Document Type : Article

**Authors**

Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

**Abstract**

Changing the structure of supply chains to move towards less polluting industries and better performance has attracted many researchers in recent studies. Design of such networks is a process associated with uncertainties and control of the uncertainties during decision-making is of particular importance. In this paper, a two-stage stochastic programming model was presented for the design of a green closed-loop supply chain network. In order to reach the environmental goals, an upper bound of emission capability that helps governments and industries to control greenhouse gas emissions was considered. During the reverse logistics of this supply chain, waste materials are returned to the forward flow by the disassembly centers. To control the uncertainty of strategic decisions, demand and the upper bound of emission capacity with three possible scenarios is considered. To solve the model, a new accelerated Benders decomposition algorithm along with Pareto-Optimal-Cut was used. The efficiency of the proposed algorithm was compared with the regular Benders algorithm. The effect of different numerical values of parameters and probabilities of scenarios on the total cost was also examined.

**Keywords**

References:

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32. Pati, R., Jans, R., and Tyagi, R.K. "Green logistics network design: a critical review", Production & Operations Management, 25, pp. 1-10 (2013).

33. Ozkir, V. and Basligil, H. "Multi objective optimization of closed loop supply chains in uncertain environment", Journal of Cleaner Production, 41, pp. 114-125 (2013).

34. Ruimin, M.A., Lifei, Y.A.O., Maozhu, J.I.N., et al. "Robust environmental closed-loop supply chain design under uncertainty", Chaos, Solitons & Fractals, 89, pp. 195-202 (2016).

35. Jerbia, R., Boujelben, M.K., Sehli, M.A., et al. "Stochastic closed-loop supply chain network design problem with multiple recovery options", Computers & Industrial Engineering, 118, pp. 23-32 (2018).

36. Mohammadi, A.S., Alemtabriz, A., Pishvaee, M.S., et al. "A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain", Scientia Iranica, 27(1), pp. 377-395 (2019).

37. Benders, J.F. "Partitioning procedures for solving mixed-variables programming problems", Numerische Mathematik, 4(1), pp. 238-252 (1962).

38. Geoffrion, A.M. and Graves, G.W. "Multi-commodity distribution system design by Benders decomposition", Management Science, 20(5), pp. 822-844 (1974).

39. Naderi, B., Govindan, K., and Soleimani, H. "A Benders decomposition approach for a real case supply chain network design with capacity acquisition and transporter planning: wheat distribution network", Annals of Operation Research, 291, pp. 685-705 (2020).

40. Hendalianpour, A., Fakhrabadi, M., Sangari, M., et al. "A combined benders decomposition and lagrangian relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system", Scientia Iranica, Trans. E, Industrial Eng., 29(1), pp. 355- 371 (2022). DOI: 10.24200/sci.2020.53644.3349.

41. Shaw, K., Irfan, M., Shankar, R., et al. "Low carbon chance constrained supply chain network design problem: A benders decomposition based approach", Computers & Industrial Engineering, 98, pp. 483-497 (2016).

42. Tsiakis, P., Shah, N., and Pantelides, C.C. "Design of multi-echelon supply chain networks under demand uncertainty", Industrial Engineering and Chemical Research, 40(16), pp. 3585-3604 (2001).

43. Google Maps, April 2019. Find local businesses, view maps and get driving directions. <https://maps. google.com>.

44. Heidelberg Cement Group, April 2019. Castlecementsustainability2007. <http:// www.heidelbergcement.com/NR/rdonlyres/ DF6E404C-8B50-4A1D-8818-671155C78236/0/ Castle cement sustainability review.pdf>.

45. UKWA, April 2019. Save energy, energy efficient warehouse operation (2010).<http://www.ukwa.org.uk/ files/23-carbon-trust- 23.pdfu>.

2. Nurjanni, K.P., Carvalho, M.S., and Costa, L. "Green supply chain design: A mathematical modeling approach based on a multi-objective optimization model", International Journal of Production Economics, 183, pp. 421-432 (2017).

3. Chopra, S. and Meindl, P., Supply Chain Management. Strategy, Planning & Operation, In: Boersch, C., and Elschen, R., Eds., Das Summa Summarum des Management. Gabler, pp. 265-275 (2007).

4. Yang, P., Wee, H., Chung, S., et al. "Sequential and global optimization for a closed-loop deteriorating inventory supply chain", Mathematical and Computer Modelling, 52(12), pp. 161-176 (2010).

5. Che, Z.-H., Chiang, T.-A., Tu, C., et al. "A supplier selection model for product design changes", International Journal Engineering Business Management, 8(1), pp. 20-30 (2010).

6. Moncayo-Martinez, L.A. and Zhang, D.Z. "Multiobjective ant colony optimisation: a meta-heuristic approach to supply chain design", International Journal of Production Economics, 131(1), pp. 407-420 (2011).

7. Jamshidi, R., Ghomi, S.F., and Karimi, B. "Multiobjective green supply chain optimization with a new hybrid memetic algorithm using the Taguchi method", Scientia Iranica, 19(6), pp. 1876-1886 (2012).

8. Tognetti, A., Grosse-Ruyken, P.T., and Wagner, S.M. "Green supply chain network optimization and the trade-off between environmental and economic objectives", Int. J. Production Economics, 170, pp. 385-392 (2015).

9. Shaw, K., Irfan, M., Shankar, R., et al. "Low carbon chance constrained supply chain network design problem: A benders decomposition based approach", Computers & Industrial Engineering, 98, pp. 483-497 (2016).

10. Varsei, M. and Polyakovskiy S. "Sustainable supply chain network design: A case of the wine industry in Australia", Omega-International Journal of Management Science, 66, pp. 236-47 (2017).

11. Devikaa, K., Jafarian, A., and Nourbakhsh, V. "Designing a sustainable closed-loop supply chain network based on triple bottom line approach", European Journal of Operational Research, 235(3), pp. 594-615 (2014).

12. Mohammed, A. and Wang, Q. "The fuzzy multiobjective distribution planner for a green meat supply chain", Int. J. Production Economics, 184, pp. 47-58 (2017).

13. Soleimani, H. and Kannan, G. "A hybrid particle swarm optimization and genetic algorithm for closedloop supply chain network design in large-scale networks", Applied Mathematical Modelling, 39(14), pp. 3990-4012 (2015).

14. Imran, M., Kang, C.W., and Ramzan M.B. "Medicine supply chain model for an integrated healthcare system with uncertain product complaints", Journal of Manufacturing Systems, 46, pp. 13-28 (2018).

15. Mirakhorli, A. "Multi-objective optimization of reverse logistics network with fuzzy demand and return- product using an interactive fuzzy goal programming approach", 40th International Conference on Computers and Industrial Engineering (CIE), pp. 1-6 (2010).

16. Paksoy, T., Pehlivan, N.Y., and Ozceylan, E. "Fuzzy multi-objective optimization of a green supply chain network with risk management that includes environmental hazards", Human and Ecological Risk Assessment: An International Journal, 18(5), pp. 1120-1151 (2012).

17. Paksoy, T., Pehlivan, N.Y., and Ozceylan, E. "A new tradeoff model for fuzzy supply chain network design and optimization", Human and Ecological Risk Assessment: An International Journal, 19(2), pp. 492-514 (2013).

18. Yilmaz, B.S. and Selim, H. "Sustainable design of renewable energy supply chains integrated with district heating systems: a fuzzy optimization approach", Journal of Cleaner Production, 133, pp. 863-885 (2016).

19. Paydar, M.M., Babaveisi, V., and Safaei, A.S. "An engine oil closed-loop supply chain design considering collection risk", Computers & Chemical Engineering,104, pp. 38-55 (2017).

20. Amin, S.H., Zhang, G., and Akhtar, P. "Effects of uncertainty on a tire closed-loop supply chain network", Expert Systems with Applications, 73, pp. 82- 91 (2017).

21. Santoso, T., Ahmed, S., Goetschalckx, M., et al. "A stochastic programming approach for supply chain network design under uncertainty", European Journal of Operational Research, 167(1), pp. 96-115 (2005).

22. Pan, F. and Nagi, R. "Robust supply chain design under uncertain demand in agile manufacturing", Computers & Operations Research, 37(4), pp. 668-683 (2010).

23. Zeballos, L.J., M endez, C.A., Barbosa-Povoa, A.P., et al. "Multi-period design and planning of closed-loop supply chains with uncertain supply and demand", Computers & Chemical Engineering, 66, pp. 151-164 (2014).

24. Khatami, M., Mahootchi, M., and Farahani, R.Z. "Benders' decomposition for concurrent redesign of forward and closed-loop supply chain network with demand and return uncertainties", Transportation Research, Part E: Logistic and Transportation Review, 79, pp. 1-21 (2015).

25. Keyvanshokooh, E., Ryan, S.M., and Kabir, E. "Hybrid robust and stochastic optimization for closed loop supply chain network design using accelerated benders decomposition", European Journal of Operational Research, 249(1), pp. 76-92 (2016).

26. Rezaee, A., Dehghanian, F., Fahimnia, B., et al. "Green supply chain network design with stochastic demand and carbon price", Annals of Operations Research, 250(2), pp. 463-485 (2017).

27. Pasandideh, S.H.R., Niaki, S.T.A., and Asadi, K. "Optimizing a bi-objective multiproduct multi-period three echelon supply chain network with warehouse reliability", Expert Systems with Applications, 42(5), pp. 2615-2623 (2015).

28. Banasik, A., Kanellopoulos, A., Claassen, G.D.H., et al. "Closing loops in agricultural supply chains using multi-objective optimization: A case study of an industrial mushroom supply chain", International Journal of Production Economics, 183, pp. 409-420 (2017).

29. Heidari-Fathian, H. and Pasandideh, S.H.R. "Greenblood supply chain network design: Robust optimization, bounded objective function & Lagrangian relaxation", Computer & Industrial Engineering, 122, pp. 95-105 (2018).

30. Ramudhin, A., Chaabane, A., and Paquet, M. "Carbon market sensitive sustainable supply chain network design", International Journal of Management Science and Engineering Management, 5(1), pp. 30-38 (2010).

31. Kamali, A., Ghomi, S.M., and Jolai, F. "A multi objective quantity discount and joint optimization model for coordination of a single-buyer multi-vendor supply chain", Computers & Mathematics with Applications, 62(8), pp. 3251-3269 (2011).

32. Pati, R., Jans, R., and Tyagi, R.K. "Green logistics network design: a critical review", Production & Operations Management, 25, pp. 1-10 (2013).

33. Ozkir, V. and Basligil, H. "Multi objective optimization of closed loop supply chains in uncertain environment", Journal of Cleaner Production, 41, pp. 114-125 (2013).

34. Ruimin, M.A., Lifei, Y.A.O., Maozhu, J.I.N., et al. "Robust environmental closed-loop supply chain design under uncertainty", Chaos, Solitons & Fractals, 89, pp. 195-202 (2016).

35. Jerbia, R., Boujelben, M.K., Sehli, M.A., et al. "Stochastic closed-loop supply chain network design problem with multiple recovery options", Computers & Industrial Engineering, 118, pp. 23-32 (2018).

36. Mohammadi, A.S., Alemtabriz, A., Pishvaee, M.S., et al. "A multi-stage stochastic programming model for sustainable closed-loop supply chain network design with financial decisions: A case study of plastic production and recycling supply chain", Scientia Iranica, 27(1), pp. 377-395 (2019).

37. Benders, J.F. "Partitioning procedures for solving mixed-variables programming problems", Numerische Mathematik, 4(1), pp. 238-252 (1962).

38. Geoffrion, A.M. and Graves, G.W. "Multi-commodity distribution system design by Benders decomposition", Management Science, 20(5), pp. 822-844 (1974).

39. Naderi, B., Govindan, K., and Soleimani, H. "A Benders decomposition approach for a real case supply chain network design with capacity acquisition and transporter planning: wheat distribution network", Annals of Operation Research, 291, pp. 685-705 (2020).

40. Hendalianpour, A., Fakhrabadi, M., Sangari, M., et al. "A combined benders decomposition and lagrangian relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system", Scientia Iranica, Trans. E, Industrial Eng., 29(1), pp. 355- 371 (2022). DOI: 10.24200/sci.2020.53644.3349.

41. Shaw, K., Irfan, M., Shankar, R., et al. "Low carbon chance constrained supply chain network design problem: A benders decomposition based approach", Computers & Industrial Engineering, 98, pp. 483-497 (2016).

42. Tsiakis, P., Shah, N., and Pantelides, C.C. "Design of multi-echelon supply chain networks under demand uncertainty", Industrial Engineering and Chemical Research, 40(16), pp. 3585-3604 (2001).

43. Google Maps, April 2019. Find local businesses, view maps and get driving directions. <https://maps. google.com>.

44. Heidelberg Cement Group, April 2019. Castlecementsustainability2007. <http:// www.heidelbergcement.com/NR/rdonlyres/ DF6E404C-8B50-4A1D-8818-671155C78236/0/ Castle cement sustainability review.pdf>.

45. UKWA, April 2019. Save energy, energy efficient warehouse operation (2010).<http://www.ukwa.org.uk/ files/23-carbon-trust- 23.pdfu>.

Transactions on Industrial Engineering (E)

September and October 2022Pages 2578-2592