PONE-D-24-18029Effect of formulations over a Periodic Capacitated Vehicle Routing Problem with Multiple Depots, Heterogeneous Fleet, and Hard Time-WindowsPLOS ONE

Dear Dr. Arenas-Vasco,

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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The paper is well-written. The authors should clarify how they produce the instances and ensure their accessibility. In addition, additional experimental evaluation is necessary to reinforce the main contribution. All reviewers'comments should be carefully considered and solved in your revised manuscript.

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Yangming Zhou, Ph.D.

Academic Editor

PLOS ONE

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"The authors want to thank Universidad EAFIT who has financed the research project

“Un estudio poliedral y m´etodos de soluci´on para problemas de enrutamiento de veh´ıculos multi-atributo con m´ultiples periodos en entornos urbanos” with internal

code 953-000020, in which this study has been developed. The authors also want to

thank Colfuturo who financed partially this project with the grant “Convocatoria"

We note that you have provided additional information within the Acknowledgements Section that is not currently declared in your Funding Statement. Please note that funding information should not appear in the Acknowledgments section or other areas of your manuscript. We will only publish funding information present in the Funding Statement section of the online submission form.

Please remove any funding-related text from the manuscript and let us know how you would like to update your Funding Statement. Currently, your Funding Statement reads as follows: "The authors want to thank Universidad EAFIT (www.eafit.edu.co) who has financed the research project "Un estudio poliedral y métodos de solución para problemas de enrutamiento de vehículos multi-atributo con múltiples periodos en entornos urbanos'' with internal code 953-000020, in which this study has been developed. The authors also want to thank Colfuturo (www.colfuturo.org) who financed partially this project with the grant "Convocatoria 909''. All grants were given to Arenas-Vasco A.

Sponsors did not play any role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript."Please include your amended statements within your cover letter; we will change the online submission form on your behalf.

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Additional Editor Comments :

This paper presents two new problem formulations for the Periodic Vehicle Routing Problem (PVRP). The paper is well-written. I have the following comments and suggestions which may further improve the manuscript. The authors should clarify how they produce the instances and ensure their accessibility. In addition, additional experimental evaluation is necessary to reinforce the main contribution.

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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: No

Reviewer #2: Yes

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

Reviewer #1: No

Reviewer #2: Yes

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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: Yes

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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

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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: The authors introduced two different but equivalent formulations for a PVRP with time windows, multiple depots, and heterogeneous fleet, considering all the particularities associated with a real-life scenario in the vending machine industry in Medellin, Colombia. The authors also performed some experiments to comprehend if the two equivalent formulations bear different performances in GUROBI.

1.The studied topic is practical. The paper is well-written. But the main contribution of this work is to propose two formulations based on classical VRP models for a real-life problem. The workload of the paper seems not enough. I suggest this work to be published in another journal.

Reviewer #2: The authors present a novel contribution to the Periodic Vehicle Routing Problem (PVRP) by introducing two new problem formulations that differ in the usage of the crucial flow variable. Experiments have demonstrated their impact on the performance of the GUROBI solver. The topic is interesting, and the manuscript is well-structured. There is only a small issue: the authors should explain in detail how they produce the instance data and ensure its accessibility. Additionally, more information is needed regarding the results on the real cases mentioned in the paper.

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Reviewer #1: No

Reviewer #2: No

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Effect of formulations over a Periodic Capacitated Vehicle Routing Problem with Multiple Depots, Heterogeneous Fleet, and Hard Time-Windows

PONE-D-24-18029R1

Dear Dr. Arenas-Vasco,

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,

Prof. Yangming Zhou,

Academic Editor, PLOS ONE

Additional Editor Comments (optional):

The authors well address all issues

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 #1: All comments have been addressed

Reviewer #2: 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 #1: Yes

Reviewer #2: (No Response)

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

Reviewer #1: Yes

Reviewer #2: (No Response)

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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 #1: Yes

Reviewer #2: (No Response)

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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 #1: Yes

Reviewer #2: (No Response)

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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 #1: The authors indicated that the proposed problem is new and provided a more complete experimentation to further strengthen the conclusions. In addition, a real-life case study data set is provided. I think that the authors have addressed all my concerns, and recommend the paper to be published.

Reviewer #2: (No Response)

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7. 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: No

Reviewer #2: No

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