Abstract
This paper aims to develop a sustainable closed-loop supply chain network model with a modular single product which is specifically designed for the automotive industry. Drawing upon sustainability criteria, three objective functions are formulated for the closed-loop network design problem including maximizing total profit across the network, minimizing the effects of environmental pollutants and maximizing employments created by the establishment of the required facilities and also maximizing the weighted sum of the minimum distance of facilities from the residential areas. In order to validate the research, a case study of the Iran’s automotive industry is also conducted. In addition, a scenario-based approach which applies the stochastic programming is used to cope with the uncertainty in both the demand and the amount of returned unusable vehicles. The results show that the stochastic programming approach is successful in mitigating the effects of uncertainties. Moreover, augmented \(\varepsilon\)-constraint methods are applied to deal with the proposed model. The preferred Pareto optimal solution achieves a 55.1% decrease in the environmental objective value, with only 0.2% increase in the economic objective value relative to the corresponding optimal value.
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Notes
Non-dominated Sorting Genetic Algorithm II.
Multi-Objective Simulated Annealing.
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Appendices
Appendix A Nomenclature
Indexes
\(t\in T\) | Index for time periods |
\(s\in S\) | Index for shredding centers |
\(r\in R\) | Index for recycling centers |
\(p\in P\) | Index for landfills for nonreusable materials |
\(n\in N\) | Index for dismantlers |
\(m\in M\) | Index for collection centers |
\(l\in L\) | Index for customer clusters |
\(k\in K\) | Index for manufacturers/ distributors |
\(j\in J\) | Index for suppliers |
\(i\in I\) | Index for parts/ materials |
\(c\in C\) | Index for technologies for the establishment of the reverse facilities (corresponding to their related emission levels) |
\(h\in \left\{\mathrm{1,2}\right\}\) | Index for transportation types |
Parameters
\({D}_{lt}\) | Demand quantity of customer cluster \(l\) in period \(t\) for new vehicles (ton) |
\({RT}_{lt}\) | Quantity of returned end-of-life vehicles by customer cluster \(l\) in period \(t\) (ton) |
\({ic}_{lt}\) | Cost incurred if one new vehicle is stored in period \(t\) at customer cluster \(l\) (IRR/ton) |
\({ic}_{mt}^{{^{\prime}}}\) | Cost incurred if one ELV is stored in period \(t\) at collection center \(m\) (IRR/ton) |
\({t}_{klth}^{1}\) | Cost incurred in period \(t\) for type \(h\) transporting new vehicles from manufacturer/distributor \(k\) to customer cluster \(l\) (IRR/ton km) |
\({t}_{lmth}^{2}\) | Cost incurred in period \(t\) for type \(h\) transporting ELVs from customer cluster \(l\) to collection center \(m\) (IRR/ton km) |
\({t}_{mnth}^{3}\) | Cost incurred in period \(t\) for type \(h\) transporting ELVs from collection center \(m\) to dismantler \(n\) (IRR/ton km) |
\({t}_{lnth}^{4}\) | Cost incurred in period \(t\) for type \(h\) transporting ELVs from customer cluster \(l\) to dismantler \(n\) (IRR/ton km) |
\({t}_{nlth}^{5}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of components/material from dismantler \(n\) to customer cluster \(l\) (IRR/ton km) |
\({t}_{nrth}^{6}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of components/material from dismantler \(n\) to recycler \(r\) (IRR/ton km) |
\({t}_{nsth}^{7}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of components/material from dismantler \(n\) to shredder \(s\) (IRR/ton km) |
\({t}_{srth}^{8}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of material from shredder \(s\) to recycler \(r\) (IRR/ton km) |
\({t}_{spth}^{9}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of ASR from shredder \(s\) to landfill \(p\) (IRR/ton km) |
\({t}_{rpth}^{10}\) | Cost incurred in period \(t\) for type \(h\) transporting one unit of material from recycler \(r\) to landfill \(p\) (IRR/ton km) |
\({sz}_{it}\) | Unit price of dismantled component/material \(i\) in period \(t\) |
\({zz}_{it}\) | Selling price of one unit of material \(i\) in period \(t\) at recycler (IRR/ton) |
\({uz}_{kt}\) | Selling price of one new vehicle in period \(t\) at manufacturer/distributor \(k\) (IRR/ton) |
\({rc}_{rt}\) | Cost incurred in period \(t\) when recycler \(r\) recycles one unit of material (IRR/ton) |
\({lc}_{pt}\) | Cost incurred in period \(t\) when landfill \(p\) disposes one unit of material (IRR/ton) |
\({sc}_{st}\) | Cost incurred in period \(t\) when shredder \(s\) shreds one unit of components/material (IRR/ton) |
\({dc}_{nt}\) | Cost incurred in period \(t\) when dismantler \(n\) dismantles ELVs (IRR/ton) |
\({cc}_{mt}\) | Cost incurred in period \(t\) when collection center \(m\) collects ELVs (IRR/ton) |
\({cc}_{nt}^{{^{\prime}}}\) | Cost incurred in period \(t\) when dismantler \(n\) collects ELVs (IRR/ton) |
\({pc}_{kt}\) | Cost incurred in period \(t\) when manufacturer/ distributor \(k\) produces new vehicles (IRR/ton) |
\({d}_{kl}^{1}\) | Distance from manufacturer/distributor \(k\) to customer cluster \(l\) (km) |
\({d}_{lm}^{2}\) | Distance from customer cluster \(l\) to collection center \(m\) (km) |
\({d}_{ln}^{3}\) | Distance from customer cluster \(l\) to dismantler \(n\) (km) |
\({d}_{mn}^{4}\) | Distance from collection center \(m\) to dismantler \(n\) (km) |
\({d}_{ns}^{5}\) | Distance from dismantler \(n\) to shredder \(s\) (km) |
\({d}_{nr}^{6}\) | Distance from dismantler \(n\) to recycler \(r\) (km) |
\({d}_{sr}^{7}\) | Distance from shredder \(s\) to recycler \(r\) (km) |
\({d}_{sp}^{8}\) | Distance from shredder \(s\) to landfill \(p\) (km) |
\({d}_{rp}^{9}\) | Distance from recycler \(r\) to landfill \(p\) (km) |
\({d}_{rj}^{10}\) | Distance from recycler \(r\) to supplier \(j\) (km) |
\({\theta }_{mc}^{1}\) | Minimum distance of collection center \(m\) with emission level \(c\) from a residential area (km) |
\({\theta }_{nc}^{2}\) | Minimum distance of dismantler \(n\) with emission level \(c\) from a residential area (km) |
\({\theta }_{sc}^{3}\) | Minimum distance of shredder \(s\) with emission level \(c\) from a residential area (km) |
\({\theta }_{rc}^{4}\) | Minimum distance of recycler \(r\) with emission level \(c\) from a residential area (km) |
\({\theta }_{pc}^{5}\) | Minimum distance of landfill \(p\) with emission level \(c\) from a residential area (km) |
\({\omega }^{1}\) | Weight for the relative importance of the distance of a collection center from a residential area in comparison with one employment opportunity |
\({\omega }^{2}\) | Weight for the relative importance of the distance of a dismantler from a residential area in comparison with one employment opportunity |
\({\omega }^{3}\) | Weight for the relative importance of the distance of a shredder from a residential area in comparison with one employment opportunity |
\({\omega }^{4}\) | Weight for the relative importance of the distance of a recycler from a residential area in comparison with one employment opportunity |
\({\omega }^{5}\) | Weight for the relative importance of the distance of a landfill from a residential area in comparison with one employment opportunity |
\({\sigma }_{i}\) | Amount of component/material \(i\) in a vehicle as weight percentage |
\(\alpha\) | Amount of hulk in an end-of-life vehicle as weight percentage |
\(\beta\) | Amount of ASR in hulk as weight percentage |
\({\mu }_{i}\) | Amount of reusable component/material \(i\) in an end-of-life vehicle as weight percentage |
\({\lambda }_{i}\) | Amount of nonreusable component/material \(i\) in an end-of-life vehicle as weight percentage |
\({\gamma }_{i}\) | Amount of recyclable component/material \(i\) in hulk as weight percentage |
\({\eta }_{i}\) | Amount of disposal component/material \(i\) in recyclable material as weight percentage |
\({\delta }_{i}\) | Amount of component/material \(i\) having economic value in recyclable material as weight percentage |
\({f}_{mc}^{1}\) | Fixed cost incurred in period \(t\) for establishing collection center \(m\) with emission level \(c\) (IRR) |
\({f}_{nc}^{2}\) | Fixed cost incurred in period \(t\) for establishing dismantler \(n\) with emission level \(c\) (IRR) |
\({f}_{sc}^{3}\) | Fixed cost incurred in period \(t\) for establishing shredder \(s\) with emission level \(c\) (IRR) |
\({f}_{rc}^{4}\) | Fixed cost incurred in period \(t\) for establishing recycler \(r\) with emission level \(c\) (IRR) |
\({f}_{pc}^{5}\) | Fixed cost incurred in period \(t\) for establishing landfill \(p\) with emission level \(c\) (IRR) |
\({Cap}_{k}^{1}\) | Maximum amount that manufacturer/distributor \(k\) can produce/distribute in period \(t\) (ton) |
\({Cap}_{mc}^{2}\) | Maximum amount that collection center \(m\) with emission level \(c\) can collect in period \(t\) (ton) |
\({Cap}_{nc}^{3}\) | Maximum amount that dismantler \(n\) with emission level \(c\) can dismantle in period \(t\) (ton) |
\({Cap}_{sc}^{4}\) | Maximum amount that shredder \(s\) with emission level \(c\) can shred in period \(t\) (ton) |
\({Cap}_{pc}^{5}\) | Maximum amount that landfill \(p\) with emission level \(c\) can dispose in period \(t\) (ton) |
\({Cap}_{irc}^{6}\) | Maximum amount that recycler \(r\) with emission level \(c\) can recycle for component/material \(i\) in period \(t\) (ton) |
\({Job}_{mc}^{1}\) | Number of employment opportunities provided by constructing collection center \(m\) with emission level \(c\) in period \(t\) |
\({Job}_{nc}^{2}\) | Number of employment opportunities provided by constructing dismantler \(n\) with emission level \(c\) in period \(t\) |
\({Job}_{sc}^{3}\) | Number of employment opportunities provided by constructing shredder \(s\) with emission level \(c\) in period \(t\) |
\({Job}_{rc}^{4}\) | Number of employment opportunities provided by constructing recycler \(r\) with emission level \(c\) in period \(t\) |
\({Job}_{pc}^{5}\) | Number of employment opportunities provided by constructing landfill \(p\) with emission level \(c\) in period \(t\) |
\({ETM}_{lmth}\) | Emissions produced by transportation type \(h\) for transferring one unit of end-of-life vehicle for one unit of distance from customer cluster \(l\) to collection center \(m\) in period \(t\) |
\({ETN}_{mnth}^{1}\) | Emissions produced by transportation type \(h\) for transferring one unit of end-of-life vehicle for one unit of distance from collection center \(m\) to dismantler \(n\) in period \(t\) |
\({ETN}_{lnth}^{2}\) | Emissions produced by transportation type \(h\) for transferring one unit of end-of-life vehicle for one unit of distance from customer cluster \(l\) to dismantler \(n\) in period \(t\) |
\({ETL}_{inlth}\) | Emissions produced by transportation type \(h\) for transferring one unit of reusable component/material \(i\) for one unit of distance from dismantler \(n\) to customer cluster \(l\) in period \(t\) |
\({ETR}_{inrth}^{1}\) | Emissions produced by transportation type \(h\) for transferring one unit of nonreuseable component/material \(i\) for one unit of distance from dismantler \(n\) to recycler \(r\) in period \(t\) |
\({ETR}_{isrth}^{2}\) | Emissions produced by transportation type \(h\) for transferring one unit of nonreusable component/material \(i\) for one unit of distance from shredder \(s\) to recycler \(r\) in period \(t\) |
\({ETS}_{nsth}\) | Emissions produced by transportation type \(h\) for transferring one unit of hulk body of end-of-life vehicle for one unit of distance from dismantler \(n\) to shredder \(s\) in period \(t\) |
\({ETP}_{irpth}^{1}\) | Emissions produced by transportation type \(h\) for transferring one unit of non-recyclable component/material \(i\) for one unit of distance from recycler \(r\) to landfill \(p\) in period \(t\) |
\({ETP}_{spth}^{2}\) | Emissions produced by transportation type \(h\) for transferring one unit of non-recyclable ASR for one unit of distance from shredder \(s\) to landfill \(p\) in period \(t\) |
\({ETJ}_{irjth}\) | Emissions produced by transportation type \(h\) for transferring one unit of recycled component/material \(i\) for one unit of distance from recycler \(r\) to supplier \(j\) in period \(t\) |
\({EFF}_{mc}^{1}\) | Emissions produced by collection center \(m\) with emission level \(c\) |
\({EFF}_{nc}^{2}\) | Emissions produced by dismantler \(n\) with emission level \(c\) |
\({EFF}_{sc}^{3}\) | Emissions produced by shredder \(s\) with emission level \(c\) |
\({EFF}_{rc}^{4}\) | Emissions produced by recycler \(r\) with emission level \(c\) |
\({EFF}_{pc}^{5}\) | Emissions produced by landfill \(p\) with emission level \(c\) |
Decision variables
\({X}_{ijkt}\) | Quantity of component/material \(i\) transferred in period \(t\) from supplier \(j\) to manufacturer/distributor \(k\) |
\({Y}_{klt}\) | Quantity of new vehicles transferred in period \(t\) from manufacturer/distributor \(k\) to customer cluster \(l\) |
\({Z}_{lmt}\) | Quantity of ELVs transferred in period \(t\) from customer cluster \(l\) to collection center \(m\) |
\({V}_{lnt}\) | Quantity of ELVs transferred in period \(t\) from customer cluster \(l\) to dismantler \(n\) |
\({W}_{mnt}\) | Quantity of ELVs transferred in period \(t\) from collection center \(m\) to dismantler \(n\) |
\({ST}_{inlt}\) | Quantity of reusable component/material \(i\) transferred in period \(t\) from dismantler \(n\) to customer cluster \(l\) |
\({A}_{inrt}\) | Quantity of nonreusable component/material \(i\) transferred in period \(t\) from dismantler \(n\) to recycler \(r\) |
\({B}_{nst}\) | Quantity of end-of-life vehicle bodies transferred in period \(t\) from dismantler \(n\) to shredder \(s\) |
\({G}_{isrt}\) | Quantity of component/material \(i\) transferred in period \(t\) from shredder \(s\) to recycler \(r\) |
\({E}_{spt}\) | Quantity of ASRs transferred in period \(t\) from shredder \(s\) to landfill \(p\) |
\({F}_{irpt}\) | Quantity of disposal component/material \(i\) transferred in period \(t\) from recycler \(r\) to landfill \(p\) |
\({H}_{irjt}\) | Quantity of component/material \(i\) transferred in period \(t\) from recycler \(r\) to supplier \(j\) |
\({I}_{lt}\) | Inventory level at customer cluster (dealership) \(l\) in period \(t\) |
\({I}_{mt}^{{^{\prime}}}\) | Inventory level at collection center \(m\) |
\({e}_{mc}^{1}\) | Binary variables for opening or closing collection center \(m\) with emission level \(c\) |
\({e}_{nc}^{2}\) | Binary variables for opening or closing dismantler \(n\) with emission level \(c\) |
\({e}_{sc}^{3}\) | Binary variables for opening or closing shredder \(s\) with emission level \(c\) in period \(t\) |
\({e}_{rc}^{4}\) | Binary variables for opening or closing recycler \(r\) with emission level \(c\) in period \(t\) |
\({e}_{pc}^{5}\) | Binary variables for opening or closing landfill \(p\) with emission level \(c\) in period \(t\) |
Notations for the stochastic programming model
Indexes
u ∈ U | Index for senarios |
Parameters
D ltu | Quantity of new vehicles demanded by customer cluster l in period t in scenario u (ton) |
RT ltu | Quantity of ELVs returned by customer cluster l in period t in scenario u (ton) |
Prob u | Probability of scenario u |
Decision variables
X ijktu | Quantity of component/material i transferred from supplier j to manufacturer/distributor k in period t in scenario u (ton) |
Y kltu | Quantity of new vehicles transferred from manufacturer/distributor k to customer cluster l in period t in scenario u (ton) |
Z lmtu | Quantity of ELVs transferred from customer cluster l to collection center m in period t in scenario u (ton) |
V lntu | Quantity of ELVs transferred from customer cluster l to dismantler n in period t in scenario u (ton) |
W mntu | Quantity of ELVs transferred from collection center m to dismantler n in period t in scenario u (ton) |
ST inltu | Quantity of reusable component/material i transferred from dismantler n to customer cluster l in period t in scenario u (ton) |
A inrtu | Quantity of nonreusable component/material i transferred from dismantler n to recycler r in period t in scenario u (ton) |
B nstu | Quantity of ELV bodies transferred from dismantler n to shredder s in period t in scenario u (ton) |
G isrtu | Quantity of component/material i transferred from shredder s to recycler r in period t in scenario u (ton) |
E sptu | Quantity of shredded residues transferred from shredder s to landfill p in period t in scenario u (ton) |
F irptu | Quantity of disposable component/material i transferred from recycler r to landfill p in period t in scenario u (ton) |
H irjtu | Quantity of component/material i transferred from recycler r to supplier j in period t in scenario u (ton) |
I ltu | Inventory level at customer cluster l in period t in scenario u (ton) |
\({I}_{mtu}^{\prime }\) | Inventory level at collection center m in period t in scenario u (ton) |
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Shahedi, A., Nasiri, M.M., Sangari, M.S. et al. A Stochastic Multi-Objective Model for a Sustainable Closed-Loop Supply Chain Network Design in the Automotive Industry. Process Integr Optim Sustain 6, 189–209 (2022). https://doi.org/10.1007/s41660-021-00204-4
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DOI: https://doi.org/10.1007/s41660-021-00204-4