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September  2021, 17(5): 2389-2414. 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  September 2021 Early access  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 and Management Optimization, 2021, 17 (5) : 2389-2414. doi: 10.3934/jimo.2020074
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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.

[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.

[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.

[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.

[5]

C. R. Carter and M. M. Jennings, Logistics social responsibility: An integrative framework, Journal of Business Logistics, 23 (2002), 145-180. 

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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. 

[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.

[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.

[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.

[18]

G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465.

[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.

[20]

M. Fleischmann, H. Krikke, R. Dekker and S. Flapper, A characterization of logistics networks for product recovery, Omega, 28 (2000), 653-666. 

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[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.

[30]

G. R. Initiative, Sustainability Reporting Guidelines (G4), Global Reporting Initiative, 2013.

[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.

[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.

[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. 

[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. 

[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.

[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.

[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.

[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.

[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.

[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.

[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.

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Figure 1.  Supply chain of closed loop for recovering machinery at the end of their life cycle based on sustainability dimensions
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Figure 2.  The change of the value of the objective function by changes in $ q_c $.
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Figure 3.  The change in the value of the objective function by changes in$ {\ DR}_c $.
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Figure 4.  The change in the value of the objective function by the changes in $ {\ V}_p $.
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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
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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} $The number of the created variable job opportunities by working in reusing centers
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$ {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} $Quantity of the remanufactured products m from D to C with transportation option td
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$ 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} $
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$ 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))
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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
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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 $ 103.245
2 $ \longrightarrow $ 2013.311
Collection & DistributionDisassemble & AssembleProduct Type 1
CentersTransportation option 1Transportation option 2
$ Q^m_{td\ d\ a} $2 $ \longrightarrow $ 1016.556
2 $ \longrightarrow $ 21.0230
Collection & Distribution Disassemble & AssembleProduct Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 21.02316.556
Collection & DistributionDisassemble & AssembleProduct Type 3
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 112.020
2 $ \longrightarrow $ 207.98
Disassemble & AssembleRemanufacturecomponent Type 1
$ Q^p_{ta\ a\ rm} $CentersTransportation option 1
2 $ \longrightarrow $ 18.897504E-4
2 $ \longrightarrow $ 20.014
Disassemble & AssembleRemanufacturecomponent Type 2
CentersTransportation option 1
2 $ \longrightarrow $ 10.006
2 $ \longrightarrow $ 20.101
Disassemble & AssembleRecyclecomponent Type 1
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 2012.429
2 $ \longrightarrow $ 10.7680
$ Q^p_{ta\ a\ rc} $Disassemble & AssembleRecyclecomponent Type 2
1 $ \longrightarrow $ 15.3780
1 $ \longrightarrow $ 2046.000
2 $ \longrightarrow $ 241.0000
Disassemble & AssembleRe-usecomponent Type 1
$ Q^p_{ta\ a\ ru} $CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 100.233
2 $ \longrightarrow $ 23.7630
Disassemble & AssembleRe-usecomponent Type 2
CentersTransportation option 2
2 $ \longrightarrow $ 11.628
2 $ \longrightarrow $ 226.341
Disassemble & AssembleDisposalcomponent Type 1
CentersTransportation option 2
$ Q^p_{ta\ a\ l} $2 $ \longrightarrow $ 10.022
2 $ \longrightarrow $ 20.350
Disassemble & AssembleDisposalcomponent Type 2
CentersTransportation option 2
2 $ \longrightarrow $ 10.151
2 $ \longrightarrow $ 22.450
SupplierDisassemble & Assemblecomponent Type 1
$ Q^p_{ts\ s\ a} $CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 24.27754.708
SupplierDisassemble & Assemblecomponent Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 24.27254.621
Re-useConsumer Zonescomponent Type 1
CentersTransportation option 1
$ Q^p_{tc\ ru\ c} $1 $ \longrightarrow $ 13.763
2 $ \longrightarrow $ 20.233
Re-useConsumer Zonescomponent Type 2
CentersTransportation option 1
1 $ \longrightarrow $ 227.969
RecycleSuppliercomponent Type 1
CentersTransportation option 1
$ Q^p_{ts\ rc\ s} $1 $ \longrightarrow $ 10.768
1 $ \longrightarrow $ 212.429
RecycleSuppliercomponent Type 2
CentersTransportation option 1
1 $ \longrightarrow $ 146.378
2 $ \longrightarrow $ 246.000
RemanufactureDisassemble & Assemblecomponent Type 1
CentersTransportation option 1Transportation option 2
$ Q^p_{ta\ rm\ a} $2 $ \longrightarrow $ 18.897504E-40.014
RemanufactureDisassemble & Assemblecomponent Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 10.0060.101
Disassemble & AssembleCollectionDistributionProduct Type 1
CentersTransportation option 1Transportation option 2
$ Q^m_{ta\ a\ d} $1 $ \longrightarrow $ 2054.722
2 $ \longrightarrow $ 14.2780
Disassemble & AssembleCollectionDistributionProduct Type 2
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 2011.560
2 $ \longrightarrow $ 15.8770
Disassemble & AssembleCollectionDistributionProduct Type 3
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 14.2780
2 $ \longrightarrow $ 2054.722
CollectionDistributionConsumer ZonesProduct Type 1
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 104.278
1 $ \longrightarrow $ 218.0000
2 $ \longrightarrow $ 2036.722
CollectionDistributionConsumer ZonesProduct Type 2
$ Q^m_{td\ d\ c} $CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 1041.000
1 $ \longrightarrow $ 24.2780
2 $ \longrightarrow $ 113.7220
CollectionDistributionConsumer ZonesProduct Type 3
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 213.72241.000
2 $ \longrightarrow $ 14.2780
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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 $ 103.245
2 $ \longrightarrow $ 2013.311
Collection & DistributionDisassemble & AssembleProduct Type 1
CentersTransportation option 1Transportation option 2
$ Q^m_{td\ d\ a} $2 $ \longrightarrow $ 1016.556
2 $ \longrightarrow $ 21.0230
Collection & Distribution Disassemble & AssembleProduct Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 21.02316.556
Collection & DistributionDisassemble & AssembleProduct Type 3
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 112.020
2 $ \longrightarrow $ 207.98
Disassemble & AssembleRemanufacturecomponent Type 1
$ Q^p_{ta\ a\ rm} $CentersTransportation option 1
2 $ \longrightarrow $ 18.897504E-4
2 $ \longrightarrow $ 20.014
Disassemble & AssembleRemanufacturecomponent Type 2
CentersTransportation option 1
2 $ \longrightarrow $ 10.006
2 $ \longrightarrow $ 20.101
Disassemble & AssembleRecyclecomponent Type 1
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 2012.429
2 $ \longrightarrow $ 10.7680
$ Q^p_{ta\ a\ rc} $Disassemble & AssembleRecyclecomponent Type 2
1 $ \longrightarrow $ 15.3780
1 $ \longrightarrow $ 2046.000
2 $ \longrightarrow $ 241.0000
Disassemble & AssembleRe-usecomponent Type 1
$ Q^p_{ta\ a\ ru} $CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 100.233
2 $ \longrightarrow $ 23.7630
Disassemble & AssembleRe-usecomponent Type 2
CentersTransportation option 2
2 $ \longrightarrow $ 11.628
2 $ \longrightarrow $ 226.341
Disassemble & AssembleDisposalcomponent Type 1
CentersTransportation option 2
$ Q^p_{ta\ a\ l} $2 $ \longrightarrow $ 10.022
2 $ \longrightarrow $ 20.350
Disassemble & AssembleDisposalcomponent Type 2
CentersTransportation option 2
2 $ \longrightarrow $ 10.151
2 $ \longrightarrow $ 22.450
SupplierDisassemble & Assemblecomponent Type 1
$ Q^p_{ts\ s\ a} $CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 24.27754.708
SupplierDisassemble & Assemblecomponent Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 24.27254.621
Re-useConsumer Zonescomponent Type 1
CentersTransportation option 1
$ Q^p_{tc\ ru\ c} $1 $ \longrightarrow $ 13.763
2 $ \longrightarrow $ 20.233
Re-useConsumer Zonescomponent Type 2
CentersTransportation option 1
1 $ \longrightarrow $ 227.969
RecycleSuppliercomponent Type 1
CentersTransportation option 1
$ Q^p_{ts\ rc\ s} $1 $ \longrightarrow $ 10.768
1 $ \longrightarrow $ 212.429
RecycleSuppliercomponent Type 2
CentersTransportation option 1
1 $ \longrightarrow $ 146.378
2 $ \longrightarrow $ 246.000
RemanufactureDisassemble & Assemblecomponent Type 1
CentersTransportation option 1Transportation option 2
$ Q^p_{ta\ rm\ a} $2 $ \longrightarrow $ 18.897504E-40.014
RemanufactureDisassemble & Assemblecomponent Type 2
CentersTransportation option 1Transportation option 2
2 $ \longrightarrow $ 10.0060.101
Disassemble & AssembleCollectionDistributionProduct Type 1
CentersTransportation option 1Transportation option 2
$ Q^m_{ta\ a\ d} $1 $ \longrightarrow $ 2054.722
2 $ \longrightarrow $ 14.2780
Disassemble & AssembleCollectionDistributionProduct Type 2
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 2011.560
2 $ \longrightarrow $ 15.8770
Disassemble & AssembleCollectionDistributionProduct Type 3
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 14.2780
2 $ \longrightarrow $ 2054.722
CollectionDistributionConsumer ZonesProduct Type 1
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 104.278
1 $ \longrightarrow $ 218.0000
2 $ \longrightarrow $ 2036.722
CollectionDistributionConsumer ZonesProduct Type 2
$ Q^m_{td\ d\ c} $CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 1041.000
1 $ \longrightarrow $ 24.2780
2 $ \longrightarrow $ 113.7220
CollectionDistributionConsumer ZonesProduct Type 3
CentersTransportation option 1Transportation option 2
1 $ \longrightarrow $ 213.72241.000
2 $ \longrightarrow $ 14.2780
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
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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
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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
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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
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