doi: 10.3934/jimo.2021198
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Effects of the carbon credits buy-back policy on manufacturing/remanufacturing decisions of the capital-constrained manufacturer

1. 

Business School, Jiangsu Normal University, Xuzhou 221116, China

2. 

National Tax Institute of STA, Yangzhou 225007, China

* Corresponding author: wyj19890823@126.com (Yongjian Wang)

Received  March 2021 Revised  August 2021 Early access November 2021

Fund Project: The research was supported by the Natural Science Research Project of the Institution of Higher Education in Jiangsu Province (No. 20KJB630014) and the National Natural Science Foundation of China (No. 71971058)

Under the emissions trading mechanism, this article explores optimal manufacturing/remanufacturing decisions considering the carbon credits buy-back policy by focusing on the value of carbon assets. First, two non-linear programming models are formulated under the cases with/without the carbon credits buy-back policy and solved using the Kuhn-Tucker Conditions (KKT). This article then systematically investigated the impacts of the carbon credits buy-back policy and related crucial parameters on production quantities, selling quantity of carbon quotas, total profits and total carbon emissions resorting to the theoretical analysis and numerical analysis. The results show that the carbon credits buy-back policy could improve operating situations, while specific implementation effect also depends on some factors. Among them, the higher value of the carbon savings of unit remanufactured product could strengthen the advantages of the carbon credits buy-back policy, and the rising carbon savings more significantly promotes the remanufacturing activities. Furthermore, both the carbon price and carbon quotas have significant effects on manufacturing/remanufacturing decisions under the carbon credits buy-back policy. Meanwhile, the carbon price can more effectively adjust production and emissions reduction activities, and consequently controls carbon emissions while protecting production activities. Finally, the results proposed in this paper provide guidance suggestions to manufacturers and policy-makers.

Citation: Yongjian Wang, Fei Wang. Effects of the carbon credits buy-back policy on manufacturing/remanufacturing decisions of the capital-constrained manufacturer. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2021198
References:
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S. S. Ahiska and E. Kurtul, Modeling and analysis of a product substitution strategy for a stochastic manufacturing/remanufacturing system, Computers & Industrial Engineering, 72 (2014), 1-11. 

[2]

S. AnB. LiD. Song and X. Chen, Green credit financing versus trade credit financing in a supply chain with carbon emission limits, European Journal of Operational Research, 292 (2021), 125-142. 

[3]

R. AyresG. Ferrer and T. Van Leynseele, Eco-efficiency, asset recovery and remanufacturing, European Management Journal, 15 (1997), 557-574. 

[4]

E. Cao, L. Du and J. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, International Journal Production Economics, 208 (2019), 383-399.

[5]

E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Computers & Industrial Engineering, 119 (2018), 50-62. 

[6]

Z. Cao, C. Zhang, J. Zhao and J. Min, Channel selection and financing strategy with a risk-averse manufacturer under the capital constraint, Chinese Journal of Management Science, 27 (2019), 30–40. (In Chinese)

[7]

Q. ChaiZ. XiaoK. Lai and G. Zhou, Can carbon cap and trade mechanism be beneficial for remanufacturing?, International Journal of Production Economics, 203 (2018), 311-321. 

[8]

X. ChangY. LiY. ZhaoW. Liu and J. Wu, Effects of carbon permits allocation methods on remanufacturing production decisions, Journal of Cleaner Production, 152 (2017), 281-294. 

[9]

X. ChangH. XiaH. ZhuT. Fan and H. Zhao, Production decisions in a hybrid manufacturing and remanufacturing system with carbon cap and trade mechanism, International Journal of Production Economics, 162 (2015), 160-173. 

[10]

Y. ChenB. LiG. Zhang and Q. Bai, Quantity and collection decisions of the remanufacturing enterprise under both the take-back and carbon emission capacity regulation, Transportation Research Part E: Logistics and Transportation Review, 141 (2020), 102032. 

[11]

D. Dash WuL. Yang and D. L. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. 

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G. Dong, L. Liang, L. Wei, J. Xie and G. Yang, Optimization model of trade credit and asset-based securitization financing in carbon emission reduction supply chain, Annals of Operations Research, 2021.

[13]

G. DouH. GuoQ. Zhang and X. Li, A two-period carbon tax regulation for manufacturing and remanufacturing production planning, Computers & Industrial Engineering, 128 (2019), 502-513. 

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S. DuL. ZhuL. Liang and F. Ma, Emission dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energy Policy, 57 (2013), 61-67. 

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B. FahimniaJ. SarkisF. DehghanianN. Banihashemi and S. Rahman, The impact of carbon pricing on a closed-loop supply chain: an Australian case study, Journal of Cleaner Production, 59 (2013), 210-225. 

[16]

L. Fang and S. Xu, Financing equilibrium in a green supply chain with capital constraint, Computers & Industrial Engineering, 143 (2020), 106390. 

[17]

G. Ferrer, The economics of tire remanufacturing, Resources, Conservation and Recycling, 19 (1997), 221-255. 

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G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26. 

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A. Haddadsisakht and S. M. Ryan, Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax, International Journal of Production Economics, 195 (2018), 118-131. 

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P. HeW. ZhangX. Xu and Y. Bian, Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations, Journal of Cleaner Production, 103 (2015), 241-248. 

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X. HuZ. YangJ. Sun and Y. Zhang, Carbon tax or cap-and-trade: Which is more viable for Chinese remanufacturing industry?, Journal of Cleaner Production, 243 (2020), 118606. 

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G. HuaT. C. E. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185. 

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S. HuangZ.-P. Fan and X. Wang, Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy, Journal of Industrial and Management Optimization, 17 (2021), 261-277. 

[24]

M. A. Ilgin and S. M. Gupta, Performance improvement potential of sensor embedded products in environmental supply chains, Resources, Conservation and Recycling, 55 (2011), 580-592. 

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K. Inderfurth, Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution, International Journal of Production Economics, 90 (2004), 325-343. 

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M. JinS. Zhao and S. C. Kumbhakar, Financial constraints and firm productivity: Evidence from Chinese manufacturing, European Journal of Operational Research, 275 (2019), 1139-1156. 

[27]

M. N. KatehakisB. Melamed and J. J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575. 

[28]

Ö. Kirca and M. M. Köksalan, An integrated production and financial planning model and an application, IIE Transactions, 28 (1996), 677-686. 

[29]

X. LiY. Li and S. Saghafian, A hybrid manufacturing/remanufacturing system with random remanufacturing yield and market-driven product acquisition, IEEE Transactions on Engineering Management, 60 (2013), 424-437.  doi: 10.1016/j.ejor.2013.05.052.

[30]

Z. LuoX. Chen and X. Wang, The role of co-opetition in low carbon manufacturing, European Journal of Operational Research, 253 (2016), 392-403. 

[31]

I. Maslennikova and D. Foley, Xerox's approach to sustainability, Interfaces, 30 (2000), 226–233.

[32]

Z. MiaoH. MaoK. Fu and Y. Wang, Remanufacturing with trade-ins under carbon regulations, Comput. Oper. Res., 89 (2018), 253-268.  doi: 10.1016/j.cor.2016.03.014.

[33]

B. Milanez and T. Bührs, Extended producer responsibility in Brazil: The case of tyre waste, Journal of Cleaner Production, 17 (2009), 608-615. 

[34]

K. NeuhoffK. K. Martinez and M. Sato, Allocation, incentives and distortions: The impact of EU ETS emissions allowance allocations to the electricity sector, Climate Policy, 6 (2006), 73-91. 

[35]

K. E. ParsopoulosI. Konstantaras and K. Skouri, Metaheuristic optimization for the single-item dynamic lot sizing problem with returns and remanufacturing, Computers & Industrial Engineering, 83 (2015), 307-315. 

[36]

J. QinY. HanG. Wei and L. Xia, The value of advance payment financing to carbon emission reduction and production in a supply chain with game theory analysis, International Journal of Production Research, 58 (2020), 1-20. 

[37]

Y. QiuJ. Qiao and P. M. Pardalos, A branch-and-price algorithm for production routing problems with carbon cap-and-trade, OMEGA, 68 (2017), 49-61. 

[38]

M. J. Retel HelmrichR. JansW. van den HeuvelErasmus and A. P. M. Wagelmans, Economic lot-sizing with remanufacturing: Complexity and efficient formulations, IIE Transaction, 46 (2014), 67-86. 

[39]

Y. ShuangA. Diabat and Y. Liao, A stochastic reverse logistics production routing model with emissions control policy selection, International Journal of Production Economics, 213 (2019), 201-216. 

[40]

N. R. Srinivasa Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. 

[41]

R. SubramanianS. Gupta and B. Talbot, Compliance strategies under permits for emissions, Production and Operations Management, 16 (2007), 763-779. 

[42]

N. Suna and L. Plambeck, Allocating emissions among co-products: Implications for procurement and climate policy, Manufacturing & Service Operations Management, 18 (2016), 414-428. 

[43]

R. Tang and L. Yang, Impacts of financing mechanism and power structure on supply chains under cap-and-trade regulation, Transportation Research Part E: Logistics and Transportation Review, 139 (2020), 101957. 

[44]

A. ToptalH. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, International Journal of Production Research, 52 (2014), 243-269. 

[45]

P. Vandenberg, Adapting to the financial landscape: Evidence from small firms in Nairobi, World Development, 31 (2003), 1829-1843. 

[46]

J. WangJ. Zhao and X. Wang, Optimum policy in hybrid manufacturing/remanufacturing system, Computers & Industrial Engineering, 60 (2011), 411-419. 

[47]

X. WangY. ZhuH. Sun and F. Jia, Production decisions of new and remanufactured products: Implications for low carbon emission economy, Journal of Cleaner Production, 171 (2018), 1225-1243. 

[48]

Y. Wang and W. Chen, Effects of emissions constraint on manufacturing and remanufacturing decisions considering capital constraint and financing, Atmospheric Pollution Research, 8 (2017), 455-464. 

[49]

Y. WangW. Chen and B. Liu, Manufacturing/remanufacturing decisions for a capital-constrained manufacturer considering carbon emission cap and trade, Journal of Cleaner Production, 140 (2017), 1118-1128. 

[50]

Y. Wang and Y. Zhang, Remanufacturer's production strategy with capital constraint and differentiated demand, Journal of Intelligent Manufacturing, 28 (2017), 869-882. 

[51]

C. S. WeiY. J. Li and X. Q. Cai, Robust optimal policies of production and inventory with uncertain returns and demand, International Journal of Production Economics, 134 (2011), 357-367. 

[52]

Z. XiaoY. Tian and Z. Yuan, The impacts of regulations and financial development on the operations of supply chains with greenhouse gas emissions, International Journal of Environmental Research and Public Health, 15 (2018), 378. 

[53]

F. XieC. Wang and L. Xu, Whether to invest in terminal efficiency: A perspective considering customer preference and capital constraint in competitive environment?, Ocean and Coastal Management, 205 (2021), 105563. 

[54]

S. Xu and L. Fang, Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint, Transportation Research Part E: Logistics and Transportation Review, 135 (2020), 101859. 

[55]

L. YangY. Hu and L. Huang, Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation, European J. Oper. Res., 287 (2020), 480-496. 

[56]

J. ZengJ. Qu and Z. Zhang, Review of the international greenhouse gas emission reduction scenario programs, Advances in Earth Science, 24 (2009), 436-443. 

[57]

J. ZhanS. Li and X. Chen, The impact of financing mechanism on supply chain sustainability and efficiency, Journal of Cleaner Production, 205 (2018), 407-418. 

[58]

D. ZhangW. DuL. ZhugeZ. M. Tong and R. B. Freeman, Do financial constraints curb firms' efforts to control pollution? Evidence from Chinese manufacturing firms, Journal of Cleaner Production, 215 (2019), 1052-1058. 

[59]

Y. Zhang and W. Chen, Optimal production and financing portfolio strategies for a capital-constrained closed-loop supply chain with OEM remanufacturing, Journal of Cleaner Production, 279 (2021), 123467. 

[60]

X. ZhuM. RenW. Chu and R. Chiong, Remanufacturing subsidy or carbon regulation? An alternative toward sustainable production, Journal of Cleaner Production, 239 (2019), 117988. 

[61]

T. ZouadiA. Yalaoui and M. Reghioui, Hybrid manufacturing/remanufacturing lot-sizing and supplier selection with returns, under carbon emission constraint, International Journal of Production Research, 56 (2018), 1233-1287. 

show all references

References:
[1]

S. S. Ahiska and E. Kurtul, Modeling and analysis of a product substitution strategy for a stochastic manufacturing/remanufacturing system, Computers & Industrial Engineering, 72 (2014), 1-11. 

[2]

S. AnB. LiD. Song and X. Chen, Green credit financing versus trade credit financing in a supply chain with carbon emission limits, European Journal of Operational Research, 292 (2021), 125-142. 

[3]

R. AyresG. Ferrer and T. Van Leynseele, Eco-efficiency, asset recovery and remanufacturing, European Management Journal, 15 (1997), 557-574. 

[4]

E. Cao, L. Du and J. Ruan, Financing preferences and performance for an emission-dependent supply chain: Supplier vs. bank, International Journal Production Economics, 208 (2019), 383-399.

[5]

E. Cao and M. Yu, Trade credit financing and coordination for an emission-dependent supply chain, Computers & Industrial Engineering, 119 (2018), 50-62. 

[6]

Z. Cao, C. Zhang, J. Zhao and J. Min, Channel selection and financing strategy with a risk-averse manufacturer under the capital constraint, Chinese Journal of Management Science, 27 (2019), 30–40. (In Chinese)

[7]

Q. ChaiZ. XiaoK. Lai and G. Zhou, Can carbon cap and trade mechanism be beneficial for remanufacturing?, International Journal of Production Economics, 203 (2018), 311-321. 

[8]

X. ChangY. LiY. ZhaoW. Liu and J. Wu, Effects of carbon permits allocation methods on remanufacturing production decisions, Journal of Cleaner Production, 152 (2017), 281-294. 

[9]

X. ChangH. XiaH. ZhuT. Fan and H. Zhao, Production decisions in a hybrid manufacturing and remanufacturing system with carbon cap and trade mechanism, International Journal of Production Economics, 162 (2015), 160-173. 

[10]

Y. ChenB. LiG. Zhang and Q. Bai, Quantity and collection decisions of the remanufacturing enterprise under both the take-back and carbon emission capacity regulation, Transportation Research Part E: Logistics and Transportation Review, 141 (2020), 102032. 

[11]

D. Dash WuL. Yang and D. L. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. 

[12]

G. Dong, L. Liang, L. Wei, J. Xie and G. Yang, Optimization model of trade credit and asset-based securitization financing in carbon emission reduction supply chain, Annals of Operations Research, 2021.

[13]

G. DouH. GuoQ. Zhang and X. Li, A two-period carbon tax regulation for manufacturing and remanufacturing production planning, Computers & Industrial Engineering, 128 (2019), 502-513. 

[14]

S. DuL. ZhuL. Liang and F. Ma, Emission dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energy Policy, 57 (2013), 61-67. 

[15]

B. FahimniaJ. SarkisF. DehghanianN. Banihashemi and S. Rahman, The impact of carbon pricing on a closed-loop supply chain: an Australian case study, Journal of Cleaner Production, 59 (2013), 210-225. 

[16]

L. Fang and S. Xu, Financing equilibrium in a green supply chain with capital constraint, Computers & Industrial Engineering, 143 (2020), 106390. 

[17]

G. Ferrer, The economics of tire remanufacturing, Resources, Conservation and Recycling, 19 (1997), 221-255. 

[18]

G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26. 

[19]

A. Haddadsisakht and S. M. Ryan, Closed-loop supply chain network design with multiple transportation modes under stochastic demand and uncertain carbon tax, International Journal of Production Economics, 195 (2018), 118-131. 

[20]

P. HeW. ZhangX. Xu and Y. Bian, Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations, Journal of Cleaner Production, 103 (2015), 241-248. 

[21]

X. HuZ. YangJ. Sun and Y. Zhang, Carbon tax or cap-and-trade: Which is more viable for Chinese remanufacturing industry?, Journal of Cleaner Production, 243 (2020), 118606. 

[22]

G. HuaT. C. E. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185. 

[23]

S. HuangZ.-P. Fan and X. Wang, Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy, Journal of Industrial and Management Optimization, 17 (2021), 261-277. 

[24]

M. A. Ilgin and S. M. Gupta, Performance improvement potential of sensor embedded products in environmental supply chains, Resources, Conservation and Recycling, 55 (2011), 580-592. 

[25]

K. Inderfurth, Optimal policies in hybrid manufacturing/remanufacturing systems with product substitution, International Journal of Production Economics, 90 (2004), 325-343. 

[26]

M. JinS. Zhao and S. C. Kumbhakar, Financial constraints and firm productivity: Evidence from Chinese manufacturing, European Journal of Operational Research, 275 (2019), 1139-1156. 

[27]

M. N. KatehakisB. Melamed and J. J. Shi, Cash-flow based dynamic inventory management, Production and Operations Management, 25 (2016), 1558-1575. 

[28]

Ö. Kirca and M. M. Köksalan, An integrated production and financial planning model and an application, IIE Transactions, 28 (1996), 677-686. 

[29]

X. LiY. Li and S. Saghafian, A hybrid manufacturing/remanufacturing system with random remanufacturing yield and market-driven product acquisition, IEEE Transactions on Engineering Management, 60 (2013), 424-437.  doi: 10.1016/j.ejor.2013.05.052.

[30]

Z. LuoX. Chen and X. Wang, The role of co-opetition in low carbon manufacturing, European Journal of Operational Research, 253 (2016), 392-403. 

[31]

I. Maslennikova and D. Foley, Xerox's approach to sustainability, Interfaces, 30 (2000), 226–233.

[32]

Z. MiaoH. MaoK. Fu and Y. Wang, Remanufacturing with trade-ins under carbon regulations, Comput. Oper. Res., 89 (2018), 253-268.  doi: 10.1016/j.cor.2016.03.014.

[33]

B. Milanez and T. Bührs, Extended producer responsibility in Brazil: The case of tyre waste, Journal of Cleaner Production, 17 (2009), 608-615. 

[34]

K. NeuhoffK. K. Martinez and M. Sato, Allocation, incentives and distortions: The impact of EU ETS emissions allowance allocations to the electricity sector, Climate Policy, 6 (2006), 73-91. 

[35]

K. E. ParsopoulosI. Konstantaras and K. Skouri, Metaheuristic optimization for the single-item dynamic lot sizing problem with returns and remanufacturing, Computers & Industrial Engineering, 83 (2015), 307-315. 

[36]

J. QinY. HanG. Wei and L. Xia, The value of advance payment financing to carbon emission reduction and production in a supply chain with game theory analysis, International Journal of Production Research, 58 (2020), 1-20. 

[37]

Y. QiuJ. Qiao and P. M. Pardalos, A branch-and-price algorithm for production routing problems with carbon cap-and-trade, OMEGA, 68 (2017), 49-61. 

[38]

M. J. Retel HelmrichR. JansW. van den HeuvelErasmus and A. P. M. Wagelmans, Economic lot-sizing with remanufacturing: Complexity and efficient formulations, IIE Transaction, 46 (2014), 67-86. 

[39]

Y. ShuangA. Diabat and Y. Liao, A stochastic reverse logistics production routing model with emissions control policy selection, International Journal of Production Economics, 213 (2019), 201-216. 

[40]

N. R. Srinivasa Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. 

[41]

R. SubramanianS. Gupta and B. Talbot, Compliance strategies under permits for emissions, Production and Operations Management, 16 (2007), 763-779. 

[42]

N. Suna and L. Plambeck, Allocating emissions among co-products: Implications for procurement and climate policy, Manufacturing & Service Operations Management, 18 (2016), 414-428. 

[43]

R. Tang and L. Yang, Impacts of financing mechanism and power structure on supply chains under cap-and-trade regulation, Transportation Research Part E: Logistics and Transportation Review, 139 (2020), 101957. 

[44]

A. ToptalH. Özlü and D. Konur, Joint decisions on inventory replenishment and emission reduction investment under different emission regulations, International Journal of Production Research, 52 (2014), 243-269. 

[45]

P. Vandenberg, Adapting to the financial landscape: Evidence from small firms in Nairobi, World Development, 31 (2003), 1829-1843. 

[46]

J. WangJ. Zhao and X. Wang, Optimum policy in hybrid manufacturing/remanufacturing system, Computers & Industrial Engineering, 60 (2011), 411-419. 

[47]

X. WangY. ZhuH. Sun and F. Jia, Production decisions of new and remanufactured products: Implications for low carbon emission economy, Journal of Cleaner Production, 171 (2018), 1225-1243. 

[48]

Y. Wang and W. Chen, Effects of emissions constraint on manufacturing and remanufacturing decisions considering capital constraint and financing, Atmospheric Pollution Research, 8 (2017), 455-464. 

[49]

Y. WangW. Chen and B. Liu, Manufacturing/remanufacturing decisions for a capital-constrained manufacturer considering carbon emission cap and trade, Journal of Cleaner Production, 140 (2017), 1118-1128. 

[50]

Y. Wang and Y. Zhang, Remanufacturer's production strategy with capital constraint and differentiated demand, Journal of Intelligent Manufacturing, 28 (2017), 869-882. 

[51]

C. S. WeiY. J. Li and X. Q. Cai, Robust optimal policies of production and inventory with uncertain returns and demand, International Journal of Production Economics, 134 (2011), 357-367. 

[52]

Z. XiaoY. Tian and Z. Yuan, The impacts of regulations and financial development on the operations of supply chains with greenhouse gas emissions, International Journal of Environmental Research and Public Health, 15 (2018), 378. 

[53]

F. XieC. Wang and L. Xu, Whether to invest in terminal efficiency: A perspective considering customer preference and capital constraint in competitive environment?, Ocean and Coastal Management, 205 (2021), 105563. 

[54]

S. Xu and L. Fang, Partial credit guarantee and trade credit in an emission-dependent supply chain with capital constraint, Transportation Research Part E: Logistics and Transportation Review, 135 (2020), 101859. 

[55]

L. YangY. Hu and L. Huang, Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation, European J. Oper. Res., 287 (2020), 480-496. 

[56]

J. ZengJ. Qu and Z. Zhang, Review of the international greenhouse gas emission reduction scenario programs, Advances in Earth Science, 24 (2009), 436-443. 

[57]

J. ZhanS. Li and X. Chen, The impact of financing mechanism on supply chain sustainability and efficiency, Journal of Cleaner Production, 205 (2018), 407-418. 

[58]

D. ZhangW. DuL. ZhugeZ. M. Tong and R. B. Freeman, Do financial constraints curb firms' efforts to control pollution? Evidence from Chinese manufacturing firms, Journal of Cleaner Production, 215 (2019), 1052-1058. 

[59]

Y. Zhang and W. Chen, Optimal production and financing portfolio strategies for a capital-constrained closed-loop supply chain with OEM remanufacturing, Journal of Cleaner Production, 279 (2021), 123467. 

[60]

X. ZhuM. RenW. Chu and R. Chiong, Remanufacturing subsidy or carbon regulation? An alternative toward sustainable production, Journal of Cleaner Production, 239 (2019), 117988. 

[61]

T. ZouadiA. Yalaoui and M. Reghioui, Hybrid manufacturing/remanufacturing lot-sizing and supplier selection with returns, under carbon emission constraint, International Journal of Production Research, 56 (2018), 1233-1287. 

Figure 1.  Operations process of the carbon credits buy-back policy
Figure 2.  Sequence of participators' decisions under no carbon credits buy-back policy
Figure 3.  Sequence of participators' decisions under the carbon credits buy-back policy
Figure 4.  Decision regions under the cases (a) without and (b) with the carbon credits buy-back policy
Figure 5.  Effects of the initial carbon price on (a) production quantities of both product types and (b) total profits, total emissions and selling quantity of carbon quotas
Figure 6.  Effects of the carbon price increasing rate on (a) production quantities of both product types and (b) total profits, total emissions and selling quantity of carbon quotas
Figure 7.  Effects of the carbon savings on (a) production quantities of both product types and (b) total profits, total emissions and selling quantity of carbon quotas
Figure 8.  Effects of the self-owned capital on (a) production quantities of both product types and (b) total profits, total emissions and selling quantity of carbon quotas
Table 1.  The relevant parameters and decision variables
Decision variables
$ q_{n}, q_{r} $ Manufacturing quantity, Remanufacturing quantity
$ Es $ selling quantity of carbon quotas
Relevant parameters
$ Q $ potential demands of new and remanufactured products
$ p_{n}, p_{r} $ Sales prices of unit new and remanufactured products, $ p_{n} $ ¿$ p_{r} $
$ c_{n}, c_{r} $ Production costs of unit new and remanufactured products, $ c_{n} $ ¿$ c_{r} $
$ e_{n}, e_{r} $ Emissions quantities of unit new and remanufactured products, $ e_{n} $ ¿$ e_{r} $
$ s $ carbon savings of unit remanufactured product (referred to as carbon savings), then the emissions quantity of unit remanufactured product is $ e_{r} $ =$ e_{n}-s $
$ p_{t} $ Carbon price at the beginning of the period, namely, the initial carbon price
$ \alpha $ Carbon price increasing rate, the enhanced emissions trading mechanism usually leads to the increasing of the carbon price, thus the final carbon price is $ p_{t} $ (1 $ + $ $ \alpha) (\alpha > $ 0)
$ B $ Self-owned capital
$ E_{0} $ Carbon quotas
$ E_{m} $ Total carbon emissions
$ \pi_{m} $ Total profit
Decision variables
$ q_{n}, q_{r} $ Manufacturing quantity, Remanufacturing quantity
$ Es $ selling quantity of carbon quotas
Relevant parameters
$ Q $ potential demands of new and remanufactured products
$ p_{n}, p_{r} $ Sales prices of unit new and remanufactured products, $ p_{n} $ ¿$ p_{r} $
$ c_{n}, c_{r} $ Production costs of unit new and remanufactured products, $ c_{n} $ ¿$ c_{r} $
$ e_{n}, e_{r} $ Emissions quantities of unit new and remanufactured products, $ e_{n} $ ¿$ e_{r} $
$ s $ carbon savings of unit remanufactured product (referred to as carbon savings), then the emissions quantity of unit remanufactured product is $ e_{r} $ =$ e_{n}-s $
$ p_{t} $ Carbon price at the beginning of the period, namely, the initial carbon price
$ \alpha $ Carbon price increasing rate, the enhanced emissions trading mechanism usually leads to the increasing of the carbon price, thus the final carbon price is $ p_{t} $ (1 $ + $ $ \alpha) (\alpha > $ 0)
$ B $ Self-owned capital
$ E_{0} $ Carbon quotas
$ E_{m} $ Total carbon emissions
$ \pi_{m} $ Total profit
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