doi: 10.3934/jimo.2021129
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

Investigating a green supply chain with product recycling under retailer's fairness behavior

Department of Mathematics, Jadavpur University, Kolkata - 700 032, India

* Corresponding author: Chirantan Mondal

Received  November 2020 Revised  April 2021 Early access August 2021

Due to the rapid increment of environmental pollution and advancement of society, recently many manufacturing firms have started greening their products and focusing on product remanufacturing. The retailing firms are also taking several efforts for marketing those products and thinking more about the fairness of the business. Keeping this in mind, this study investigates the effect of recycling activity and the retailer's fairness behavior on pricing, green improvement, and marketing effort in a closed-loop green supply chain. In the forward channel, the manufacturer sells the green product through the retailer while in the reverse channel, either the manufacturer or the retailer or an independent third-party collects used products. The centralized model and six decentralized models are developed depending on the retailer's fairness behavior and/or product recycling. The optimal results are derived and compared analytically. The analytical results are verified by exemplifying a numerical example. A restitution-based wholesale price contract is developed to resolve the channel conflicts and coordinate the supply chain. Our results reveal that (ⅰ) the manufacturer never selects the third-party as a collector of used products under fair-neutral retailer, (ⅱ) the fairness behavior of the retailer improves her profitability but it diminishes the manufacturer's profit, and (ⅲ) if the manufacturer does not pay much transfer price, then the collection through the third-party is preferable to the fair-minded retailer.

Citation: Chirantan Mondal, Bibhas C. Giri. Investigating a green supply chain with product recycling under retailer's fairness behavior. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021129
References:
[1]

Q. BaiM. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.   Google Scholar

[2]

Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with substitutable products, Journal of Cleaner Production, 145 (2017), 232-249.  doi: 10.1016/j.jclepro.2017.01.060.  Google Scholar

[3]

O. Caliskan-DemiragY. Chen and J. Li, Channel coordination under fairness concerns and nonlinear demand, European J. Oper. Res., 207 (2010), 1321-1326.  doi: 10.1016/j.ejor.2010.07.017.  Google Scholar

[4]

C.-K. Chen and M. Akmalul'Ulya, Analyses of the reward-penalty mechanism in green closed-loop supply chains with product remanufacturing, International Journal of Production Economics, 210 (2019), 211-223.  doi: 10.1016/j.ijpe.2019.01.006.  Google Scholar

[5]

C.-K. ChenM. Akmalul'Ulya and and U. A. Mancasari, A study of product quality and marketing efforts in closed-loop supply chains with remanufacturing, IEEE Transactions on Systems, Man and Cybernatics: Systems, 50 (2020), 4870-4881.  doi: 10.1109/TSMC.2018.2883984.  Google Scholar

[6]

H. T. CuiJ. S. Raju and Z. J. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314.   Google Scholar

[7]

S. DuL. WeiY. Zhu and T. Nie, Peer-regarding fairness in supply chain, International Journal of Production Research, 56 (2018), 3384-3396.  doi: 10.1080/00207543.2016.1257872.  Google Scholar

[8]

S. F. DuT. NieC. Chu and Y. Yu, Newsvendor model for a dyadic supply chain with Nash bargaining fairness concerns, International Journal of Production Research, 52 (2014), 5070-5085.   Google Scholar

[9]

X. Du and W. Zhao, Managing a dual-channel supply chain with fairness and channel preference, Math. Probl. Eng., (2021), Article ID: 6614692, 1–10. doi: 10.1155/2021/6614692.  Google Scholar

[10]

T. S. Genc and P. De Giovanni, Trade-in and save: A two-period closed-loop supply chain game with price and technology dependent returns, International Journal of Production Economics, 183 (2017), 514-527.   Google Scholar

[11]

D. Ghosh and J. Shah, Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164 (2015), 319-329.  doi: 10.1016/j.ijpe.2014.11.005.  Google Scholar

[12]

B. C. GiriC. Mondal and T. Maiti, Analysing a closed-loop supply chain with selling price, warranty period and green sensitive consumer demand under revenue sharing contract, Journal of Cleaner Production, 190 (2018), 822-837.  doi: 10.1016/j.jclepro.2018.04.092.  Google Scholar

[13]

V. D. R. Jr. Guide, Production planning and control for remanufacturing: Industry practice and research needs, Journal of Operations Management, 18 (2000), 467-483.  doi: 10.1016/S0272-6963(00)00034-6.  Google Scholar

[14]

J. HeydariK. Govindan and Z. Basiri, Balancing price and green quality in presence of consumer environmental awareness: a green supply chain coordination approach, International Journal of Production Research, 59 (2021), 1957-1975.   Google Scholar

[15]

X. HongL. XuP. Du and W. Wang, Joint advertising, pricing and collection decisions in a closed-loop supply chain, International Journal of Production Economics, 167 (2015), 12-22.  doi: 10.1016/j.ijpe.2015.05.001.  Google Scholar

[16]

Z. Hong and X. Guo, Green product supply chain contracts considering environmental responsibilities, Omega, 83 (2019), 155-166.  doi: 10.1016/j.omega.2018.02.010.  Google Scholar

[17]

M. HuangM. SongL. H. Lee and W. K. Ching, Analysis for strategy of closed-loop supply chain with dual recycling channel, International Journal of Production Economics, 144 (2013), 510-520.  doi: 10.1016/j.ijpe.2013.04.002.  Google Scholar

[18]

J. Jian, B. Li, N. Zhang and J. Su, Decision-making and coordination of green closed-loop supply chain with fairness concern, Journal of Cleaner Production, 298 (2021), 126779. Google Scholar

[19]

Y. LiL. FengK. Govindan and F. Xu, Effects of a secondary market on original equipment manufactures' pricing, trade-in remanufacturing, and entry decisions, European J. Oper. Res., 279 (2019), 751-766.  doi: 10.1016/j.ejor.2019.03.039.  Google Scholar

[20]

L. LiuZ. WangL. XuX. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.   Google Scholar

[21]

W. Liu, S. Wang and D. Zhu, The more supply chain control power, the better? A comparison among four kinds of cooperation models, Math. Probl. Eng., (2015), Article ID: 290912, 1–19. doi: 10.1155/2015/290912.  Google Scholar

[22]

Z. LiuK. W. LiB.-Y. LiJ. Huang and J. Tang, Impact of product-design strategies on the operations of a closed-loop supply chain, Transportation Research Part E: Logistics and Transportation Review, 124 (2019), 75-91.  doi: 10.1016/j.tre.2019.02.007.  Google Scholar

[23]

Z. Liu, K. W. Li, J. Tang, B. Gong and J. Huang, Optimal operations of a closed-loop supply chain under a dual regulation, International Journal of Production Economics, 233 (2021), 107991. Google Scholar

[24]

Z. Liu, X.-X. Zheng, B.-G. Gong and Y.-M. Gui, Joint decision-making and the coordination of a sustainable supply chain in the context of carbon tax regulation and fairness concerns, Int. J. Environ. Res. Public Health, 14 (2017), 1464. doi: 10.3390/ijerph14121464.  Google Scholar

[25]

P. MaK. W. Li and Z.-J. Wang, Pricing decisions in closed-loop supply chains with marketing effort and fairness concerns, International Journal of Production Research, 55 (2017), 6710-6731.  doi: 10.1080/00207543.2017.1346324.  Google Scholar

[26]

P. MaH. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581.   Google Scholar

[27]

T. Maiti and B. C. Giri, A closed-loop supply chain under retail price and product quality dependent demand, Journal of Manufacturing Systems, 37 (2015), 624-637.  doi: 10.1016/j.jmsy.2014.09.009.  Google Scholar

[28]

T. Maiti and B. C. Giri, Two-way product recovery in a closed-loop supply chain with variable markup under price and quality dependent demand, International Journal of Production Economics, 183 (2017), 259-272.   Google Scholar

[29]

N. M. ModakN. Kazemi and L. E. Cárdenas-Barrón, Investigating structure of a two-echelon closed-loop supply chain using social work donation as a Corporate Social Responsibility practice, International Journal of Production Economics, 207 (2019), 19-33.  doi: 10.1016/j.ijpe.2018.10.009.  Google Scholar

[30]

N. M. ModakN. ModakS. Panda and S. S. Sana, Analyzing structure of two-echelon closed-loop supply chain for pricing, quality and recycling management, Journal of Cleaner Production, 171 (2018), 512-528.  doi: 10.1016/j.jclepro.2017.10.033.  Google Scholar

[31]

C. Mondal and B. C. Giri, Pricing and used product collection strategies in a two-period closed-loop supply chain under greening level and effort dependent demand, Journal of Cleaner Production, 265 (2020), 121335. Google Scholar

[32]

C. Mondal and B. C. Giri, Retailers' competition and cooperation in a closed-loop green supply chain under governmental intervention and cap-and-trade policy, Operational Research, (2020). doi: 10.1007/s12351-020-00596-0.  Google Scholar

[33]

C. Mondal, B. C. Giri and S. Biswas, Integrating corporate social responsibility in a closed-loop supply chain under government subsidy and used products collection strategies, Flexible Services and Manufacturing Journal, (2021). doi: 10.1007/s10696-021-09404-z.  Google Scholar

[34]

T. Nie and S. Du, Dual-fairness supply chain with quantity discount contracts, European J. Oper. Res., 258 (2017), 491-500.  doi: 10.1016/j.ejor.2016.08.051.  Google Scholar

[35]

X. Qian, F. T. S. Chan, J. Zhang, M. Yin and Q. Zhang, Channel coordination of a two-echelon sustainable supply chain with a fair-minded retailer under cap-and-trade regulation, Journal of Cleaner Production, 244 (2020), 118715. doi: 10.1016/j.jclepro.2019.118715.  Google Scholar

[36]

A. Ranjan and J. K. Jha, Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort, Journal of Cleaner Production, 218 (2019), 409-424.  doi: 10.1016/j.jclepro.2019.01.297.  Google Scholar

[37]

Y. Ranjbar, H. Sahebi, J. Ashayeri and A. Teymouri, A competitive dual recycling channel in a three-level closed loop supply chain under different power structures: pricing and collecting decisions, Journal of Cleaner Production, 272 (2020), 122623. doi: 10.1016/j.jclepro.2020.122623.  Google Scholar

[38]

R. C. SavaskanS. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[39]

E. Shama, Ford, BMW, Honda, and Volkswagen agree to California emissions framework, (2019), https://www.cnbc.com/2019/07/25/ford-bmw-honda-and-volkswagen-agree-to-california-emissions-rules.html. Google Scholar

[40]

H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[41]

Y. SongJ. ChenY. YangC. Jia and J. Su, A dual-channel supply chain model considering supplier's mental accounting and retailer's fairness concerns, Procedia Computer Science, 139 (2018), 347-355.  doi: 10.1016/j.procs.2018.10.280.  Google Scholar

[42]

A. A. TaleizadehM. S. Moshtagh and I. Moon, Pricing, product quality, and collection optimization in a decentralized closed-loop supply chain with different channel structures: Game theoretical approach, Journal of Cleaner Production, 189 (2018), 406-431.  doi: 10.1016/j.jclepro.2018.02.209.  Google Scholar

[43]

Q. WangD. Zhao and L. He, Contracting emission reduction for supply chains considering market low-carbon preference, Journal of Cleaner Production, 120 (2016), 72-84.  doi: 10.1016/j.jclepro.2015.11.049.  Google Scholar

[44]

S. Y. Wang and S. H. Choi, Pareto-efficient coordination of the contract-based MTO supply chain under flexible cap-and-trade emission constraint, Journal of Cleaner Production, 250 (2020), 119571. doi: 10.1016/j.jclepro.2019.119571.  Google Scholar

[45]

Y. WangR. FanL. Shen and M. Jin, Decisions and coordination of green e-commerce supply chain considering green manufacturer's fairness concerns, International Journal of Production Research, 58 (2020), 7471-7489.   Google Scholar

[46]

Y. WangZ. Yu and L. Shen, Study on the decision-making and coordination of an e-commerce supply chain with manufacturer fairness concerns, International Journal of Production Research, 57 (2019), 2788-2808.   Google Scholar

[47]

W. Wu, Q. Zhang and Z. Liang, Environmentally responsible closed-loop supply chain models for joint environmental responsibility investment, recycling and pricing decisions, Journal of Cleaner Production, 259 (2020), 120776. doi: 10.1016/j.jclepro.2020.120776.  Google Scholar

[48]

J. YangJ. XieX. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European J. Oper. Res., 227 (2013), 401-407.  doi: 10.1016/j.ejor.2012.12.011.  Google Scholar

[49]

L. ZhangH. ZhouY. Liu and R. Lu, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, Journal of Cleaner Production, 213 (2019), 1063-1079.  doi: 10.1016/j.jclepro.2018.12.187.  Google Scholar

[50]

X.-M. Zhang, Q.-W. Li, Z. Liu and C.-T. Chang, Optimal pricing and remanufacturing mode in a closed-loop supply chain of WEEE under government fund policy, Computers & Industrial Engineering, 151 (2021), 106951. Google Scholar

[51]

X. Zhang, Q. Li and G. Qi, Decision-making of a dual-channel closed-loop supply chain in the context government policy: a dynamic game theory, Discrete Dyn. Nat. Soc., (2020), Article ID: 2313698, 1–19. doi: 10.1155/2020/2313698.  Google Scholar

[52]

X. Zhang, C. Ma, H. Chen and G. Qi, Impact of retailer's vertical and horizontal fairness concerns on manufacturer's online channel mode, Discrete Dyn. Nat. Soc., (2021), Article ID: 6692582, 1–12. doi: 10.1155/2021/6692582.  Google Scholar

[53]

X. ZhangM. Song and G. Liu, Service product pricing strategies based on time-sensitive customer choice behavior, J. Ind. Manag. Optim., 13 (2017), 297-312.  doi: 10.3934/jimo.2016018.  Google Scholar

[54]

Z.-C. ZhangH.-Y. Xu and K.-B. Chen, Operational decisions and financing strategies in a capital-constrained closed-loop supply chain, International Journal of Production Research, 59 (2021), 4690-4710.  doi: 10.1080/00207543.2020.1770356.  Google Scholar

[55]

X. Zhen, D. Shi, S.-B. Tsai and W. Wang, Pricing decisions of a supply chain with multichannel retailer under fairness concerns, Math. Probl. Eng., (2019), Article ID: 9547302, 1–22. doi: 10.1155/2019/9547302.  Google Scholar

[56]

X.-X. ZhengD.-F. LiZ. LiuF. Jia and J.-B. Sheu, Coordinating a closed-loop supply chain with fairness concerns through variable-weighted Shapley values, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 227-253.  doi: 10.1016/j.tre.2019.04.006.  Google Scholar

[57]

X.-X. ZhengZ. LiuK. W. LiJ. Huang and J. Chen, Cooperative game approaches to coordinating a three-echelon closed-loop supply chain with fairness concerns, International Journal of Production Economics, 212 (2019), 92-110.  doi: 10.1016/j.ijpe.2019.01.011.  Google Scholar

[58]

Y. ZhouM. BaoX. Chen and X. Xu, Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns, Journal of Cleaner Production, 133 (2016), 402-412.  doi: 10.1016/j.jclepro.2016.05.097.  Google Scholar

show all references

References:
[1]

Q. BaiM. Chen and L. Xu, Revenue and promotional cost-sharing contract versus two-part tariff contract in coordinating sustainable supply chain systems with deteriorating items, International Journal of Production Economics, 187 (2017), 85-101.   Google Scholar

[2]

Z. Basiri and J. Heydari, A mathematical model for green supply chain coordination with substitutable products, Journal of Cleaner Production, 145 (2017), 232-249.  doi: 10.1016/j.jclepro.2017.01.060.  Google Scholar

[3]

O. Caliskan-DemiragY. Chen and J. Li, Channel coordination under fairness concerns and nonlinear demand, European J. Oper. Res., 207 (2010), 1321-1326.  doi: 10.1016/j.ejor.2010.07.017.  Google Scholar

[4]

C.-K. Chen and M. Akmalul'Ulya, Analyses of the reward-penalty mechanism in green closed-loop supply chains with product remanufacturing, International Journal of Production Economics, 210 (2019), 211-223.  doi: 10.1016/j.ijpe.2019.01.006.  Google Scholar

[5]

C.-K. ChenM. Akmalul'Ulya and and U. A. Mancasari, A study of product quality and marketing efforts in closed-loop supply chains with remanufacturing, IEEE Transactions on Systems, Man and Cybernatics: Systems, 50 (2020), 4870-4881.  doi: 10.1109/TSMC.2018.2883984.  Google Scholar

[6]

H. T. CuiJ. S. Raju and Z. J. Zhang, Fairness and channel coordination, Management Science, 53 (2007), 1303-1314.   Google Scholar

[7]

S. DuL. WeiY. Zhu and T. Nie, Peer-regarding fairness in supply chain, International Journal of Production Research, 56 (2018), 3384-3396.  doi: 10.1080/00207543.2016.1257872.  Google Scholar

[8]

S. F. DuT. NieC. Chu and Y. Yu, Newsvendor model for a dyadic supply chain with Nash bargaining fairness concerns, International Journal of Production Research, 52 (2014), 5070-5085.   Google Scholar

[9]

X. Du and W. Zhao, Managing a dual-channel supply chain with fairness and channel preference, Math. Probl. Eng., (2021), Article ID: 6614692, 1–10. doi: 10.1155/2021/6614692.  Google Scholar

[10]

T. S. Genc and P. De Giovanni, Trade-in and save: A two-period closed-loop supply chain game with price and technology dependent returns, International Journal of Production Economics, 183 (2017), 514-527.   Google Scholar

[11]

D. Ghosh and J. Shah, Supply chain analysis under green sensitive consumer demand and cost sharing contract, International Journal of Production Economics, 164 (2015), 319-329.  doi: 10.1016/j.ijpe.2014.11.005.  Google Scholar

[12]

B. C. GiriC. Mondal and T. Maiti, Analysing a closed-loop supply chain with selling price, warranty period and green sensitive consumer demand under revenue sharing contract, Journal of Cleaner Production, 190 (2018), 822-837.  doi: 10.1016/j.jclepro.2018.04.092.  Google Scholar

[13]

V. D. R. Jr. Guide, Production planning and control for remanufacturing: Industry practice and research needs, Journal of Operations Management, 18 (2000), 467-483.  doi: 10.1016/S0272-6963(00)00034-6.  Google Scholar

[14]

J. HeydariK. Govindan and Z. Basiri, Balancing price and green quality in presence of consumer environmental awareness: a green supply chain coordination approach, International Journal of Production Research, 59 (2021), 1957-1975.   Google Scholar

[15]

X. HongL. XuP. Du and W. Wang, Joint advertising, pricing and collection decisions in a closed-loop supply chain, International Journal of Production Economics, 167 (2015), 12-22.  doi: 10.1016/j.ijpe.2015.05.001.  Google Scholar

[16]

Z. Hong and X. Guo, Green product supply chain contracts considering environmental responsibilities, Omega, 83 (2019), 155-166.  doi: 10.1016/j.omega.2018.02.010.  Google Scholar

[17]

M. HuangM. SongL. H. Lee and W. K. Ching, Analysis for strategy of closed-loop supply chain with dual recycling channel, International Journal of Production Economics, 144 (2013), 510-520.  doi: 10.1016/j.ijpe.2013.04.002.  Google Scholar

[18]

J. Jian, B. Li, N. Zhang and J. Su, Decision-making and coordination of green closed-loop supply chain with fairness concern, Journal of Cleaner Production, 298 (2021), 126779. Google Scholar

[19]

Y. LiL. FengK. Govindan and F. Xu, Effects of a secondary market on original equipment manufactures' pricing, trade-in remanufacturing, and entry decisions, European J. Oper. Res., 279 (2019), 751-766.  doi: 10.1016/j.ejor.2019.03.039.  Google Scholar

[20]

L. LiuZ. WangL. XuX. Hong and K. Govindan, Collection effort and reverse channel choices in a closed-loop supply chain, Journal of Cleaner Production, 144 (2017), 492-500.   Google Scholar

[21]

W. Liu, S. Wang and D. Zhu, The more supply chain control power, the better? A comparison among four kinds of cooperation models, Math. Probl. Eng., (2015), Article ID: 290912, 1–19. doi: 10.1155/2015/290912.  Google Scholar

[22]

Z. LiuK. W. LiB.-Y. LiJ. Huang and J. Tang, Impact of product-design strategies on the operations of a closed-loop supply chain, Transportation Research Part E: Logistics and Transportation Review, 124 (2019), 75-91.  doi: 10.1016/j.tre.2019.02.007.  Google Scholar

[23]

Z. Liu, K. W. Li, J. Tang, B. Gong and J. Huang, Optimal operations of a closed-loop supply chain under a dual regulation, International Journal of Production Economics, 233 (2021), 107991. Google Scholar

[24]

Z. Liu, X.-X. Zheng, B.-G. Gong and Y.-M. Gui, Joint decision-making and the coordination of a sustainable supply chain in the context of carbon tax regulation and fairness concerns, Int. J. Environ. Res. Public Health, 14 (2017), 1464. doi: 10.3390/ijerph14121464.  Google Scholar

[25]

P. MaK. W. Li and Z.-J. Wang, Pricing decisions in closed-loop supply chains with marketing effort and fairness concerns, International Journal of Production Research, 55 (2017), 6710-6731.  doi: 10.1080/00207543.2017.1346324.  Google Scholar

[26]

P. MaH. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581.   Google Scholar

[27]

T. Maiti and B. C. Giri, A closed-loop supply chain under retail price and product quality dependent demand, Journal of Manufacturing Systems, 37 (2015), 624-637.  doi: 10.1016/j.jmsy.2014.09.009.  Google Scholar

[28]

T. Maiti and B. C. Giri, Two-way product recovery in a closed-loop supply chain with variable markup under price and quality dependent demand, International Journal of Production Economics, 183 (2017), 259-272.   Google Scholar

[29]

N. M. ModakN. Kazemi and L. E. Cárdenas-Barrón, Investigating structure of a two-echelon closed-loop supply chain using social work donation as a Corporate Social Responsibility practice, International Journal of Production Economics, 207 (2019), 19-33.  doi: 10.1016/j.ijpe.2018.10.009.  Google Scholar

[30]

N. M. ModakN. ModakS. Panda and S. S. Sana, Analyzing structure of two-echelon closed-loop supply chain for pricing, quality and recycling management, Journal of Cleaner Production, 171 (2018), 512-528.  doi: 10.1016/j.jclepro.2017.10.033.  Google Scholar

[31]

C. Mondal and B. C. Giri, Pricing and used product collection strategies in a two-period closed-loop supply chain under greening level and effort dependent demand, Journal of Cleaner Production, 265 (2020), 121335. Google Scholar

[32]

C. Mondal and B. C. Giri, Retailers' competition and cooperation in a closed-loop green supply chain under governmental intervention and cap-and-trade policy, Operational Research, (2020). doi: 10.1007/s12351-020-00596-0.  Google Scholar

[33]

C. Mondal, B. C. Giri and S. Biswas, Integrating corporate social responsibility in a closed-loop supply chain under government subsidy and used products collection strategies, Flexible Services and Manufacturing Journal, (2021). doi: 10.1007/s10696-021-09404-z.  Google Scholar

[34]

T. Nie and S. Du, Dual-fairness supply chain with quantity discount contracts, European J. Oper. Res., 258 (2017), 491-500.  doi: 10.1016/j.ejor.2016.08.051.  Google Scholar

[35]

X. Qian, F. T. S. Chan, J. Zhang, M. Yin and Q. Zhang, Channel coordination of a two-echelon sustainable supply chain with a fair-minded retailer under cap-and-trade regulation, Journal of Cleaner Production, 244 (2020), 118715. doi: 10.1016/j.jclepro.2019.118715.  Google Scholar

[36]

A. Ranjan and J. K. Jha, Pricing and coordination strategies of a dual-channel supply chain considering green quality and sales effort, Journal of Cleaner Production, 218 (2019), 409-424.  doi: 10.1016/j.jclepro.2019.01.297.  Google Scholar

[37]

Y. Ranjbar, H. Sahebi, J. Ashayeri and A. Teymouri, A competitive dual recycling channel in a three-level closed loop supply chain under different power structures: pricing and collecting decisions, Journal of Cleaner Production, 272 (2020), 122623. doi: 10.1016/j.jclepro.2020.122623.  Google Scholar

[38]

R. C. SavaskanS. Bhattacharya and L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Management Science, 50 (2004), 239-252.  doi: 10.1287/mnsc.1030.0186.  Google Scholar

[39]

E. Shama, Ford, BMW, Honda, and Volkswagen agree to California emissions framework, (2019), https://www.cnbc.com/2019/07/25/ford-bmw-honda-and-volkswagen-agree-to-california-emissions-rules.html. Google Scholar

[40]

H. Song and X. Gao, Green supply chain game model and analysis under revenue-sharing contract, Journal of Cleaner Production, 170 (2018), 183-192.  doi: 10.1016/j.jclepro.2017.09.138.  Google Scholar

[41]

Y. SongJ. ChenY. YangC. Jia and J. Su, A dual-channel supply chain model considering supplier's mental accounting and retailer's fairness concerns, Procedia Computer Science, 139 (2018), 347-355.  doi: 10.1016/j.procs.2018.10.280.  Google Scholar

[42]

A. A. TaleizadehM. S. Moshtagh and I. Moon, Pricing, product quality, and collection optimization in a decentralized closed-loop supply chain with different channel structures: Game theoretical approach, Journal of Cleaner Production, 189 (2018), 406-431.  doi: 10.1016/j.jclepro.2018.02.209.  Google Scholar

[43]

Q. WangD. Zhao and L. He, Contracting emission reduction for supply chains considering market low-carbon preference, Journal of Cleaner Production, 120 (2016), 72-84.  doi: 10.1016/j.jclepro.2015.11.049.  Google Scholar

[44]

S. Y. Wang and S. H. Choi, Pareto-efficient coordination of the contract-based MTO supply chain under flexible cap-and-trade emission constraint, Journal of Cleaner Production, 250 (2020), 119571. doi: 10.1016/j.jclepro.2019.119571.  Google Scholar

[45]

Y. WangR. FanL. Shen and M. Jin, Decisions and coordination of green e-commerce supply chain considering green manufacturer's fairness concerns, International Journal of Production Research, 58 (2020), 7471-7489.   Google Scholar

[46]

Y. WangZ. Yu and L. Shen, Study on the decision-making and coordination of an e-commerce supply chain with manufacturer fairness concerns, International Journal of Production Research, 57 (2019), 2788-2808.   Google Scholar

[47]

W. Wu, Q. Zhang and Z. Liang, Environmentally responsible closed-loop supply chain models for joint environmental responsibility investment, recycling and pricing decisions, Journal of Cleaner Production, 259 (2020), 120776. doi: 10.1016/j.jclepro.2020.120776.  Google Scholar

[48]

J. YangJ. XieX. Deng and H. Xiong, Cooperative advertising in a distribution channel with fairness concerns, European J. Oper. Res., 227 (2013), 401-407.  doi: 10.1016/j.ejor.2012.12.011.  Google Scholar

[49]

L. ZhangH. ZhouY. Liu and R. Lu, Optimal environmental quality and price with consumer environmental awareness and retailer's fairness concerns in supply chain, Journal of Cleaner Production, 213 (2019), 1063-1079.  doi: 10.1016/j.jclepro.2018.12.187.  Google Scholar

[50]

X.-M. Zhang, Q.-W. Li, Z. Liu and C.-T. Chang, Optimal pricing and remanufacturing mode in a closed-loop supply chain of WEEE under government fund policy, Computers & Industrial Engineering, 151 (2021), 106951. Google Scholar

[51]

X. Zhang, Q. Li and G. Qi, Decision-making of a dual-channel closed-loop supply chain in the context government policy: a dynamic game theory, Discrete Dyn. Nat. Soc., (2020), Article ID: 2313698, 1–19. doi: 10.1155/2020/2313698.  Google Scholar

[52]

X. Zhang, C. Ma, H. Chen and G. Qi, Impact of retailer's vertical and horizontal fairness concerns on manufacturer's online channel mode, Discrete Dyn. Nat. Soc., (2021), Article ID: 6692582, 1–12. doi: 10.1155/2021/6692582.  Google Scholar

[53]

X. ZhangM. Song and G. Liu, Service product pricing strategies based on time-sensitive customer choice behavior, J. Ind. Manag. Optim., 13 (2017), 297-312.  doi: 10.3934/jimo.2016018.  Google Scholar

[54]

Z.-C. ZhangH.-Y. Xu and K.-B. Chen, Operational decisions and financing strategies in a capital-constrained closed-loop supply chain, International Journal of Production Research, 59 (2021), 4690-4710.  doi: 10.1080/00207543.2020.1770356.  Google Scholar

[55]

X. Zhen, D. Shi, S.-B. Tsai and W. Wang, Pricing decisions of a supply chain with multichannel retailer under fairness concerns, Math. Probl. Eng., (2019), Article ID: 9547302, 1–22. doi: 10.1155/2019/9547302.  Google Scholar

[56]

X.-X. ZhengD.-F. LiZ. LiuF. Jia and J.-B. Sheu, Coordinating a closed-loop supply chain with fairness concerns through variable-weighted Shapley values, Transportation Research Part E: Logistics and Transportation Review, 126 (2019), 227-253.  doi: 10.1016/j.tre.2019.04.006.  Google Scholar

[57]

X.-X. ZhengZ. LiuK. W. LiJ. Huang and J. Chen, Cooperative game approaches to coordinating a three-echelon closed-loop supply chain with fairness concerns, International Journal of Production Economics, 212 (2019), 92-110.  doi: 10.1016/j.ijpe.2019.01.011.  Google Scholar

[58]

Y. ZhouM. BaoX. Chen and X. Xu, Co-op advertising and emission reduction cost sharing contracts and coordination in low-carbon supply chain based on fairness concerns, Journal of Cleaner Production, 133 (2016), 402-412.  doi: 10.1016/j.jclepro.2016.05.097.  Google Scholar

Figure 1.  Proposed closed-loop supply chain models
Figure 2.  Availability of remanufactured products in the primary market
Figure 3.  Win-win situation for the manufacturer and the retailer
Figure 4.  Sensitivity of optimal results w.r.t. $ B $
Figure 5.  Sensitivity of optimal results w.r.t. $ \xi $
Table 1.  A comparison of the present study with related existing literatures
Author(s) Demand sensitivity Carbon Collector Retailer's Loop type Channel
price quality effort emission M R T fairness concern open closed coordination
Maiti and Giri [27] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Hong et al. [15] $ \times $ $ \times $ $ \times $ $ \times $
Nie and Du [34] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Liu et al. [24] $ \times $ $ \times $ $ \times $ $ \times $
Ma et al. [25] $ \times $ $ \times $ $ \times $ $ \times $
Chen et al. [5] $ \times $ $ \times $ $ \times $ $ \times $
Modak et al. [30] $ \times $ $ \times $ $ \times $ $ \times $
Song et al. [41] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Chen and Akmalul'Ulya [4] $ \times $ $ \times $ $ \times $ $ \times $
Modak et al. [29] $ \times $ $ \times $ $ \times $ $ \times $
Zhang et al. [49] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Zheng et al. [57] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Zheng et al. [56] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Mondal and Giri [31] $ \times $ $ \times $ $ \times $
Zhang et al. [54] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Qian et al. [35] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Jian et al. [18] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Du and Zhao [9] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Mondal et al. [33] $ \times $ $ \times $ $ \times $ $ \times $
Present study $ \times $
Note: M - Manufacturer; R - Retailer; T - Third-party.
Here, quality includes greening level, sustainability level, emission reduction level, etc. and effort includes sales, marketing, greening, CSR effort, etc.
Author(s) Demand sensitivity Carbon Collector Retailer's Loop type Channel
price quality effort emission M R T fairness concern open closed coordination
Maiti and Giri [27] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Hong et al. [15] $ \times $ $ \times $ $ \times $ $ \times $
Nie and Du [34] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Liu et al. [24] $ \times $ $ \times $ $ \times $ $ \times $
Ma et al. [25] $ \times $ $ \times $ $ \times $ $ \times $
Chen et al. [5] $ \times $ $ \times $ $ \times $ $ \times $
Modak et al. [30] $ \times $ $ \times $ $ \times $ $ \times $
Song et al. [41] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Chen and Akmalul'Ulya [4] $ \times $ $ \times $ $ \times $ $ \times $
Modak et al. [29] $ \times $ $ \times $ $ \times $ $ \times $
Zhang et al. [49] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Zheng et al. [57] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Zheng et al. [56] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Mondal and Giri [31] $ \times $ $ \times $ $ \times $
Zhang et al. [54] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Qian et al. [35] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Jian et al. [18] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Du and Zhao [9] $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $ $ \times $
Mondal et al. [33] $ \times $ $ \times $ $ \times $ $ \times $
Present study $ \times $
Note: M - Manufacturer; R - Retailer; T - Third-party.
Here, quality includes greening level, sustainability level, emission reduction level, etc. and effort includes sales, marketing, greening, CSR effort, etc.
Table 2.  Decision variables and parameters
Notations Description
Decision variables
$ w $ unit wholesale price of the manufacturer.
$ p $ unit selling price of the retailer.
$ \theta $ level of green innovation.
$ e $ marketing effort level of the retailer.
$ \tau $ collection rate of used products.
Parameters
$ D $ market demand.
$ D_r $ return quantity.
$ c_m (c_r) $ unit manufacturing (remanufacturing) cost of the new (returned) product.
$ D_0 $ basic market demand.
$ E_0 $ basic carbon emission during production.
$ E_u (E_t) $ unit (total) carbon emission during production.
$ \rho $ fraction of remanufactured products available for selling in the primary market.
$ w_1 $ unit selling price of the remanufactured product in the secondary market.
$ \lambda $ green investment-related cost coefficient.
$ \eta $ marketing effort-related cost coefficient.
$ \mu $ collection cost coefficient.
$ A $ unit price paid to the customer for used products.
$ B $ unit transfer price of the used products ($ B> A $).
$ \Pi_i^j $ profit function where superscript $ j $ denotes the supply chain models
($ j = C, MN, RN, TN, MF, RF, TF, CO $) while the subscript $ i $ denotes the
supply chain members and the entire supply chain, respectively ($ i = m, r, t, w $).
$ (.)^j $ optimal decisions under model $ j $.
Notations Description
Decision variables
$ w $ unit wholesale price of the manufacturer.
$ p $ unit selling price of the retailer.
$ \theta $ level of green innovation.
$ e $ marketing effort level of the retailer.
$ \tau $ collection rate of used products.
Parameters
$ D $ market demand.
$ D_r $ return quantity.
$ c_m (c_r) $ unit manufacturing (remanufacturing) cost of the new (returned) product.
$ D_0 $ basic market demand.
$ E_0 $ basic carbon emission during production.
$ E_u (E_t) $ unit (total) carbon emission during production.
$ \rho $ fraction of remanufactured products available for selling in the primary market.
$ w_1 $ unit selling price of the remanufactured product in the secondary market.
$ \lambda $ green investment-related cost coefficient.
$ \eta $ marketing effort-related cost coefficient.
$ \mu $ collection cost coefficient.
$ A $ unit price paid to the customer for used products.
$ B $ unit transfer price of the used products ($ B> A $).
$ \Pi_i^j $ profit function where superscript $ j $ denotes the supply chain models
($ j = C, MN, RN, TN, MF, RF, TF, CO $) while the subscript $ i $ denotes the
supply chain members and the entire supply chain, respectively ($ i = m, r, t, w $).
$ (.)^j $ optimal decisions under model $ j $.
Table 3.  Optimal results under retailer's fairness concern
Model-MF Model-RF Model-TF
$ w^* $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta (X - A)^2\big]</td> </tr> <tr> <td>+ \mu c_m \alpha \big[\lambda (1 + 2 \xi) \Psi_1 - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}} $ $ \frac{ \begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta \Psi_2\big(\Psi_2 + 2(1 + \xi)(X - B)\big)\big]</td> </tr> <tr> <td>+ c_m \alpha \big[\mu \big(\lambda \Psi_1(1 + 2\xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda \Psi_2\big(\Psi_2 + 2 \xi (B - A)\big)\big]\end{array} }{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - 2 \alpha^2 \eta \Psi_3\big]</td> </tr> <tr> <td>+ c_m \alpha \big[\mu \big(\lambda (1 + 2 \xi)\Psi_1 - \eta \beta^2\big) + 2 \alpha^2 \eta \lambda \xi^2 \Psi_3\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}} $
$ p^* $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - \alpha^2 \eta (X - A)^2\big]</td> </tr> <tr> <td>+ \mu c_m \alpha \big[\lambda (1 + \xi)(2 \alpha \eta - \gamma^2) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda (1 + \xi)\big[\mu (6 \alpha \eta - \gamma^2) + 2 \alpha^2 \eta (X - A)\Psi_2\big]</td> </tr> <tr> <td>+ c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - 2 \alpha^2 \eta (1 - \xi^2) \Psi_3\big]</td> </tr> <tr> <td>+ c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \theta^* $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ e^* $ $ \frac{\alpha \eta \lambda (1 + \xi) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\gamma \lambda \mu (1 + \xi) \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\gamma \lambda \mu (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \tau^* $ $ \frac{\alpha \eta \lambda (X - A) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\alpha \eta \lambda (1 + \xi)\Psi_2 \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\alpha \lambda \eta (B - A) (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}} $
$ \Pi_m^* $ $ \frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{D\eta \lambda \mu (1 + \xi)\Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \Pi_r^* $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu^2 \Psi_1 \Psi_4^2(1 + \xi) (1 + 3 \xi)\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi)\Psi_4^2 \big[\mu \Psi_1(1 + 3\xi)</td> </tr> <tr> <td>+ \alpha^2 \eta \Psi_2\big((B - A)(1 + 3\xi) + (X - B)\xi (1 - \xi)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi) \big(\mu \Psi_1 (1 + 3 \xi) + 4 \alpha^2 \eta \xi^2 \Psi_3\big) \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]^2\end{array}} $
$ \Pi_t^* $ $ \frac{\begin{array}{c}\alpha^2 \lambda^2 \eta^2 \mu (1 + \xi)^2 (B - A)^2 \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]^2\end{array}} $
$ \Pi_w^* $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2\big[\mu \big(3 \lambda (1 + \xi)^2 \Psi_1 - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big)</td> </tr> <tr> <td>- \alpha^2 \eta \lambda (1 + \xi)^2 \Psi_2 \big(\Psi_2 + 2 (X - A)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big)</td> </tr> <tr> <td>+ \alpha^2 \eta \lambda (1 + \xi)^2\big((B - A)^2 - 2 (1 - 2 \xi)\Psi_3\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3 \big]^2\end{array}} $
$ E_t^* $ $ (E_0 - \delta \theta^{MF})D^{MF} $ $ (E_0 - \delta \theta^{RF})D^{RF} $ $ (E_0 - \delta \theta^{TF})D^{TF} $
Model-MF Model-RF Model-TF
$ w^* $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta (X - A)^2\big]</td> </tr> <tr> <td>+ \mu c_m \alpha \big[\lambda (1 + 2 \xi) \Psi_1 - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}} $ $ \frac{ \begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - \alpha^2 \eta \Psi_2\big(\Psi_2 + 2(1 + \xi)(X - B)\big)\big]</td> </tr> <tr> <td>+ c_m \alpha \big[\mu \big(\lambda \Psi_1(1 + 2\xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda \Psi_2\big(\Psi_2 + 2 \xi (B - A)\big)\big]\end{array} }{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu \Psi_1 - 2 \alpha^2 \eta \Psi_3\big]</td> </tr> <tr> <td>+ c_m \alpha \big[\mu \big(\lambda (1 + 2 \xi)\Psi_1 - \eta \beta^2\big) + 2 \alpha^2 \eta \lambda \xi^2 \Psi_3\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}} $
$ p^* $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - \alpha^2 \eta (X - A)^2\big]</td> </tr> <tr> <td>+ \mu c_m \alpha \big[\lambda (1 + \xi)(2 \alpha \eta - \gamma^2) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda (1 + \xi)\big[\mu (6 \alpha \eta - \gamma^2) + 2 \alpha^2 \eta (X - A)\Psi_2\big]</td> </tr> <tr> <td>+ c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]\end{array}} $ $ \frac{\begin{array}{c}D_0 \lambda \big[\mu (6 \alpha \eta - \gamma^2)(1 + \xi) - 2 \alpha^2 \eta (1 - \xi^2) \Psi_3\big]</td> </tr> <tr> <td>+ c_m \alpha \mu \big[\lambda (2 \alpha \eta - \gamma^2)(1 + \xi) - \eta \beta^2\big]\end{array}}{\begin{array}{c}\alpha \big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \theta^* $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\beta \eta \mu \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ e^* $ $ \frac{\alpha \eta \lambda (1 + \xi) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\gamma \lambda \mu (1 + \xi) \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\gamma \lambda \mu (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \tau^* $ $ \frac{\alpha \eta \lambda (X - A) \Psi_4}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\alpha \eta \lambda (1 + \xi)\Psi_2 \Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{\alpha \lambda \eta (B - A) (1 + \xi)\Psi_4}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]\end{array}} $
$ \Pi_m^* $ $ \frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\end{array}} $ $ \frac{\lambda \eta \mu \Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]\end{array}} $ $ \frac{D\eta \lambda \mu (1 + \xi)\Psi_4^2}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]\end{array}} $
$ \Pi_r^* $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu^2 \Psi_1 \Psi_4^2(1 + \xi) (1 + 3 \xi)\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi)\Psi_4^2 \big[\mu \Psi_1(1 + 3\xi)</td> </tr> <tr> <td>+ \alpha^2 \eta \Psi_2\big((B - A)(1 + 3\xi) + (X - B)\xi (1 - \xi)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2\big]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda^2 \eta \mu (1 + \xi) \big(\mu \Psi_1 (1 + 3 \xi) + 4 \alpha^2 \eta \xi^2 \Psi_3\big) \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3\big]^2\end{array}} $
$ \Pi_t^* $ $ \frac{\begin{array}{c}\alpha^2 \lambda^2 \eta^2 \mu (1 + \xi)^2 (B - A)^2 \Psi_4^2\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2) \Psi_3\big]^2\end{array}} $
$ \Pi_w^* $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2\big[\mu \big(3 \lambda (1 + \xi)^2 \Psi_1 - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2\big]\end{array}}{\begin{array}{c}[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - \alpha^2 \eta \lambda (X - A)^2]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big)</td> </tr> <tr> <td>- \alpha^2 \eta \lambda (1 + \xi)^2 \Psi_2 \big(\Psi_2 + 2 (X - A)\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1(1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 + \xi) (X - A) \Psi_2 \big]^2\end{array}} $ $ \frac{\begin{array}{c}\lambda \eta \mu \Psi_4^2 \big[\mu \big(3 \lambda \Psi_1(1 + \xi)^2 - \eta \beta^2\big)</td> </tr> <tr> <td>+ \alpha^2 \eta \lambda (1 + \xi)^2\big((B - A)^2 - 2 (1 - 2 \xi)\Psi_3\big)\big]\end{array}}{\begin{array}{c}\big[\mu\big(2 \lambda \Psi_1 (1 + \xi) - \eta \beta^2\big) - 2 \alpha^2 \eta \lambda (1 - \xi^2)\Psi_3 \big]^2\end{array}} $
$ E_t^* $ $ (E_0 - \delta \theta^{MF})D^{MF} $ $ (E_0 - \delta \theta^{RF})D^{RF} $ $ (E_0 - \delta \theta^{TF})D^{TF} $
Table 4.  Optimal results of the proposed models
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 525.499 529.530 529.530 484.279 488.405 488.222 - 372.201
$ p $ 720.948 719.742 722.926 720.817 719.514 722.601 522.136 522.136
$ \theta $ 0.83066 0.83599 0.82193 0.73948 0.74459 0.73247 1.70843 1.70843
$ e $ 0.32575 0.32784 0.32233 0.32479 0.32704 0.32171 0.66997 0.66997
$ \tau $ 0.32249 0.21637 0.21274 0.28709 0.20289 0.21233 0.66327 0.66327
$ \Pi_m $ 8160.02 8212.36 8074.27 7264.27 7314.53 7195.46 - 9973.38
$ \Pi_r $ 4192.51 4176.24 4104.85 5060.96 5048.37 4967.26 - 6809.43
$ \Pi_t $ - - 67.8844 - - 67.6264 - -
$ \Pi_w $ 12352.5 12388.6 12247.0 12325.2 12362.9 12230.3 16782.8 16782.8
$ E_u $ 0.83387 0.83280 0.83561 0.85211 0.85108 0.85351 0.65831 0.65831
$ E_t $ 17.9277 18.0196 17.7764 18.2658 18.3701 18.1225 29.1094 29.1094
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 525.499 529.530 529.530 484.279 488.405 488.222 - 372.201
$ p $ 720.948 719.742 722.926 720.817 719.514 722.601 522.136 522.136
$ \theta $ 0.83066 0.83599 0.82193 0.73948 0.74459 0.73247 1.70843 1.70843
$ e $ 0.32575 0.32784 0.32233 0.32479 0.32704 0.32171 0.66997 0.66997
$ \tau $ 0.32249 0.21637 0.21274 0.28709 0.20289 0.21233 0.66327 0.66327
$ \Pi_m $ 8160.02 8212.36 8074.27 7264.27 7314.53 7195.46 - 9973.38
$ \Pi_r $ 4192.51 4176.24 4104.85 5060.96 5048.37 4967.26 - 6809.43
$ \Pi_t $ - - 67.8844 - - 67.6264 - -
$ \Pi_w $ 12352.5 12388.6 12247.0 12325.2 12362.9 12230.3 16782.8 16782.8
$ E_u $ 0.83387 0.83280 0.83561 0.85211 0.85108 0.85351 0.65831 0.65831
$ E_t $ 17.9277 18.0196 17.7764 18.2658 18.3701 18.1225 29.1094 29.1094
Table 5.  Optimal results of the proposed models when $ \rho = 0 $
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 532.607 537.992 537.853 491.302 497.210 496.564 - 385.372
$ p $ 724.435 723.963 727.008 723.929 723.400 726.202 536.602 536.602
$ \theta $ 0.81527 0.81735 0.80391 0.72725 0.72933 0.71833 1.64456 1.64456
$ e $ 0.31971 0.32053 0.31525 0.31942 0.32033 0.31550 0.64493 0.64493
$ \tau $ 0.03517 0.21155 0.20807 0.03137 0.23256 0.20823 0.07094 0.07094
$ \Pi_m $ 8008.80 8029.26 7897.21 7144.19 7164.59 7056.50 - 9672.70
$ \Pi_r $ 4038.56 3992.09 3926.80 4895.02 4839.26 4772.80 - 6482.72
$ \Pi_t $ - - 64.9398 - - 65.0397 - -
$ \Pi_w $ 12047.4 12021.4 11889.0 12039.2 12003.9 11894.3 16155.4 16155.4
$ E_u $ 0.83695 0.83653 0.83922 0.85455 0.85413 0.85634 0.67109 0.67109
$ E_t $ 17.6604 17.6967 17.4616 18.0154 18.0581 17.8315 28.5650 28.5650
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 532.607 537.992 537.853 491.302 497.210 496.564 - 385.372
$ p $ 724.435 723.963 727.008 723.929 723.400 726.202 536.602 536.602
$ \theta $ 0.81527 0.81735 0.80391 0.72725 0.72933 0.71833 1.64456 1.64456
$ e $ 0.31971 0.32053 0.31525 0.31942 0.32033 0.31550 0.64493 0.64493
$ \tau $ 0.03517 0.21155 0.20807 0.03137 0.23256 0.20823 0.07094 0.07094
$ \Pi_m $ 8008.80 8029.26 7897.21 7144.19 7164.59 7056.50 - 9672.70
$ \Pi_r $ 4038.56 3992.09 3926.80 4895.02 4839.26 4772.80 - 6482.72
$ \Pi_t $ - - 64.9398 - - 65.0397 - -
$ \Pi_w $ 12047.4 12021.4 11889.0 12039.2 12003.9 11894.3 16155.4 16155.4
$ E_u $ 0.83695 0.83653 0.83922 0.85455 0.85413 0.85634 0.67109 0.67109
$ E_t $ 17.6604 17.6967 17.4616 18.0154 18.0581 17.8315 28.5650 28.5650
Table 6.  Optimal results of the proposed models when $ \rho = 1 $
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 521.843 527.354 527.391 480.679 486.583 486.085 - 360.962
$ p $ 719.155 718.656 721.876 719.221 718.735 721.678 514.474 514.474
$ \theta $ 0.83858 0.84078 0.82656 0.74574 0.74766 0.73610 1.74226 1.74226
$ e $ 0.32885 0.32972 0.32414 0.32754 0.32838 0.32331 0.68324 0.68324
$ \tau $ 0.39791 0.21761 0.21393 0.35386 0.19506 0.21338 0.82672 0.82672
$ \Pi_m $ 8237.79 8259.44 8119.78 7325.84 7344.61 7231.05 - 10141.5
$ \Pi_r $ 4272.81 4224.26 4151.26 5147.11 5091.53 5017.71 - 6973.61
$ \Pi_t $ - - 68.6518 - - 68.2972 - -
$ \Pi_w $ 12510.6 12483.7 12339.7 12473.0 12436.1 12317.1 17115.1 17115.1
$ E_u $ 0.83228 0.83184 0.83469 0.85085 0.85047 0.85278 0.65155 0.65155
$ E_t $ 18.0642 18.1021 17.8568 18.3935 18.4324 18.1967 29.3808 29.3808
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 521.843 527.354 527.391 480.679 486.583 486.085 - 360.962
$ p $ 719.155 718.656 721.876 719.221 718.735 721.678 514.474 514.474
$ \theta $ 0.83858 0.84078 0.82656 0.74574 0.74766 0.73610 1.74226 1.74226
$ e $ 0.32885 0.32972 0.32414 0.32754 0.32838 0.32331 0.68324 0.68324
$ \tau $ 0.39791 0.21761 0.21393 0.35386 0.19506 0.21338 0.82672 0.82672
$ \Pi_m $ 8237.79 8259.44 8119.78 7325.84 7344.61 7231.05 - 10141.5
$ \Pi_r $ 4272.81 4224.26 4151.26 5147.11 5091.53 5017.71 - 6973.61
$ \Pi_t $ - - 68.6518 - - 68.2972 - -
$ \Pi_w $ 12510.6 12483.7 12339.7 12473.0 12436.1 12317.1 17115.1 17115.1
$ E_u $ 0.83228 0.83184 0.83469 0.85085 0.85047 0.85278 0.65155 0.65155
$ E_t $ 18.0642 18.1021 17.8568 18.3935 18.4324 18.1967 29.3808 29.3808
Table 7.  Optimal results of the proposed models when $ w_1 = 0 $
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 530.503 533.809 533.738 489.220 492.515 492.433 - 384.801
$ p $ 723.403 721.876 724.989 723.006 721.308 724.419 532.377 532.377
$ \theta $ 0.81982 0.82656 0.81282 0.73088 0.73755 0.72533 1.66322 1.66322
$ e $ 0.32150 0.32414 0.31875 0.32101 0.32394 0.31858 0.65224 0.65224
$ \tau $ 0.17682 0.21393 0.21038 0.15764 0.21808 0.21026 0.35873 0.35873
$ \Pi_m $ 8053.58 8119.78 7984.76 7179.79 7245.31 7125.30 - 9753.86
$ \Pi_r $ 4083.84 4082.61 4014.35 4943.93 4950.75 4868.60 - 6584.80
$ \Pi_t $ - - 66.3876 - - 66.3141 - -
$ \Pi_w $ 12137.4 12202.4 12065.5 12123.7 12196.1 12060.2 16338.7 16338.7
$ E_u $ 0.83604 0.83469 0.83744 0.85382 0.85249 0.85493 0.66736 0.66736
$ E_t $ 17.7398 17.8568 17.6177 18.0898 18.2264 17.9759 28.7283 28.7283
Optimal Without fairness With fairness
results Model-MN Model-RN Model-TN Model-MF Model-RF Model-TF Model-C Model-CO
$ w $ 530.503 533.809 533.738 489.220 492.515 492.433 - 384.801
$ p $ 723.403 721.876 724.989 723.006 721.308 724.419 532.377 532.377
$ \theta $ 0.81982 0.82656 0.81282 0.73088 0.73755 0.72533 1.66322 1.66322
$ e $ 0.32150 0.32414 0.31875 0.32101 0.32394 0.31858 0.65224 0.65224
$ \tau $ 0.17682 0.21393 0.21038 0.15764 0.21808 0.21026 0.35873 0.35873
$ \Pi_m $ 8053.58 8119.78 7984.76 7179.79 7245.31 7125.30 - 9753.86
$ \Pi_r $ 4083.84 4082.61 4014.35 4943.93 4950.75 4868.60 - 6584.80
$ \Pi_t $ - - 66.3876 - - 66.3141 - -
$ \Pi_w $ 12137.4 12202.4 12065.5 12123.7 12196.1 12060.2 16338.7 16338.7
$ E_u $ 0.83604 0.83469 0.83744 0.85382 0.85249 0.85493 0.66736 0.66736
$ E_t $ 17.7398 17.8568 17.6177 18.0898 18.2264 17.9759 28.7283 28.7283
[1]

Zhidan Wu, Xiaohu Qian, Min Huang, Wai-Ki Ching, Hanbin Kuang, Xingwei Wang. Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3247-3268. doi: 10.3934/jimo.2020116

[2]

Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021035

[3]

Dingzhong Feng, Xiaofeng Zhang, Ye Zhang. Collection decisions and coordination in a closed-loop supply chain under recovery price and service competition. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021117

[4]

Maedeh Agahgolnezhad Gerdrodbari, Fatemeh Harsej, Mahboubeh Sadeghpour, Mohammad Molani Aghdam. A robust multi-objective model for managing the distribution of perishable products within a green closed-loop supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021107

[5]

Ziyuan Zhang, Liying Yu. Joint emission reduction dynamic optimization and coordination in the supply chain considering fairness concern and reference low-carbon effect. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021155

[6]

Jian Liu, Xin Wu, Jiang-Ling Lei. The combined impacts of consumer green preference and fairness concern on the decision of three-party supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021090

[7]

Yi Jing, Wenchuan Li. Integrated recycling-integrated production - distribution planning for decentralized closed-loop supply chain. Journal of Industrial & Management Optimization, 2018, 14 (2) : 511-539. doi: 10.3934/jimo.2017058

[8]

Wenbin Wang, Peng Zhang, Junfei Ding, Jian Li, Hao Sun, Lingyun He. Closed-loop supply chain network equilibrium model with retailer-collection under legislation. Journal of Industrial & Management Optimization, 2019, 15 (1) : 199-219. doi: 10.3934/jimo.2018039

[9]

Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023

[10]

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

[11]

Guangzhou Yan, Qinyu Song, Yaodong Ni, Xiangfeng Yang. Pricing, carbon emission reduction and recycling decisions in a closed-loop supply chain under uncertain environment. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021181

[12]

Masoud Mohammadzadeh, Alireza Arshadi Khamseh, Mohammad Mohammadi. A multi-objective integrated model for closed-loop supply chain configuration and supplier selection considering uncertain demand and different performance levels. Journal of Industrial & Management Optimization, 2017, 13 (2) : 1041-1064. doi: 10.3934/jimo.2016061

[13]

Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker, Guo-Qiang Yang. Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021014

[14]

Fatemeh Kangi, Seyed Hamid Reza Pasandideh, Esmaeil Mehdizadeh, Hamed Soleimani. The optimization of a multi-period multi-product closed-loop supply chain network with cross-docking delivery strategy. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021118

[15]

Chong Zhang, Yaxian Wang, Ying Liu, Haiyan Wang. Coordination contracts for a dual-channel supply chain under capital constraints. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1485-1504. doi: 10.3934/jimo.2020031

[16]

Wei Chen, Fuying Jing, Li Zhong. Coordination strategy for a dual-channel electricity supply chain with sustainability. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021139

[17]

Yanhua Feng, Xuhui Xia, Lei Wang, Zelin Zhang. Pricing and coordination of competitive recycling and remanufacturing supply chain considering the quality of recycled products. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021089

[18]

Huimin Liu, Hui Yu. Fairness and retailer-led supply chain coordination under two different degrees of trust. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1347-1364. doi: 10.3934/jimo.2016076

[19]

Simon Hochgerner. Symmetry actuated closed-loop Hamiltonian systems. Journal of Geometric Mechanics, 2020, 12 (4) : 641-669. doi: 10.3934/jgm.2020030

[20]

Xiaohong Chen, Kui Li, Fuqiang Wang, Xihua Li. Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1389-1414. doi: 10.3934/jimo.2019008

2020 Impact Factor: 1.801

Article outline

Figures and Tables

[Back to Top]