IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v12y2021i1p15-d492635.html
   My bibliography  Save this article

Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach

Author

Listed:
  • Gila E. Fruchter

    (The Graduate School of Business Administration, Bar-Ilan University, Ramat Gan 5290002, Israel)

  • Hussein Naseraldin

    (Department of Industrial Engineering and Management, ORT Braude College, Karmiel 2161002, Israel)

Abstract

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies exogenously given demands in separate markets. The two firms can build up or rundown stocks (full backlogging), both of which are costly. The emission cost depends on the total output of the two firms. We develop Nash equilibrium feedback strategies, where each firm decides on its output based on its inventory or the inventories of both. We also develop a social planning solution where decisions are centralized. We present the analytic results for the total profits in these settings. The results show the benefits of a decentralized approach over a centralized one, provided there is a mechanism for coordination. Finally, emission costs are compared for the various solution concepts.

Suggested Citation

  • Gila E. Fruchter & Hussein Naseraldin, 2021. "Coordinating Carbon Emissions via Production Quantities: A Differential Game Approach," Games, MDPI, vol. 12(1), pages 1-16, February.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:15-:d:492635
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/12/1/15/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/12/1/15/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Glock, C. H. & Jaber, M. Y. & Searcy, C., 2012. "Sustainability strategies in an EPQ model with price- and quality-sensitive demand," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 59335, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    2. Battini, Daria & Persona, Alessandro & Sgarbossa, Fabio, 2014. "A sustainable EOQ model: Theoretical formulation and applications," International Journal of Production Economics, Elsevier, vol. 149(C), pages 145-153.
    3. Feichtinger, Gustav & Hartl, Richard, 1985. "Optimal pricing and production in an inventory model," European Journal of Operational Research, Elsevier, vol. 19(1), pages 45-56, January.
    4. Zied Jemai & Y Bouchery & Asma Ghaffari & Yves Dallery, 2012. "Including sustainability criteria into inventory models," Post-Print hal-01672398, HAL.
    5. Bouchery, Yann & Ghaffari, Asma & Jemai, Zied & Dallery, Yves, 2012. "Including sustainability criteria into inventory models," European Journal of Operational Research, Elsevier, vol. 222(2), pages 229-240.
    6. Zanoni, Simone & Bettoni, Laura & Glock, Christoph H., 2014. "Energy implications in a two-stage production system with controllable production rates," International Journal of Production Economics, Elsevier, vol. 149(C), pages 164-171.
    7. Erickson, Gary M., 2011. "A differential game model of the marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 211(2), pages 394-402, June.
    8. Felix Papier, 2016. "Managing Electricity Peak Loads in Make-To-Stock Manufacturing Lines," Production and Operations Management, Production and Operations Management Society, vol. 25(10), pages 1709-1726, October.
    9. Ross Baldick & Sergey Kolos & Stathis Tompaidis, 2006. "Interruptible Electricity Contracts from an Electricity Retailer's Point of View: Valuation and Optimal Interruption," Operations Research, INFORMS, vol. 54(4), pages 627-642, August.
    10. Xiuli Chao & Frank Y. Chen, 2005. "An Optimal Production and Shutdown Strategy when a Supplier Offers an Incentive Program," Manufacturing & Service Operations Management, INFORMS, vol. 7(2), pages 130-143, March.
    11. Dov Pekelman, 1974. "Simultaneous Price-Production Decisions," Operations Research, INFORMS, vol. 22(4), pages 788-794, August.
    12. Zanoni, S. & Bettoni, L. & Glock, C. H., 2014. "Energy Implications in a Two-Stage Production System with Controllable Production Rates," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 62117, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    13. Yevgenia Mikhaylidi & Hussein Naseraldin & Liron Yedidsion, 2015. "Operations scheduling under electricity time-varying prices," International Journal of Production Research, Taylor & Francis Journals, vol. 53(23), pages 7136-7157, December.
    14. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    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. Battini, Daria & Glock, Christoph H. & Grosse, Eric H. & Persona, Alessandro & Sgarbossa, Fabio, 2017. "Reprint of “Ergo-lot-sizing: An approach to integrate ergonomic and economic objectives in manual materials handling”," International Journal of Production Economics, Elsevier, vol. 194(C), pages 32-42.
    2. Vahid Reza Soleymanfar & Ahmad Makui & Ata Allah Taleizadeh & Reza Tavakkoli-Moghaddam, 2022. "Sustainable EOQ and EPQ models for a two-echelon multi-product supply chain with return policy," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(4), pages 5317-5343, April.
    3. Hovelaque, Vincent & Bironneau, Laurent, 2015. "The carbon-constrained EOQ model with carbon emission dependent demand," International Journal of Production Economics, Elsevier, vol. 164(C), pages 285-291.
    4. Jia-Liang Pan & Chui-Yu Chiu & Kun-Shan Wu & Chih-Te Yang & Yen-Wen Wang, 2021. "Optimal Pricing, Advertising, Production, Inventory and Investing Policies in a Multi-Stage Sustainable Supply Chain," Energies, MDPI, vol. 14(22), pages 1-20, November.
    5. Daria Battini & Martina Calzavara & Ilaria Isolan & Fabio Sgarbossa & Francesco Zangaro, 2018. "Sustainability in Material Purchasing: A Multi-Objective Economic Order Quantity Model under Carbon Trading," Sustainability, MDPI, vol. 10(12), pages 1-15, November.
    6. Konstantin Biel & Christoph H. Glock, 2017. "Prerequisites of efficient decentralized waste heat recovery and energy storage in production planning," Journal of Business Economics, Springer, vol. 87(1), pages 41-72, January.
    7. Jin-Kyung Kwak, 2021. "An Order-Up-to Inventory Model with Sustainability Consideration," Sustainability, MDPI, vol. 13(23), pages 1-8, December.
    8. Andriolo, Alessandro & Battini, Daria & Persona, Alessandro & Sgarbossa, Fabio, 2015. "Haulage sharing approach to achieve sustainability in material purchasing: New method and numerical applications," International Journal of Production Economics, Elsevier, vol. 164(C), pages 308-318.
    9. Tapan Kumar Datta & Sayantan Datta & Adrijit Goswami, 2024. "A sustainable bi-objective inventory model with source-based emissions and plan-based green investments under inflation and the present value of money," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(1), pages 91-117.
    10. Khan, Mehmood & Hussain, Matloub & Saber, Hussein M., 2016. "Information sharing in a sustainable supply chain," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 208-214.
    11. Yann Bouchery & Asma Ghaffari & Zied Jemai & Jan Fransoo, 2016. "Sustainable transportation and order quantity: insights from multiobjective optimization," Flexible Services and Manufacturing Journal, Springer, vol. 28(3), pages 367-396, September.
    12. Soon-Kyo Lee & Seung Ho Yoo & Taesu Cheong, 2017. "Sustainable EOQ under Lead-Time Uncertainty and Multi-Modal Transport," Sustainability, MDPI, vol. 9(3), pages 1-22, March.
    13. Andriolo, Alessandro & Battini, Daria & Grubbström, Robert W. & Persona, Alessandro & Sgarbossa, Fabio, 2014. "A century of evolution from Harris׳s basic lot size model: Survey and research agenda," International Journal of Production Economics, Elsevier, vol. 155(C), pages 16-38.
    14. YuJan Shen & KuanFu Shen & ChihTe Yang, 2019. "A Production Inventory Model for Deteriorating Items with Collaborative Preservation Technology Investment Under Carbon Tax," Sustainability, MDPI, vol. 11(18), pages 1-18, September.
    15. Erickson, Gary M., 2012. "Transfer pricing in a dynamic marketing-operations interface," European Journal of Operational Research, Elsevier, vol. 216(2), pages 326-333.
    16. Suchitra Pattnaik & Mitali Madhusmita Nayak & Stefano Abbate & Piera Centobelli, 2021. "Recent Trends in Sustainable Inventory Models: A Literature Review," Sustainability, MDPI, vol. 13(21), pages 1-20, October.
    17. Marco Trost & Enrico Teich & Thorsten Claus & Frank Herrmann, 2017. "Ein lineares Optimierungsmodell zur Hauptproduktionsprogrammplanung mit Berücksichtigung sozialer Größen [A linear optimisation model for master production scheduling including social criteria]," Sustainability Nexus Forum, Springer, vol. 25(1), pages 71-80, June.
    18. Y Bouchery & Asma Ghaffari & Zied Jemai & Jan C Fransoo, 2016. "Sustainable transportation and order quantity: insights from multiobjective optimization," Post-Print hal-01954465, HAL.
    19. Kim, Taebok & Glock, Christoph H., 2018. "Production planning for a two-stage production system with multiple parallel machines and variable production rates," International Journal of Production Economics, Elsevier, vol. 196(C), pages 284-292.
    20. Jialiang Pan & Kun-Shan Wu & Chih-Te Yang & Chi-Jie Lu & Shin Lu, 2024. "Using Game Theory to Explore the Multinational Supply Chain Production Inventory Models of Various Carbon Emission Policy Combinations," Mathematics, MDPI, vol. 12(10), pages 1-18, May.

    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:gam:jgames:v:12:y:2021:i:1:p:15-:d:492635. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.