doi: 10.3934/jimo.2021181
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Pricing, carbon emission reduction and recycling decisions in a closed-loop supply chain under uncertain environment

1. 

College of Science, Hebei Agricultural University, Baoding 071001, China

2. 

Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China

3. 

School of Information Technology and Management, University of International Business and Economics, Beijing 100029, China

* Corresponding author: Yaodong Ni

Received  June 2021 Revised  September 2021 Early access October 2021

This paper studies the pricing and recycling decision problems in a closed-loop supply chain (CLSC) containing a manufacturer, a downstream retailer, and a third-party recycling left. The manufacturer is subjected to the cap-and-trade regulation and determines the wholesale price of products and carbon emission reduction rate. The retailer determines its resale price to meet customer demands. The third-party recycling left determines the collection rate of recycling and remanufacturing used products. The new product demands, total carbon emissions, and recovery of these products are characterized as uncertain variables due to lack of historical data or insufficient data collected for research. By constructing three decentralized game models, we explore the equilibrium solutions under the corresponding decision-making situation and the corresponding analytical solutions. Finally, numerical experiments are performed to show the total profit of supply chain members for each structure and some special insights are drawn.

Citation: 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, doi: 10.3934/jimo.2021181
References:
[1]

E. BazanM. Jaber and A. Saadany, Carbon emissions and energy effects on manufacturing-remanufacturing inventory models, Computers and Industrial Engineering, 88 (2015), 307-316.  doi: 10.1016/j.cie.2015.07.002.  Google Scholar

[2]

S. BenjaafarY. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2013), 99-116.  doi: 10.1109/TASE.2012.2203304.  Google Scholar

[3]

J. Chen and C. Chang, Dynamic pricing for new and remanufactured products in a closed-loop supply chain, International Journal of Production Economics, 146 (2013), 153-160.  doi: 10.1016/j.ijpe.2013.06.017.  Google Scholar

[4]

J. Cruz, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European J. Oper. Res., 184 (2008), 1005-1031.  doi: 10.1016/j.ejor.2006.12.012.  Google Scholar

[5]

V. DanielR. Guide and J. Li, The potential for cannibalization of new products sales by remanufactured products, Decision Sciences, 41 (2010), 547-572.   Google Scholar

[6]

S. Ding, Uncertain multi-product newsboy problem with chance constraint, Appl. Math. Comput., 223 (2013), 139-146.  doi: 10.1016/j.amc.2013.07.083.  Google Scholar

[7]

S. DuL. ZhuZ. FuL. Liang and F. Ma, Emission-dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energy Policy, 57 (2013), 61-67.  doi: 10.1016/j.enpol.2012.09.042.  Google Scholar

[8]

S. DuF. MaZ. FuL. Zhu and J. Zhang, Game-theoretic analysis for an emission-dependent supply chain in a 'cap-and-trade' system, Ann. Oper. Res., 228 (2015), 135-149.  doi: 10.1007/s10479-011-0964-6.  Google Scholar

[9]

G. Ferrer and M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465.  Google Scholar

[10]

S. GanI. PujawanSu parno and B. Widodo, Pricing decision model for new and remanufactured short-life cycle products with time-dependent demand, Oper. Res. Perspect., 2 (2015), 1-12.  doi: 10.1016/j.orp.2014.11.001.  Google Scholar

[11]

S. GanI. PujawanSu parno and B. Widodo, Pricing decision for new and remanufactured product in a closed-loop supply chain with separate sales-channel, International Journal of Production Economics, 190 (2017), 120-132.  doi: 10.1016/j.ijpe.2016.08.016.  Google Scholar

[12]

D. Ghosh and J. Shah, A comparative analysis of greening policies across supply chain structures, International Journal of Production Economics, 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027.  Google Scholar

[13]

B. GiriA. Chakraborty and T. Maiti, Pricing and return product collection decisions in a closed-loop supply chain with dual-channel in both forward and reverse logistics, Journal of Manufacturing Systems, 42 (2017), 104-123.  doi: 10.1016/j.jmsy.2016.11.007.  Google Scholar

[14]

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

[15]

G. HuaT. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185.  doi: 10.1016/j.ijpe.2011.03.024.  Google Scholar

[16]

M. HuangM. SongL. Lee and W. 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

[17]

J. JiZ. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, International Journal of Production Economics, 187 (2017), 68-84.  doi: 10.1016/j.ijpe.2017.02.011.  Google Scholar

[18]

J. M. Jose, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European J. Oper. Res., 184 (2008), 1005-1031.  doi: 10.1016/j.ejor.2006.12.012.  Google Scholar

[19]

H. KeY. WuH. Huang and Z. Chen, Pricing decision in a two-echelon supply chain with competing retailers under uncertain environment, Journal of Uncertainty Analysis and Applications, 5 (2017), 1-5.  doi: 10.1186/s40467-017-0059-2.  Google Scholar

[20]

M. Kotchen, Impure public goods and the comparative statics of environmentally friendly consumption, Journal of Environmental Economics and Management, 49 (2005), 281-300.  doi: 10.1016/j.jeem.2004.05.003.  Google Scholar

[21]

H. LiC. WangM. Shang and W. Ou, Pricing, carbon emission reduction, low-carbon promotion and returning decision in a closed-loop supply chain under vertical and horizontal cooperation, International Journal of Environmental Research and Public Health, 14 (2017), 13-32.  doi: 10.3390/ijerph14111332.  Google Scholar

[22]

X. LiY. Li and X. Cai, Remanufacturing and pricing decisions with random yield and random demand, Comput. Oper. Res., 54 (2015), 195-203.  doi: 10.1016/j.cor.2014.01.005.  Google Scholar

[23]

B. Liu, Uncertainty Theory, 1$^nd$ edition, Springer Berlin Heidelberg, 2007. Google Scholar

[24]

B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (2009), 3-10.   Google Scholar

[25]

B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, DBLP, 2010. Google Scholar

[26]

B. Liu, Uncertainty Theory, 4$^nd$ edition, Springer Berlin Heidelberg, 2015. doi: 10.1007/978-3-662-44354-5.  Google Scholar

[27]

S. Liu and Z. Xu, Stackelberg game models between two competitive retailers in fuzzy decision environment, Fuzzy Optim. Decis. Mak., 13 (2014), 33-48.  doi: 10.1007/s10700-013-9165-x.  Google Scholar

[28]

Y. Liu and M. Ha, Expected value of function of uncertain variables, Journal of Uncertain Systems, 4 (2010), 181-186.   Google Scholar

[29]

K. MengP. LouX. Peng and V. Prybutok, Multi-objective optimization decision-making of quality dependent product recovery for sustainability, International Journal of Production Economics, 188 (2017), 72-85.  doi: 10.1016/j.ijpe.2017.03.017.  Google Scholar

[30]

J. ShiG. Zhang and J. Sha, Optimal production and pricing policy for a closed loop system, Resources Conservation and Recycling, 55 (2011), 639-647.  doi: 10.1016/j.resconrec.2010.05.016.  Google Scholar

[31]

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

[32]

R. Savaskan and L. Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[33]

Q. SongY. Ni and R. Dan, The impact of lead-time uncertainty in product configuration, International Journal of Production Research, 59 (2020), 1-23.  doi: 10.1080/00207543.2020.1715506.  Google Scholar

[34]

G. Souza, Remanufacturing in closed-loop supply chains, Production and Inventory Management Journal, 45 (2009), 56-66.   Google Scholar

[35]

A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and Service Operations Management, 2 (2000), 372-391.  doi: 10.1287/msom.2.4.372.12342.  Google Scholar

[36]

J. Vorasayan and S. Ryan, Optimal price and quantity of refurbished products, Production and Operations Management, 15 (2010), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[37]

C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, 69 (2018), 1-11.  doi: 10.1057/s41274-017-0228-1.  Google Scholar

[38]

J. WeiJ. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, Journal of Cleaner Production, 105 (2015), 86-102.  doi: 10.1016/j.jclepro.2014.09.059.  Google Scholar

[39]

J. Wei and J. Zhao, Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments, Ann. Oper. Res., 242 (2016), 505-528.  doi: 10.1007/s10479-014-1541-6.  Google Scholar

[40]

T. Xiao and D. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200.  doi: 10.1016/j.ijpe.2008.01.006.  Google Scholar

[41]

Y. XiongQ. Zhao and Y. Zhou, Manufacturer-remanufacturing vs supplier-remanufacturing in a closed-loop supply chain, International Journal of Production Economics, 176 (2016), 21-28.  doi: 10.1016/j.ijpe.2016.03.001.  Google Scholar

[42]

X. XuW. ZhangP. He and X. Xu, Production and pricing problems in make-to-order supply chain with cap-and-trade regulation, Omega, 66 (2017), 248-257.  doi: 10.1016/j.omega.2015.08.006.  Google Scholar

[43]

G. YanY. Ni and X. Yang, Optimal pricing in recycling and remanufacturing in uncertain environments, Sustainability, 12 (2020), 1-16.  doi: 10.3390/su12083199.  Google Scholar

[44]

D. Yang and T. Xiao, Pricing and green level decisions of a green supply chain with governmental interventions under fuzzy uncertainties, Journal of Cleaner Production, 149 (2017), 1174-1187.  doi: 10.1016/j.jclepro.2017.02.138.  Google Scholar

[45]

L. YangC. Zheng and M. Xu, Comparisons of low carbon policies in supply chain coordination, Journal of Systems Science and Systems Engineering, 23 (2014), 342-361.  doi: 10.1007/s11518-014-5249-6.  Google Scholar

[46]

L. YangQ. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, International Journal of Production Economics, 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021.  Google Scholar

[47]

K. Yao, A formula to calculate the variance of uncertain variable, Soft Computing, 19 (2015), 2947-2953.  doi: 10.1007/s00500-014-1457-8.  Google Scholar

[48]

P. YiM. HuangL. Guo and T. Shi, Dual recycling channel decision in retailer oriented closed-loop supply chain for construction machinery remanufacturing, Journal of Cleaner Production, 137 (2016), 1393-1405.  doi: 10.1016/j.jclepro.2016.07.104.  Google Scholar

[49]

J. ZhaoW. TangR. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European J. Oper. Res., 216 (2012), 409-419.  doi: 10.1016/j.ejor.2011.07.026.  Google Scholar

show all references

References:
[1]

E. BazanM. Jaber and A. Saadany, Carbon emissions and energy effects on manufacturing-remanufacturing inventory models, Computers and Industrial Engineering, 88 (2015), 307-316.  doi: 10.1016/j.cie.2015.07.002.  Google Scholar

[2]

S. BenjaafarY. Li and M. Daskin, Carbon footprint and the management of supply chains: Insights from simple models, IEEE Transactions on Automation Science and Engineering, 10 (2013), 99-116.  doi: 10.1109/TASE.2012.2203304.  Google Scholar

[3]

J. Chen and C. Chang, Dynamic pricing for new and remanufactured products in a closed-loop supply chain, International Journal of Production Economics, 146 (2013), 153-160.  doi: 10.1016/j.ijpe.2013.06.017.  Google Scholar

[4]

J. Cruz, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European J. Oper. Res., 184 (2008), 1005-1031.  doi: 10.1016/j.ejor.2006.12.012.  Google Scholar

[5]

V. DanielR. Guide and J. Li, The potential for cannibalization of new products sales by remanufactured products, Decision Sciences, 41 (2010), 547-572.   Google Scholar

[6]

S. Ding, Uncertain multi-product newsboy problem with chance constraint, Appl. Math. Comput., 223 (2013), 139-146.  doi: 10.1016/j.amc.2013.07.083.  Google Scholar

[7]

S. DuL. ZhuZ. FuL. Liang and F. Ma, Emission-dependent supply chain and environment-policy-making in the 'cap-and-trade' system, Energy Policy, 57 (2013), 61-67.  doi: 10.1016/j.enpol.2012.09.042.  Google Scholar

[8]

S. DuF. MaZ. FuL. Zhu and J. Zhang, Game-theoretic analysis for an emission-dependent supply chain in a 'cap-and-trade' system, Ann. Oper. Res., 228 (2015), 135-149.  doi: 10.1007/s10479-011-0964-6.  Google Scholar

[9]

G. Ferrer and M. Swaminathan, Managing new and remanufactured products, Management Science, 52 (2006), 15-26.  doi: 10.1287/mnsc.1050.0465.  Google Scholar

[10]

S. GanI. PujawanSu parno and B. Widodo, Pricing decision model for new and remanufactured short-life cycle products with time-dependent demand, Oper. Res. Perspect., 2 (2015), 1-12.  doi: 10.1016/j.orp.2014.11.001.  Google Scholar

[11]

S. GanI. PujawanSu parno and B. Widodo, Pricing decision for new and remanufactured product in a closed-loop supply chain with separate sales-channel, International Journal of Production Economics, 190 (2017), 120-132.  doi: 10.1016/j.ijpe.2016.08.016.  Google Scholar

[12]

D. Ghosh and J. Shah, A comparative analysis of greening policies across supply chain structures, International Journal of Production Economics, 135 (2012), 568-583.  doi: 10.1016/j.ijpe.2011.05.027.  Google Scholar

[13]

B. GiriA. Chakraborty and T. Maiti, Pricing and return product collection decisions in a closed-loop supply chain with dual-channel in both forward and reverse logistics, Journal of Manufacturing Systems, 42 (2017), 104-123.  doi: 10.1016/j.jmsy.2016.11.007.  Google Scholar

[14]

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

[15]

G. HuaT. Cheng and S. Wang, Managing carbon footprints in inventory management, International Journal of Production Economics, 132 (2011), 178-185.  doi: 10.1016/j.ijpe.2011.03.024.  Google Scholar

[16]

M. HuangM. SongL. Lee and W. 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

[17]

J. JiZ. Zhang and L. Yang, Comparisons of initial carbon allowance allocation rules in an O2O retail supply chain with the cap-and-trade regulation, International Journal of Production Economics, 187 (2017), 68-84.  doi: 10.1016/j.ijpe.2017.02.011.  Google Scholar

[18]

J. M. Jose, Dynamics of supply chain networks with corporate social responsibility through integrated environmental decision-making, European J. Oper. Res., 184 (2008), 1005-1031.  doi: 10.1016/j.ejor.2006.12.012.  Google Scholar

[19]

H. KeY. WuH. Huang and Z. Chen, Pricing decision in a two-echelon supply chain with competing retailers under uncertain environment, Journal of Uncertainty Analysis and Applications, 5 (2017), 1-5.  doi: 10.1186/s40467-017-0059-2.  Google Scholar

[20]

M. Kotchen, Impure public goods and the comparative statics of environmentally friendly consumption, Journal of Environmental Economics and Management, 49 (2005), 281-300.  doi: 10.1016/j.jeem.2004.05.003.  Google Scholar

[21]

H. LiC. WangM. Shang and W. Ou, Pricing, carbon emission reduction, low-carbon promotion and returning decision in a closed-loop supply chain under vertical and horizontal cooperation, International Journal of Environmental Research and Public Health, 14 (2017), 13-32.  doi: 10.3390/ijerph14111332.  Google Scholar

[22]

X. LiY. Li and X. Cai, Remanufacturing and pricing decisions with random yield and random demand, Comput. Oper. Res., 54 (2015), 195-203.  doi: 10.1016/j.cor.2014.01.005.  Google Scholar

[23]

B. Liu, Uncertainty Theory, 1$^nd$ edition, Springer Berlin Heidelberg, 2007. Google Scholar

[24]

B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3 (2009), 3-10.   Google Scholar

[25]

B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, DBLP, 2010. Google Scholar

[26]

B. Liu, Uncertainty Theory, 4$^nd$ edition, Springer Berlin Heidelberg, 2015. doi: 10.1007/978-3-662-44354-5.  Google Scholar

[27]

S. Liu and Z. Xu, Stackelberg game models between two competitive retailers in fuzzy decision environment, Fuzzy Optim. Decis. Mak., 13 (2014), 33-48.  doi: 10.1007/s10700-013-9165-x.  Google Scholar

[28]

Y. Liu and M. Ha, Expected value of function of uncertain variables, Journal of Uncertain Systems, 4 (2010), 181-186.   Google Scholar

[29]

K. MengP. LouX. Peng and V. Prybutok, Multi-objective optimization decision-making of quality dependent product recovery for sustainability, International Journal of Production Economics, 188 (2017), 72-85.  doi: 10.1016/j.ijpe.2017.03.017.  Google Scholar

[30]

J. ShiG. Zhang and J. Sha, Optimal production and pricing policy for a closed loop system, Resources Conservation and Recycling, 55 (2011), 639-647.  doi: 10.1016/j.resconrec.2010.05.016.  Google Scholar

[31]

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

[32]

R. Savaskan and L. Wassenhove, Reverse channel design: The case of competing retailers, Management Science, 52 (2006), 1-14.  doi: 10.1287/mnsc.1050.0454.  Google Scholar

[33]

Q. SongY. Ni and R. Dan, The impact of lead-time uncertainty in product configuration, International Journal of Production Research, 59 (2020), 1-23.  doi: 10.1080/00207543.2020.1715506.  Google Scholar

[34]

G. Souza, Remanufacturing in closed-loop supply chains, Production and Inventory Management Journal, 45 (2009), 56-66.   Google Scholar

[35]

A. Tsay and N. Agrawal, Channel dynamics under price and service competition, Manufacturing and Service Operations Management, 2 (2000), 372-391.  doi: 10.1287/msom.2.4.372.12342.  Google Scholar

[36]

J. Vorasayan and S. Ryan, Optimal price and quantity of refurbished products, Production and Operations Management, 15 (2010), 369-383.  doi: 10.1111/j.1937-5956.2006.tb00251.x.  Google Scholar

[37]

C. Wang and X. Chen, Joint order and pricing decisions for fresh produce with put option contracts, Journal of the Operational Research Society, 69 (2018), 1-11.  doi: 10.1057/s41274-017-0228-1.  Google Scholar

[38]

J. WeiJ. Zhao and Y. Li, Price and warranty period decisions for complementary products with horizontal firms' cooperation/noncooperation strategies, Journal of Cleaner Production, 105 (2015), 86-102.  doi: 10.1016/j.jclepro.2014.09.059.  Google Scholar

[39]

J. Wei and J. Zhao, Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments, Ann. Oper. Res., 242 (2016), 505-528.  doi: 10.1007/s10479-014-1541-6.  Google Scholar

[40]

T. Xiao and D. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty, International Journal of Production Economics, 114 (2008), 187-200.  doi: 10.1016/j.ijpe.2008.01.006.  Google Scholar

[41]

Y. XiongQ. Zhao and Y. Zhou, Manufacturer-remanufacturing vs supplier-remanufacturing in a closed-loop supply chain, International Journal of Production Economics, 176 (2016), 21-28.  doi: 10.1016/j.ijpe.2016.03.001.  Google Scholar

[42]

X. XuW. ZhangP. He and X. Xu, Production and pricing problems in make-to-order supply chain with cap-and-trade regulation, Omega, 66 (2017), 248-257.  doi: 10.1016/j.omega.2015.08.006.  Google Scholar

[43]

G. YanY. Ni and X. Yang, Optimal pricing in recycling and remanufacturing in uncertain environments, Sustainability, 12 (2020), 1-16.  doi: 10.3390/su12083199.  Google Scholar

[44]

D. Yang and T. Xiao, Pricing and green level decisions of a green supply chain with governmental interventions under fuzzy uncertainties, Journal of Cleaner Production, 149 (2017), 1174-1187.  doi: 10.1016/j.jclepro.2017.02.138.  Google Scholar

[45]

L. YangC. Zheng and M. Xu, Comparisons of low carbon policies in supply chain coordination, Journal of Systems Science and Systems Engineering, 23 (2014), 342-361.  doi: 10.1007/s11518-014-5249-6.  Google Scholar

[46]

L. YangQ. Zhang and J. Ji, Pricing and carbon emission reduction decisions in supply chains with vertical and horizontal cooperation, International Journal of Production Economics, 191 (2017), 286-297.  doi: 10.1016/j.ijpe.2017.06.021.  Google Scholar

[47]

K. Yao, A formula to calculate the variance of uncertain variable, Soft Computing, 19 (2015), 2947-2953.  doi: 10.1007/s00500-014-1457-8.  Google Scholar

[48]

P. YiM. HuangL. Guo and T. Shi, Dual recycling channel decision in retailer oriented closed-loop supply chain for construction machinery remanufacturing, Journal of Cleaner Production, 137 (2016), 1393-1405.  doi: 10.1016/j.jclepro.2016.07.104.  Google Scholar

[49]

J. ZhaoW. TangR. Zhao and J. Wei, Pricing decisions for substitutable products with a common retailer in fuzzy environments, European J. Oper. Res., 216 (2012), 409-419.  doi: 10.1016/j.ejor.2011.07.026.  Google Scholar

Figure 1.  The CLSC structure
Table 1.  Notations
$ \bullet $ Decision variables
$ \omega $: Unit wholesale price to retailer, the manufacturer's decision variable.
$ r $: Unit markup price of retailer, the retailer's decision variable.
$ p $: Unit retail price of retailer, where $ p=\omega+r $.
$ \tau $: Recovery rate through third-party channel,
$ \tau\in[0,1] $, the third-party's decision variable.
$ \theta $: Carbon emission reduction rate of manufacturer,
$ \theta\in[0,1] $, the manufacturer's decision variable.
$ \bullet $ Parameters
$ c_{n} $: Unit cost of manufacturing the product from raw materials.
$ c_{r} $: Unit manufacturing cost of the product from return products.
$ \widetilde{s_{r}} $: Unit sales cost of retailer, an uncertain variable.
$ \widetilde{d} $: The market base of product, an uncertain variable.
$ \widetilde{C} $: Total emissions of the manufacturer, an uncertain variable.
$ p_{c} $: Average recycling price for used product from the third-party to the manufacturer.
$ A $: Average recycling price for used products through the third-party channel.
$ e $: Initial carbon emission of unit product.
$ \Omega $: Total carbon free permits from government.
$ \rho $: Cost coefficient of emissions reduction investment.
$ \lambda $: Coefficient of carbon emissions reduction unit recovery rate.
$ b $: Carbon buying price of unit product.
$ s $: Carbon selling price of unit product.
$ \bullet $ Decision variables
$ \omega $: Unit wholesale price to retailer, the manufacturer's decision variable.
$ r $: Unit markup price of retailer, the retailer's decision variable.
$ p $: Unit retail price of retailer, where $ p=\omega+r $.
$ \tau $: Recovery rate through third-party channel,
$ \tau\in[0,1] $, the third-party's decision variable.
$ \theta $: Carbon emission reduction rate of manufacturer,
$ \theta\in[0,1] $, the manufacturer's decision variable.
$ \bullet $ Parameters
$ c_{n} $: Unit cost of manufacturing the product from raw materials.
$ c_{r} $: Unit manufacturing cost of the product from return products.
$ \widetilde{s_{r}} $: Unit sales cost of retailer, an uncertain variable.
$ \widetilde{d} $: The market base of product, an uncertain variable.
$ \widetilde{C} $: Total emissions of the manufacturer, an uncertain variable.
$ p_{c} $: Average recycling price for used product from the third-party to the manufacturer.
$ A $: Average recycling price for used products through the third-party channel.
$ e $: Initial carbon emission of unit product.
$ \Omega $: Total carbon free permits from government.
$ \rho $: Cost coefficient of emissions reduction investment.
$ \lambda $: Coefficient of carbon emissions reduction unit recovery rate.
$ b $: Carbon buying price of unit product.
$ s $: Carbon selling price of unit product.
Table 2.  Parameters for the model
Parameters $ c_{n} $ $ c_{r} $ $ p_{c} $ $ A $ $ b $ $ s $ $ e $ $ k $ $ \lambda $ $ \rho $ $ \Omega $
Value 20 10 7 5 13 6 2.5 1200 1500 10000 5000
Parameters $ c_{n} $ $ c_{r} $ $ p_{c} $ $ A $ $ b $ $ s $ $ e $ $ k $ $ \lambda $ $ \rho $ $ \Omega $
Value 20 10 7 5 13 6 2.5 1200 1500 10000 5000
Table 3.  Distributions of uncertain variables
Parameters Distribution Expected value
$ \tilde{\beta} $ $ \mathcal{L} $(0.4, 0.8) 0.6
$ \tilde{\gamma} $ $ \mathcal{L} $(0.2, 0.4) 0.3
$ \tilde{d} $ $ \mathcal{Z} $(700,950, 1000) 900
$ \tilde{s_{r}} $ $ \mathcal{L} $(3, 5) 4
Parameters Distribution Expected value
$ \tilde{\beta} $ $ \mathcal{L} $(0.4, 0.8) 0.6
$ \tilde{\gamma} $ $ \mathcal{L} $(0.2, 0.4) 0.3
$ \tilde{d} $ $ \mathcal{Z} $(700,950, 1000) 900
$ \tilde{s_{r}} $ $ \mathcal{L} $(3, 5) 4
Table 4.  The optimal decisions of the three structures under buying carbon quotas
Structure $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi^{b}_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
RS 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
VN 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
Structure $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi^{b}_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
RS 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
VN 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
Table 5.  The optimal decisions of the three structures under selling carbon quotas
Structure $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi^{b}_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS 758.6526 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7821
RS 1156.2150 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9213
VN 516.9945 0.4553 174966.9000 493.6749 143955.4000 0.2448 71.9002
Structure $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi^{b}_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS 758.6526 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7821
RS 1156.2150 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9213
VN 516.9945 0.4553 174966.9000 493.6749 143955.4000 0.2448 71.9002
Table 6.  Effects of the retailer sales costs $ \tilde{s}_r $ on the optimal results under buying carbon quotas
Structure $ \tilde{s}_{r} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(2.5, 5.5) 753.7724 0.7351 224152.9000 375.4051 82890.7900 0.1856 41.3454
$ \mathcal{L} $(3, 5) 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
$ \mathcal{L} $(3.5, 4.5) 753.7789 0.7351 224176.7000 375.3218 82777.9400 0.1856 41.3517
RS $ \mathcal{L} $(2.5, 5.5) 1161.6360 0.2598 143442.6000 222.7092 15407.3100 0.0579 4.0218
$ \mathcal{L} $(3, 5) 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
$ \mathcal{L} $(3.5, 4.5) 1161.6620 0.2599 143464.5000 222.6533 15264.5700 0.0579 4.0239
VN $ \mathcal{L} $(2.5, 5.5) 512.1714 0.9743 210333.8000 496.2412 145507.4000 0.2460 72.6412
$ \mathcal{L} $(3, 5) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(3.5, 4.5) 512.2070 0.9743 210355.9000 496.1676 145379.4000 0.2460 72.6524
Structure $ \tilde{s}_{r} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(2.5, 5.5) 753.7724 0.7351 224152.9000 375.4051 82890.7900 0.1856 41.3454
$ \mathcal{L} $(3, 5) 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
$ \mathcal{L} $(3.5, 4.5) 753.7789 0.7351 224176.7000 375.3218 82777.9400 0.1856 41.3517
RS $ \mathcal{L} $(2.5, 5.5) 1161.6360 0.2598 143442.6000 222.7092 15407.3100 0.0579 4.0218
$ \mathcal{L} $(3, 5) 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
$ \mathcal{L} $(3.5, 4.5) 1161.6620 0.2599 143464.5000 222.6533 15264.5700 0.0579 4.0239
VN $ \mathcal{L} $(2.5, 5.5) 512.1714 0.9743 210333.8000 496.2412 145507.4000 0.2460 72.6412
$ \mathcal{L} $(3, 5) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(3.5, 4.5) 512.2070 0.9743 210355.9000 496.1676 145379.4000 0.2460 72.6524
Table 7.  Effects of the retailer sales costs $ \tilde{s}_r $ on the optimal results under selling carbon quotas
Structure $ \tilde{s}_{r} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(2.5, 5.5) 758.6278 0.3429 193450.0000 372.8552 81758.7700 0.1840 40.7793
$ \mathcal{L} $(3, 5) 758.6526 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7821
$ \mathcal{L} $(3.5, 4.5) 758.6834 0.3429 193474.6000 372.7715 80964.4000 0.1844 40.7856
RS $ \mathcal{L} $(2.5, 5.5) 1158.2020 0.1368 107475.7000 229.5509 15952.6800 0.0572 3.9204
$ \mathcal{L} $(3, 5) 1156.2150 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9213
$ \mathcal{L} $(3.5, 4.5) 1156.2300 0.1368 107496.8000 229.4951 15541.0800 0.0572 3.9223
VN $ \mathcal{L} $(2.5, 5.5) 516.9780 0.4553 174957.1000 493.7081 143955.3000 0.2448 71.8953
$ \mathcal{L} $(3, 5) 516.9945 0.4553 174966.9000 493.6749 143889.4000 0.2448 71.9002
$ \mathcal{L} $(3.5, 4.5) 517.0149 0.4553 174979.1000 493.6339 143887.0000 0.2448 71.9062
Structure $ \tilde{s}_{r} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(2.5, 5.5) 758.6278 0.3429 193450.0000 372.8552 81758.7700 0.1840 40.7793
$ \mathcal{L} $(3, 5) 758.6526 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7821
$ \mathcal{L} $(3.5, 4.5) 758.6834 0.3429 193474.6000 372.7715 80964.4000 0.1844 40.7856
RS $ \mathcal{L} $(2.5, 5.5) 1158.2020 0.1368 107475.7000 229.5509 15952.6800 0.0572 3.9204
$ \mathcal{L} $(3, 5) 1156.2150 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9213
$ \mathcal{L} $(3.5, 4.5) 1156.2300 0.1368 107496.8000 229.4951 15541.0800 0.0572 3.9223
VN $ \mathcal{L} $(2.5, 5.5) 516.9780 0.4553 174957.1000 493.7081 143955.3000 0.2448 71.8953
$ \mathcal{L} $(3, 5) 516.9945 0.4553 174966.9000 493.6749 143889.4000 0.2448 71.9002
$ \mathcal{L} $(3.5, 4.5) 517.0149 0.4553 174979.1000 493.6339 143887.0000 0.2448 71.9062
Table 8.  Effects of the greening level elastic coefficient $ \tilde{\gamma} $ on the optimal results under buying carbon quotas
Structure $ \tilde{\gamma} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(0.15, 0.45) 753.7486 0.7351 224163.5000 375.3678 82826.4400 0.1856 41.3482
$ \mathcal{L} $(0.2, 0.4) 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
$ \mathcal{L} $(0.25, 0.35) 753.7486 0.7351 224163.5000 375.3678 82851.4700 0.1856 41.3482
RS $ \mathcal{L} $(0.15, 0.45) 1161.6480 0.2598 143452.4000 222.6842 15340.7800 0.0579 4.0227
$ \mathcal{L} $(0.2, 0.4) 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
$ \mathcal{L} $(0.25, 0.35) 1161.6480 0.2598 143452.4000 222.6841 15340.7900 0.0579 4.0227
VN $ \mathcal{L} $(0.15, 0.45) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(0.2, 0.4) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(0.25, 0.35) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
Structure $ \tilde{\gamma} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(0.15, 0.45) 753.7486 0.7351 224163.5000 375.3678 82826.4400 0.1856 41.3482
$ \mathcal{L} $(0.2, 0.4) 753.7486 0.7351 224163.5012 375.3678 82851.5121 0.1856 41.3482
$ \mathcal{L} $(0.25, 0.35) 753.7486 0.7351 224163.5000 375.3678 82851.4700 0.1856 41.3482
RS $ \mathcal{L} $(0.15, 0.45) 1161.6480 0.2598 143452.4000 222.6842 15340.7800 0.0579 4.0227
$ \mathcal{L} $(0.2, 0.4) 1161.6480 0.2598 143452.4000 222.6841 15340.8000 0.0579 4.0227
$ \mathcal{L} $(0.25, 0.35) 1161.6480 0.2598 143452.4000 222.6841 15340.7900 0.0579 4.0227
VN $ \mathcal{L} $(0.15, 0.45) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(0.2, 0.4) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
$ \mathcal{L} $(0.25, 0.35) 512.1873 0.9743 210343.7000 496.2082 145447.5000 0.2460 72.6462
Table 9.  Effects of the greening level elastic coefficient $ \tilde{\gamma} $ on the optimal results under selling carbon quotas
Structure $ \tilde{\gamma} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(0.15, 0.45) 758.6554 0.3429 193462.2000 372.8136 81714.9800 0.1844 40.7825
$ \mathcal{L} $(0.2, 0.4) 758.6554 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7825
$ \mathcal{L} $(0.25, 0.35) 758.6554 0.3429 193462.2000 372.8136 81714.9600 0.1844 40.7825
RS $ \mathcal{L} $(0.15, 0.45) 1156.2160 0.1368 107486.2000 229.5232 15612.7900 0.0572 3.9214
$ \mathcal{L} $(0.2, 0.4) 1156.2160 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9214
$ \mathcal{L} $(0.25, 0.35) 1156.2160 0.1368 107486.1000 229.5232 15612.7800 0.0572 3.9214
VN $ \mathcal{L} $(0.15, 0.45) 516.9964 0.4553 174968.0000 493.6712 143951.5000 0.2448 71.9007
$ \mathcal{L} $(0.2, 0.4) 516.9964 0.4553 174966.9000 493.6749 143955.4000 0.2448 71.9007
$ \mathcal{L} $(0.25, 0.35) 516.9964 0.4553 174968.0000 493.6712 143951.5000 0.2448 71.9007
Structure $ \tilde{\gamma} $ $ \omega^{\ast} $ $ \theta^{\ast} $ $ \pi_{m} $ $ r^{\ast} $ $ \pi_{r} $ $ \tau^{\ast} $ $ \pi_{t} $
MS $ \mathcal{L} $(0.15, 0.45) 758.6554 0.3429 193462.2000 372.8136 81714.9800 0.1844 40.7825
$ \mathcal{L} $(0.2, 0.4) 758.6554 0.3429 193461.0000 372.8177 81719.3100 0.1844 40.7825
$ \mathcal{L} $(0.25, 0.35) 758.6554 0.3429 193462.2000 372.8136 81714.9600 0.1844 40.7825
RS $ \mathcal{L} $(0.15, 0.45) 1156.2160 0.1368 107486.2000 229.5232 15612.7900 0.0572 3.9214
$ \mathcal{L} $(0.2, 0.4) 1156.2160 0.1368 107485.1000 229.5259 15617.3600 0.0572 3.9214
$ \mathcal{L} $(0.25, 0.35) 1156.2160 0.1368 107486.1000 229.5232 15612.7800 0.0572 3.9214
VN $ \mathcal{L} $(0.15, 0.45) 516.9964 0.4553 174968.0000 493.6712 143951.5000 0.2448 71.9007
$ \mathcal{L} $(0.2, 0.4) 516.9964 0.4553 174966.9000 493.6749 143955.4000 0.2448 71.9007
$ \mathcal{L} $(0.25, 0.35) 516.9964 0.4553 174968.0000 493.6712 143951.5000 0.2448 71.9007
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