IDEAS home Printed from https://ideas.repec.org/a/spr/snopef/v6y2025i2d10.1007_s43069-025-00470-9.html
   My bibliography  Save this article

A Three-Level Refrigeration Supply Chain Inventory Model Including Linear Time-Dependent Demand for Temperature-Sensitive Items Considering Carbon Tax Regulations

Author

Listed:
  • Ranu

    (Lovely Professional University)

  • Nitin Kumar Mishra

    (Lovely Professional University)

Abstract

In this inventory model, a production process system is explained. In this research, we investigate a retailer, supplier, and manufacturer’s combined inventory replenishment decisions or production and besides this, the incentive to invest in reducing carbon emissions underneath the greenhouse gas emission regulation strategy. This research looks at some temperature-sensitive item that deteriorates at a constant rate. A “break-even” point is established in this article where Q1 + Q2 is the optimal quantity produced by the manufacturer until the “break-even” point. Thereafter Q2 amount is to be spent in the remaining ongoing unequal cycles until the produced total quantity Q2 is transported to the retailer. Q1 is required to be larger than Q2. Furthermore, the demand rate is a linear function dependent upon time under a finite period. To satisfy customer demand, the manufacturing rate is postulated to be larger than the demand rate. To exhibit the proposed model, a numerical instance, scenario analysis, and their tabular, as well as graphical representation, are furnished. With the help of Mathematica software, optimality was also discussed for unequal replenishment time over the finite planning horizon. The present research in this kind of area has been rigorously analyzed and summarized. Eventually, managerial suggestions and future recommendations have been also explained.

Suggested Citation

  • Ranu & Nitin Kumar Mishra, 2025. "A Three-Level Refrigeration Supply Chain Inventory Model Including Linear Time-Dependent Demand for Temperature-Sensitive Items Considering Carbon Tax Regulations," SN Operations Research Forum, Springer, vol. 6(2), pages 1-30, June.
  • Handle: RePEc:spr:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00470-9
    DOI: 10.1007/s43069-025-00470-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s43069-025-00470-9
    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/s43069-025-00470-9?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. Sarkar, Biswajit & Sarkar, Mitali & Ganguly, Baishakhi & Cárdenas-Barrón, Leopoldo Eduardo, 2021. "Combined effects of carbon emission and production quality improvement for fixed lifetime products in a sustainable supply chain management," International Journal of Production Economics, Elsevier, vol. 231(C).
    2. Min Wang & Lindu Zhao & Michael Herty, 2018. "Modelling carbon trading and refrigerated logistics services within a fresh food supply chain under carbon cap-and-trade regulation," International Journal of Production Research, Taylor & Francis Journals, vol. 56(12), pages 4207-4225, June.
    3. Liu, Zugang (Leo) & Anderson, Trisha D. & Cruz, Jose M., 2012. "Consumer environmental awareness and competition in two-stage supply chains," European Journal of Operational Research, Elsevier, vol. 218(3), pages 602-613.
    4. Songyi Wang & Fengming Tao & Yuhe Shi & Haolin Wen, 2017. "Optimization of Vehicle Routing Problem with Time Windows for Cold Chain Logistics Based on Carbon Tax," Sustainability, MDPI, vol. 9(5), pages 1-23, April.
    5. Bae, Sang Hoo & Sarkis, Joseph & Yoo, Chung Sik, 2011. "Greening transportation fleets: Insights from a two-stage game theoretic model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 793-807.
    6. Neeraj Kumar & S.R. Singh & Rachna Kumari, 2012. "Three echelon supply chain inventory model for deteriorating items with limited storage facility and lead-time under inflation," International Journal of Services and Operations Management, Inderscience Enterprises Ltd, vol. 13(1), pages 98-118.
    7. Giulio Quaglini & Simon Pezzutto & Andrea Grotto & Eric Wilczynski, 2022. "Assessment of Final Space Cooling Consumption in the European Transportation Sector," Sustainability, MDPI, vol. 14(3), pages 1-20, January.
    8. Bin Hu & Bangtong Huang & Zheng Liu & Hangxin Guo & Zihong Chen & Lihua Shi, 2021. "Optimization Model of Carbon Footprint of Fresh Products in Cold Chain from the Energy Conservation and Emission Reduction Perspective," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, April.
    9. Saif, Ahmed & Elhedhli, Samir, 2016. "Cold supply chain design with environmental considerations: A simulation-optimization approach," European Journal of Operational Research, Elsevier, vol. 251(1), pages 274-287.
    10. Volha Yakavenka & Ioannis Mallidis & Dimitrios Vlachos & Eleftherios Iakovou & Zafeiriou Eleni, 2020. "Development of a multi-objective model for the design of sustainable supply chains: the case of perishable food products," Annals of Operations Research, Springer, vol. 294(1), pages 593-621, November.
    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. Abdul Salam Khan & Bashir Salah & Dominik Zimon & Muhammad Ikram & Razaullah Khan & Catalin I. Pruncu, 2020. "A Sustainable Distribution Design for Multi-Quality Multiple-Cold-Chain Products: An Integrated Inspection Strategies Approach," Energies, MDPI, vol. 13(24), pages 1-25, December.
    2. Konur, Dinçer, 2014. "Carbon constrained integrated inventory control and truckload transportation with heterogeneous freight trucks," International Journal of Production Economics, Elsevier, vol. 153(C), pages 268-279.
    3. Tapan Kumar Datta & Prasanta Nath & Karabi Dutta Choudhury, 2020. "A hybrid carbon policy inventory model with emission source-based green investments," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 202-220, March.
    4. Juanjuan Qin & Liguo Ren & Liangjie Xia, 2017. "Carbon Emission Reduction and Pricing Strategies of Supply Chain under Various Demand Forecasting Scenarios," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-27, February.
    5. Andrea Gallo & Riccardo Accorsi & Giulia Baruffaldi & Riccardo Manzini, 2017. "Designing Sustainable Cold Chains for Long-Range Food Distribution: Energy-Effective Corridors on the Silk Road Belt," Sustainability, MDPI, vol. 9(11), pages 1-20, November.
    6. Prem Vrat & Rachita Gupta & Aman Bhatnagar & Devendra Kumar Pathak & Vijayta Fulzele, 2018. "Literature review analytics (LRA) on sustainable cold-chain for perishable food products: research trends and future directions," OPSEARCH, Springer;Operational Research Society of India, vol. 55(3), pages 601-627, November.
    7. Ge, Houtian & Baker, Quinton J. & Gomez, Miguel I. & Jaromczyk, Jerzy & Yi, Jing, 2022. "Assessing the carbon footprint of fresh produce assembly and distribution in the U.S," 2022 Annual Meeting, July 31-August 2, Anaheim, California 322537, Agricultural and Applied Economics Association.
    8. Hota, Soumya Kanti & Sarkar, Biswajit & Ghosh, Santanu Kumar & Cheikhrouhou, Naoufel & Treviño-Garza, Gerardo, 2024. "What should be the best retail strategy to deal with an unequal shipment from an unreliable manufacturer?," Journal of Retailing and Consumer Services, Elsevier, vol. 76(C).
    9. Avinadav, Tal & Levy, Priel, 2023. "The effect of an uncertain commission rate on the decisions of a capital-constrained developer," Operations Research Perspectives, Elsevier, vol. 11(C).
    10. Yi Zheng & Huchang Liao & Xue Yang, 2016. "Stochastic Pricing and Order Model with Transportation Mode Selection for Low-Carbon Retailers," Sustainability, MDPI, vol. 8(1), pages 1-19, January.
    11. Wang, Moran & Guo, Xiaolong & Wang, Shouyang, 2022. "Financial hedging in two-stage sustainable commodity supply chains," European Journal of Operational Research, Elsevier, vol. 303(2), pages 803-818.
    12. Yang, Yuxiang & Goodarzi, Shadi & Jabbarzadeh, Armin & Fahimnia, Behnam, 2022. "In-house production and outsourcing under different emissions reduction regulations: An equilibrium decision model for global supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    13. Zhaofu Hong & Hao Wang & Yeming Gong, 2019. "Green product design considering functional-product reference," Post-Print hal-02312293, HAL.
    14. Yuxiang Sun & Xiaopu Zhang & Xirou Huang & Wenbin Cao, 2025. "Research on Logistics Service Supply Chain Coordination in the Context of Green Innovation," Sustainability, MDPI, vol. 17(2), pages 1-28, January.
    15. Xu, Xiaoping & He, Ping & Zhou, Li & Cheng, T.C.E., 2023. "Coordination of a platform-based supply chain in the marketplace or reselling mode considering cross-channel effect and blockchain technology," European Journal of Operational Research, Elsevier, vol. 309(1), pages 170-187.
    16. Fateme Souri & S. M. T. Fatemi Ghomi, 2025. "Design of sustainable perishable food supply chain network under uncertainty," OPSEARCH, Springer;Operational Research Society of India, vol. 62(1), pages 406-422, March.
    17. Prudence Dato, 2018. "Investment in Energy Efficiency, Adoption of Renewable Energy and Household Behavior: Evidence from OECD Countries," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    18. Zhang, Dengjun & Xie, Yifan, 2022. "Customer environmental concerns and profit margin: Evidence from manufacturing firms," Journal of Economics and Business, Elsevier, vol. 120(C).
    19. Yumin Fu & Jianyun Wu & Cheng Ma & Xiaoyu Fu, 2023. "Agency, Reselling, or Hybrid: Strategic Channel Selection in a Green Supply Chain," Sustainability, MDPI, vol. 15(3), pages 1-21, January.
    20. Hamed Nozari & Esmaeil Najafi & Mohammad Fallah & Farhad Hosseinzadeh Lotfi, 2019. "Quantitative Analysis of Key Performance Indicators of Green Supply Chain in FMCG Industries Using Non-Linear Fuzzy Method," Mathematics, MDPI, vol. 7(11), pages 1-19, October.

    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:snopef:v:6:y:2025:i:2:d:10.1007_s43069-025-00470-9. 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.