Sustainable and reliable closed-loop supply chain network design: Normalized Normal Constraint (NNC) method application

Document Type : Research Paper


Department of Industrial Management, Faculty of Management and Accounting, Allameh Tabataba'i University, Tehran, Iran


The competitive environment of the present age has focused the attention of organizations on meeting the requirements of quality and socially responsible, because organizations that adhere to the quality management framework achieve a higher level of customer satisfaction. In addition, the shorter product life due to the development of technology and changing customer needs reveals the need to pay attention to the concepts of sustainability and reliability in the design of the supply chain network. In this paper, the convergence of sustainability and reliability in supply chains is considered and a model of economic, responsible, and reliable supply chain is comprehensively and efficiently modeled. For this purpose, a nonlinear mixed-integer programming model for the supply chain network design problem is considered as three-objective, multi-product, multi-level, multi-source, multi-capacity, and multi-stage. In this study, the normalized normal constraint (NNC) method is used to solve the proposed multi-objective optimization problem and find Pareto optimal solutions. In addition, numerical examples with random data in different dimensions have been considered to measure the accuracy and overall performance of the proposed model and by changing the various parameters of the model, the sensitivity analysis of target functions has been performed to analyze the model behavior.


Main Subjects

Ahmadigorji, M., Amjady, N., & Dehghan, S. (2017). A robust model for multiyear distribution network reinforcement planning based on information-gap decision theory. IEEE Transactions on Power Systems, 33(2), 1339-1351.
Aksoy, A., Küçükoğlu, İ., Ene, S., & Öztürk, N. (2014). Integrated emission and fuel consumption calculation model for green supply chain management. Procedia-Social and Behavioral Sciences109, 1106-1109.
Alkawaleet, N., Hsieh, Y. F., & Wang, Y. (2014). Inventory routing problem with CO 2 emissions consideration. In Logistics operations, supply chain management and sustainability (pp. 611-619). Springer, Cham.
Altmann, M., & Bogaschewsky, R. (2014). An environmentally conscious robust closed-loop supply chain design. Journal of Business Economics84(5), 613-637.
Ballou, R. H. (2004). Business logistics, supply chain management. Upper Saddle River, NJ: 5. internat. Aufl.
Bektaş, T., & Laporte, G. (2011). The pollution-routing problem. Transportation Research Part B: Methodological45(8), 1232-1250.
Cascini, A., Mora, C., Pareschi, A., & Ferrari, E. (2014). Multi-objective Optimisation modelling for green supply chain management. Proceedings of XIX Summer School AIDI “Francesco Turco”, Industrial Mechanical Plants. Senigallia (AN), Italy.
Chen, C. L., & Lee, W. C. (2004). Multi-objective optimization of multi-echelon supply chain networks with uncertain product demands and prices. Computers & Chemical Engineering28(6-7), 1131-1144.
Chen, Z. L. (2004). Integrated production and distribution operations. In Handbook of quantitative supply chain analysis (pp. 711-745). Springer, Boston, MA.
Chopra, S., & Meindl, P. (2007). Supply chain management. Strategy, planning & operation. In Das summa summarum des management (pp. 265-275). Gabler.
Dakov, I., & Novkov, S. (2008, May). Sustainable Supply chain management–Scope, activities and interrelations with other concepts. In 5th International Conference on Business and Management (pp. 16-17).
Das, I., & Dennis, J. E. (1998). Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems. SIAM journal on optimization8(3), 631-657.
Eskandarpour, M., Dejax, P., Miemczyk, J., & Péton, O. (2015). Sustainable supply chain network design: An optimization-oriented review. Omega54, 11-32.
Fahimnia, B., & Jabbarzadeh, A. (2016). Marrying supply chain sustainability and resilience: A match made in heaven. Transportation Research Part E: Logistics and Transportation Review91, 306-324.
Fakhrzad, M. B., & Goodarzian, F. (2019). A fuzzy multi-objective programming approach to develop a green closed-loop supply chain network design problem under uncertainty: modifications of imperialist competitive algorithm. RAIRO-Operations Research, 53(3), 963-990.
Fattahi, M., & Govindan, K. (2018). A multi-stage stochastic program for the sustainable design of biofuel supply chain networks under biomass supply uncertainty and disruption risk: A real-life case study. Transportation Research Part E: Logistics and Transportation Review118, 534-567.
Fazli-Khalaf, M., Mirzazadeh, A., & Pishvaee, M. S. (2017). A robust fuzzy stochastic programming model for the design of a reliable green closed-loop supply chain network. Human and ecological risk assessment: an international journal23(8), 2119-2149.
Fazli-Khalaf, M., Naderi, B., Mohammadi, M., & Pishvaee, M. S. (2020). Design of a sustainable and reliable hydrogen supply chain network under mixed uncertainties: A case study. International Journal of Hydrogen Energy45(59), 34503-34531.
Gaur, J., Amini, M., & Rao, A. K. (2017). Closed-loop supply chain configuration for new and reconditioned products: An integrated optimization model. Omega, 66, 212-223.
Ghayebloo, S., Tarokh, M. J., Venkatadri, U., & Diallo, C. (2015). Developing a bi-objective model of the closed-loop supply chain network with green supplier selection and disassembly of products: the impact of parts reliability and product greenness on the recovery network. Journal of Manufacturing Systems36, 76-86.
Gong, D. C., Chen, P. S., & Lu, T. Y. (2017). Multi-objective optimization of green supply chain network designs for transportation mode selection. Scientia Iranica, 24(6), 3355-3370.
Govindan, K., Fattahi, M., & Keyvanshokooh, E. (2017). Supply chain network design under uncertainty: A comprehensive review and future research directions. European Journal of Operational Research263(1), 108-141.
Gulati, R., Puranam, P., & Tushman, M. (2012). Meta‐organization design: Rethinking design in interorganizational and community contexts. Strategic management journal33(6), 571-586.
Hamidieh, A., Naderi, B., Mohammadi, M., & Fazli-Khalaf, M. (2017). A robust possibilistic programming model for a responsive closed loop supply chain network design. Cogent Mathematics4(1), 1329886.
Hoen, K. M. R., Tan, T., Fransoo, J. C., & Houtum, G. (2010). Effect of carbon emission regulations on transport mode selection in supply chains [Z]. Eindhoven: Eindhoven University of Technology.
Hosseini-Motlagh, S. M., Samani, M. R. G., & Shahbazbegian, V. (2020). Innovative strategy to design a mixed resilient-sustainable electricity supply chain network under uncertainty. Applied Energy, 280, 115921.
Ismail-Yahaya, A., & Messac, A. (2002). Effective generation of the Pareto frontier using the normal constraint method. In 40th AIAA Aerospace Sciences Meeting & Exhibit (p. 178).
Jabali, O., Van Woensel, T., & De Kok, A. G. (2012). Analysis of travel times and CO2 emissions in time‐dependent vehicle routing. Production and Operations Management, 21(6), 1060-1074.
Jabbarzadeh, A., Fahimnia, B., & Sabouhi, F. (2018). Resilient and sustainable supply chain design: sustainability analysis under disruption risks. International Journal of Production Research, 56(17), 5945-5968.
Kabadurmus, O., & Erdogan, M. S. (2020). Sustainable, multimodal and reliable supply chain design. Annals of Operations Research292(1), 47-70.
Khalifehzadeh, S., Seifbarghy, M., & Naderi, B. (2015). A four-echelon supply chain network design with shortage: Mathematical modeling and solution methods. Journal of Manufacturing Systems35, 164-175.
Kim, J., Xu, M., Kahhat, R., Allenby, B., & Williams, E. (2009). Designing and assessing a sustainable networked delivery (SND) system: Hybrid business-to-consumer book delivery case study. Environmental science & technology43(1), 181-187.
Kuo, Y. (2010). Using simulated annealing to minimize fuel consumption for the time-dependent vehicle routing problem. Computers & Industrial Engineering59(1), 157-165.
Lakin, N., & Scheubel, V. (2017). Corporate community involvement: The definitive guide to maximizing your business' societal engagement. Routledge.
Li, Q., Loy-Benitez, J., Nam, K., Hwangbo, S., Rashidi, J., & Yoo, C. (2019). Sustainable and reliable design of reverse osmosis desalination with hybrid renewable energy systems through supply chain forecasting using recurrent neural networks. Energy178, 277-292.
Li, Y., Liu, B., & Huan, T. C. T. (2019). Renewal or not? Consumer response to a renewed corporate social responsibility strategy: Evidence from the coffee shop industry. Tourism Management72, 170-179.
Liu, J., Feng, Y., Zhu, Q., & Sarkis, J. (2018). Green supply chain management and the circular economy: Reviewing theory for advancement of both fields. International Journal of Physical Distribution & Logistics Management.
Lotfi, R., Kheiri, K., Sadeghi, A., & Babaee Tirkolaee, E. (2022). An extended robust mathematical model to project the course of COVID-19 epidemic in Iran. Annals of Operations Research, 1-25.
Lotfi, R., Kargar, B., Gharehbaghi, A., & Weber, G. W. (2021a). Viable medical waste chain network design by considering risk and robustness. Environmental Science and Pollution Research, 1-16.
Lotfi, R., Mardani, N., & Weber, G. W. (b. Robust bi-level programming for renewable energy location. International Journal of Energy Research, 45(5), 7521-7534.
Marchi, B., Zanoni, S., Zavanella, L. E., & Jaber, M. Y. (2019). Supply chain models with greenhouse gases emissions, energy usage, imperfect process under different coordination decisions. International Journal of Production Economics211, 145-153.
Mavrotas, G. (2009). Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied mathematics and computation213(2), 455-465.
Max Shen, Z. J. (2007). Integrated supply chain design models: a survey and future research directions. Journal of Industrial & Management Optimization3(1), 1.
Messac, A., & Mattson, C. A. (2002). Generating well-distributed sets of Pareto points for engineering design using physical programming. Optimization and Engineering, 3(4), 431-450.
Messac, A., & Mattson, C. A. (2004). Normal constraint method with guarantee of even representation of complete Pareto frontier. AIAA journal, 42(10), 2101-2111.
Messac, A., Ismail-Yahaya, A., & Mattson, C. A. (2003). The normalized normal constraint method for generating the Pareto frontier. Structural and multidisciplinary optimization25(2), 86-98.
Mirzapour Al-e-hashem, S. M. J., & Rekik, Y. (2014). Multi-product multi-period Inventory Routing Problem with a transshipment option: A green approach. International Journal of Production Economics157, 80-88.
Moradi, S., & Sangari, M. S. (2021). A robust optimisation approach for designing a multi-echelon, multi-product, multi-period supply chain network with outsourcing. International Journal of Logistics Systems and Management38(4), 488-505.
Mousavi Ahranjani, P., Ghaderi, S. F., Azadeh, A., & Babazadeh, R. (2020). Robust design of a sustainable and resilient bioethanol supply chain under operational and disruption risks. Clean Technologies and Environmental Policy22(1), 119-151.
Nosrati, M., & Khamseh, A. (2020). Reliability optimization in a four-echelon green closed-loop supply chain network considering stochastic demand and carbon price. Uncertain Supply Chain Management8(3), 457-472.
Nurjanni, K. P., Carvalho, M. S., & Costa, L. (2017). Green supply chain design: A mathematical modeling approach based on a multi-objective optimization model. International Journal of Production Economics183, 421-432.
Pan, F., & Nagi, R. (2013). Multi-echelon supply chain network design in agile manufacturing. Omega41(6), 969-983.
Pasandideh, S. H. R., Niaki, S. T. A., & Asadi, K. (2015). Bi-objective optimization of a multi-product multi-period three-echelon supply chain problem under uncertain environments: NSGA-II and NRGA. Information Sciences292, 57-74.
Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2012). Robust possibilistic programming for socially responsible supply chain network design: A new approach. Fuzzy sets and systems206, 1-20.
Pishvaee, M. S., Razmi, J., & Torabi, S. A. (2014). An accelerated Benders decomposition algorithm for sustainable supply chain network design under uncertainty: A case study of medical needle and syringe supply chain. Transportation Research Part E: Logistics and Transportation Review67, 14-38.
Pourghader Chobar, A., Adibi, M. A., & Kazemi, A. (2021). A novel multi-objective model for hub location problem considering dynamic demand and environmental issues. Journal of Industrial Engineering and Management Studies, 8(1), 1-31.
Rahmani, D., & Mahoodian, V. (2017). Strategic and operational supply chain network design to reduce carbon emission considering reliability and robustness. Journal of Cleaner Production149, 607-620.
Rahmani, S., & Amjady, N. (2018). Improved normalised normal constraint method to solve multi-objective optimal power flow problem. IET generation, transmission & distribution, 12(4), 859-872.
Rezaei Kallaj, M., Abolghasemian, M., Moradi Pirbalouti, S., Sabk Ara, M., & Pourghader Chobar, A. (2021). Vehicle Routing Problem in Relief Supply under a Crisis Condition considering Blood Types. Mathematical Problems in Engineering, 2021.
Rizk, N., Martel, A., & D’Amours, S. (2006). Multi-item dynamic production-distribution planning in process industries with divergent finishing stages. Computers & Operations Research, 33(12), 3600-3623.
Sahraeian, R., Bashiri, M., & Taheri-Moghadam, A. (2013). Capacitated multimodal structure of a green supply chain network considering multiple objectives. International Journal of Engineering Transactions B: Applications, 9(26).
Snyder, L. V., & Daskin, M. S. (2005). Reliability models for facility location: the expected failure cost case. Transportation Science39(3), 400-416.
Sundarakani, B., De Souza, R., Goh, M., Wagner, S. M., & Manikandan, S. (2010). Modeling carbon footprints across the supply chain. International Journal of Production Economics128(1), 43-50.
Taleizadeh, A. A., Haghighi, F., & Niaki, S. T. A. (2019). Modeling and solving a sustainable closed loop supply chain problem with pricing decisions and discounts on returned products. Journal of cleaner production207, 163-181.
Tao, J., Shao, L., Guan, Z., Ho, W., & Talluri, S. (2020). Incorporating risk aversion and fairness considerations into procurement and distribution decisions in a supply chain. International Journal of Production Research, 58(7), 1950-1967.
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 Production250, 119517.
Tsao, Y. C., Thanh, V. V., Lu, J. C., & Yu, V. (2018). Designing sustainable supply chain networks under uncertain environments: Fuzzy multi-objective programming. Journal of Cleaner Production174, 1550-1565.
Wang, B., Zhang, H., Yuan, M., Guo, Z., & Liang, Y. (2020). Sustainable refined products supply chain: a reliability assessment for demand‐side management in primary distribution processes. Energy Science & Engineering8(4), 1029-1049.
Wang, F., Lai, X., & Shi, N. (2011). A multi-objective optimization for green supply chain network design. Decision support systems, 51(2), 262-269.
Yousefi-Babadi, A., Tavakkoli-Moghaddam, R., Bozorgi-Amiri, A., & Seifi, S. (2017). Designing a reliable multi-objective queuing model of a petrochemical supply chain network under uncertainty: a case study. Computers & Chemical Engineering100, 177-197.
Zahiri, B., Zhuang, J., & Mohammadi, M. (2017). Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study. Transportation Research Part E: Logistics and Transportation Review, 103, 109-142.
Zhalechian, M., Tavakkoli-Moghaddam, R., Zahiri, B., & Mohammadi, M. (2016). Sustainable design of a closed-loop location-routing-inventory supply chain network under mixed uncertainty. Transportation Research Part E: Logistics and Transportation Review89, 182-214.