. Environ Dev Sustain 2022;24:2193-2224 [in persian].
[3] Moradi H, Rabbani M, Babaei Meybodi H, Honari MT. Sustainable Supplier Selection : A New Integrated Approach of Fuzzy Interpretive Structural Modeling and Dynamic Network Data Envelopment Analysis 2021;12:14–36.
[4] Kou M, Chen K, Wang S, Shao Y. Measuring efficiencies of multi-period and multi-division systems associated with DEA : An application to OECD countries ’ national innovation systems Measuring efficiencies of multi-period and multi-division systems associated with DEA : An application t. Expert Syst Appl 2015;46:494–510.
[5] Paul S, Ali SM, Hasan MA, Paul SK, Kabir G. Critical Success Factors for Supply Chain Sustainability in the Wood Industry: An Integrated PCA-ISM Model. Sustain 2022;14.
[6] Elmsalmi M, Hachicha W, Aljuaid AM. Modeling sustainable risks mitigation strategies using a morphological analysis-based approach: A real case study. Sustain 2021;13.
[7] Kalantary M, Farzipoor Saen R, Toloie Eshlaghy A. Sustainability assessment of supply chains by inverse network dynamic data envelopment analysis. Sci Iran 2018;25:3723-3743 [in persian].
[8] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision making units. Eur J Oper Res 1978;2:429–44.
[9] Banker RD, Charnes A, Cooper WW. Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Manage Sci 1984;30:1078–92.
[10]         Ouyang W, Yang J. The network energy and environment efficiency analysis of 27 OECD countries: A multiplicative network DEA model. Energy 2020;197:117161.
[11]         Färe R. Measuring farrell efficiency for a firm with intermediate inputs. Acad Econ Pap 1991;19:329–40.
[12]         Chen Y, Cook WD, Li N, Zhu J. Additive efficiency decomposition in two-stage DEA. Eur J Oper Res 2009;196:1170–6.
[13]         Fare R, Whittaker G, Fare F. AN INTERMEDIATE INPUT MODEL 1995;46:201–13.
[14]         Färe R, Grosskopf S, Letters EE. Productivity and intermediate products : A frontier approach. Econ Lett 1996;50:65–70.
[15]         Fukuyama H, Weber WL. A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega 2010;38:398–409.
[16]         Tone K, Tsutsui M. Network DEA : A slacks-based measure approach. Eur J Oper Res 2009;197:243–52.
[17]         Nemoto J, Goto M. Measurement of Dynamic Efficiency in Production : An Application of Data Envelopment Analysis 2003:191–210.
[18]         Färe R, Grosskopf S, Whittaker G. Chapter 12 NETWORK DEA. Model. Data Irregularities Struct. Complexities Data Envel. Anal., 2007, p. 209–40.
[19]         Tone K, Tsutsui M. Dynamic DEA with network structure : A slacks-based measure approach. Omega 2014;42:124–31.
[21]         Avkiran NK, McCrystal A. Intertemporal analysis of organizational productivity in residential aged care networks: scenario analyses for setting policy targets. Health Care Manag Sci 2014;17:113–25.
[22]         Warfield JN, Member S. Developing Interconnection Matrices in Structural Modeling 1974:81–7.
[23]         Kumar S, Janu N, Raja L, Kumar A. A fuzzy ISM analysis of factors in growth of initial coin offerings (ICOs). J Interdiscip Math 2022:1–11.
[24]         Sindhu S. Cause-related marketing—an interpretive structural model approach. J Nonprofit Public Sect Mark 2022;34:102–28.
[25]         Yadav S, Sharma A. Modelling of Enablers for Maintenance Management by ISM Method. Ind Eng Manag 2017;06.
[26]         Jamwal A, Agrawal R, Gupta S, Dangayach GS, Sharma M, Sohag MAZ. Modelling of Sustainable Manufacturing Barriers in Pharmaceutical Industries of Himachal Pradesh: An ISM-Fuzzy Approach. Smart Innov Syst Technol 2020;174:157–67.
[27]         Lamba K, Singh SP. Modeling big data enablers for operations and supply chain management. Int J Logist Manag 2018;29:629–58.
[28]         Srivastava A, Dashora K. A Fuzzy ISM approach for modeling electronic traceability in agri-food supply chain in India. Ann Oper Res 2021.
[29]         Cooper WW, JESUS T.Pastor. Range Adjusted Measure of Inefficiency for Use with Additive Models , and Relations to Other Models and Measures in DEA. J Product Anal 1999;11:5–42.
[30]         Longoni A, Cagliano R. Environmental and social sustainability priorities: Their integration in operations strategies. Int J Oper Prod Manag 2016;35:282–315.
[31]         Sy M. Impact Of Sustainability Practices On The Firms ’ Performance. Asia Pacific Bus Econ Perspect 2016;4:4–21.
[32]         Krysiak FC. Risk management as a tool for sustainability. J Bus Ethics 2009;85:483–92.
[33]         Salimian S, Mousavi SM, Antucheviciene J. An Interval-Valued Intuitionistic Fuzzy Model Based on Extended VIKOR and MARCOS for Sustainable Supplier Selection in Organ Transplantation Networks for Healthcare Devices. Sustain 2022;14:[in persian].
[34]         Zhang D, Wang H, Wang W. The Influence of Relational Capital on the Sustainability Risk: Findings from Chinese Non-State-Owned Manufacturing Enterprises. Sustainability 2022;14:6904.
[35]         Lai HF. Determining the sustainability of virtual learning communities in E-learning platform 2010:1581–6.
[36]         Cook WD, Zhu J, Bi G, Yang F. Network DEA: Additive efficiency decomposition. Eur J Oper Res 2010;207:1122–9.
[37]         Zhu L, Zhu D, Wang X, Cunningham SW, Wang Z. An integrated solution for detecting rising technology stars in co-inventor networks. vol. 121. Springer International Publishing; 2019.
[38]         Moradi H, Rabbani M, Babaei Meybodi H, Honari M. T. Development of a Hybrid Model for Sustainable Supply Chain Evaluation with Dynamic Network Data Envelopment Analysis Approach. Iran J Oper Res 2021;12:1–13.