Research on low-carbon closed-loop supply chain strategy based on differential games-dynamic optimization analysis of new and remanufactured products

Jun Wang; Dan Wang; Yuan Yuan; Jun Wang; Dan Wang; Yuan Yuan

doi:10.3934/math.20241540

AIMS Mathematics

2024, Volume 9, Issue 11: 32076-32101. doi: 10.3934/math.20241540

Previous Article Next Article

Research article Topical Sections

Research on low-carbon closed-loop supply chain strategy based on differential games-dynamic optimization analysis of new and remanufactured products

School of Mathematics and Statistics, Changchun University of Technology, Changchun 130012, China

Received: 27 July 2024 Revised: 17 October 2024 Accepted: 31 October 2024 Published: 11 November 2024
MSC : 91A23

With the current increasing global demand for low-carbon and environmentally friendly products, promoting the sustainability of closed-loop supply chains has become one of the key measures. However, consumers often do not regard remanufactured products as equivalent to new products. Therefore, this paper proposes a dynamic closed-loop supply chain that incorporates consumers' purchasing preferences to model a long-term game with product differentiation. Moreover, to enhance consumer acceptance of remanufactured products and reduce manufacturers' costs, low-carbon technologies and cost-sharing mechanisms are introduced. In this way, we construct a differential game in which the manufacturer sells new and remanufactured products through a retailer and makes decisions about the level of low-carbon technology in the remanufacturing process. Based on the theory of differential games, this paper analyzes three different power structures: the manufacturer-dominated Stackelberg game, the Nash game, and the retailer-dominated Stackelberg game. The optimal low-carbon technology level and pricing strategy are obtained by applying Pontryagin's maximum principle. The study shows that the retailer-led Stackelberg game helps retailers maximize profits, while the Nash game enables the entire closed-loop supply chain system to achieve the highest overall profits. This paper innovatively integrates low-carbon technologies into the dynamic game model of the remanufacturing process and reveals how the game behavior of supply chain participants affects the application of low-carbon technologies and the overall profit of the supply chain by comparing the cost-sharing mechanisms under different power structures. The results provide important theoretical support and practical references for closed-loop supply chain management with product differentiation.
- closed-loop supply chain,
- differential game,
- power structure,
- cost-sharing
Citation: Jun Wang, Dan Wang, Yuan Yuan. Research on low-carbon closed-loop supply chain strategy based on differential games-dynamic optimization analysis of new and remanufactured products[J]. AIMS Mathematics, 2024, 9(11): 32076-32101. doi: 10.3934/math.20241540

Related Papers:

Abstract

With the current increasing global demand for low-carbon and environmentally friendly products, promoting the sustainability of closed-loop supply chains has become one of the key measures. However, consumers often do not regard remanufactured products as equivalent to new products. Therefore, this paper proposes a dynamic closed-loop supply chain that incorporates consumers' purchasing preferences to model a long-term game with product differentiation. Moreover, to enhance consumer acceptance of remanufactured products and reduce manufacturers' costs, low-carbon technologies and cost-sharing mechanisms are introduced. In this way, we construct a differential game in which the manufacturer sells new and remanufactured products through a retailer and makes decisions about the level of low-carbon technology in the remanufacturing process. Based on the theory of differential games, this paper analyzes three different power structures: the manufacturer-dominated Stackelberg game, the Nash game, and the retailer-dominated Stackelberg game. The optimal low-carbon technology level and pricing strategy are obtained by applying Pontryagin's maximum principle. The study shows that the retailer-led Stackelberg game helps retailers maximize profits, while the Nash game enables the entire closed-loop supply chain system to achieve the highest overall profits. This paper innovatively integrates low-carbon technologies into the dynamic game model of the remanufacturing process and reveals how the game behavior of supply chain participants affects the application of low-carbon technologies and the overall profit of the supply chain by comparing the cost-sharing mechanisms under different power structures. The results provide important theoretical support and practical references for closed-loop supply chain management with product differentiation.

References

[1]	V. D. R. Guide, T. P. Harrison, L. N. Van Wassenhove, The challenge of closed-loop supply chains, Interfaces, 33 (2003), 3–6. https://doi.org/10.1287/inte.33.6.3.25182 doi: 10.1287/inte.33.6.3.25182
[2]	A. Atasu, V. D. R. Guide, L. N. Van Wassenhove, Product reuse economics in closed‐loop supply chain research, Prod. Oper. Manage., 17 (2008), 483–496. https://doi.org/10.3401/poms.1080.0051 doi: 10.3401/poms.1080.0051
[3]	Z. Zhang, L. Yu, Dynamic decision-making and coordination of low-carbon closed-loop supply chain considering different power structures and government double subsidy, Clean Technol. Environ. Policy, 25 (2023), 143–171. https://doi.org/10.1016/j.ijpe.2009.02.012 doi: 10.1016/j.ijpe.2009.02.012
[4]	X. Wang, Y. Zhu, H. Sun, F. Jia, Production decisions of new and remanufactured products: Implications for low carbon emission economy, J. Clean. Prod., 171 (2018), 1225–1243. https://doi.org/10.1016/j.jclepro.2017.10.053 doi: 10.1016/j.jclepro.2017.10.053
[5]	L. Yang, Y. Hu, L. Huang, Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation, Eur. J. Oper. Res., 287 (2020), 480–496. https://doi.org/10.1016/j.ejor.2020.04.006 doi: 10.1016/j.ejor.2020.04.006
[6]	R. C. Savaskan, S. Bhattacharya, L. N. Van Wassenhove, Closed-loop supply chain models with product remanufacturing, Manage. Sci., 50 (2004), 239–252. https://doi.org/10.1287/mnsc.1030.0186 doi: 10.1287/mnsc.1030.0186
[7]	M. Fleischmann, P. Beullens, J. M. Bloemhof-Ruwaard, L. N. Van Wassenhove, The impact of product recovery on logistics network design, Prod. Oper. Manage., 10 (2003), 156–173. https://doi.org/10.1111/j.1937-5956.2001.tb00076.x doi: 10.1111/j.1937-5956.2001.tb00076.x
[8]	V. D. R. Guide, V. Jayaraman, J. D. Linton, Building contingency planning for closed-loop supply chains with product recovery, J. Oper. Manage., 21 (2003), 259–279. https://doi.org/10.1016/S0272-6963(02)00110-9 doi: 10.1016/S0272-6963(02)00110-9
[9]	T. M. Choi, Y. Li, L. Xu, Channel leadership, performance and coordination in closed loop supply chains, Int. J. Prod. Econ., 146 (2013), 371–380. https://doi.org/10.1016/j.ijpe.2013.08.002 doi: 10.1016/j.ijpe.2013.08.002
[10]	Y. Feng, X. Xia, X. Yin, L. Wang, Z. Zhang, Pricing and coordination of remanufacturing supply chain with government participation considering consumers' preferences and quality of recycled products, Complexity, 2022, 8378639. https://doi.org/10.1155/2022/8378639 doi: 10.1155/2022/8378639
[11]	J. Vorasayan, S. M. Ryan, Optimal price and quantity of refurbished products, Prod. Oper. Manage., 15 (2006), 69–383. https://doi.org/10.1111/j.1937-5956.2006.tb00251.x doi: 10.1111/j.1937-5956.2006.tb00251.x
[12]	P. D. Giovanni, P. V. Reddy, G. Zaccour, Incentive strategies for an optimal recovery program in a closed-loop supply chain, Eur. J. Oper. Res., 249 (2016), 605–617. https://doi.org/10.1016/j.ejor.2015.09.021 doi: 10.1016/j.ejor.2015.09.021
[13]	H. Guo, Z. Liu, B. Hu, H. Lin, Pricing and coordination mechanism of supply chain considering product recycling under asymmetric power, Math. Probl. Eng., 2021 (2021), 5579655. https://doi.org/10.1155/2021/5579655 doi: 10.1155/2021/5579655
[14]	J. H. Ma, L. Xie, The comparison and complex analysis on dual-channel supply chain under different channel power structures and uncertain demand, Nonlinear Dyn., 83 (2016), 1379–1393. https://doi.org/10.1007/s11071-015-2410-9 doi: 10.1007/s11071-015-2410-9
[15]	R. Harms, J. D. Linton, Willingness to pay for eco-certified refurbished products: the effects of environmental attitudes and knowledge, J. Ind. Ecol., 20 (2016), 893–904. https://doi.org/10.1111/jiec.12301 doi: 10.1111/jiec.12301
[16]	J. Ni, J. Zhao, L. K. Chu, Supply contracting and process innovation in a dynamic supply chain with information asymmetry, Eur. J. Oper. Res., 288 (2021), 552–562. https://doi.org/10.1016/j.ejor.2020.06.008 doi: 10.1016/j.ejor.2020.06.008
[17]	Q. Xia, M. Jin, H. Wu, C. Yang, A DEA-based decision framework to determine the subsidy rate of emission reduction for local government, J. Clean. Prod., 202 (2018), 846–852. https://doi.org/10.1016/j.jclepro.2018.08.171 doi: 10.1016/j.jclepro.2018.08.171
[18]	N. Wang, Q. He, B. Jiang, Hybrid closed-loop supply chains with competition in recycling and product markets, Int. J. Prod. Econ., 217 (2019), 246–258. https://doi.org/10.1016/j.ijpe.2018.01.002 doi: 10.1016/j.ijpe.2018.01.002
[19]	W. Wang, Y. Zhang, K. Zhang, T. Bai, J. Shang, Reward-penalty mechanism for closed-loop supply chains under responsibility-sharing and different power structures, Int. J. Prod. Econ., 170 (2015), 178–190. https://doi.org/10.1016/j.ijpe.2015.09.003 doi: 10.1016/j.ijpe.2015.09.003
[20]	Z. Liu, J. Chen, C. Diallo, Optimal production and pricing strategies for a remanufacturing firm, Int. J. Prod. Econ., 204 (2018), 290–315. https://doi.org/10.1016/j.ijpe.2018.07.015 doi: 10.1016/j.ijpe.2018.07.015
[21]	S. Liu, F. Yao, D. Chen, CSR investment decision and coordination strategy for closed-loop supply chain with two competing retailers, J. Clean. Prod., 310 (2021), 1–10. https://doi.org/10.1016/j.jclepro.2021.127378 doi: 10.1016/j.jclepro.2021.127378
[22]	Y. Zhang, Y. He, J. Yue, Q. Gou, Pricing decisions for a supply chain with refurbished products, Int. J. Prod. Res., 57 (2019), 2867–2900. https://doi.org/10.1080/00207543.2018.1543968 doi: 10.1080/00207543.2018.1543968
[23]	X. P. Hong, L. Xu, P. Du, W. J. Wang, Joint advertising, pricing and collection decisions in a closed-loop supply chain, Int. J. Prod. Econ., 167 (2015), 12–22. https://doi.org/10.1016/j.ijpe.2015.05.001 doi: 10.1016/j.ijpe.2015.05.001
[24]	H. Chen, Z. Dong, G. Li, K. He, Remanufacturing process innovation in closed-loop supply chain under cost-sharing mechanism and different power structures, Comput. Ind. Eng., 162 (2021), 107743. https://doi.org/10.1016/j.cie.2021.107743 doi: 10.1016/j.cie.2021.107743
[25]	J. Wei, K. Govindan, Y. Li, J. Zhao, Pricing and collecting decisions in a closed-loop supply chain with symmetric and asymmetric information, Comput. Oper. Res., 54 (2015), 257–265. https://doi.org/10.1016/j.cor.2013.11.021 doi: 10.1016/j.cor.2013.11.021
[26]	J. Gao, X. Wang, Q. Yang, Q. Zhong, Pricing decisions of a dual-channel closed-loop supply chain under uncertain demand of indirect channel, Math. Probl. Eng., 2016 (2016), 6053510. https://doi.org/10.1155/2016/6053510 doi: 10.1155/2016/6053510
[27]	Z. J. Ma, N. Zhang, Y. Dai, S. Hu, Managing channel profits of different cooperative models in closed-loop supply chains, Omega, 59 (2016), 251–262. https://doi.org/10.1016/j.omega.2015.06.013 doi: 10.1016/j.omega.2015.06.013
[28]	Z. Zhang, L. Yu, Altruistic mode selection and coordination in a low-carbon closed-loop supply chain under the government's compound subsidy: a differential game analysis, J. Clean. Prod., 336 (2022), 132863. https://doi.org/10.1016/j.jclepro.2022.132863 doi: 10.1016/j.jclepro.2022.132863
[29]	T. Xu, J. H. Ma, Feed-in tariff or tax-rebate regulation? Dynamic decision model for the solar photovoltaic supply chain, Appl. Math. Modell., 89 (2021), 1106–1123. https://doi.org/10.1016/j.apm.2020.08.007 doi: 10.1016/j.apm.2020.08.007
[30]	J. H. Ma, T. Xu, Optimal strategy of investing in solar energy for meeting the renewable portfolio standard requirement in America, J. Oper. Res. Soc., 74 (2023), 181–194. https://doi.org/10.1080/01605682.2022.2032427 doi: 10.1080/01605682.2022.2032427
[31]	Z. Xiang, M. Xu, Dynamic cooperation strategies of the closed-loop supply chain involving the internet service platform, J. Clean. Prod., 220 (2019), 1180–1193. https://doi.org/10.1016/j.jclepro.2019.01.310 doi: 10.1016/j.jclepro.2019.01.310
[32]	D. Ma, J. Hu, Research on collaborative management strategies of closed-loop supply chain under the influence of big-data marketing and reference price effect, Sustainability, 12 (2020), 1685. https://doi.org/10.3390/su12041685 doi: 10.3390/su12041685
[33]	L. Liu, L. Wang, T. Huang, J. Pang, The differential game of a closed-loop supply chain with manufacturer competition considering goodwill, Mathematics, 10 (2022), 1795. https://doi.org/10.3390/math10111795 doi: 10.3390/math10111795
[34]	L. Guo, Y. Qu, M. L. Tseng, C. Wu, X. Wang, Two-echelon reverse supply chain in collecting waste electrical and electronic equipment: a game theory model, Comput. Ind. Eng., 126 (2018), 187–195. https://doi.org/10.1016/j.cie.2018.09.036 doi: 10.1016/j.cie.2018.09.036
[35]	Y. Yang, X. Xu, A differential game model for closed-loop supply chain participants under carbon emission permits, Comput. Ind. Eng., 135 (2019), 1077–1090. https://doi.org/10.1016/j.cie.2019.03.049 doi: 10.1016/j.cie.2019.03.049
[36]	C. H. Wu, A dynamic perspective of government intervention in a competitive closed-loop supply chain, Eur. J. Oper. Res., 294 (2021), 122–137. https://doi.org/10.1016/j.ejor.2021.01.014 doi: 10.1016/j.ejor.2021.01.014
[37]	J. H. Ma, F. Zhang, H. Jiang, Dynamic pricing game under different channel power structures in a closed-loop supply chain, Int. J. Bifurcation Chaos, 30 (2020), 2050052. https://doi.org/10.1142/S0218127420500522 doi: 10.1142/S0218127420500522
[38]	Z. H. Xiang, M. L. Xu, Dynamic game strategies of a two-stage remanufacturing closed-loop supply chain considering big data marketing, Technol. Innovation Overconfidence, 145 (2020), 106538. https://doi.org/10.1016/j.cie.2020.106538 doi: 10.1016/j.cie.2020.106538
[39]	D. W. K. Yeung, L. A. Petrosyan, Cooperative stochastic differential games, Springer, 2006. https://doi.org/10.1007/0-387-27622-X

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)