The Regression Model and the Problem of Inventory Centralization: Is the “Square Root Law” Applicable?

Round 1

Reviewer 1 Report

The manuscript is well written. However, some of the contents of the manuscript require citation. E.g. statement in lines 81 to 84, lines 193 to 195, etc. Also, it requires minor formatting. Literature review on page 2 should be moved to page 3—the same thing for materials and Methods in line 253.
I encourage the author(s) to provide a summary of the paper at the end of the introduction section.

Author Response

Thank you Professor for your valuable comments to improve the paper. We changed the following things in the article:

- a newly written abstract,

- changed elements in the introduction,

- the literature review section was divided and reorganized. New positions were added to the review,

- missing citations added,

- conclusion section was divided and rewritten.

Reviewer 2 Report

This paper describes the results of research on optimizing the number of warehouses in the supply chain with the use of various methods (simulation, modeling, etc.). The authors analyze and describe in detail the process carried out, thus facilitating the understanding of the content.

The abstract must include the main contributions of the authors to the problem addressed. In this summary, it is not very clear what the main contributions have been. Likewise, the main results obtained are not indicated. It would be advisable to rewrite the abstract to include these details.

The state of the art is included in the literature review section. It is usually advisable to list the different bibliographical references according to the order in which they appear in the text. For example by placing the citation number in square brackets [a] in your citation. This nomenclature makes it easier for the reader to search for it in the corresponding section. It is recommended to go deeper into this section. For example, showing the differences or advantages with respect to other related scientific documents. As a suggestion, perhaps the development of a table can give clarity to the state of the art. It is also recommended to increase the number of bibliographical references in the document. This will help to delve into the state of the art.

On the other hand, the document is technically sound, since it contains an analysis of the state of the art of the problem addressed. It also incorporates different mathematical expressions and diagrams associated with the development of the model. Similarly, it includes some estimated results that support the analysis shown.

Concepts are presented comprehensively. The different figures, tables, diagrams, and schemes facilitate the understanding of the contents presented by the authors in the paper. 

Likewise, the results obtained support the comments made by the authors. All this makes it easier for the reader to follow the paper.

It is recommended to unify the font type and size in the footnotes of the figures. Sometimes different font sizes appear and there is no separation between the images. It is advisable to review the magazine's layout regulations before publication.

Finally, it is advisable to separate the "results, conclusions, and recommendations" section. It makes no sense to mix the conclusions with results or the discussion forum. All these points indicate concepts and contents are different. It is convenient to indicate on the one hand the results obtained and ideas extracted from the figures and graphs shown. indicating the mathematical model used, errors, statistical data, estimates, and other items deemed appropriate.

The conclusions must clearly describe the main contributions of the authors to the topic addressed. As well as the summary of the main contents with respect to other research papers. Thus, it is considered necessary for the authors to rewrite this last section in its entirety.

The number of bibliographic references provided is insufficient. It is advisable to increase their number in order to improve the state of the art.

Author Response

Thank you Professor for your valuable comments to improve the paper. We changed the following things in the article:

- a newly written abstract,

- changed elements in the introduction,

- the literature review section was divided and reorganized. New positions were added to the literature review. The number of items in the bibliography has increased

- missing citations added,

- conclusion section was divided and rewritten

Reviewer 3 Report

The article The regression model and the problem of inventory centralization. Is the "Square Root Law" applicable?“ is original and actual. The research methods chosen are appropriate.

But I have some remarks:

1. In the abstract of the article, you must describe the relevance of your topic, what kind of problem do you raise. And briefly describe your article results.
2. In the introduction to the article, I propose you to write what kind of tasks you have risen and what you need to achieve your purpose.
3. In the literature review, you must use more newer references.
4. In line 195, I cannot see the citation.
5. I propose that the metology in your manuscript is written concisely, with the execution of a stage.
6. Chapter 'Results, Conclusions, and Recommendations' I propose to split into three separate chapters.
7. Research results I propose to describe the event of stage as in the methology chapter.
8. Conclusions must be numeric according to the tasks.
9. The article must review the article to meet the template.

Author Response

Thank you Professor for your valuable comments to improve the paper. We changed the following things in the article:

- a newly written abstract,

- changed elements in the introduction,

- the literature review section was divided and reorganized. New positions were added to the literature review. The number of items in the bibliography has increased

- missing citations added,

- conclusion section was divided and rewritten

Round 2

Reviewer 2 Report

First of all, I congratulate the authors for the research work presented.

The authors have incorporated in the document the different observations and recommendations made by the reviewers. In this way, the abstract and the conclusions of the paper have been rewritten. In the same way, the state of the art has been improved by incorporating a greater number of bibliographical references. The authors have also indicated their contributions to the topic analyzed. The results have also been rewritten encouraging discussion of them.