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

Abdolhossein Sadrnia; Amirreza Payandeh Sani; Najme Roghani Langarudi

doi:10.3934/jimo.2020074

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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 & Management Optimization, 2021, 17 (5) : 2389-2414. doi: 10.3934/jimo.2020074

References:

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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. Google Scholar
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[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
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[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
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[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
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[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
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[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
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[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
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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 $ 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

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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 $ 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

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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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2020 Impact Factor: 1.801

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2020 Impact Factor: 1.801

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2020 Impact Factor: 1.801

American Institute of Mathematical Sciences

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

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American Institute of Mathematical Sciences

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

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