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doi: 10.3934/jimo.2020074

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

 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

Received  January 2019 Revised  January 2020 Published  June 2020

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

Citation: Abdolhossein Sadrnia, Amirreza Payandeh Sani, Najme Roghani Langarudi. Sustainable closed-loop supply chain network optimization for construction machinery recovering. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020074
References:
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References:
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Relvas, Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty, European Journal of Operational Research, 226 (2013), 436-451.  doi: 10.1016/j.ejor.2012.11.035.  Google Scholar [4] C. R. Carter and M. M. Jennings, Social responsibility and supply chain relationships, Transportation Research Part E: Logistics and Transportation Review, 38 (2002), 37-52.  doi: 10.1016/S1366-5545(01)00008-4.  Google Scholar [5] C. R. Carter and M. M. Jennings, Logistics social responsibility: An integrative framework, Journal of Business Logistics, 23 (2002), 145-180.   Google Scholar [6] A. Chaabane, A. Ramudhin and M. Paquet, Design of sustainable supply chains under the emission trading scheme, International Journal of Production Economics, 135 (2012), 37-49.  doi: 10.1016/j.ijpe.2010.10.025.  Google Scholar [7] H. K. Chan and V. 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Jha, A multi-criteria optimization approach to manage environmental issues in closed loop supply chain network design, Journal of Cleaner Production, 100 (2015), 297-314.  doi: 10.1016/j.jclepro.2015.02.075.  Google Scholar [24] S. Giarola, A. Zamboni and F. Bezzo, Spatially explicit multi-objective optimization for design and planning of hybrid ïrst and second generation bioreïneries, Computers & Chemical Engineering, 35 (2011), 1782–1797, energy Systems Engineering. doi: 10.1016/j.compchemeng.2011.01.020.  Google Scholar [25] M. Goetschalcks and B. Fleischmann, Strategic network design, Supply Chain Management and Advanced Planning, (2008), 117–132. doi: 10.1007/978-3-540-74512-9_7.  Google Scholar [26] Jr. V. D. R. Guide and L. N. Van Wassenhove, Closed-loop supply chains, quantitative approaches to distribution logistics and supply chain management, Springer, 47–60. Google Scholar [27] T. G. Gutowski, C. F. Murphy, D. T. Allen and et al, WTEC Panel Report on: Environmentally Benign Manufacturing (EBM), International Technology Research Institute, World Technology (WTEC) Division, Baltimore, Maryland. Google Scholar [28] P. Hasanov, M. Y. Jaber, S. Zanoni, L. E. Zavanella, Closed-loop supphy chain system with energy, transportation and waste disposal costs, International Journal of Sustainable Engineering, (2013), 352–358. doi: 10.1080/19397038.2012.762433.  Google Scholar [29] M. A. Ilgin and S. M. Gupta, Environmentally conscious manufacturing and product recovery (ECMPRO): A review of the state of the art, Journal of Environmental Management, 91 (2010), 563-591.  doi: 10.1016/j.jenvman.2009.09.037.  Google Scholar [30] G. R. Initiative, Sustainability Reporting Guidelines (G4), Global Reporting Initiative, 2013. Google Scholar [31] R. Jamshidi, S. F. Ghomi and B. Karimi, Multi-objective green supply chain optimization with a new hybrid memetic algorithm using the taguchi method, Scientia Iranica, 19 (2012), 1876-1886.  doi: 10.1016/j.scient.2012.07.002.  Google Scholar [32] V. Jayaraman, Jr. V. D. R. Guide and R. Srivastava, Closed-loop logistics model for remanufacturing, Journal of the Operational Research Society, 50 (1999), 497-508.  doi: 10.1057/palgrave.jors.2600716.  Google Scholar [33] A. Jindal and K. S. Sangwan, Closed loop supply chain network design and optimization using Fuzzy mixed integer linear programming model, International Journal of Production Research, 52 (2013), 4156-4173.   Google Scholar [34] W. Kerr and C. Ryan, Eco-efficiency gains from remanufacturing: A case study of photocopier remanufacturing at Fuji Xerox Australia, Journal of Cleaner Production, 9 (2001), 75-81.   Google Scholar [35] G. Kizilboga, G. Mandil, M. E. Genevois and P. 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Supply chain of closed loop for recovering machinery at the end of their life cycle based on sustainability dimensions
The change of the value of the objective function by changes in $q_c$.
The change in the value of the objective function by changes in${\ DR}_c$.
The change in the value of the objective function by the changes in ${\ V}_p$.
 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
 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
 ${CTR}^m_{tc\ c\ d}$ 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
 ${CTR}^m_{tc\ c\ d}$ 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
 $Q^m_{tc\ c\ d}$ 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
 $Q^m_{tc\ c\ d}$ 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
 $X_a$ ${{\rm X}}_{{\rm a}}{\rm = 1\ }$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$.{\rm Otherwise,}{\rm \ }{{\rm W}}_{{\rm ru}}{\rm = 0}$
 $X_a$ ${{\rm X}}_{{\rm a}}{\rm = 1\ }$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$.{\rm Otherwise,}{\rm \ }{{\rm W}}_{{\rm ru}}{\rm = 0}$
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))
 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))
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
 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
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
 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
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
 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
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
 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
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
 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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