IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v199y2023i2d10.1007_s10957-023-02305-1.html
   My bibliography  Save this article

Emission Reduction of Low-Carbon Supply Chain Based on Uncertain Differential Game

Author

Listed:
  • Xiangfeng Yang

    (University of International Business and Economics)

  • Peng Zhang

    (University of International Business and Economics)

Abstract

This paper studies the low-carbon production problem based on an uncertain differential game. In a two-stage low-carbon product supply chain consisting of a single supplier and a single manufacturer, we construct an uncertain differential equation by taking the emission reduction efforts of the supplier and manufacturer as decision variables and product emission reduction as a state variable. Based on the uncertain differential game, we obtain the supply chain’s dynamic equilibrium strategy, emission reduction, and revenue trajectory under non-cooperative and cooperative situations. By comparison, cooperation leads to more effort on both sides of the supply chain, more carbon emission reduction, and higher profits than non-cooperative ones. To further illustrate the supply chain game in the cooperative situation, we give different income situations under the two distribution methods of Nash bargaining solution and Shapley value, respectively.

Suggested Citation

  • Xiangfeng Yang & Peng Zhang, 2023. "Emission Reduction of Low-Carbon Supply Chain Based on Uncertain Differential Game," Journal of Optimization Theory and Applications, Springer, vol. 199(2), pages 732-765, November.
    • Handle: RePEc:spr:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02305-1
    DOI: 10.1007/s10957-023-02305-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-023-02305-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-023-02305-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Papers 2102.09851, arXiv.org, revised Feb 2021.
    2. Benchekroun, Hassan & Martín-Herrán, Guiomar, 2016. "The impact of foresight in a transboundary pollution game," European Journal of Operational Research, Elsevier, vol. 251(1), pages 300-309.
    3. Shaofu Du & Jun Qian & Tianzhuo Liu & Li Hu, 2020. "Emission allowance allocation mechanism design: a low-carbon operations perspective," Annals of Operations Research, Springer, vol. 291(1), pages 247-280, August.
    4. Feng Zhang, 2022. "Sufficient Maximum Principle for Stochastic Optimal Control Problems with General Delays," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 678-701, February.
    5. William Lefebvre & Enzo Miller, 2021. "Linear-Quadratic Stochastic Delayed Control and Deep Learning Resolution," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 134-168, October.
    6. Ting Ji & Xiaoping Xu & Xiaoming Yan & Yugang Yu, 2020. "The production decisions and cap setting with wholesale price and revenue sharing contracts under cap-and-trade regulation," International Journal of Production Research, Taylor & Francis Journals, vol. 58(1), pages 128-147, January.
    7. Plambeck, Erica L., 2012. "Reducing greenhouse gas emissions through operations and supply chain management," Energy Economics, Elsevier, vol. 34(S1), pages 64-74.
    8. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Post-Print hal-03145949, HAL.
    9. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    10. Yi Zhang & Jinwu Gao & Xiang Li & Xiangfeng Yang, 2021. "Two-person cooperative uncertain differential game with transferable payoffs," Fuzzy Optimization and Decision Making, Springer, vol. 20(4), pages 567-594, December.
    11. Shaofu Du & Jiaang Zhu & Huifang Jiao & Wuyi Ye, 2015. "Game-theoretical analysis for supply chain with consumer preference to low carbon," International Journal of Production Research, Taylor & Francis Journals, vol. 53(12), pages 3753-3768, June.
    12. Liangjie Xia & Yongwan Bai & Sanjoy Ghose & Juanjuan Qin, 2022. "Differential game analysis of carbon emissions reduction and promotion in a sustainable supply chain considering social preferences," Annals of Operations Research, Springer, vol. 310(1), pages 257-292, March.
    13. William Lefebvre & Enzo Miller, 2021. "Linear-quadratic stochastic delayed control and deep learning resolution," Working Papers hal-03145949, HAL.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Xuefeng & Li, Zhe & Li, Guo, 2024. "Grandfather-based or benchmark-based: Strategy choice for carbon quota allocation methods in the carbon neutrality era," Renewable and Sustainable Energy Reviews, Elsevier, vol. 192(C).
    2. Liangjie Xia & Yongwan Bai & Sanjoy Ghose & Juanjuan Qin, 2022. "Differential game analysis of carbon emissions reduction and promotion in a sustainable supply chain considering social preferences," Annals of Operations Research, Springer, vol. 310(1), pages 257-292, March.
    3. Peng Liu & Ying Chen, 2022. "Differential Game Model of Shared Manufacturing Supply Chain Considering Low-Carbon Emission Reduction," Sustainability, MDPI, vol. 14(18), pages 1-24, September.
    4. Weihao Wang & Deqing Ma & Jinsong Hu, 2022. "Dynamic Carbon Reduction and Marketing Strategies with Consumers’ Environmental Awareness under Cap-and-Trade Regulation," Sustainability, MDPI, vol. 14(16), pages 1-31, August.
    5. Shoufeng Ji & Dan Zhao & Xiaoshuai Peng, 2018. "Joint Decisions on Emission Reduction and Inventory Replenishment with Overconfidence and Low-Carbon Preference," Sustainability, MDPI, vol. 10(4), pages 1-21, April.
    6. Yang, Lei & Hu, Yijuan & Huang, Lijuan, 2020. "Collecting mode selection in a remanufacturing supply chain under cap-and-trade regulation," European Journal of Operational Research, Elsevier, vol. 287(2), pages 480-496.
    7. Xu, Song & Govindan, Kannan & Wang, Wanru & Yang, Wenting, 2024. "Supply chain management under cap-and-trade regulation: A literature review and research opportunities," International Journal of Production Economics, Elsevier, vol. 271(C).
    8. Wen, Wen & Zhou, P. & Zhang, Fuqiang, 2018. "Carbon emissions abatement: Emissions trading vs consumer awareness," Energy Economics, Elsevier, vol. 76(C), pages 34-47.
    9. Jinjin Liu & Hua Ke & Yuan Gao, 2022. "Manufacturer’s R &D cooperation contract: linear fee or revenue-sharing payment in a low-carbon supply chain," Annals of Operations Research, Springer, vol. 318(1), pages 323-355, November.
    10. Chao Lu & Weilai Huang & Haifang Cheng, 2021. "Comparative Analysis of Government Subsidy Policies in a Dynamic Green Supply Chain Considering Consumers Preference," Sustainability, MDPI, vol. 13(21), pages 1-26, October.
    11. Jiaping Xie & Jing Li & Ling Liang & Xu Fang & Guang Yang & Lihong Wei, 2020. "Contracting Emissions Reduction Supply Chain Based on Market Low-Carbon Preference and Carbon Intensity Constraint," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(02), pages 1-34, March.
    12. Wang, Yong & Sun, Weixin & Abedin, Mohammad Zoynul & Hajek, Petr & Xue, Wenting, 2025. "A multi-objective lot sizing procurement model for multi-period cold chain management including supplier and carrier selection," Omega, Elsevier, vol. 130(C).
    13. Konur, Dinçer, 2017. "Non-collaborative emission targets joining and quantity flow decisions in a Stackelberg setting," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 60-82.
    14. Qiang Han & Yuyan Wang, 2018. "Decision and Coordination in a Low-Carbon E-Supply Chain Considering the Manufacturer’s Carbon Emission Reduction Behavior," Sustainability, MDPI, vol. 10(5), pages 1-23, May.
    15. Cai, Jianhu & Jiang, Feiying, 2023. "Decision models of pricing and carbon emission reduction for low-carbon supply chain under cap-and-trade regulation," International Journal of Production Economics, Elsevier, vol. 264(C).
    16. Limin Su & Yongchao Cao & Wenjuan Zhang, 2023. "Low-Carbon Supply Chain Operation Decisions and Coordination Strategies Considering the Consumers’ Preferences," Sustainability, MDPI, vol. 15(14), pages 1-20, July.
    17. Junlong Peng & Zhuo Su & Xiao Liu & Chongsen Ma, 2025. "Promoting Low-Carbonization in the Construction Supply Chain: Key Influencing Factors and Sustainable Practices," Sustainability, MDPI, vol. 17(8), pages 1-36, April.
    18. Chan, Ying Tung & Zhao, Hong, 2023. "Optimal carbon tax rates in a dynamic stochastic general equilibrium model with a supply chain," Economic Modelling, Elsevier, vol. 119(C).
    19. Ji, Guojun & Gunasekaran, Angappa & Yang, Guangyong, 2014. "Constructing sustainable supply chain under double environmental medium regulations," International Journal of Production Economics, Elsevier, vol. 147(PB), pages 211-219.
    20. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2021. "From firm to global-level pollution control: The case of transboundary pollution," European Journal of Operational Research, Elsevier, vol. 290(1), pages 331-345.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:199:y:2023:i:2:d:10.1007_s10957-023-02305-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.