-->PONE-D-25-40047-->

Strategies for carbon reduction and advertising investments in partially centralized supply chains

PLOS ONE

Dear Dr. Kong,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Academic Editor

PLOS ONE

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The rejection point is significant by a reviewer. However, I would like to give the authors the opportunity to revise the paper for publication. Thus, the authors must revise properly based on the reviewer's comments.

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Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.-->

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Partly

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-->2. Has the statistical analysis been performed appropriately and rigorously?-->

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: N/A

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Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: No

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Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: Reviewer Comments for Manuscript PONE-D-25-40047

Title: Strategies for Carbon Reduction and Advertising Investments in Partially Centralized Supply Chains

General Assessment:

The manuscript addresses an important and timely topic, exploring the interplay between carbon reduction efforts, green advertising, and cost-sharing contracts in supply chains under cap-and-trade policies. The study is theoretically grounded and provides valuable insights into supply chain coordination mechanisms. However, there are several areas where the manuscript could be improved to enhance clarity, rigor, and practical relevance.

Major Comments:

Clarity of Model Assumptions and Justifications:

The assumptions underlying the demand function (e.g., linearity in price, carbon reduction rate, and advertising efforts) should be more thoroughly justified. Are there empirical studies or real-world data supporting these assumptions? If not, the authors should discuss the limitations of these simplifications.

The cost functions for carbon reduction ((ke^2)/2) and green advertising ((vγ^2)/2) are standard in the literature but may not capture real-world complexities. The authors should justify these choices and discuss potential alternatives (e.g., non-quadratic costs).

Empirical Validation:

While the numerical simulations are useful, the manuscript would benefit from empirical validation or case studies to demonstrate the practical applicability of the findings. For instance, could the authors provide examples of firms or industries where the proposed models align with observed behavior?

Policy and Managerial Implications:

The discussion on policy implications is somewhat limited. How might governments design cap-and-trade policies to incentivize the optimal cost-sharing ratios identified in the study?

The managerial insights could be expanded to provide clearer guidance for supply chain managers. For example, what specific steps should managers take to determine the most suitable cost-sharing model for their context?

Comparative Analysis of Models:

The comparison between the RC, MC, and DC models is a strength of the study, but the thresholds (e.g., θ^h,δ^m) are not intuitively explained. The authors should provide more intuitive interpretations of these thresholds and their practical significance.

Dynamic Considerations:

The study assumes static conditions, but carbon trading prices and consumer preferences are dynamic in reality. How might the findings change if dynamic or stochastic elements were incorporated? This could be a valuable direction for future research.

Minor Comments:

Writing and Organization:

The manuscript is well-structured but could benefit from tighter editing for clarity. Some sentences are overly complex (e.g., in the abstract and introduction).

The figures (e.g., Figures 3–10) are informative but could be improved with clearer labels.

Literature Review:

The literature review is comprehensive but could better highlight the novel contributions of this study relative to prior work. For example, how does this study advance beyond the findings of [3], [28], or other cited papers?

Parameter Sensitivity:

The sensitivity of results to parameter choices (e.g., k,v,P_c) should be discussed further. Are the findings robust to variations in these parameters, or do they hold only under specific conditions?

Recommendation:

The manuscript makes a valuable contribution to the literature on green supply chain management and cost-sharing contracts. However, the revisions suggested above would significantly strengthen its theoretical rigor, practical relevance, and clarity. I recommend major revisions before acceptance.

Additional Suggestions:

Include a table summarizing the key findings and managerial insights.

Consider adding a section on limitations and future research directions.

Ensure all mathematical derivations are clearly presented in the appendices.

Overall, this study has the potential to be a strong addition to the field, and I look forward to seeing the revised version.

Reviewer #2: Thanks to the respected authors for trying to fill the research gap in the study. There is a concern about the presentation of the article, which has lowered its quality, it is better to try to rewrite the article in accordance with the standards.

Reviewer #3: This manuscript examines carbon reduction and green advertising strategies in supply chains under a cap-and-trade policy through game theory modelling of four coordination scenarios. While the research addresses an important and timely topic with a generally sound mathematical framework, several critical issues require revision before the manuscript meets publication standards.

The mathematical verification in this manuscript is incomplete. The Hessian matrix analysis provided in the Appendix, Proof of Corollary 3, only verifies second-order conditions for the manufacturer's profit optimisation but omits the retailer's second-order conditions in both RC and MC scenarios. This incomplete verification raises questions about whether the presented solutions truly represent optimal decisions for both parties in the supply chain.

The model adopts standard assumptions of linear demand and quadratic cost functions in Section 3.2 without justification. While these are common in the game theory literature, the authors should at least briefly explain why these functional forms are appropriate for their context or acknowledge them as limitations. The analysis is also limited to a single manufacturer-retailer dyad without discussion of how competition might affect results.

The finding that high carbon trading prices combined with high reduction cost coefficients may decrease emission reduction efforts (shown in Figure 3) is counterintuitive and important for policy. While the authors provide some economic reasoning about manufacturers shifting strategies, this paradoxical result would benefit from a clearer presentation of the parameter ranges where it occurs and a brief discussion of policy implications.

The comparative analysis in Propositions 1-3 provides useful theoretical insights but could benefit from brief discussion of what drives these threshold conditions. For instance, what market characteristics favor the RC model over the MC model?

Regarding data availability, the statement "Data will be made available on request" does not meet PLOS ONE policy, which requires that all data necessary to replicate the study be publicly available at publication. Please deposit the simulation code and parameters in a public repository or include them as Supporting Information, and update the Data Availability Statement accordingly. While not required, providing full simulation scripts would substantially strengthen reproducibility. Additionally, Table 1 is incomplete, missing definitions for profit notation (πm, πr, π) and threshold parameters (δm, δr, θh, θm, θr¹, θr³) that appear in later propositions. Please complete these definitions. Also, the terminology "grandfather law" should be corrected to "grandfathering provisions" throughout the manuscript.

Despite these concerns, the manuscript has notable strengths, including its novel partial centralisation framework comparing RC and MC models, comprehensive analysis across four coordination structures, and integration of both carbon reduction and advertising decisions within a unified framework. The core gam theory approach appears well, and the research questions are relevant to current sustainability challenges in supply chain management.

The manuscript requires major revision to address these fundamental issues. Specifically, the authors must provide complete mathematical verification including all second order conditions for both manufacturer and retailer, add brief justification for key assumptions or acknowledge their limitations, provide clearer presentation of the paradoxical carbon price effect with discussion of when it occurs and its policy implications, and ensure proper data availability by providing simulation code and parameters in supplementary materials or a public repository.

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Reviewer #1: Yes:  Mohamed A.Wahab ALI

Reviewer #2: No

Reviewer #3: No

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Attachments

Attachment

Submitted filename: Reviewers Comments.docx

-->PONE-D-25-40047R1-->-->Strategies for carbon reduction and advertising investments in partially centralized supply chains-->-->PLOS One

Dear Dr. Liu,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

-->-->According to the reviewers’ comments, there are several issues that should be addressed prior to any form of acceptance. Although these were classified as minor revisions, I consider them to be major, as they involve adding citations to the reviewers’ own work, which is not permitted under PLOS policies. As a result, such statements have been removed. If, for any reason, any of them remain, they should be disregarded.

Please submit your revised manuscript by Jun 05 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:-->

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

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We look forward to receiving your revised manuscript.

Kind regards,

João Zambujal-Oliveira

Academic Editor

PLOS One

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #4: All comments have been addressed

Reviewer #5: (No Response)

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #4: Yes

Reviewer #5: Yes

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-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #4: N/A

Reviewer #5: N/A

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-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #4: Yes

Reviewer #5: No

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #4: Yes

Reviewer #5: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #4: In this paper, the authors introduce four models that analyze different supply chain models with real life examples which is praiseworthy. This approach is distinct from other papers on cost-sharing mechanisms, as it explores a partially centralized model. Furthermore, applicable conditions for the models are discussed that provides a clear understanding of practical application.

Following feedbacks may be helpful to improve the manuscript:

1. On page 33, regarding the Hessian matrix of the manufacturer's profit, could the author clarify how they conclude on the non-negativity of the numerator?

2. The author focuses on two types of cost-sharing mechanism (i.e., RC and MC). It would be appreciated if the author could mention some of the challenges of these mechanisms.

3. This study conducted numerical simulations for four models (e.g., centralized, decentralized, and two partially centralized models) based on assumed parametric values. How do these parametric values change or react to different market conditions?

4. There are several repeating statements in the abstract, introduction, and conclusion. Revise or rephrase these sections to improve the readability of the manuscript and maintain a clear and focused narrative.

5. In the bibliography, it is evident that no recent (since 2024 to date) paper has been cited. I recommend to cite recent relevant articles, particularly from 2024 to 2026.

Reviewer #5: This manuscript studies carbon reduction and green advertising decisions in a supply chain under cap-and-trade regulation, considering different cost-sharing mechanisms. The topic is relevant, and the paper provides a structured analytical model with some potentially useful managerial insights. The framework is generally clear, and the combination of carbon reduction and advertising decisions is meaningful. However, there are several issues that should be addressed before the paper can be considered for publication.

1. The paper states that existing studies have not systematically explored the interaction between different supply chain structures and emission reduction strategies. However, there is already a substantial literature on cost-sharing contracts, emission reduction, and supply chain coordination. The current wording somewhat overstates the gap. It would be better to moderate the claim and clarify that prior work has partially addressed these issues, but not in the specific setting considered here (e.g., combining cap-and-trade, green advertising, and partial centralization). A more careful positioning would improve the credibility of the contribution.

2.Some assumptions are standard but should still be better explained, especially for a broad audience such as PLOS ONE, These assumptions are reasonable, but brief economic intuition or references should be added to improve clarity.

3.While the analytical derivations are detailed, the explanation of results is sometimes too long and repetitive. In particular: the economic intuition behind key findings (e.g., non-monotonic effect of carbon price) could be explained more directly. It would help to summarize the main mechanisms more clearly instead of repeating mathematical interpretations.

4.The conclusions provide reasonable insights, but they remain relatively broad. The paper could be improved by: Linking specific findings to concrete managerial decisions and explaining under what conditions each cost-sharing model should be used in practice.

5.Some related paper are listed for your consideration:

A.Low-carbon supply policies and supply chain performance with carbon concerned demand

B.Production optimization considering environmental performance and preference in the cap-and-trade system

6.Language is generally understandable but would benefit from light editing for clarity and conciseness.

Overall Recommendation: The paper addresses a relevant topic and presents a coherent analytical model. With revisions to improve clarity, positioning, and interpretation, it could be suitable for publication.

Recommendation: Minor Revision

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Reviewer #4: Yes:  ZIAUL HAQ ADNAN

Reviewer #5: No

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Strategies for carbon reduction and advertising investments in partially centralized supply chains

PONE-D-25-40047R2

Dear Dr. Liu,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

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Kind regards,

João Zambujal-Oliveira

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #4: All comments have been addressed

Reviewer #5: All comments have been addressed

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-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #4: Yes

Reviewer #5: Yes

**********

-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #4: N/A

Reviewer #5: Yes

**********

-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #4: Yes

Reviewer #5: Yes

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #4: Yes

Reviewer #5: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #4: The author has revised the manuscript in accordance with all my previous comments, effectively addressing each point raised. The revisions have improved the clarity and quality of the manuscript. All concerns have been adequately addressed. I find the responses satisfactory, and there are no major unresolved issues. Therefore, I recommend the manuscript for further editorial consideration and possible acceptance.

Reviewer #5: All my questions have been well addressed. It is recommended that the author carefully review the entire article before the journal accept it.

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Reviewer #4: No

Reviewer #5: No

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