# Recycling Pricing and Government Subsidy Strategy for End-of-Life Vehicles in a Reverse Supply Chain under Consumer Recycling Channel Preferences

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Recycling Channels of the Reverse Supply Chain

#### 2.2. Recycling Pricing of the Reverse Supply Chain

#### 2.3. Consumer Behavior in the Reverse Supply Chain

## 3. Problem Description

#### 3.1. Parameter Setting

#### 3.2. Model Gssumptions

## 4. Model Construction and Solution

#### 4.1. Government Non-Subsidy—Model d

**Theorem**

**1.**

**Lemma**

**1.**

#### 4.2. Government Subsidy for Remanufacturers—Model G

**Theorem**

**2.**

**Lemma**

**2.**

#### 4.3. Government Subsidy for Consumers—Model C

**Theorem**

**3.**

**Lemma**

**3.**

## 5. Comparative Analysis of Models

**Conclusion**

**1.**

**Conclusion**

**2.**

**Conclusion**

**3.**

**Conclusion**

**4.**

**Conclusion**

**5.**

## 6. Numerical Analysis

## 7. Conclusions

- The increase in consumer preferences for online recycling has a positive effect on the recycling volume and profit of the reverse supply chain of ELVs, which is reflected in three models: government non-subsidy, government subsidy for remanufacturers, and government subsidy for consumers. When formulating subsidy methods, the government should give priority to subsidizing and encouraging the productivity brought about by technological progress. In the discussion of this paper, the online recycling platform based on Internet technology provides a convenient one-stop recycling service for consumers who need to deal with ELVs, and consumer preferences for online recycling make the online recycling platform enter the recycling practice.
- Both government subsidies for remanufacturers and consumers have an impact on the RSC. Does the government subsidize remanufacturers or consumers? It depends on the intensity of government subsidies under a certain consumer preference. From the point of view of RSC recycling, when the subsidy intensity is small, the subsidy method of subsidizing remanufacturers can bring more recycling for the RSC, while the subsidy method of subsidizing consumers can bring more recycling when the subsidy intensity is increased. The purpose of government subsidy is not only to increase the recycling volume to increase the utilization rate of resources but also to encourage the development of the remanufacturing industry. In this case, it is necessary to consider the subsidy method from the perspective of RSC profit. When subsidies are given at the lower middle level, higher profits can be earned by subsidizing remanufacturers, and, on the contrary, higher RSC profits can be earned by subsidizing consumers.

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Proof.**

**Proof of Theorem**

**1.**

**Proof of Lemma**

**1.**

**Proof of Theorem**

**2.**

**Proof of Lemma**

**2.**

**Proof of Theorem**

**3.**

**Proof of Lemma**

**3.**

**Proof of Conclusion**

**1.**

**Proof of Conclusion**

**2.**

**Proof of Conclusion**

**3.**

**Proof of Conclusion**

**4.**

**Proof of Conclusion**

**5.**

## References

- Van Engeland, J.; Belien, J.; De Boeck, L.; De Jaeger, S. Literature review: Strategic network optimization models in waste reverse supply chains. Omega-Int. J. Manag. Sci.
**2020**, 91, 102012. [Google Scholar] [CrossRef] - de Souza, J.A.F.; Silva, M.M.; Rodrigues, S.G.; Santos, S.M. A forecasting model based on ARIMA and artificial neural networks for end-OF-life vehicles. J. Environ. Manag.
**2022**, 318, 115616. [Google Scholar] [CrossRef] [PubMed] - Zhou, F.; Lim, M.K.; He, Y.; Lin, Y.; Chen, S. End-of-life vehicle (ELV) recycling management: Improving performance using an ISM approach. J. Clean. Prod.
**2019**, 228, 231–243. [Google Scholar] [CrossRef] - Zhou, F.; Wang, X.; Lim, M.K.; He, Y.; Li, L. Sustainable recycling partner selection using fuzzy DEMATEL-AEW-FVIKOR: A case study in small-and-medium enterprises (SMEs). J. Clean. Prod.
**2018**, 196, 489–504. [Google Scholar] [CrossRef] - Martin Gomez, A.M.; Aguayo Gonzalez, F.; Marcos Barcena, M. Smart eco-industrial parks: A circular economy implementation based on industrial metabolism. Resour. Conserv. Recycl.
**2018**, 135, 58–69. [Google Scholar] [CrossRef] - Yuik, C.J.; Saman, M.Z.M.; Ngadiman, N.H.A.; Hamzah, H.S. Supply chain optimisation for recycling and remanufacturing sustainable management in end-of-life vehicles: A mini-review and classification. Waste Manag. Res.
**2023**, 41, 554–565. [Google Scholar] [CrossRef] [PubMed] - Gerrard, J.; Kandlikar, M. Is European end-of-life vehicle legislation living up to expectations? Assessing the impact of the ELV Directive on ‘green’ innovation and vehicle recovery. J. Clean. Prod.
**2007**, 15, 17–27. [Google Scholar] [CrossRef] - Council, S. Administrative Measures for End of Life Vehicles. Available online: https://www.gov.cn/zhengce/content/2019-05/06/content_5389079.htm (accessed on 6 May 2019).
- Xiao, Y.; Li, C.; Song, L.; Yang, J.; Su, J. A Multidimensional Information Fusion-Based Matching Decision Method for Manufacturing Service Resource. IEEE Access
**2021**, 9, 39839–39851. [Google Scholar] [CrossRef] - Özceylan, E.; Demirel, N.; Çetinkaya, C.; Demirel, E. A closed-loop supply chain network design for automotive industry in Turkey. Comput. Ind. Eng.
**2017**, 113, 727–745. [Google Scholar] [CrossRef] - Gorji, M.A.; Jamali, M.B.; Iranpoor, M. A game-theoretic approach for decision analysis in end-of-life vehicle reverse supply chain regarding government subsidy. Waste Manag.
**2021**, 120, 734–747. [Google Scholar] [CrossRef] - Zhu, X.; Ren, M.; Chu, W.; Chiong, R. Remanufacturing subsidy or carbon regulation? An alternative toward sustainable production. J. Clean. Prod.
**2019**, 239, 117988. [Google Scholar] [CrossRef] - Hong, Z.; Zhang, Y.; Yu, Y.; Chu, C. Dynamic pricing for remanufacturing within socially environmental incentives. Int. J. Prod. Res.
**2020**, 58, 3976–3997. [Google Scholar] [CrossRef] - Liu, Y.Z.; Xiao, T.J. Pricing and Collection Rate Decisions and Reverse Channel Choice in a Socially Responsible Supply Chain With Green Consumers. Ieee Trans. Eng. Manag.
**2020**, 67, 483–495. [Google Scholar] [CrossRef] - ATRenew. To Give a Second Life to All Idle Goods. Available online: https://ir.atrenew.com/ (accessed on 1 January 2023).
- Alahb. Alahb Profile. Available online: https://www.sohu.com/a/147286807_99895762 (accessed on 8 June 2017).
- Aitedaxiang. End-of-Life Vehicles Recycling Service Platform. Available online: https://www.daxiangshouche.com/about (accessed on 1 April 2020).
- Zhou, F.; Chen, T.; Tiwari, S.; Si, D.; Pratap, S.; Mahto, R.V. Pricing and Quality Improvement Decisions in the End-of-Life Vehicle Closed-Loop Supply Chain Considering Collection Quality. IEEE Trans. Eng. Manag.
**2023**, 1–15. [Google Scholar] [CrossRef] - Li, Y.J.; Xu, F.C.; Zhao, X.K. Governance mechanisms of dual-channel reverse supply chains with informal collection channel. J. Clean. Prod.
**2017**, 155, 125–140. [Google Scholar] [CrossRef] - Geng, D.; Lai, K.-h.; Zhu, Q. Eco-innovation and its role for performance improvement among Chinese small and medium-sized manufacturing enterprises. Int. J. Prod. Econ.
**2021**, 231, 107869. [Google Scholar] [CrossRef] - Govindan, K.; Paam, P.; Abtahi, A.-R. A fuzzy multi-objective optimization model for sustainable reverse logistics network design. Ecol. Indic.
**2016**, 67, 753–768. [Google Scholar] [CrossRef] - Mahdiraji, H.A.; Govindan, K.; Madadi, S.; Garza-Reyes, J.A. Coordination in a closed-loop sustainable supply chain considering dual-channel and cost-sharing contract: Evidence from an emerging economy. J. Oper. Res. Soc.
**2023**, 74, 2362–2381. [Google Scholar] [CrossRef] - Bakhshi, A.; Heydari, J. An optimal put option contract for a reverse supply chain: Case of remanufacturing capacity uncertainty. Ann. Oper. Res.
**2023**, 324, 37–60. [Google Scholar] [CrossRef] - Wei, J.; Wang, Y.; Zhao, J.; Santibanez Gonzalez, E.D.R. Analyzing the performance of a two-period remanufacturing supply chain with dual collecting channels. Comput. Ind. Eng.
**2019**, 135, 1188–1202. [Google Scholar] [CrossRef] - Suvadarshini, P.; Biswas, I.; Srivastava, S.K. Impact of reverse channel competition, individual rationality, and information asymmetry on multi-channel closed-loop supply chain design. Int. J. Prod. Econ.
**2023**, 259, 108818. [Google Scholar] [CrossRef] - Yan, G.Z.; Ni, Y.D.; Yang, X.F. Pricing and recovery in a dual-channel closed-loop supply chain under uncertain environment. Soft Comput.
**2021**, 25, 13679–13694. [Google Scholar] [CrossRef] - He, P.; He, Y.; Xu, H. Channel structure and pricing in a dual-channel closed-loop supply chain with government subsidy. Int. J. Prod. Econ.
**2019**, 213, 108–123. [Google Scholar] [CrossRef] - Wang, M.M.; Yang, F.; Xia, Q. Design of the reverse channel for the third-party remanufacturing considering consumer education. Rairo-Oper. Res.
**2021**, 55, 3513–3540. [Google Scholar] [CrossRef] - Hosseini-Motlagh, S.M.; Johari, M.; Nematollahi, M.; Pazari, P. Reverse supply chain management with dual channel and collection disruptions: Supply chain coordination and game theory approaches. Ann. Oper. Res.
**2023**, 324, 215–248. [Google Scholar] [CrossRef] - Wang, Y.Y.; Yu, Z.Q.; Shen, L.; Jin, M.Z. Operational modes of E-closed loop supply chain considering platforms? services. Int. J. Prod. Econ.
**2022**, 251, 108551. [Google Scholar] [CrossRef] - Wan, N.N.; Li, L.; Fan, J.C.; Chen, W. The choice of the collection channel in an O2O closed-loop supply chain. Environ. Dev. Sustain.
**2023**, 25, 5009–5051. [Google Scholar] [CrossRef] - Matsui, K. Dual-recycling channel reverse supply chain design of recycling platforms under acquisition price competition. Int. J. Prod. Econ.
**2023**, 259, 108769. [Google Scholar] [CrossRef] - Li, Z.; Zhao, J.; Meng, Q.F. Dual-channel recycling e-waste pricing decision under the impact of recyclers’ loss aversion and consumers’ bargaining power. Environ. Dev. Sustain.
**2022**, 24, 11697–11720. [Google Scholar] [CrossRef] - Zhu, M.H.; Li, X.; Ma, J.H.; Xu, T.T.; Zhu, L.Q. Study on complex dynamics for the waste electrical and electronic equipment recycling activities oligarchs closed-loop supply chain. Environ. Sci. Pollut. Res.
**2022**, 29, 4519–4539. [Google Scholar] [CrossRef] - Zheng, B.R.; Huang, S.J.; Jin, L. The bright side of online recycling: Perspectives of customer’s channel preference and competition. Electron. Commer. Res. Appl.
**2021**, 50, 101102. [Google Scholar] [CrossRef] - Feng, L.; Govindan, K.; Li, C. Strategic planning: Design and coordination for dual-recycling channel reverse supply chain considering consumer behavior. Eur. J. Oper. Res.
**2017**, 260, 601–612. [Google Scholar] [CrossRef] - Zand, F.; Yaghoubi, S.; Sadjadi, S.J. Impacts of government direct limitation on pricing, greening activities and recycling management in an online to offline closed loop supply chain. J. Clean. Prod.
**2019**, 215, 1327–1340. [Google Scholar] [CrossRef] - Sarkar, B.; Ullah, M.; Choi, S.-B. Joint Inventory and Pricing Policy for an Online to Offline Closed-Loop Supply Chain Model with Random Defective Rate and Returnable Transport Items. Mathematics
**2019**, 7, 497. [Google Scholar] [CrossRef] - Fleischmann, M.; Bloemhof-Ruwaard, J.M.; Dekker, R.; van der Laan, E.; van Nunen, J.A.E.E.; Van Wassenhove, L.N. Quantitative models for reverse logistics: A review. Eur. J. Oper. Res.
**1997**, 103, 1–17. [Google Scholar] [CrossRef] - Savaskan, R.C.; Bhattacharya, S.; Van Wassenhove, L.N. Closed-Loop Supply Chain Models with Product Remanufacturing. Manag. Sci.
**2004**, 50, 239–252. [Google Scholar] [CrossRef] - Savaskan, R.C.; Van Wassenhove, L.N. Reverse Channel Design: The Case of Competing Retailers. Manag. Sci.
**2006**, 52, 1–14. [Google Scholar] [CrossRef] - Xiang, Z.; Xu, M. Dynamic game strategies of a two-stage remanufacturing closed-loop supply chain considering Big Data marketing, technological innovation and overconfidence. Comput. Ind. Eng.
**2020**, 145, 106538. [Google Scholar] [CrossRef] - Wang, Y.; Su, M.; Shen, L.; Tang, R. Decision-making of closed-loop supply chain under Corporate Social Responsibility and fairness concerns. J. Clean. Prod.
**2021**, 284, 125373. [Google Scholar] [CrossRef] - Zhang, Q.; Tang, Y.; Bunn, D.; Li, H.; Li, Y. Comparative evaluation and policy analysis for recycling retired EV batteries with different collection modes. Appl. Energy
**2021**, 303, 117614. [Google Scholar] [CrossRef] - Wang, T.-Y.; Wang, Z.-Q.; He, P. Impact of Information Sharing Modes on the Dual-Channel Closed Loop Supply Chains Under Different Power Structures. Asia-Pac. J. Oper. Res.
**2021**, 38, 2050051. [Google Scholar] [CrossRef] - Xiao, T.; Choi, T.-M.; Cheng, T.C.E. Collection Responsibility Choice for Competing E-Tailing Supply Chains With Consumer Returns. IEEE Trans. Eng. Manag.
**2021**, 71, 283–295. [Google Scholar] [CrossRef] - Zhao, J.; Wei, J.; Li, M. Collecting channel choice and optimal decisions on pricing and collecting in a remanufacturing supply chain. J. Clean. Prod.
**2017**, 167, 530–544. [Google Scholar] [CrossRef] - Taleizadeh, A.A.; Sadeghi, R. Pricing strategies in the competitive reverse supply chains with traditional and e-channels: A game theoretic approach. Int. J. Prod. Econ.
**2019**, 215, 48–60. [Google Scholar] [CrossRef] - Xu, L. Analysis for Waste Collection and Management of Closed-Loop Supply Chain with Dual-Channel forward Logistics. Int. J. Ind. Eng.-Theory Appl. Pract.
**2020**, 27, 124–139. [Google Scholar] - Li, Y.; Liu, L.; Li, W. Quality control strategies of the supply chain based on stochastic differential game. Evol. Intell.
**2021**, 1–12. [Google Scholar] [CrossRef] - Yang, W.; Zhang, J.; Yan, H. Impacts of online consumer reviews on a dual-channel supply chain. Omega-Int. J. Manag. Sci.
**2021**, 101, 102266. [Google Scholar] [CrossRef] - Jin, L.; Zheng, B.R.; Huang, S.J. Pricing and coordination in a reverse supply chain with online and offline recycling channels: A power perspective. J. Clean. Prod.
**2021**, 298, 126786. [Google Scholar] [CrossRef] - Liu, H.; Ye, L.L.; Sun, J.A. Automotive parts remanufacturing models: Consequences for ELV take-back under government regulations. J. Clean. Prod.
**2023**, 416, 137760. [Google Scholar] [CrossRef] - Feng, D.Z.; Shen, C.; Pei, Z. Production decisions of a closed-loop supply chain considering remanufacturing and refurbishing under government subsidy. Sustain. Prod. Consump.
**2021**, 27, 2058–2074. [Google Scholar] [CrossRef] - Liu, Z.; Qian, Q.S.; Hu, B.; Shang, W.L.; Li, L.L.; Zhao, Y.J.; Zhao, Z.; Han, C.J. Government regulation to promote coordinated emission reduction among enterprises in the green supply chain based on evolutionary game analysis. Resour. Conserv. Recycl.
**2022**, 182, 106290. [Google Scholar] [CrossRef] - Ullah, M. Impact of transportation and carbon emissions on reverse channel selection in closed-loop supply chain management. J. Clean. Prod.
**2023**, 394, 136370. [Google Scholar] [CrossRef] - Xie, L.; Ma, J.H. Study the complexity and control of the recycling-supply chain of China’s color TVs market based on the government subsidy. Commun. Nonlinear Sci. Numer. Simul.
**2016**, 38, 102–116. [Google Scholar] [CrossRef] - Song, H.Z.; Zhang, J.T.; Li, J.C. The impacts of subsidy strategies and recycling modes on the closed-loop supply chain. Manag. Decis. Econ.
**2022**, 43, 4106–4123. [Google Scholar] [CrossRef] - Wan, N.; Hong, D. The impacts of subsidy policies and transfer pricing policies on the closed-loop supply chain with dual collection channels. J. Clean. Prod.
**2019**, 224, 881–891. [Google Scholar] [CrossRef] - Chen, C.-K.; Ulya, M.A. Analyses of the reward-penalty mechanism in green closed-loop supply chains with product remanufacturing. Int. J. Prod. Econ.
**2019**, 210, 211–223. [Google Scholar] [CrossRef] - Zhang, Z.Y.; Yu, L.Y. Dynamic decision-making and coordination of low-carbon closed-loop supply chain considering different power structures and government double subsidy. Clean Technol. Environ. Policy
**2023**, 25, 143–171. [Google Scholar] [CrossRef] - Zhao, J.; Sun, N. Government subsidies-based profits distribution pattern analysis in closed-loop supply chain using game theory. Neural Comput. Appl.
**2020**, 32, 1715–1724. [Google Scholar] [CrossRef] - Wu, C.H. A dynamic perspective of government intervention in a competitive closed-loop supply chain. Eur. J. Oper. Res.
**2021**, 294, 122–137. [Google Scholar] [CrossRef] - Yang, H.; Chen, W. Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing. Omega-Int. J. Manag. Sci.
**2018**, 78, 179–191. [Google Scholar] [CrossRef] - Chang, X.; Wu, J.; Li, T.; Fan, T.-J. The joint tax-subsidy mechanism incorporating extended producer responsibility in a manufacturing-recycling system. J. Clean. Prod.
**2019**, 210, 821–836. [Google Scholar] [CrossRef] - Zhang, M.Y.; Wang, Y.; Qian, X.W.; Zhao, J.; Nie, Y.Y.; Qian, G.R. Competition and price strategies of hazardous waste collection for small and micro enterprises based on dual-channel reverse supply chain. J. Clean. Prod.
**2023**, 386, 135714. [Google Scholar] [CrossRef] - Xu, H.; Liu, Z.Z.; Zhang, S.H. A strategic analysis of dual-channel supply chain design with price and delivery lead time considerations. Int. J. Prod. Econ.
**2012**, 139, 654–663. [Google Scholar] [CrossRef] - Li, C.; Feng, L.; Luo, S. Strategic introduction of an online recycling channel in the reverse supply chain with a random demand. J. Clean. Prod.
**2019**, 236, 117683. [Google Scholar] [CrossRef] - Chiang, W.-y.K.; Chhajed, D.; Hess, J.D. Direct Marketing, Indirect Profits: A Strategic Analysis of Dual-Channel Supply-Chain Design. Manag. Sci.
**2003**, 49, 1–20. [Google Scholar] [CrossRef]

Parameter | Definition |
---|---|

${Q}_{c}$ | Recycling volume of offline recyclers |

${Q}_{e}$ | Online recycling |

${I}_{c}$ | Input cost of offline recycling channels |

${I}_{e}$ | Input cost of offline recycling channels |

$\mathsf{\omega}$ | Income from dismantling ELVs and remanufacturing parts |

$\mathrm{s}$ | per unit to remanufacturers and consumers |

$\upsilon $ | Consumer value perception of ELVs |

$\theta $ | Consumer behavior preferences for online recycling channels |

$\phi $ | Convenience value of online recycling channels for consumers |

Decision variable | |

${p}_{r}$ | Offline recyclers transfer payment prices to remanufacturers |

${p}_{c}$ | Offline recyclers’ recycling price |

${p}_{e}$ | Online recycling price |

Variable | $\mathbf{Model}\mathbf{d}$ | Model G |
---|---|---|

${{p}_{r}}^{\ast}$ | $\frac{{I}_{c}+\omega}{2}$ | $\frac{{I}_{c}+\omega}{2}$ |

${{p}_{e}}^{\ast}$ | $\frac{{-I}_{e}+\omega -\phi}{2}$ | $\frac{\omega -\phi}{2}$ |

${{p}_{c}}^{\ast}$ | $\frac{{-I}_{e}+\omega -{I}_{c}\theta +\omega \theta +\phi}{4\theta}$ | $\frac{\omega -{I}_{c}\theta +\omega \theta +\phi}{4\theta}$ |

${{Q}_{c}}^{\ast}$ | $-\frac{{-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi}{4(-1+\theta )}$ | $-\frac{\omega +{I}_{c}\theta -\omega \theta +\phi}{4-4\theta}$ |

${{Q}_{e}}^{\ast}$ | $\frac{{I}_{e}+\omega \left(-1+\theta \right)+{I}_{c}\theta -{2I}_{e}\theta -\phi +2\theta \phi}{4(-1+\theta )\theta}$ | $\frac{\omega -{I}_{c}\theta -\omega \theta +\phi -2\theta \phi}{4(1-\theta )\theta}$ |

${{\Pi}_{\mathrm{r}}}^{\ast}$ | $\begin{array}{c}\frac{({I}_{e}-\omega -\phi )(\omega -{I}_{c}\theta -\omega \theta -{I}_{e}+2{I}_{e}\theta +\phi -2\theta \phi )}{8\left(-1+\theta \right)\theta}\hfill \\ +\frac{({I}_{c}-\omega )({-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi )}{8(-1+\theta )}\hfill \end{array}$ | $\begin{array}{c}\frac{{{I}_{c}}^{2}{\theta}^{2}+{\omega}^{2}\left(-1+{\theta}^{2}\right)-2\omega \left(-1+\theta \right)\left({I}_{c}\theta -\phi \right)}{8(-1+\theta )\theta}\hfill \\ \hfill +\frac{{2I}_{c}\theta \phi +\left(-1+2\theta \right){\phi}^{2}}{8(-1+\theta )\theta}\end{array}$ |

${{\Pi}_{\mathrm{c}}}^{\ast}$ | $\frac{{\left({-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi \right)}^{2}}{16(-1+\theta )\theta}$ | $\frac{{\left(\omega +{I}_{c}\theta -\omega \theta +\phi \right)}^{2}}{16(-1+\theta )\theta}$ |

Variable | $\mathbf{Model}\mathbf{d}$ | Model G |
---|---|---|

${{p}_{r}}^{\ast}$ | $\frac{{I}_{c}+\omega}{2}$ | $\frac{{I}_{c}-s+\omega}{2}$ |

${{p}_{e}}^{\ast}$ | $\frac{{-I}_{e}+\omega -\phi}{2}$ | $\frac{{-I}_{e}-s+\omega -\phi}{2}$ |

${{p}_{c}}^{\ast}$ | $\frac{{-I}_{e}+\omega -{I}_{c}\theta +\omega \theta +\phi}{4\theta}$ | $\frac{{-I}_{e}+s+\omega -{I}_{c}\theta -3s\theta +\omega \theta +\phi}{4\theta}$ |

${{Q}_{c}}^{\ast}$ | $-\frac{{-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi}{4(-1+\theta )}$ | $-\frac{{-I}_{e}+s+\omega +{I}_{c}\theta -s\theta -\omega \theta +\phi}{4(-1+\theta )}$ |

${{Q}_{e}}^{\ast}$ | $\frac{{I}_{e}+\omega \left(-1+\theta \right)+{I}_{c}\theta -{2I}_{e}\theta -\phi +2\theta \phi}{4(-1+\theta )\theta}$ | $\frac{{I}_{e}+\left(s+\omega \right)\left(-1+\theta \right)+{I}_{c}\theta -{2I}_{e}\theta -\phi +2\theta \phi}{4(-1+\theta )\theta}$ |

${{\Pi}_{\mathrm{r}}}^{\ast}$ | $\begin{array}{l}\frac{({I}_{e}-\omega -\phi )(\omega -{I}_{c}\theta -\omega \theta -{I}_{e}+2{I}_{e}\theta +\phi -2\theta \phi )}{8\left(-1+\theta \right)\theta}\\ +\frac{({I}_{c}-\omega )({-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi )}{8(-1+\theta )}\end{array}$ | $\begin{array}{l}\frac{({I}_{e}-s-\omega -\phi )(s+\omega -{I}_{c}\theta -s\theta -\omega \theta -{I}_{e}+2{I}_{e}\theta +\phi -2\theta \phi )}{8(-1+\theta )\theta}\\ +\frac{({I}_{e}-s-\omega )({-I}_{e}+s+\omega +{I}_{c}\theta -s\theta -\omega \theta +\phi )}{8(-1+\theta )}\end{array}$ |

${{\Pi}_{\mathrm{c}}}^{\ast}$ | $\frac{{\left({-I}_{e}+\omega +{I}_{c}\theta -\omega \theta +\phi \right)}^{2}}{16(-1+\theta )\theta}$ | $\frac{{\left({-I}_{e}+s+\omega +{I}_{c}\theta -s\theta -\omega \theta +\phi \right)}^{2}}{16(-1+\theta )\theta}$ |

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## Share and Cite

**MDPI and ACS Style**

Wang, Z.
Recycling Pricing and Government Subsidy Strategy for End-of-Life Vehicles in a Reverse Supply Chain under Consumer Recycling Channel Preferences. *Mathematics* **2024**, *12*, 35.
https://doi.org/10.3390/math12010035

**AMA Style**

Wang Z.
Recycling Pricing and Government Subsidy Strategy for End-of-Life Vehicles in a Reverse Supply Chain under Consumer Recycling Channel Preferences. *Mathematics*. 2024; 12(1):35.
https://doi.org/10.3390/math12010035

**Chicago/Turabian Style**

Wang, Zhiguo.
2024. "Recycling Pricing and Government Subsidy Strategy for End-of-Life Vehicles in a Reverse Supply Chain under Consumer Recycling Channel Preferences" *Mathematics* 12, no. 1: 35.
https://doi.org/10.3390/math12010035