Sustainable closed-loop supply chain network optimization for construction machinery recovering

Abdolhossein Sadrnia; Amirreza Payandeh Sani; Najme Roghani Langarudi

doi:10.3934/jimo.2020074

Previous Article
Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization
JIMO Home
This Issue
Next Article
Dynamic network flow location models and algorithms for quickest evacuation planning

doi: 10.3934/jimo.2020074

Sustainable closed-loop supply chain network optimization for construction machinery recovering

Abdolhossein Sadrnia ^1,, , Amirreza Payandeh Sani ^2, and Najme Roghani Langarudi ^2,

1.	Assistant professor of department of Industrial Engineering, Quchan University of Technology, P.O. Box: 94771-67335, Quchan, Iran
2.	Islamic Azad University of Semnan branch, Amirkabir University of Technology-Tehran Polytechnic, Iran

^* Corresponding author: Abdolhossein sadrnia

Received January 2019 Revised January 2020 Published June 2020

With regard to environmental pressures and economic benefits, some original construction equipment manufacturers, have focused on collecting and recovering construction machinery at the end of their life. The present study aimed to focus on Sustainable closed-loop supply chain network optimization for construction machinery recovering. To this purpose, different recovery options such as remanufacturing, recycling and reusing were implemented. A mixed integer linear programming model (MILP) including three objective functions was proposed in this regard. Based on the model, all three dimensions of sustainability including economic, environmental, and social dimensions were considered and could successfully determine the optimal values of the flow of used products, remanufactured products, recycled parts, re-usable parts. In order to demonstrate the applicability of the proposed model, a numerical example was used with the help of GAMS software to obtain the supply chain structure with the lowest cost and reduce the pollution caused by CO₂. Finally, the model could maximize fixed and variable job opportunities.

Keywords: Closed-loop supply chain, Sustainable supply chain, Construction machinery recovering, Remanufacturing, Recycling, Re-use.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

Citation: Abdolhossein Sadrnia, Amirreza Payandeh Sani, Najme Roghani Langarudi. Sustainable closed-loop supply chain network optimization for construction machinery recovering. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020074

References:

[1]	F. Altiparmak, M. Gen, L. Lin and T. Paksoy, A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers & Industrial Engineering, 51 (2006), 196–215, special Issue on Computational Intelligence and Information Technology: Applications to Industrial Engineering 33rd. ICC & amp; IE - Computational Intelligence & amp; Information. doi: 10.1016/j.cie.2006.07.011. Google Scholar
[2]	Y. Cardona-ValdÂes, A. Âlvarez and D. Ozdemir, A bi objective supply chain design problem with uncertainty, Transportation Research Part C: Emerging Technologies19, 5 (2011), 821–832, freight Transportation and Logistics(selected papers from{ODYSSEUS}2009-the4th International Work shop on Freight Transportation and Logistics). doi: 10.1016/j.trc.2010.04.003. Google Scholar
[3]	S. R. Cardoso, A. P. F. Barbosa-Povoa and S. Relvas, Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty, European Journal of Operational Research, 226 (2013), 436-451. doi: 10.1016/j.ejor.2012.11.035. Google Scholar
[4]	C. R. Carter and M. M. Jennings, Social responsibility and supply chain relationships, Transportation Research Part E: Logistics and Transportation Review, 38 (2002), 37-52. doi: 10.1016/S1366-5545(01)00008-4. Google Scholar
[5]	C. R. Carter and M. M. Jennings, Logistics social responsibility: An integrative framework, Journal of Business Logistics, 23 (2002), 145-180. Google Scholar
[6]	A. Chaabane, A. Ramudhin and M. Paquet, Design of sustainable supply chains under the emission trading scheme, International Journal of Production Economics, 135 (2012), 37-49. doi: 10.1016/j.ijpe.2010.10.025. Google Scholar
[7]	H. K. Chan and V. Jain, A framework of reverse logistics for the automobile industry, International Journal of Production Research, 50 (2012), 1318-1331. doi: 10.1080/00207543.2011.571929. Google Scholar
[8]	Z. Che and C. Chiang, A modiiï ed Pareto genetic algorithm for multi-objective build-to-order supply chain planning with product assembly, Advances in Engineering Software, 41 (78) (2010), 1011–1022, advances in Structural Optimization. doi: 10.1016/j.advengsoft.2010.04.001. Google Scholar
[9]	S. Chopra and P. Meindl, Supply chain management: Strategy, planning, and operation, Das Summa Summarum des Management, 2007,265–275. doi: 10.1007/978-3-8349-9320-5_22. Google Scholar
[10]	J. M. Cruz, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European Journal of Operational Research, 184 (2008), 1005-1031. doi: 10.1016/j.ejor.2006.12.012. Google Scholar
[11]	R. Cruz-Rivera and J. Ertel, Reverse logistics network design for the collection of End-of-Life Vehicles in Mexico, European Journal of Operational Research, 196 (2009), 930-939. doi: 10.1016/j.ejor.2008.04.041. Google Scholar
[12]	J. M. Cruz and T. Wakolbinger, Multiperiod effects of corporate social responsibility on supply chain networks, transaction costs, emissions, and risk, International Journal of Production Economics, 116 (2008), 61-74. doi: 10.1016/j.ijpe.2008.07.011. Google Scholar
[13]	J. M. Cruz, The impact of corporate social responsibility in supply chain management: Multicriteria decision-making approach, Decision Support Systems, 48 (2009), 224-236. doi: 10.1016/j.dss.2009.07.013. Google Scholar
[14]	S. K. Das and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment, Computers & Industrial Engineering, 132 (2019), 311-324. Google Scholar
[15]	S. K. Das, S. K. Roy and G. W. Weber, Heuristic approaches for solid transportation-P-facility location problem, Central European Journal of Operations Research, (2019), 1–23. doi: 10.1007/s10100-019-00610-7. Google Scholar
[16]	N. Demirel and H. GÚkÃen, A mixed integer programming model for remanufacturing in reverse logistics environment, International Journal of Advanced Manufacturing Technology, 39 (2008), 1197-1206. doi: 10.1007/s00170-007-1290-7. Google Scholar
[17]	M. Eskandarpour, P. Dejax, J. Miemczyk and O. Peton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32. doi: 10.1016/j.omega.2015.01.006. Google Scholar
[18]	G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26. doi: 10.1287/mnsc.1050.0465. Google Scholar
[19]	M. Fleischmann, P. Beullens, J. M. Bloemhof-Ruwaard and L. N. Van Wassenhove, The impact of product recovery on logistics network design, Production and Operations Management, 10 (2001), 156-173. doi: 10.1111/j.1937-5956.2001.tb00076.x. Google Scholar
[20]	M. Fleischmann, H. Krikke, R. Dekker and S. Flapper, A characterization of logistics networks for product recovery, Omega, 28 (2000), 653-666. Google Scholar
[21]	R. B. Franca, E. C. Jones, C. N. Richards and J. P. Carlson, Multi-objective stochastic supply chain modeling to evaluate tradeoïs between proït and quality, International Journal of Production Economics 127 ({2}) (2010), 292–299, supply Chain Planning and Conïguration in the Global Arena. Google Scholar
[22]	J. Q. Frota Neto, J. M. Bloemhof-Ruwaard and et al, Designing and evaluating sustainable logistics networks, International Journal of Production Economics, 111 (2008), 195-208. doi: 10.1016/j.ijpe.2006.10.014. Google Scholar
[23]	K. Garg, D. Kannan, A. Diabat and P. C. Jha, A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design, Journal of Cleaner Production, 100 (2015), 297-314. doi: 10.1016/j.jclepro.2015.02.075. Google Scholar
[24]	S. Giarola, A. Zamboni and F. Bezzo, Spatially explicit multi-objective optimization for design and planning of hybrid ïrst and second generation bioreïneries, Computers & Chemical Engineering, 35 (2011), 1782–1797, energy Systems Engineering. doi: 10.1016/j.compchemeng.2011.01.020. Google Scholar
[25]	M. Goetschalcks and B. Fleischmann, Strategic network design, Supply Chain Management and Advanced Planning, (2008), 117–132. doi: 10.1007/978-3-540-74512-9_7. Google Scholar
[26]	Jr. V. D. R. Guide and L. N. Van Wassenhove, Closed-loop supply chains, quantitative approaches to distribution logistics and supply chain management, Springer, 47–60. Google Scholar
[27]	T. G. Gutowski, C. F. Murphy, D. T. Allen and et al, WTEC Panel Report on: Environmentally Benign Manufacturing (EBM), International Technology Research Institute, World Technology (WTEC) Division, Baltimore, Maryland. Google Scholar
[28]	P. Hasanov, M. Y. Jaber, S. Zanoni, L. E. Zavanella, Closed-loop supphy chain system with energy, transportation and waste disposal costs, International Journal of Sustainable Engineering, (2013), 352–358. doi: 10.1080/19397038.2012.762433. Google Scholar
[29]	M. A. Ilgin and S. M. Gupta, Environmentally conscious manufacturing and product recovery (ECMPRO): A review of the state of the art, Journal of Environmental Management, 91 (2010), 563-591. doi: 10.1016/j.jenvman.2009.09.037. Google Scholar
[30]	G. R. Initiative, Sustainability Reporting Guidelines (G4), Global Reporting Initiative, 2013. Google Scholar
[31]	R. Jamshidi, S. F. Ghomi and B. Karimi, Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the taguchi method, Scientia Iranica, 19 (2012), 1876-1886. doi: 10.1016/j.scient.2012.07.002. Google Scholar
[32]	V. Jayaraman, Jr. V. D. R. Guide and R. Srivastava, Closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, 50 (1999), 497-508. doi: 10.1057/palgrave.jors.2600716. Google Scholar
[33]	A. Jindal and K. S. Sangwan, Closed loop supply chain network design and optimization using Fuzzy mixed integer linear programming model, International Journal of Production Research, 52 (2013), 4156-4173. Google Scholar
[34]	W. Kerr and C. Ryan, Eco-efficiency gains from remanufacturing: A case study of photocopier remanufacturing at Fuji Xerox Australia, Journal of Cleaner Production, 9 (2001), 75-81. Google Scholar
[35]	G. Kizilboga, G. Mandil, M. E. Genevois and P. Zwolinski, Remanufacturing network design modeling: A case of diesel particulate filter, Procedia CIRP, 11 (2013), 163-168. doi: 10.1016/j.procir.2013.07.048. Google Scholar
[36]	D. H. Lee and M. Dong, A heuristic approach to logistics network design for end-of-lease Computer products recovery, Transportation Research Part E: Logistics and Transportation Review, 44 (2008), 455-474. doi: 10.1016/j.tre.2006.11.003. Google Scholar
[37]	S. Liu and L. G. Papageorgiou, Multi objective optimization of production, distribution and capacity planning of global supply chains in the process industry, Omega, 41 (2013), 369–382, management science and environmental issues. https://doi.org/10.1016/j.omega.2012.03.007. Google Scholar
[38]	D. Mathivathanan, D. Kannan and A. N. Haq, Sustainable supply chain management practices in Indian automotive industry: A multi-stakeholder view, Resources, Conservation and Recycling, 128 (2018), 284-305. doi: 10.1016/j.resconrec.2017.01.003. Google Scholar
[39]	L. A. Moncayo-MartÁnez and D. Z. Zhang, Multi-objective ant colony optimisation: A meta-heuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407–420, innsbruck 2008. https://doi.org/10.1016/j.ijpe.2010.11.026. Google Scholar
[40]	B. Mota, M. I. Gomes, A. Carvalho and A. P. Barbosa-Povoa, Towards supply chain sustainability: Economic, environmental and social design and planning, Journal of Cleaner Production, 105 (2015), 14-27. doi: 10.1016/j.jclepro.2014.07.052. Google Scholar
[41]	A. Mutha and S. Pokharel, Strategic network design for reverse logistics and remanufacturing using new and old product modules, Computers & Industrial Engineering, 56 (2009), 334-346. doi: 10.1016/j.cie.2008.06.006. Google Scholar
[42]	E. $ \phi $zceylan and T. Paksoy, A mixed integer programming model for a closed-loop supply-chain network, International Journal of Production Research, 51 (2012), 718-734. doi: 10.1080/00207543.2012.661090. Google Scholar
[43]	A. Pedram, N. Bin Yusoff, O. Ezutah Udoncy, A. B. Mahat, P. Pedram and A. Babaloha, Integrated forward and reverse supply chain: A tier case study.Waste Management, Waste Management, 60 (2017), 460-470. doi: 10.1016/j.wasman.2016.06.029. Google Scholar
[44]	R. Piplani and A. Saraswat, Robust optimization approach to the design of service networks for reverse logistics, International Journal of Production Research, 50 (2012), 1424–1437. https://doi.org/10.1080/00207543.2011.571942. Google Scholar
[45]	M. S. Pishvaee, J. Razmi and S. A. Torabi, Robust possibilistic programming for socially responsible supply chain network design: A new approach, Fuzzy Sets and Systems, 206 (2012), 1-20. doi: 10.1016/j.fss.2012.04.010. Google Scholar
[46]	E. N. Pistikopoulos and A. Hugo, Environmentally conscious long-range planning and design of supply chain networks, Journal of Cleaner Production, 13 (2005), 1471-1491. doi: 10.1016/j.jclepro.2005.04.011. Google Scholar
[47]	C. Pozo, R. Ruz-Femenia, J. Caballero, G. Guilln Goslbez and L. Jimnez, On the use of principal component analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains, Chemical Engineering Science, 69 (2012), 146-158. doi: 10.1016/j.ces.2011.10.018. Google Scholar
[48]	L. C. Roca and C. Searcy, An analysis of indicators disclosed in corporate sustainability reports, Journal of Cleaner Production, 20 (2012), 103-118. doi: 10.1016/j.jclepro.2011.08.002. Google Scholar
[49]	S. K. Roy, G. Maity, G. W. Weber and S. Z. A. GÚk, Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal, Annals of Operations Research, 253 (2017), 599-620. doi: 10.1007/s10479-016-2283-4. Google Scholar
[50]	S. K. Roy and S. Midya, Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment, Applied Intelligence, 49 (2019), 3524–3538. https://doi.org/10.1007/s10489-019-01466-9. Google Scholar
[51]	S. K. Roy, G. Maity and G.-W. Weber, Multi-objective two-stage grey transportation problem using utility function with goals, Central European Journal of Operations Research, 25 (2017), 417-439. doi: 10.1007/s10100-016-0464-5. Google Scholar
[52]	N. Sabio, A. Kostin, G. Guilln-Goslbez and L. Jimnez, Holistic minimization of the life cycle environmental impact of hydrogen infrastructures using multi-objective optimization and principal component analysis, International Journal of Hydrogen Energy, 37 (2012), 5385–5405, optimization Approaches to Hydrogen Logistics. doi: 10.1016/j.ijhydene.2011.09.039. Google Scholar
[53]	F. Schultmann, M. Zumkeller and et al., Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry, European Journal of Operational Research, 171 (2006), 1033-1050. doi: 10.1016/j.ejor.2005.01.016. Google Scholar
[54]	L. H. Shih, Reverse logistics system planning for recycling electrical appliances and computers in Taiwan, Resources, Conservation and Recycling, 32 (2001), 55-72. doi: 10.1016/S0921-3449(00)00098-7. Google Scholar
[55]	H. Úster, G. Easwaran, E. AkÃali and S. Cetinkaya, Benders decomposition with alternative Multiple cuts for a multi$\hat{a}$product closed$\hat{a}$loop supply chain network design model, Naval Research Logistics, 54 (2007), 890-907. doi: 10.1002/nav.20262. Google Scholar
[56]	F. Wang, X. Lai and N. Shi, A multi-objective optimization for green supply chain network design, Decision Support Systems, 51 (2011), 262–269, multiple Criteria Decision Making and Decision Support Systems. doi: 10.1016/j.dss.2010.11.020. Google Scholar
[57]	C. D. White, E. Masanet and et al., Product recovery with some byte: An overview of management challenges and environmental consequences in reverse manufacturing for the computer industry, Journal of Cleaner Production, 11 (2003), 445-458. doi: 10.1016/S0959-6526(02)00066-5. Google Scholar
[58]	P. Yi, M. Huang, L. Guo and T. Shi, A retailer oriented closed-loop supply chain network design for end of life construction machinery remanufacturing, Journal of Cleaner Production, 124 (2016), 191-203. doi: 10.1016/j.jclepro.2016.02.070. Google Scholar
[59]	M. Zhang, Y. K. Tse, B. Doherty, S. Li and P. Akhtar, Sustainable supply chain management: Confirmation of a higher-order model, Resources, Conservation and Recycling, 128 (2018), 206-221. doi: 10.1016/j.resconrec.2016.06.015. Google Scholar
[60]	Q. Zhao and M. Chen, A comparison of ELV recycling system in China and Japan and China's strategies, Resources, Conservation and Recycling, 57 (2011), 15-21. doi: 10.1016/j.resconrec.2011.09.010. Google Scholar

show all references

References:

[1]	F. Altiparmak, M. Gen, L. Lin and T. Paksoy, A genetic algorithm approach for multi-objective optimization of supply chain networks, Computers & Industrial Engineering, 51 (2006), 196–215, special Issue on Computational Intelligence and Information Technology: Applications to Industrial Engineering 33rd. ICC & amp; IE - Computational Intelligence & amp; Information. doi: 10.1016/j.cie.2006.07.011. Google Scholar
[2]	Y. Cardona-ValdÂes, A. Âlvarez and D. Ozdemir, A bi objective supply chain design problem with uncertainty, Transportation Research Part C: Emerging Technologies19, 5 (2011), 821–832, freight Transportation and Logistics(selected papers from{ODYSSEUS}2009-the4th International Work shop on Freight Transportation and Logistics). doi: 10.1016/j.trc.2010.04.003. Google Scholar
[3]	S. R. Cardoso, A. P. F. Barbosa-Povoa and S. Relvas, Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty, European Journal of Operational Research, 226 (2013), 436-451. doi: 10.1016/j.ejor.2012.11.035. Google Scholar
[4]	C. R. Carter and M. M. Jennings, Social responsibility and supply chain relationships, Transportation Research Part E: Logistics and Transportation Review, 38 (2002), 37-52. doi: 10.1016/S1366-5545(01)00008-4. Google Scholar
[5]	C. R. Carter and M. M. Jennings, Logistics social responsibility: An integrative framework, Journal of Business Logistics, 23 (2002), 145-180. Google Scholar
[6]	A. Chaabane, A. Ramudhin and M. Paquet, Design of sustainable supply chains under the emission trading scheme, International Journal of Production Economics, 135 (2012), 37-49. doi: 10.1016/j.ijpe.2010.10.025. Google Scholar
[7]	H. K. Chan and V. Jain, A framework of reverse logistics for the automobile industry, International Journal of Production Research, 50 (2012), 1318-1331. doi: 10.1080/00207543.2011.571929. Google Scholar
[8]	Z. Che and C. Chiang, A modiiï ed Pareto genetic algorithm for multi-objective build-to-order supply chain planning with product assembly, Advances in Engineering Software, 41 (78) (2010), 1011–1022, advances in Structural Optimization. doi: 10.1016/j.advengsoft.2010.04.001. Google Scholar
[9]	S. Chopra and P. Meindl, Supply chain management: Strategy, planning, and operation, Das Summa Summarum des Management, 2007,265–275. doi: 10.1007/978-3-8349-9320-5_22. Google Scholar
[10]	J. M. Cruz, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European Journal of Operational Research, 184 (2008), 1005-1031. doi: 10.1016/j.ejor.2006.12.012. Google Scholar
[11]	R. Cruz-Rivera and J. Ertel, Reverse logistics network design for the collection of End-of-Life Vehicles in Mexico, European Journal of Operational Research, 196 (2009), 930-939. doi: 10.1016/j.ejor.2008.04.041. Google Scholar
[12]	J. M. Cruz and T. Wakolbinger, Multiperiod effects of corporate social responsibility on supply chain networks, transaction costs, emissions, and risk, International Journal of Production Economics, 116 (2008), 61-74. doi: 10.1016/j.ijpe.2008.07.011. Google Scholar
[13]	J. M. Cruz, The impact of corporate social responsibility in supply chain management: Multicriteria decision-making approach, Decision Support Systems, 48 (2009), 224-236. doi: 10.1016/j.dss.2009.07.013. Google Scholar
[14]	S. K. Das and S. K. Roy, Effect of variable carbon emission in a multi-objective transportation-p-facility location problem under neutrosophic environment, Computers & Industrial Engineering, 132 (2019), 311-324. Google Scholar
[15]	S. K. Das, S. K. Roy and G. W. Weber, Heuristic approaches for solid transportation-P-facility location problem, Central European Journal of Operations Research, (2019), 1–23. doi: 10.1007/s10100-019-00610-7. Google Scholar
[16]	N. Demirel and H. GÚkÃen, A mixed integer programming model for remanufacturing in reverse logistics environment, International Journal of Advanced Manufacturing Technology, 39 (2008), 1197-1206. doi: 10.1007/s00170-007-1290-7. Google Scholar
[17]	M. Eskandarpour, P. Dejax, J. Miemczyk and O. Peton, Sustainable supply chain network design: An optimization-oriented review, Omega, 54 (2015), 11-32. doi: 10.1016/j.omega.2015.01.006. Google Scholar
[18]	G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26. doi: 10.1287/mnsc.1050.0465. Google Scholar
[19]	M. Fleischmann, P. Beullens, J. M. Bloemhof-Ruwaard and L. N. Van Wassenhove, The impact of product recovery on logistics network design, Production and Operations Management, 10 (2001), 156-173. doi: 10.1111/j.1937-5956.2001.tb00076.x. Google Scholar
[20]	M. Fleischmann, H. Krikke, R. Dekker and S. Flapper, A characterization of logistics networks for product recovery, Omega, 28 (2000), 653-666. Google Scholar
[21]	R. B. Franca, E. C. Jones, C. N. Richards and J. P. Carlson, Multi-objective stochastic supply chain modeling to evaluate tradeoïs between proït and quality, International Journal of Production Economics 127 ({2}) (2010), 292–299, supply Chain Planning and Conïguration in the Global Arena. Google Scholar
[22]	J. Q. Frota Neto, J. M. Bloemhof-Ruwaard and et al, Designing and evaluating sustainable logistics networks, International Journal of Production Economics, 111 (2008), 195-208. doi: 10.1016/j.ijpe.2006.10.014. Google Scholar
[23]	K. Garg, D. Kannan, A. Diabat and P. C. Jha, A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design, Journal of Cleaner Production, 100 (2015), 297-314. doi: 10.1016/j.jclepro.2015.02.075. Google Scholar
[24]	S. Giarola, A. Zamboni and F. Bezzo, Spatially explicit multi-objective optimization for design and planning of hybrid ïrst and second generation bioreïneries, Computers & Chemical Engineering, 35 (2011), 1782–1797, energy Systems Engineering. doi: 10.1016/j.compchemeng.2011.01.020. Google Scholar
[25]	M. Goetschalcks and B. Fleischmann, Strategic network design, Supply Chain Management and Advanced Planning, (2008), 117–132. doi: 10.1007/978-3-540-74512-9_7. Google Scholar
[26]	Jr. V. D. R. Guide and L. N. Van Wassenhove, Closed-loop supply chains, quantitative approaches to distribution logistics and supply chain management, Springer, 47–60. Google Scholar
[27]	T. G. Gutowski, C. F. Murphy, D. T. Allen and et al, WTEC Panel Report on: Environmentally Benign Manufacturing (EBM), International Technology Research Institute, World Technology (WTEC) Division, Baltimore, Maryland. Google Scholar
[28]	P. Hasanov, M. Y. Jaber, S. Zanoni, L. E. Zavanella, Closed-loop supphy chain system with energy, transportation and waste disposal costs, International Journal of Sustainable Engineering, (2013), 352–358. doi: 10.1080/19397038.2012.762433. Google Scholar
[29]	M. A. Ilgin and S. M. Gupta, Environmentally conscious manufacturing and product recovery (ECMPRO): A review of the state of the art, Journal of Environmental Management, 91 (2010), 563-591. doi: 10.1016/j.jenvman.2009.09.037. Google Scholar
[30]	G. R. Initiative, Sustainability Reporting Guidelines (G4), Global Reporting Initiative, 2013. Google Scholar
[31]	R. Jamshidi, S. F. Ghomi and B. Karimi, Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the taguchi method, Scientia Iranica, 19 (2012), 1876-1886. doi: 10.1016/j.scient.2012.07.002. Google Scholar
[32]	V. Jayaraman, Jr. V. D. R. Guide and R. Srivastava, Closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, 50 (1999), 497-508. doi: 10.1057/palgrave.jors.2600716. Google Scholar
[33]	A. Jindal and K. S. Sangwan, Closed loop supply chain network design and optimization using Fuzzy mixed integer linear programming model, International Journal of Production Research, 52 (2013), 4156-4173. Google Scholar
[34]	W. Kerr and C. Ryan, Eco-efficiency gains from remanufacturing: A case study of photocopier remanufacturing at Fuji Xerox Australia, Journal of Cleaner Production, 9 (2001), 75-81. Google Scholar
[35]	G. Kizilboga, G. Mandil, M. E. Genevois and P. Zwolinski, Remanufacturing network design modeling: A case of diesel particulate filter, Procedia CIRP, 11 (2013), 163-168. doi: 10.1016/j.procir.2013.07.048. Google Scholar
[36]	D. H. Lee and M. Dong, A heuristic approach to logistics network design for end-of-lease Computer products recovery, Transportation Research Part E: Logistics and Transportation Review, 44 (2008), 455-474. doi: 10.1016/j.tre.2006.11.003. Google Scholar
[37]	S. Liu and L. G. Papageorgiou, Multi objective optimization of production, distribution and capacity planning of global supply chains in the process industry, Omega, 41 (2013), 369–382, management science and environmental issues. https://doi.org/10.1016/j.omega.2012.03.007. Google Scholar
[38]	D. Mathivathanan, D. Kannan and A. N. Haq, Sustainable supply chain management practices in Indian automotive industry: A multi-stakeholder view, Resources, Conservation and Recycling, 128 (2018), 284-305. doi: 10.1016/j.resconrec.2017.01.003. Google Scholar
[39]	L. A. Moncayo-MartÁnez and D. Z. Zhang, Multi-objective ant colony optimisation: A meta-heuristic approach to supply chain design, International Journal of Production Economics, 131 (2011), 407–420, innsbruck 2008. https://doi.org/10.1016/j.ijpe.2010.11.026. Google Scholar
[40]	B. Mota, M. I. Gomes, A. Carvalho and A. P. Barbosa-Povoa, Towards supply chain sustainability: Economic, environmental and social design and planning, Journal of Cleaner Production, 105 (2015), 14-27. doi: 10.1016/j.jclepro.2014.07.052. Google Scholar
[41]	A. Mutha and S. Pokharel, Strategic network design for reverse logistics and remanufacturing using new and old product modules, Computers & Industrial Engineering, 56 (2009), 334-346. doi: 10.1016/j.cie.2008.06.006. Google Scholar
[42]	E. $ \phi $zceylan and T. Paksoy, A mixed integer programming model for a closed-loop supply-chain network, International Journal of Production Research, 51 (2012), 718-734. doi: 10.1080/00207543.2012.661090. Google Scholar
[43]	A. Pedram, N. Bin Yusoff, O. Ezutah Udoncy, A. B. Mahat, P. Pedram and A. Babaloha, Integrated forward and reverse supply chain: A tier case study.Waste Management, Waste Management, 60 (2017), 460-470. doi: 10.1016/j.wasman.2016.06.029. Google Scholar
[44]	R. Piplani and A. Saraswat, Robust optimization approach to the design of service networks for reverse logistics, International Journal of Production Research, 50 (2012), 1424–1437. https://doi.org/10.1080/00207543.2011.571942. Google Scholar
[45]	M. S. Pishvaee, J. Razmi and S. A. Torabi, Robust possibilistic programming for socially responsible supply chain network design: A new approach, Fuzzy Sets and Systems, 206 (2012), 1-20. doi: 10.1016/j.fss.2012.04.010. Google Scholar
[46]	E. N. Pistikopoulos and A. Hugo, Environmentally conscious long-range planning and design of supply chain networks, Journal of Cleaner Production, 13 (2005), 1471-1491. doi: 10.1016/j.jclepro.2005.04.011. Google Scholar
[47]	C. Pozo, R. Ruz-Femenia, J. Caballero, G. Guilln Goslbez and L. Jimnez, On the use of principal component analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains, Chemical Engineering Science, 69 (2012), 146-158. doi: 10.1016/j.ces.2011.10.018. Google Scholar
[48]	L. C. Roca and C. Searcy, An analysis of indicators disclosed in corporate sustainability reports, Journal of Cleaner Production, 20 (2012), 103-118. doi: 10.1016/j.jclepro.2011.08.002. Google Scholar
[49]	S. K. Roy, G. Maity, G. W. Weber and S. Z. A. GÚk, Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal, Annals of Operations Research, 253 (2017), 599-620. doi: 10.1007/s10479-016-2283-4. Google Scholar
[50]	S. K. Roy and S. Midya, Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment, Applied Intelligence, 49 (2019), 3524–3538. https://doi.org/10.1007/s10489-019-01466-9. Google Scholar
[51]	S. K. Roy, G. Maity and G.-W. Weber, Multi-objective two-stage grey transportation problem using utility function with goals, Central European Journal of Operations Research, 25 (2017), 417-439. doi: 10.1007/s10100-016-0464-5. Google Scholar
[52]	N. Sabio, A. Kostin, G. Guilln-Goslbez and L. Jimnez, Holistic minimization of the life cycle environmental impact of hydrogen infrastructures using multi-objective optimization and principal component analysis, International Journal of Hydrogen Energy, 37 (2012), 5385–5405, optimization Approaches to Hydrogen Logistics. doi: 10.1016/j.ijhydene.2011.09.039. Google Scholar
[53]	F. Schultmann, M. Zumkeller and et al., Modeling reverse logistic tasks within closed-loop supply chains: An example from the automotive industry, European Journal of Operational Research, 171 (2006), 1033-1050. doi: 10.1016/j.ejor.2005.01.016. Google Scholar
[54]	L. H. Shih, Reverse logistics system planning for recycling electrical appliances and computers in Taiwan, Resources, Conservation and Recycling, 32 (2001), 55-72. doi: 10.1016/S0921-3449(00)00098-7. Google Scholar
[55]	H. Úster, G. Easwaran, E. AkÃali and S. Cetinkaya, Benders decomposition with alternative Multiple cuts for a multi$\hat{a}$product closed$\hat{a}$loop supply chain network design model, Naval Research Logistics, 54 (2007), 890-907. doi: 10.1002/nav.20262. Google Scholar
[56]	F. Wang, X. Lai and N. Shi, A multi-objective optimization for green supply chain network design, Decision Support Systems, 51 (2011), 262–269, multiple Criteria Decision Making and Decision Support Systems. doi: 10.1016/j.dss.2010.11.020. Google Scholar
[57]	C. D. White, E. Masanet and et al., Product recovery with some byte: An overview of management challenges and environmental consequences in reverse manufacturing for the computer industry, Journal of Cleaner Production, 11 (2003), 445-458. doi: 10.1016/S0959-6526(02)00066-5. Google Scholar
[58]	P. Yi, M. Huang, L. Guo and T. Shi, A retailer oriented closed-loop supply chain network design for end of life construction machinery remanufacturing, Journal of Cleaner Production, 124 (2016), 191-203. doi: 10.1016/j.jclepro.2016.02.070. Google Scholar
[59]	M. Zhang, Y. K. Tse, B. Doherty, S. Li and P. Akhtar, Sustainable supply chain management: Confirmation of a higher-order model, Resources, Conservation and Recycling, 128 (2018), 206-221. doi: 10.1016/j.resconrec.2016.06.015. Google Scholar
[60]	Q. Zhao and M. Chen, A comparison of ELV recycling system in China and Japan and China's strategies, Resources, Conservation and Recycling, 57 (2011), 15-21. doi: 10.1016/j.resconrec.2011.09.010. Google Scholar

Figure 1. Supply chain of closed loop for recovering machinery at the end of their life cycle based on sustainability dimensions

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2. The change of the value of the objective function by changes in $ q_c $.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3. The change in the value of the objective function by changes in$ {\ DR}_c $.

Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4. The change in the value of the objective function by the changes in $ {\ V}_p $.

Figure Options

Download full-size image

Download as PowerPoint slide

Table111

C = $ \left\{1,2,\dots ,c\right\} $	Set of consumer zone
D = $ \left\{1,2,\dots ,d\right\} $	Set of collection /distribution centers
A = $ \left\{1,2,\dots ,a\right\} $	Set of potential Assembly / Disassembly centers locations
RM = $ \left\{1,2,\dots ,rm\right\} $	Set of potential remanufacture centers locations
RC = $ \left\{1,2,\dots ,rc\right\} $	Set of potential recycling centers locations
RU = $ \left\{1,2,\dots ,ru\right\} $	Set of potential reusing centers locations
L = $ \left\{1,2,\dots ,l\right\} $	Set of disposal centers
S = $ \left\{1,2,\dots ,s\right\} $	Set of suppliers
TC = $ \left\{1,2,\dots ,tc\right\} $	Transportation options from consumers
TD = $ \left\{1,2,\dots ,td\right\} $	Transportation options from collection /distribution centers
TA = $ \left\{1,2,\dots ,ta\right\} $	Transportation options from Assembly / Disassembly centers
TS = $ \left\{1,2,\dots ,ts\right\} $	Transportation options from suppliers
M = $ \left\{1,2,\dots ,m\right\} $	Set of products
P = $ \left\{1,2,\dots ,p\right\} $	Set of components

Table Options

Download as excel

C = $ \left\{1,2,\dots ,c\right\} $	Set of consumer zone
D = $ \left\{1,2,\dots ,d\right\} $	Set of collection /distribution centers
A = $ \left\{1,2,\dots ,a\right\} $	Set of potential Assembly / Disassembly centers locations
RM = $ \left\{1,2,\dots ,rm\right\} $	Set of potential remanufacture centers locations
RC = $ \left\{1,2,\dots ,rc\right\} $	Set of potential recycling centers locations
RU = $ \left\{1,2,\dots ,ru\right\} $	Set of potential reusing centers locations
L = $ \left\{1,2,\dots ,l\right\} $	Set of disposal centers
S = $ \left\{1,2,\dots ,s\right\} $	Set of suppliers
TC = $ \left\{1,2,\dots ,tc\right\} $	Transportation options from consumers
TD = $ \left\{1,2,\dots ,td\right\} $	Transportation options from collection /distribution centers
TA = $ \left\{1,2,\dots ,ta\right\} $	Transportation options from Assembly / Disassembly centers
TS = $ \left\{1,2,\dots ,ts\right\} $	Transportation options from suppliers
M = $ \left\{1,2,\dots ,m\right\} $	Set of products
P = $ \left\{1,2,\dots ,p\right\} $	Set of components

Table112

$ {CTR}^m_{tc\ c\ d} $	The transportation cost of used products per km between consumer zone and collection /distribution centers with transportation option tc.
$ {CTR}^m_{td\ d\ a} $	The transportation cost of used products per km between collection /distribution centers and Assembly / Disassembly centers with transportation option td.
$ {CTR}^p_{ta\ a\ rm} $	The transportation cost of used parts per km between Assembly/ Disassembly centers and remanufacturing centers with transportation option ta.
$ {CTR}^p_{ta\ a\ rc} $	The transportation cost of used parts per km between Assembly/ Disassembly centers and recycling centers with transportation option ta.
$ {CTR}^p_{ta\ a\ ru} $	The transportation cost of reusable parts per km between Assembly/ Disassembly centers and reusing centers with transportation option ta.
$ {CTR}^p_{ta\ a\ l} $	The transportation cost of disposal parts per km between Assembly/ Disassembly centers and disposal centers with transportation option ta.
$ {CTR}^p_{ts\ \ s\ a} $	The transportation cost of new parts per km between suppliers and Assembly / Disassembly centers with transportation option ts.
$ {CTR}^p_{tc\ ru\ c} $	The transportation cost of reusable parts per km between reusing centers and consumer zone with transportation option tc.
$ {CTR}^p_{ts\ rc\ s} $	The transportation cost of recycled parts per km between recycle centers and suppliers with transportation option ts.
$ {CTR}^p_{ta\ rm\ a} $	The transportation cost of remanufactured parts per km between remanufacturing centers and Assembly/ Disassembly centers with transportation option ta.
$ {CTR}^m_{ta\ a\ d} $	The transportation cost of remanufactured products per km between Assembly / Disassembly centers and collection /distribution centers with transportation option ta.
$ {CTR}^m_{td\ d\ c} $	The transportation cost of remanufactured products per km between collection /distribution centers and consumer zone with transportation option td.
$ {dis}_{c\ d} $	Distance from c to d
$ {dis}_{d\ a} $	Distance from d to a
$ {dis}_{a\ l} $	Distance from a to l
$ {dis}_{a\ rm} $	Distance from a to rm
$ {dis}_{a\ rc} $	Distance from a to rc
$ {dis}_{a\ ru} $	Distance from a to ru
$ {dis}_{rc\ s} $	Distance from rc to s
$ {dis}_{s\ a} $	Distance from s to a
$ {CAP}_a $	Capacity of Assembly / Disassembly centers
$ {CAP}_{rm} $	Capacity of remanufacturing centers for parts
$ {CAP}_{rc} $	Capacity of recycling centers for parts
$ {CAP}_{ru} $	Capacity of reusing centers for parts
$ {cd}_m $	Unit dismantling cost for product m in Assembly / Disassembly centers
$ {ca}_m $	Unit assembling cost for product m in Assembly / Disassembly centers
$ c_i $	Unit inspection cost for parts
$ {crm}_p $	Unit remanufacturing costs for part p in remanufacturing centers
$ {crc}_p $	Unit recycling costs for part p in recycling centers
$ {cru}_p $	Unit preparing cost for reusing the parts in reusing center
$ {cs}_p $	Unit supplying cost for the parts
$ F_a $	Fixed cost for opening Assembly / Disassembly centers
$ F_{rm} $	Fixed cost for opening remanufacturing centers
$ F_{rc} $	Fixed cost for opening recycling centers
$ F_{ru} $	Fixed cost for opening reusing centers
$ F_d $	Cost for expanding a distribution center to a combined collection / distribution facility
$ {\lambda }_c $	Collection ratio in the consumer's zone
$\hat I$	Badly-damaged ratio of the used part
$\hat I$	Remanufacturing ratio of the used part
$\hat I$	Recycling ratio of the used part
${\hat I}_{¸} $	Reusing ratio of the used part
$ q_c $	Supply for the used product in the consumer's zone
$ {DR}_c $	Demand for the remanufactured product in the consumer's zone
$ V_p $	Unit volume of the part in product
$ e_{rm} $	Rate of released $ {CO}_2 $ to remanufacture one unit of the product in remanufacturing centers
$ {eCD}^{tc} $	The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the used product from the consumer's zone to collection /distribution centers for a unit distance.
$ {eDA}^{td} $	The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the used product from collection /distribution centers to Assembly / Disassembly centers for a unit distance.
$ {eARM}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to remanufacturing centers for a unit distance.
$ {eARC}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to recycling centers for a unit distance.
$ {eARU}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to reusing centers for a unit distance.
$ {eAL}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the disposal part from Assembly / Disassembly centers to disposal centers for a unit distance.
$ {eSA}^{ts} $	The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the new part from suppliers to Assembly / Disassembly centers for a unit distance.
$ {eRUC}^{tc} $	The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the reusable part from reusing centers to the consumer's zone for a unit distance.
$ {eRCS}^{ts} $	The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the recycled part from recycling centers to suppliers for a unit distance.
$ {eRMA}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured part from remanufacturing centers to Assembly / Disassembly centers for a unit distance.
$ {eAD}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured product from Assembly / Disassembly centers to collection /distribution centers for a unit distance.
$ {eDC}^{td} $	The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the remanufactured product from collection /distribution centers to the consumer's zone for a unit distance.
$ H_{tc} $	Capacity of transportation option tc
$ H_{td} $	Capacity of transportation option td
$ H_{ta} $	Capacity of transportation option ta
$ H_{ts} $	Capacity of transportation option ts
$ {\varphi }_a $	The number of the fixed job opportunities created by launching the Assembly / Disassembly centers
$ {\varphi }_{rm} $	The number of the fixed job opportunities created by launching the remanufacturing centers
$ {\varphi }_{rc} $	The number of the fixed job opportunities created by launching the recycling centers
$ {\varphi }_{ru} $	The number of the fixed job opportunities created by launching the reusing centers
$ {\mu }_a $	The number of the created variable job opportunities by working in Assembly / Disassembly centers
$ {\mu }_{rm} $	The number of the created variable job opportunities by working in remanufacturing centers
$ {\mu }_{rc} $	The number of the created variable job opportunities by working in recycling centers
$ {\mu }_{ru} $	The number of the created variable job opportunities by working in reusing centers

Table Options

Download as excel

$ {CTR}^m_{tc\ c\ d} $	The transportation cost of used products per km between consumer zone and collection /distribution centers with transportation option tc.
$ {CTR}^m_{td\ d\ a} $	The transportation cost of used products per km between collection /distribution centers and Assembly / Disassembly centers with transportation option td.
$ {CTR}^p_{ta\ a\ rm} $	The transportation cost of used parts per km between Assembly/ Disassembly centers and remanufacturing centers with transportation option ta.
$ {CTR}^p_{ta\ a\ rc} $	The transportation cost of used parts per km between Assembly/ Disassembly centers and recycling centers with transportation option ta.
$ {CTR}^p_{ta\ a\ ru} $	The transportation cost of reusable parts per km between Assembly/ Disassembly centers and reusing centers with transportation option ta.
$ {CTR}^p_{ta\ a\ l} $	The transportation cost of disposal parts per km between Assembly/ Disassembly centers and disposal centers with transportation option ta.
$ {CTR}^p_{ts\ \ s\ a} $	The transportation cost of new parts per km between suppliers and Assembly / Disassembly centers with transportation option ts.
$ {CTR}^p_{tc\ ru\ c} $	The transportation cost of reusable parts per km between reusing centers and consumer zone with transportation option tc.
$ {CTR}^p_{ts\ rc\ s} $	The transportation cost of recycled parts per km between recycle centers and suppliers with transportation option ts.
$ {CTR}^p_{ta\ rm\ a} $	The transportation cost of remanufactured parts per km between remanufacturing centers and Assembly/ Disassembly centers with transportation option ta.
$ {CTR}^m_{ta\ a\ d} $	The transportation cost of remanufactured products per km between Assembly / Disassembly centers and collection /distribution centers with transportation option ta.
$ {CTR}^m_{td\ d\ c} $	The transportation cost of remanufactured products per km between collection /distribution centers and consumer zone with transportation option td.
$ {dis}_{c\ d} $	Distance from c to d
$ {dis}_{d\ a} $	Distance from d to a
$ {dis}_{a\ l} $	Distance from a to l
$ {dis}_{a\ rm} $	Distance from a to rm
$ {dis}_{a\ rc} $	Distance from a to rc
$ {dis}_{a\ ru} $	Distance from a to ru
$ {dis}_{rc\ s} $	Distance from rc to s
$ {dis}_{s\ a} $	Distance from s to a
$ {CAP}_a $	Capacity of Assembly / Disassembly centers
$ {CAP}_{rm} $	Capacity of remanufacturing centers for parts
$ {CAP}_{rc} $	Capacity of recycling centers for parts
$ {CAP}_{ru} $	Capacity of reusing centers for parts
$ {cd}_m $	Unit dismantling cost for product m in Assembly / Disassembly centers
$ {ca}_m $	Unit assembling cost for product m in Assembly / Disassembly centers
$ c_i $	Unit inspection cost for parts
$ {crm}_p $	Unit remanufacturing costs for part p in remanufacturing centers
$ {crc}_p $	Unit recycling costs for part p in recycling centers
$ {cru}_p $	Unit preparing cost for reusing the parts in reusing center
$ {cs}_p $	Unit supplying cost for the parts
$ F_a $	Fixed cost for opening Assembly / Disassembly centers
$ F_{rm} $	Fixed cost for opening remanufacturing centers
$ F_{rc} $	Fixed cost for opening recycling centers
$ F_{ru} $	Fixed cost for opening reusing centers
$ F_d $	Cost for expanding a distribution center to a combined collection / distribution facility
$ {\lambda }_c $	Collection ratio in the consumer's zone
$\hat I$	Badly-damaged ratio of the used part
$\hat I$	Remanufacturing ratio of the used part
$\hat I$	Recycling ratio of the used part
${\hat I}_{¸} $	Reusing ratio of the used part
$ q_c $	Supply for the used product in the consumer's zone
$ {DR}_c $	Demand for the remanufactured product in the consumer's zone
$ V_p $	Unit volume of the part in product
$ e_{rm} $	Rate of released $ {CO}_2 $ to remanufacture one unit of the product in remanufacturing centers
$ {eCD}^{tc} $	The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the used product from the consumer's zone to collection /distribution centers for a unit distance.
$ {eDA}^{td} $	The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the used product from collection /distribution centers to Assembly / Disassembly centers for a unit distance.
$ {eARM}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to remanufacturing centers for a unit distance.
$ {eARC}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to recycling centers for a unit distance.
$ {eARU}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the used part from Assembly / Disassembly centers to reusing centers for a unit distance.
$ {eAL}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the disposal part from Assembly / Disassembly centers to disposal centers for a unit distance.
$ {eSA}^{ts} $	The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the new part from suppliers to Assembly / Disassembly centers for a unit distance.
$ {eRUC}^{tc} $	The amount of CO$ {}_{2} $ released by transportation option tc to send a unit of the reusable part from reusing centers to the consumer's zone for a unit distance.
$ {eRCS}^{ts} $	The amount of CO$ {}_{2} $ released by transportation option ts to send a unit of the recycled part from recycling centers to suppliers for a unit distance.
$ {eRMA}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured part from remanufacturing centers to Assembly / Disassembly centers for a unit distance.
$ {eAD}^{ta} $	The amount of CO$ {}_{2} $ released by transportation option ta to send a unit of the remanufactured product from Assembly / Disassembly centers to collection /distribution centers for a unit distance.
$ {eDC}^{td} $	The amount of CO$ {}_{2} $ released by transportation option td to send a unit of the remanufactured product from collection /distribution centers to the consumer's zone for a unit distance.
$ H_{tc} $	Capacity of transportation option tc
$ H_{td} $	Capacity of transportation option td
$ H_{ta} $	Capacity of transportation option ta
$ H_{ts} $	Capacity of transportation option ts
$ {\varphi }_a $	The number of the fixed job opportunities created by launching the Assembly / Disassembly centers
$ {\varphi }_{rm} $	The number of the fixed job opportunities created by launching the remanufacturing centers
$ {\varphi }_{rc} $	The number of the fixed job opportunities created by launching the recycling centers
$ {\varphi }_{ru} $	The number of the fixed job opportunities created by launching the reusing centers
$ {\mu }_a $	The number of the created variable job opportunities by working in Assembly / Disassembly centers
$ {\mu }_{rm} $	The number of the created variable job opportunities by working in remanufacturing centers
$ {\mu }_{rc} $	The number of the created variable job opportunities by working in recycling centers
$ {\mu }_{ru} $	The number of the created variable job opportunities by working in reusing centers

Table1112

$ Q^m_{tc\ c\ d} $	Quantity of the used products m from C to D with transportation option tc
$ Q^m_{td\ d\ a} $	Quantity of the used products m from D to A with transportation option td
$ Q^p_{ta\ a\ rm} $	Quantity of the used parts p from A to RM with transportation option ta
$ Q^p_{ta\ a\ rc} $	Quantity of the used parts p from A to RC with transportation option ta
$ Q^p_{ta\ a\ ru} $	Quantity of the reusable parts p from A to RU with transportation option ta
$ Q^p_{ta\ a\ l} $	Quantity of the disposal parts p from A to L with transportation option ta
$ Q^p_{ts\ s\ a} $	Quantity of the new parts p from S to A with transportation option ts
$ Q^p_{tc\ ru\ c} $	Quantity of the reusable parts p from RU to C with transportation option tc
$ Q^p_{ts\ rc\ s} $	Quantity of the recycled parts p from RC to S with transportation option ts
$ Q^p_{ta\ rm\ a} $	Quantity of the remanufactured parts p from RM to A with transportation option ta
$ Q^m_{ta\ a\ d} $	Quantity of the remanufactured products m from A to D with transportation option ta
$ Q^m_{td\ d\ c} $	Quantity of the remanufactured products m from D to C with transportation option td

Table Options

Download as excel

$ Q^m_{tc\ c\ d} $	Quantity of the used products m from C to D with transportation option tc
$ Q^m_{td\ d\ a} $	Quantity of the used products m from D to A with transportation option td
$ Q^p_{ta\ a\ rm} $	Quantity of the used parts p from A to RM with transportation option ta
$ Q^p_{ta\ a\ rc} $	Quantity of the used parts p from A to RC with transportation option ta
$ Q^p_{ta\ a\ ru} $	Quantity of the reusable parts p from A to RU with transportation option ta
$ Q^p_{ta\ a\ l} $	Quantity of the disposal parts p from A to L with transportation option ta
$ Q^p_{ts\ s\ a} $	Quantity of the new parts p from S to A with transportation option ts
$ Q^p_{tc\ ru\ c} $	Quantity of the reusable parts p from RU to C with transportation option tc
$ Q^p_{ts\ rc\ s} $	Quantity of the recycled parts p from RC to S with transportation option ts
$ Q^p_{ta\ rm\ a} $	Quantity of the remanufactured parts p from RM to A with transportation option ta
$ Q^m_{ta\ a\ d} $	Quantity of the remanufactured products m from A to D with transportation option ta
$ Q^m_{td\ d\ c} $	Quantity of the remanufactured products m from D to C with transportation option td

Table1113

$ X_a $	$ {{\rm X}}_{{\rm a}}{\rm = 1\ } $if Assembly / Disassembly center is open. Otherwise, $ {\rm \ }{{\rm X}}_{{\rm a}}{\rm = 0} $
$ Y_{rm} $	$ {{\rm Y}}_{{\rm rm}}{\rm = 1} $ if remanufacturing center is open. Otherwise, $ {{\rm Y}}_{{\rm rm}}{\rm = 0} $
$ Z_{rc} $	$ {{\rm Z}}_{{\rm rc}}{\rm = 1} $ if recycling center is open$ .\ {\rm Otherwise,\ }{\rm \ }{{\rm Z}}_{{\rm rc}}{\rm = 0} $
$ W_{ru} $	$ {{\rm W}}_{{\rm ru}}{\rm = 1} $ if reusing center is open$ .{\rm Otherwise,}{\rm \ }{{\rm W}}_{{\rm ru}}{\rm = 0} $

Table Options

Download as excel

$ X_a $	$ {{\rm X}}_{{\rm a}}{\rm = 1\ } $if Assembly / Disassembly center is open. Otherwise, $ {\rm \ }{{\rm X}}_{{\rm a}}{\rm = 0} $
$ Y_{rm} $	$ {{\rm Y}}_{{\rm rm}}{\rm = 1} $ if remanufacturing center is open. Otherwise, $ {{\rm Y}}_{{\rm rm}}{\rm = 0} $
$ Z_{rc} $	$ {{\rm Z}}_{{\rm rc}}{\rm = 1} $ if recycling center is open$ .\ {\rm Otherwise,\ }{\rm \ }{{\rm Z}}_{{\rm rc}}{\rm = 0} $
$ W_{ru} $	$ {{\rm W}}_{{\rm ru}}{\rm = 1} $ if reusing center is open$ .{\rm Otherwise,}{\rm \ }{{\rm W}}_{{\rm ru}}{\rm = 0} $

Table 1. The initial values of parameters

parameter	value	parameter	value
$ {CTR}^m_{tc\ c\ d} $	floor(uniform(1, 1500))	$ F_d $	floor(uniform(1, 8000000))
$ {CTR}^m_{td\ d\ a} $	floor(uniform(1, 1650))	$ q_c $	floor(uniform(1, 25))
$ {CTR}^p_{ta\ a\ rm} $	floor(uniform(1, 1867))	$ {DR}_c $	floor(uniform(1,100))
$ {CTR}^p_{ta\ a\ rc} $	floor(uniform(1, 1900))	$ V_p $	floor(uniform(1, 10))
$ {CTR}^p_{ta\ a\ ru} $	floor(uniform(1, 1972))	$ e_{rm} $	floor(uniform(1, 10))
$ {CTR}^p_{ta\ a\ l} $	floor(uniform(1, 2000))	$ {eCD}^{tc} $	floor(uniform(1, 30))
$ {CTR}^p_{ts\ \ s\ a} $	floor(uniform(1, 3613))	$ {eDA}^{td} $	floor(uniform(1, 40))
$ {CTR}^p_{tc\ ru\ c} $	floor(uniform(1, 2890))	$ {eARM}^{ta} $	floor(uniform(1, 50))
$ {CTR}^p_{ts\ rc\ s} $	floor(uniform(1, 4561))	$ {eARC}^{ta} $	floor(uniform(1, 90))
$ {CTR}^p_{ta\ rm\ a} $	floor(uniform(1, 3000))	$ {eARU}^{ta} $	floor(uniform(1, 80))
$ {CTR}^m_{ta\ a\ d} $	floor(uniform(1, 3700))	$ {eAL}^{ta} $	floor(uniform(1,100))
$ {CTR}^m_{td\ d\ c} $	floor(uniform(1, 9000))	$ {eSA}^{ts} $	floor(uniform(1, 70))
$ {dis}_{c\ d} $	floor(uniform(1,100))	$ {eRUC}^{tc} $	floor(uniform(1,120))
$ {dis}_{d\ a} $	floor(uniform(1,150))	$ {eRCS}^{ts} $	floor(uniform(1,150))
$ {dis}_{a\ l} $	floor(uniform(1,200))	$ {eRMA}^{ta} $	floor(uniform(1,190))
$ {dis}_{a\ rm} $	floor(uniform(1,300))	$ {eAD}^{ta} $	floor(uniform(1, 60))
$ {dis}_{a\ rc} $	floor(uniform(1,450))	$ {eDC}^{td} $	floor(uniform(1,170))
$ {dis}_{a\ ru} $	floor(uniform(1,700))	$ H_{tc} $	floor (uniform(1, 5))
$ {dis}_{rc\ s} $	floor(uniform(1,950))	$ H_{td} $	floor (uniform(1, 5))
$ {dis}_{s\ a} $	floor(uniform(1,800))	$ H_{ta} $	floor (uniform(1, 5))
$ {CAP}_a $	floor(uniform(120,150))	$ H_{ts} $	floor (uniform(1, 5))
$ {CAP}_{rm} $	floor(uniform(10, 50))	$ {\varphi }_a $	floor(uniform(1, 6000)
$ {CAP}_{rc} $	floor(uniform(10, 50))	$ {\varphi }_{rm} $	floor(uniform(1, 8500))
$ {CAP}_{ru} $	floor(uniform(10, 50))	$ {\varphi }_{rc} $	floor(uniform(1, 7000))
$ {cd}_m $	floor(uniform(1,100))	$ {\varphi }_{ru} $	floor(uniform(1, 9500))
$ {ca}_m $	floor(uniform(1,130))	$ {\mu }_a $	floor(uniform(1, 5000))
$ c_i $	floor(uniform(1, 90))	$ {\mu }_{rm} $	floor(uniform(1, 7000))
$ {crm}_p $	floor(uniform(1,170))	$ {\mu }_{rc} $	floor(uniform(1, 9000))
$ {crc}_p $	floor(uniform(1,200))	$ {\mu }_{ru} $	floor(uniform(1, 1000))
$ {cru}_p $	floor(uniform(1,350))	$ {\lambda }_c $	uniform(0, 1)
$ {cs}_p $	floor(uniform(1,100))	$\hat I$	uniform(0, 1)
$ F_a $	floor(uniform(1, 1000000))	$\hat I$	uniform(0, 0.001)
$ F_{rm} $	floor(uniform(1, 3000000))	$\hat I$	uniform(0, 1)
$ F_{rc} $	floor(uniform(1, 5000000))	${\hat I}_¸ $	uniform(0, 0.001)
$ F_{ru} $	floor(uniform(1, 4000000))

Table Options

Download as excel

parameter	value	parameter	value
$ {CTR}^m_{tc\ c\ d} $	floor(uniform(1, 1500))	$ F_d $	floor(uniform(1, 8000000))
$ {CTR}^m_{td\ d\ a} $	floor(uniform(1, 1650))	$ q_c $	floor(uniform(1, 25))
$ {CTR}^p_{ta\ a\ rm} $	floor(uniform(1, 1867))	$ {DR}_c $	floor(uniform(1,100))
$ {CTR}^p_{ta\ a\ rc} $	floor(uniform(1, 1900))	$ V_p $	floor(uniform(1, 10))
$ {CTR}^p_{ta\ a\ ru} $	floor(uniform(1, 1972))	$ e_{rm} $	floor(uniform(1, 10))
$ {CTR}^p_{ta\ a\ l} $	floor(uniform(1, 2000))	$ {eCD}^{tc} $	floor(uniform(1, 30))
$ {CTR}^p_{ts\ \ s\ a} $	floor(uniform(1, 3613))	$ {eDA}^{td} $	floor(uniform(1, 40))
$ {CTR}^p_{tc\ ru\ c} $	floor(uniform(1, 2890))	$ {eARM}^{ta} $	floor(uniform(1, 50))
$ {CTR}^p_{ts\ rc\ s} $	floor(uniform(1, 4561))	$ {eARC}^{ta} $	floor(uniform(1, 90))
$ {CTR}^p_{ta\ rm\ a} $	floor(uniform(1, 3000))	$ {eARU}^{ta} $	floor(uniform(1, 80))
$ {CTR}^m_{ta\ a\ d} $	floor(uniform(1, 3700))	$ {eAL}^{ta} $	floor(uniform(1,100))
$ {CTR}^m_{td\ d\ c} $	floor(uniform(1, 9000))	$ {eSA}^{ts} $	floor(uniform(1, 70))
$ {dis}_{c\ d} $	floor(uniform(1,100))	$ {eRUC}^{tc} $	floor(uniform(1,120))
$ {dis}_{d\ a} $	floor(uniform(1,150))	$ {eRCS}^{ts} $	floor(uniform(1,150))
$ {dis}_{a\ l} $	floor(uniform(1,200))	$ {eRMA}^{ta} $	floor(uniform(1,190))
$ {dis}_{a\ rm} $	floor(uniform(1,300))	$ {eAD}^{ta} $	floor(uniform(1, 60))
$ {dis}_{a\ rc} $	floor(uniform(1,450))	$ {eDC}^{td} $	floor(uniform(1,170))
$ {dis}_{a\ ru} $	floor(uniform(1,700))	$ H_{tc} $	floor (uniform(1, 5))
$ {dis}_{rc\ s} $	floor(uniform(1,950))	$ H_{td} $	floor (uniform(1, 5))
$ {dis}_{s\ a} $	floor(uniform(1,800))	$ H_{ta} $	floor (uniform(1, 5))
$ {CAP}_a $	floor(uniform(120,150))	$ H_{ts} $	floor (uniform(1, 5))
$ {CAP}_{rm} $	floor(uniform(10, 50))	$ {\varphi }_a $	floor(uniform(1, 6000)
$ {CAP}_{rc} $	floor(uniform(10, 50))	$ {\varphi }_{rm} $	floor(uniform(1, 8500))
$ {CAP}_{ru} $	floor(uniform(10, 50))	$ {\varphi }_{rc} $	floor(uniform(1, 7000))
$ {cd}_m $	floor(uniform(1,100))	$ {\varphi }_{ru} $	floor(uniform(1, 9500))
$ {ca}_m $	floor(uniform(1,130))	$ {\mu }_a $	floor(uniform(1, 5000))
$ c_i $	floor(uniform(1, 90))	$ {\mu }_{rm} $	floor(uniform(1, 7000))
$ {crm}_p $	floor(uniform(1,170))	$ {\mu }_{rc} $	floor(uniform(1, 9000))
$ {crc}_p $	floor(uniform(1,200))	$ {\mu }_{ru} $	floor(uniform(1, 1000))
$ {cru}_p $	floor(uniform(1,350))	$ {\lambda }_c $	uniform(0, 1)
$ {cs}_p $	floor(uniform(1,100))	$\hat I$	uniform(0, 1)
$ F_a $	floor(uniform(1, 1000000))	$\hat I$	uniform(0, 0.001)
$ F_{rm} $	floor(uniform(1, 3000000))	$\hat I$	uniform(0, 1)
$ F_{rc} $	floor(uniform(1, 5000000))	${\hat I}_¸ $	uniform(0, 0.001)
$ F_{ru} $	floor(uniform(1, 4000000))

Table 2. Optimal values of the objective functions

The optimal value of the first objective	The optimal value of the second objective function	The optimal value of the third objective function
2.764708E+8	6.2554E+9	47600.110

Table Options

Download as excel

The optimal value of the first objective	The optimal value of the second objective function	The optimal value of the third objective function
2.764708E+8	6.2554E+9	47600.110

Table 3. The values obtained from the GAMS software for variables

	Consumer Zones	Collection & Distribution	Product Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		3.245	0
$ Q^m_{tc\ c\ d} $	1 $ \longrightarrow $ 2		0	1.023
	2 $ \longrightarrow $ 2		13.311	0
	Consumer Zones	Collection & Distribution	Product Type 2
	Centers		Transportation option 2
	1 $ \longrightarrow $ 1		3.245
	2 $ \longrightarrow $ 2		14.334
	Consumer Zones	Collection & Distribution	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		1.023	0
	2 $ \longrightarrow $ 1		0	3.245
	2 $ \longrightarrow $ 2		0	13.311
	Collection & Distribution	Disassemble & Assemble	Product Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^m_{td\ d\ a} $	2 $ \longrightarrow $ 1		0	16.556
	2 $ \longrightarrow $ 2		1.023	0
	Collection & Distribution	Disassemble & Assemble	Product Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		1.023	16.556
	Collection & Distribution	Disassemble & Assemble	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 1		12.02	0
	2 $ \longrightarrow $ 2		0	7.98
	Disassemble & Assemble	Remanufacture	component Type 1
$ Q^p_{ta\ a\ rm} $	Centers		Transportation option 1
	2 $ \longrightarrow $ 1		8.897504E-4
	2 $ \longrightarrow $ 2		0.014
	Disassemble & Assemble	Remanufacture	component Type 2
	Centers		Transportation option 1
	2 $ \longrightarrow $ 1		0.006
	2 $ \longrightarrow $ 2		0.101
	Disassemble & Assemble	Recycle	component Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		0	12.429
	2 $ \longrightarrow $ 1		0.768	0
$ Q^p_{ta\ a\ rc} $	Disassemble & Assemble	Recycle	component Type 2
	1 $ \longrightarrow $ 1		5.378	0
	1 $ \longrightarrow $ 2		0	46.000
	2 $ \longrightarrow $ 2		41.000	0
	Disassemble & Assemble	Re-use	component Type 1
$ Q^p_{ta\ a\ ru} $	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	0.233
	2 $ \longrightarrow $ 2		3.763	0
	Disassemble & Assemble	Re-use	component Type 2
	Centers		Transportation option 2
	2 $ \longrightarrow $ 1		1.628
	2 $ \longrightarrow $ 2		26.341
	Disassemble & Assemble	Disposal	component Type 1
	Centers		Transportation option 2
$ Q^p_{ta\ a\ l} $	2 $ \longrightarrow $ 1		0.022
	2 $ \longrightarrow $ 2		0.350
	Disassemble & Assemble	Disposal	component Type 2
	Centers		Transportation option 2
	2 $ \longrightarrow $ 1		0.151
	2 $ \longrightarrow $ 2		2.450
	Supplier	Disassemble & Assemble	component Type 1
$ Q^p_{ts\ s\ a} $	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		4.277	54.708
	Supplier	Disassemble & Assemble	component Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		4.272	54.621
	Re-use	Consumer Zones	component Type 1
	Centers		Transportation option 1
$ Q^p_{tc\ ru\ c} $	1 $ \longrightarrow $ 1		3.763
	2 $ \longrightarrow $ 2		0.233
	Re-use	Consumer Zones	component Type 2
	Centers		Transportation option 1
	1 $ \longrightarrow $ 2		27.969
	Recycle	Supplier	component Type 1
	Centers		Transportation option 1
$ Q^p_{ts\ rc\ s} $	1 $ \longrightarrow $ 1		0.768
	1 $ \longrightarrow $ 2		12.429
	Recycle	Supplier	component Type 2
	Centers		Transportation option 1
	1 $ \longrightarrow $ 1		46.378
	2 $ \longrightarrow $ 2		46.000
	Remanufacture	Disassemble & Assemble	component Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^p_{ta\ rm\ a} $	2 $ \longrightarrow $ 1		8.897504E-4	0.014
	Remanufacture	Disassemble & Assemble	component Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 1		0.006	0.101
	Disassemble & Assemble	Collection	Distribution	Product Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^m_{ta\ a\ d} $		1 $ \longrightarrow $ 2	0	54.722
	2 $ \longrightarrow $ 1		4.278	0
	Disassemble & Assemble	Collection	Distribution	Product Type 2
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		0	11.560
	2 $ \longrightarrow $ 1		5.877	0
	Disassemble & Assemble	Collection	Distribution	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		4.278	0
	2 $ \longrightarrow $ 2		0	54.722
	Collection	Distribution	Consumer Zones	Product Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	4.278
	1 $ \longrightarrow $ 2		18.000	0
	2 $ \longrightarrow $ 2		0	36.722
	Collection	Distribution	Consumer Zones	Product Type 2
$ Q^m_{td\ d\ c} $	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	41.000
	1 $ \longrightarrow $ 2		4.278	0
	2 $ \longrightarrow $ 1		13.722	0
	Collection	Distribution	Consumer Zones	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		13.722	41.000
	2 $ \longrightarrow $ 1		4.278	0

Table Options

Download as excel

	Consumer Zones	Collection & Distribution	Product Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		3.245	0
$ Q^m_{tc\ c\ d} $	1 $ \longrightarrow $ 2		0	1.023
	2 $ \longrightarrow $ 2		13.311	0
	Consumer Zones	Collection & Distribution	Product Type 2
	Centers		Transportation option 2
	1 $ \longrightarrow $ 1		3.245
	2 $ \longrightarrow $ 2		14.334
	Consumer Zones	Collection & Distribution	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		1.023	0
	2 $ \longrightarrow $ 1		0	3.245
	2 $ \longrightarrow $ 2		0	13.311
	Collection & Distribution	Disassemble & Assemble	Product Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^m_{td\ d\ a} $	2 $ \longrightarrow $ 1		0	16.556
	2 $ \longrightarrow $ 2		1.023	0
	Collection & Distribution	Disassemble & Assemble	Product Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		1.023	16.556
	Collection & Distribution	Disassemble & Assemble	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 1		12.02	0
	2 $ \longrightarrow $ 2		0	7.98
	Disassemble & Assemble	Remanufacture	component Type 1
$ Q^p_{ta\ a\ rm} $	Centers		Transportation option 1
	2 $ \longrightarrow $ 1		8.897504E-4
	2 $ \longrightarrow $ 2		0.014
	Disassemble & Assemble	Remanufacture	component Type 2
	Centers		Transportation option 1
	2 $ \longrightarrow $ 1		0.006
	2 $ \longrightarrow $ 2		0.101
	Disassemble & Assemble	Recycle	component Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		0	12.429
	2 $ \longrightarrow $ 1		0.768	0
$ Q^p_{ta\ a\ rc} $	Disassemble & Assemble	Recycle	component Type 2
	1 $ \longrightarrow $ 1		5.378	0
	1 $ \longrightarrow $ 2		0	46.000
	2 $ \longrightarrow $ 2		41.000	0
	Disassemble & Assemble	Re-use	component Type 1
$ Q^p_{ta\ a\ ru} $	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	0.233
	2 $ \longrightarrow $ 2		3.763	0
	Disassemble & Assemble	Re-use	component Type 2
	Centers		Transportation option 2
	2 $ \longrightarrow $ 1		1.628
	2 $ \longrightarrow $ 2		26.341
	Disassemble & Assemble	Disposal	component Type 1
	Centers		Transportation option 2
$ Q^p_{ta\ a\ l} $	2 $ \longrightarrow $ 1		0.022
	2 $ \longrightarrow $ 2		0.350
	Disassemble & Assemble	Disposal	component Type 2
	Centers		Transportation option 2
	2 $ \longrightarrow $ 1		0.151
	2 $ \longrightarrow $ 2		2.450
	Supplier	Disassemble & Assemble	component Type 1
$ Q^p_{ts\ s\ a} $	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		4.277	54.708
	Supplier	Disassemble & Assemble	component Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 2		4.272	54.621
	Re-use	Consumer Zones	component Type 1
	Centers		Transportation option 1
$ Q^p_{tc\ ru\ c} $	1 $ \longrightarrow $ 1		3.763
	2 $ \longrightarrow $ 2		0.233
	Re-use	Consumer Zones	component Type 2
	Centers		Transportation option 1
	1 $ \longrightarrow $ 2		27.969
	Recycle	Supplier	component Type 1
	Centers		Transportation option 1
$ Q^p_{ts\ rc\ s} $	1 $ \longrightarrow $ 1		0.768
	1 $ \longrightarrow $ 2		12.429
	Recycle	Supplier	component Type 2
	Centers		Transportation option 1
	1 $ \longrightarrow $ 1		46.378
	2 $ \longrightarrow $ 2		46.000
	Remanufacture	Disassemble & Assemble	component Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^p_{ta\ rm\ a} $	2 $ \longrightarrow $ 1		8.897504E-4	0.014
	Remanufacture	Disassemble & Assemble	component Type 2
	Centers		Transportation option 1	Transportation option 2
	2 $ \longrightarrow $ 1		0.006	0.101
	Disassemble & Assemble	Collection	Distribution	Product Type 1
	Centers		Transportation option 1	Transportation option 2
$ Q^m_{ta\ a\ d} $		1 $ \longrightarrow $ 2	0	54.722
	2 $ \longrightarrow $ 1		4.278	0
	Disassemble & Assemble	Collection	Distribution	Product Type 2
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		0	11.560
	2 $ \longrightarrow $ 1		5.877	0
	Disassemble & Assemble	Collection	Distribution	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		4.278	0
	2 $ \longrightarrow $ 2		0	54.722
	Collection	Distribution	Consumer Zones	Product Type 1
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	4.278
	1 $ \longrightarrow $ 2		18.000	0
	2 $ \longrightarrow $ 2		0	36.722
	Collection	Distribution	Consumer Zones	Product Type 2
$ Q^m_{td\ d\ c} $	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 1		0	41.000
	1 $ \longrightarrow $ 2		4.278	0
	2 $ \longrightarrow $ 1		13.722	0
	Collection	Distribution	Consumer Zones	Product Type 3
	Centers		Transportation option 1	Transportation option 2
	1 $ \longrightarrow $ 2		13.722	41.000
	2 $ \longrightarrow $ 1		4.278	0

Table 4. The amount of changes in the objective function for changes in $ q_c $

*Changes in*$ {\mathbf \ \ }{{\mathbf q}}_{{\mathbf c}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*	*Numerical example 4*
10	1868132000	2619831	393784200	17291600
15	1917029000	3027281	406228600	17744600
20	1973978000	3497575	424883000	18274400
28	2323844000	6807494	439768100	21675600
36	3050361000	13929150	458673000	28832300
40	3491321000	18206340	469234000	33176500
46	3976855000	22915890	469987000	37959900

Table Options

Download as excel

*Changes in*$ {\mathbf \ \ }{{\mathbf q}}_{{\mathbf c}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*	*Numerical example 4*
10	1868132000	2619831	393784200	17291600
15	1917029000	3027281	406228600	17744600
20	1973978000	3497575	424883000	18274400
28	2323844000	6807494	439768100	21675600
36	3050361000	13929150	458673000	28832300
40	3491321000	18206340	469234000	33176500
46	3976855000	22915890	469987000	37959900

Table 5. The amount of changes in the objective function for the changes in$ \ \ {DR}_c $

*Changes in* $ {{\mathbf DR}}_{{\mathbf c}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*	*Numerical example 4*
10	440529700	21170450	347895400	183145000
50	1172853000	21968080	348972000	252260000
100	2042508000	22915890	359998700	331765000
150	2944460000	23905960	379543900	415302000
212	4289378000	24850110	391134100	494550000

Table Options

Download as excel

*Changes in* $ {{\mathbf DR}}_{{\mathbf c}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*	*Numerical example 4*
10	440529700	21170450	347895400	183145000
50	1172853000	21968080	348972000	252260000
100	2042508000	22915890	359998700	331765000
150	2944460000	23905960	379543900	415302000
212	4289378000	24850110	391134100	494550000

Table 6. The amount of changes in the objective function due to the changes in$ {\ V}_p $

*Changes in*$ {{\mathbf \ \ }{\mathbf V}}_{{\mathbf p}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*
5	4086738000	101785170	237854320
10	4289378000	139202200	259873270
15	5201699000	189831200	267134010
19	6184267000	248501100	281294130

Table Options

Download as excel

*Changes in*$ {{\mathbf \ \ }{\mathbf V}}_{{\mathbf p}} $	*Objective function*
	*Numerical example 1*	*Numerical example 2*	*Numerical example 3*
5	4086738000	101785170	237854320
10	4289378000	139202200	259873270
15	5201699000	189831200	267134010
19	6184267000	248501100	281294130

[1]	Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker, Guo-Qiang Yang. Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2021014
[2]	Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020165
[3]	Honglin Yang, Jiawu Peng. Coordinating a supply chain with demand information updating. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020181
[4]	Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020173
[5]	Wenyan Zhuo, Honglin Yang, Leopoldo Eduardo Cárdenas-Barrón, Hong Wan. Loss-averse supply chain decisions with a capital constrained retailer. Journal of Industrial & Management Optimization, 2021, 17 (2) : 711-732. doi: 10.3934/jimo.2019131
[6]	Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030
[7]	Zonghong Cao, Jie Min. Selection and impact of decision mode of encroachment and retail service in a dual-channel supply chain. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020167
[8]	Wei Chen, Yongkai Ma, Weihao Hu. Electricity supply chain coordination with carbon abatement technology investment under the benchmarking mechanism. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020175
[9]	Feimin Zhong, Jinxing Xie, Yuwei Shen. Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020172
[10]	Hongxia Sun, Yao Wan, Yu Li, Linlin Zhang, Zhen Zhou. Competition in a dual-channel supply chain considering duopolistic retailers with different behaviours. Journal of Industrial & Management Optimization, 2021, 17 (2) : 601-631. doi: 10.3934/jimo.2019125
[11]	Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026
[12]	Mahir Demir, Suzanne Lenhart. A spatial food chain model for the Black Sea Anchovy, and its optimal fishery. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 155-171. doi: 10.3934/dcdsb.2020373
[13]	Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020359
[14]	Juhua Shi, Feida Jiang. The degenerate Monge-Ampère equations with the Neumann condition. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020297
[15]	Wenbin Li, Jianliang Qian. Simultaneously recovering both domain and varying density in inverse gravimetry by efficient level-set methods. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2020073
[16]	Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, 2021, 20 (1) : 449-465. doi: 10.3934/cpaa.2020276
[17]	Andrea Malchiodi. Perturbative techniques for the construction of spike-layers. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3767-3787. doi: 10.3934/dcds.2020055
[18]	Yanjun He, Wei Zeng, Minghui Yu, Hongtao Zhou, Delie Ming. Incentives for production capacity improvement in construction supplier development. Journal of Industrial & Management Optimization, 2021, 17 (1) : 409-426. doi: 10.3934/jimo.2019118
[19]	Peter Giesl, Sigurdur Hafstein. System specific triangulations for the construction of CPA Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020378
[20]	Mengni Li. Global regularity for a class of Monge-Ampère type equations with nonzero boundary conditions. Communications on Pure & Applied Analysis, 2021, 20 (1) : 301-317. doi: 10.3934/cpaa.2020267

2019 Impact Factor: 1.366

Tools

Metrics

Tools

Article outline

Figures and Tables

2019 Impact Factor: 1.366

Tools

Figures and Tables

2019 Impact Factor: 1.366

American Institute of Mathematical Sciences

Sustainable closed-loop supply chain network optimization for construction machinery recovering

References:

References:

Tools

Metrics

Other articles
by authors

Tools

Tools

Tools

Metrics

Other articles
by authors

American Institute of Mathematical Sciences

Sustainable closed-loop supply chain network optimization for construction machinery recovering

References:

References:

Tools

Metrics

Other articlesby authors

Tools

Tools

Tools

Metrics

Other articlesby authors

Other articles
by authors

Other articles
by authors