Semigroup-theoretic analysis of supply-chain disruptions and resilience

Job Agba Opue; Marshal I. Sampson; Otobong J. Tom; Uchechukwu E. Okorie

doi:10.1371/journal.pone.0350123

Peer Review History

Original SubmissionJanuary 31, 2026
2 Apr 2026 Decision Letter - Fucai Lin, Editor -->PONE-D-26-05436--> Semigroup-Theoretic Analysis of Supply-Chain Disruptions and Resilience PLOS One Dear Dr. Opue, 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. Please submit your revised manuscript by May 16 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. 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Please ensure that you refer to Figures 3-8 in your text as, if accepted, production will need this reference to link the reader to the figure. 6. We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to Table 1-3 in your text; if accepted, production will need this reference to link the reader to the Table. 7. If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: 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: Yes ******** -->2. Has the statistical analysis been performed appropriately and rigorously?--> Reviewer #1: Yes Reviewer #2: N/A ****** -->3. 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 #1: Yes Reviewer #2: No ****** -->4. 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 #1: Yes Reviewer #2: Yes ****** -->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: Paper is good, it is better if you add some application.The framework is illustrated with examples spanning manufacturing, agricultural, and e-commerce logistics systems. Analytical results, algorithmic procedures, and case studies demonstrate how semigroup properties map to measurable resilience indicators, providing interpretable, computationally tractable tools for assessing shock containment strategies in real-world networks. Reviewer #2: This is a completely theoretic paper with interesting applications of semi-group analysis to supply chains. It is interesting how authors relate the algebraic structure to disruptions and residence of supply chains in particular theoretic escenarios. However, some comments point out changes that should be made in order to be suited for publication. The theoretic analysis presented in the paper does complement existing literature such as network analysis and operational modeling. However, the paper is missing a review of related literature of such analyses. Authors should include in this literature review advances in network propagation models and application using data. Make a clearer presentation of contribution in contrast to network analysis. My main concern is regarding practical applicability to non-mathematicians. Despite the good theoretic presentation, authors should improve the explanation and intuition behind applied examples of supply chains. Supply chains are an important subject in economics and, as the paper currently stands, it will be hard for economists to follow and apply the algorithms proposed. This will be even harder for policy makers. In complement with my previous point, authors should improve presentation of the case study considering the analysis of economic situations. All theoretic data should be publicly available through a repository such as an Open Science Framework. Recommendation: addressed all comments before being suited for publication. ****** -->6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.--> Reviewer #1: Yes: E Keshava Reddy Reviewer #2: Yes: Martha G. Alatriste Contreras ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures You may also use PLOS’s free figure tool, NAAS, to help you prepare publication quality figures: https://journals.plos.org/plosone/s/figures#loc-tools-for-figure-preparation. NAAS will assess whether your figures meet our technical requirements by comparing each figure against our figure specifications. Attachments Attachment Submitted filename: Review_PlosOne_SemigroupTheoreticAnalysis.pdf https://doi.org/10.1371/journal.pone.0350123.r001
Revision 1
15 Apr 2026 Author Response Response to Reviewer Manuscript Title: Semigroup Theoretic Analysis of Supply-Chain Disruptions and Resilience Journal: PLOS ONE We sincerely thank the reviewer for the careful reading of our manuscript and for the constructive suggestions provided. We have revised the manuscript accordingly and addressed each comment in detail below. All changes have been incorporated into the revised manuscript to improve clarity, practical interpretation, and reproducibility. Reviewer Comment 1 “The theoretic analysis presented in the paper does complement existing literature such as network analysis and operational modeling. However, the paper is missing a review of related literature of such analyses. Authors should include in this literature review advances in network propagation models and application using data.” Response We appreciate this important suggestion. In response, we have expanded the Introduction to include a discussion of recent advances in network propagation models and data-driven disruption analysis. The revised text now situates the semigroup-based framework within the broader context of supply-chain modeling approaches, including network-based and simulation-based methods. These additions clarify how algebraic transformation models provide complementary structural insights beyond probabilistic or graph-based propagation models. Location in Manuscript Introduction section - literature review paragraph discussing network propagation and data-driven disruption models, with additional references included. Reviewer Comment 2 “Make a clearer presentation of contribution in contrast to network analysis.” Response We have revised the final paragraph of the Introduction to explicitly state the distinct contribution of the semigroup-theoretic approach relative to traditional network-based models. The revised text now emphasizes that the proposed framework focuses on structural properties of disruption transformations, including collapse states, reachability, and stabilisation behaviour, which are not directly captured by standard network flow or simulation models. This clarification strengthens the positioning of the work within the broader supply-chain modeling literature. Location in Manuscript Introduction section - concluding paragraph describing the theoretical and operational contributions of the proposed framework. Reviewer Comment 3 “My main concern is regarding practical applicability to non-mathematicians. Despite the good theoretic presentation, authors should improve the explanation and intuition behind applied examples of supply chains. Supply chains are an important subject in economics and, as the paper currently stands, it will be hard for economists to follow and apply the algorithms proposed. This will be even harder for policy makers.” Response We thank the reviewer for highlighting the importance of accessibility for practitioners and policy-oriented readers. To address this concern, we introduced additional explanatory text throughout the examples and case discussions to provide operational interpretation of the mathematical constructs. Specifically, we added descriptive paragraphs explaining: • how disruptions correspond to operational events such as port closures or logistics failures, • how repeated disruptions lead to backlog accumulation, • how stabilisation corresponds to restoration of operational capacity, • how collapse states represent conditions requiring external intervention. These additions provide intuitive explanations linking the algebraic framework to real-world supply-chain behaviour. Location in Manuscript Immediately before the manufacturing disruption example - new subsection titled: Operational Interpretation Reviewer Comment 4 “In complement with my previous point, authors should improve presentation of the case study considering the analysis of economic situations.” Response In response to this suggestion, we strengthened the practical interpretation of the case study examples by explicitly linking the mathematical framework to observable economic and logistics disruptions. The revised manuscript now includes: • clearer descriptions of production and delivery interruptions, • interpretation of collapse states as operational failure scenarios, • examples of corrective actions such as rerouting shipments or restoring infrastructure, • structured transformation examples representing logistics disruptions. In addition, we included a supplementary appendix containing illustrative transformation matrices and reachability tables that demonstrate how disruptions propagate through supply-chain states. These additions improve the economic relevance and interpretability of the examples while preserving the theoretical rigor of the model. Location in Manuscript Case study and example sections - expanded explanatory paragraphs. Appendix - supplementary transformation and reachability examples. Reviewer Comment 5 “All theoretic data should be publicly available through a repository such as an Open Science Framework.” Response We appreciate this recommendation regarding transparency and reproducibility. In response, we have added a formal Data Availability section to the manuscript describing how the data underlying the practical illustrations can be accessed. The revised manuscript now states that: • theoretical examples and computational materials are available from the corresponding author upon reasonable request, • practical disruption illustrations are based on publicly available logistics and port performance datasets. The dataset sources are now explicitly cited in the manuscript. To support reproducibility, we also included supplementary materials in the appendix containing: • representative transformation matrices, • reachability tables, • minimal collapse-inducing generator sets, • sample computational scripts. These materials allow readers to reproduce the structural analyses presented in the paper. Location in Manuscript Data Availability section - newly added. Appendix - supplementary transformation data and computational procedures. Summary of Revisions The revised manuscript now includes: • Expanded literature review on network propagation and data-driven supply-chain analysis, • Clearer statement of the contribution of semigroup-based modeling, • Improved operational interpretation of mathematical examples, • Stronger economic and logistics context for case studies, • Formal data availability statement and supplementary materials supporting reproducibility. We believe these revisions fully address the reviewer’s concerns and significantly strengthen the clarity, applicability, and transparency of the manuscript. We sincerely thank the reviewer for the thoughtful comments that helped improve the quality and accessibility of this work. Attachments Attachment Submitted filename: Response to Reviewer-Semigroup in Supply Chain.pdf https://doi.org/10.1371/journal.pone.0350123.r002
10 May 2026 Decision Letter - Fucai Lin, Editor Semigroup-Theoretic Analysis of Supply-Chain Disruptions and Resilience PONE-D-26-05436R1 Dear Dr. Opue, 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. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. For questions related to billing, please contact billing support. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Fucai Lin, Ph.D. Academic Editor PLOS One ******** -->Review Comments to the Author--> Reviewer #1: Application of problem taken as paper may be mention in the paper and paper can be made more effective using new technique. Reviewer #2: Literature review is limited but enough. Authors should make all data surrounding results fully available, not under reasonable request. ******** https://doi.org/10.1371/journal.pone.0350123.r003
Formally Accepted
Acceptance Letter - Fucai Lin, Editor PONE-D-26-05436R1 PLOS One Dear Dr. Opue, I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS One. Congratulations! Your manuscript is now being handed over to our production team. At this stage, our production department will prepare your paper for publication. This includes ensuring the following: * All references, tables, and figures are properly cited * All relevant supporting information is included in the manuscript submission, * There are no issues that prevent the paper from being properly typeset You will receive further instructions from the production team, including instructions on how to review your proof when it is ready. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few days to review your paper and let you know the next and final steps. Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. You will receive an invoice from PLOS for your publication fee after your manuscript has reached the completed accept phase. If you receive an email requesting payment before acceptance or for any other service, this may be a phishing scheme. Learn how to identify phishing emails and protect your accounts at https://explore.plos.org/phishing. If we can help with anything else, please email us at customercare@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Professor Fucai Lin Academic Editor PLOS One https://doi.org/10.1371/journal.pone.0350123.r004

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