Developing a Fuzzy Green Supply Chain Management Problem Considering Location Allocation Routing Problem: Hybrid Meta-Heuristic Approach

Document Type : Original Manuscript


1 Department of Industrial Engineering,Central Tehan Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Masjed-Soleiman Branch, Islamic Azad University, Masjed-Soleiman, Iran

3 Department of Industrial Engineering, Firouzabad Institute of Higher Education, Firouzabad, Fars, Iran


Nowadays, the internationalization of supply chains makes the management of operation affairs face a great challenge. On the other hand, vague parameters have challenged decision-makers to drive decision-making. To cope with these challenges, this study tries to model a green SCM (GSCM) model which considers fuzzy parameters. The objective function of our model is to minimize total fuzzy cost including fuzzy establishment costs of the plants and distribution centers, fuzzy transportation costs among the suppliers, facilities, and customers, fuzzy hiring cost of the transportation facilities, and miscellaneous fuzzy environmental impact costs. The developed model also includes facilities location constraints, material flow constraints, open transportation routing from plants to customers and from distribution centers to customers. Also, determining alternative products for customers has not been addressed in the literature.  Therefore, this paper tries to focus on the mentioned complex problem and develop a comprehensive model. Because of the level of complexity of the developed model, two empowered meta-heuristic approaches, named fuzzy hybrid genetic algorithm (FHGA) and fuzzy hybrid biogeography-based optimization algorithm (FHBBO), are implemented to solve the NP-hard developed problem. According to the best of our knowledge, the proposed FHGA is not addressed in the literature in this way. For instance, most of the fuzzy algorithms either are not hybrid or get out of the fuzzy environment in one of their complex evolution processes. However, our fuzzy hybrid algorithms follow a fuzzy environment from beginning test initialization to calculating the objective function and presenting the convergence plots and none of our parameters are defuzzied in all steps of these processes. Besides, miscellaneous Figures, illustrations, and tables support the explanations of results.  

Graphical Abstract

Developing a Fuzzy Green Supply Chain Management Problem Considering Location Allocation Routing Problem: Hybrid Meta-Heuristic Approach


  • Modelling supply chain with fuzzy parameters
  • Considering various environmental issues
  • Considering transportation and location affairs
  • Developing fuzzy hybrid meta-heuristic algorithms


Amiri, M., Hashemi-Tabatabaei, M., Ghahremanloo. M., Keshavarz-Ghorabaee. M., Zavadskas. E. K., & Banaitis. A. (2021). A new fuzzy BWM approach for evaluating and selecting a sustainable supplier in supply chain management. International Journal of Sustainable Development & World Ecology, 28(2), 125-142.
Buckley, J. J. (2005). Fuzzy statistics: hypothesis testing. Soft Computing, 9(7), 512-518.
Büyüközkan, G., & Çifçi, G. (2012). A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers. Expert Systems with Applications, 39(3), 3000-3011
Deng, X., & Jiang, W. (2019). Evaluating green supply chain management practices under fuzzy environment: a novel method based on D number theory. International Journal of Fuzzy Systems, 21(5), 1389-1402.
Giallanza, A., & Puma, G. L. (2020). Fuzzy green vehicle routing problem for designing a three echelons supply chain. Journal of Cleaner Production, 259, 120774.
Govindan, K., Khodaverdi, R., & Vafadarnikjoo, A. (2015). Intuitionistic fuzzy based DEMATEL method for developing green practices and performances in a green supply chain. Expert Systems with Applications, 42(20), 7207-7220.
Kannan, D., Khodaverdi, R., Olfat, L., Jafarian, A., & Diabat, A. (2013). Integrated fuzzy multi criteria decision making method and multi-objective programming approach for supplier selection and order allocation in a green supply chain. Journal of Cleaner production, 47, 355-367.
Kumar, D., Rahman, Z., & Chan, F. T. (2017). A fuzzy AHP and fuzzy multi-objective linear programming model for order allocation in a sustainable supply chain: A case study. International Journal of Computer Integrated Manufacturing, 30(6), 535-551.
Lin, R. J. (2013). Using fuzzy DEMATEL to evaluate the green supply chain management practices. Journal of Cleaner Production, 40, 32-39.
Mangla, S. K., Kumar, P., & Barua, M. K. (2015). Flexible decision modeling for evaluating the risks in green supply chain using fuzzy AHP and IRP methodologies. Global Journal of Flexible Systems Management, 16(1), 19-35.
Mangla, S. K., Kumar, P., & Barua, M. K. (2015). Risk analysis in green supply chain using fuzzy AHP approach: A case study. Resources, Conservation and Recycling, 104, 375-390.
Midya, S., Roy, S. K., & Vincent, F. Y. (2021). Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain. International Journal of Machine Learning and Cybernetics, 12(3), 699-717.
Nayeri, S., Paydar, M. M., Asadi-Gangraj, E., & Emami, S. (2020). Multi-objective fuzzy robust optimization approach to sustainable closed-loop supply chain network design. Computers & Industrial Engineering, 148, 106716.
Noh, J., & Kim, J. S. (2019). Cooperative green supply chain management with greenhouse gas emissions and fuzzy demand. Journal of Cleaner Production, 208, 1421-1435.
Pourjavad, E., & Shahin, A. (2018). The application of Mamdani fuzzy inference system in evaluating green supply chain management performance. International Journal of Fuzzy Systems, 20(3), 901-912.
Rahmati, S. H. A., & Zandieh, M. (2012). A new biogeography-based optimization (BBO) algorithm for the flexible job shop scheduling problem. The International Journal of Advanced Manufacturing Technology, 58(9), 1115-1129.
Rostamzadeh, R., Govindan, K., Esmaeili, A., & Sabaghi, M. (2015). Application of fuzzy VIKOR for evaluation of green supply chain management practices. Ecological Indicators, 49, 188-203.
Shen, L., Olfat, L., Govindan, K., Khodaverdi, R., & Diabat, A. (2013). A fuzzy multi criteria approach for evaluating green supplier's performance in green supply chain with linguistic preferences. Resources, Conservation and Recycling, 74, 170-179.
Tirkolaee, E. B., Mardani, A., Dashtian, Z., Soltani, M., & Weber, G. W. (2020). A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design. Journal of Cleaner Production, 250, 119517.
Tseng, M. L., Lim, M., Wu, K. J., Zhou, L., & Bui, D. T. D. (2018). A novel approach for enhancing green supply chain management using converged interval-valued triangular fuzzy numbers-grey relation analysis. Resources, Conservation and Recycling, 128, 122-133.
Tsai, W. H., & Hung, S. J. (2009). A fuzzy goal programming approach for green supply chain optimisation under activity-based costing and performance evaluation with a value-chain structure. International Journal of Production Research, 47(18), 4991-5017.
Uygun, Ö., & Dede, A. (2016). Performance evaluation of green supply chain management using integrated fuzzy multi-criteria decision-making techniques. Computers & Industrial Engineering, 102, 502-511.
Wang, X., & Chan, H. K. (2013). A hierarchical fuzzy TOPSIS approach to assess improvement areas when implementing green supply chain initiatives. International Journal of Production Research, 51(10), 3117-3130.
Wu, K. J., Liao, C. J., Tseng, M. L., & Chiu, A. S. (2015). Exploring decisive factors in green supply chain practices under uncertainty. International Journal of Production Economics, 159, 147-157.