Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

Round 1

Reviewer 1 Report

The paper offers two models related to mathematical programming formulations for the berth allocation in container terminals. From the viewpoint of logistics the paper is interesting, useful and well structured. I have some minor comments for its improvements:

- it would be very useful to indicate trends in container shipping in the Introduction (it is relatively dynamic market with respect to ship size which further affects all other aspects - maybe this reference could be useful to strengthen the reference list: Vladimir, N., Ančić, I. & Šestan, A. Effect of ship size on EEDI requirements for large container ships. J Mar Sci Technol 23, 42–51 (2018). https://doi.org/10.1007/s00773-017-0453-y - anyhow, please, look for additional 2-3 references),

- same statements on the paper aims are repeated several times throughout the paper - it is enough to stress the paper aims in the Introduction and maybe to leave it again in the Conclusion, but no more is needed,

- as far as I understand the paper targets some very small container vessels - it is not an issue itself, but I would like authors to discuss whether the model is independent on the ship and port technical properties

- it is necessary to provide more input data on the considered technical cases, even some geographical map would be useful to provide readers more information - this way is slightly difficult to read and interpret 

Author Response

Responses to the reviewer 1 comment's

Manuscript ID: logistics-2796399

Title: Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. Every change in the text is colored in red

Author Response File: Author Response.pdf

Reviewer 2 Report

The work, in its entirety, is well-structured and described in detail. The case study is well-detailed, and the modeling domain is well-structured. However, scientific progress is limited or, in some cases, dissonant. For example, introducing more than a company should ensure that cooperation and negotiation are introduced into the model to give a hierarchical structure to the different priorities and the weight of management.

1. Please insert the bibliographic reference for what is stated on lines 295-297.
2. The assignment values between the model and the actual case are identical in tables 3 and 4, as in tables 7 and 8. How do the authors justify this accuracy? What data set was the calibration done on?
3. The authors must also highlight carefully the improvements introduced by their modeling in compliance with the previously observed cases, highlighting why reproduced results are effective only in some scenarios. (see the attached "supplementary tables")

"While" is often misused, the term does not have a disjunctive or comparative value but only a temporal one. It should be better modified with whatever, whereas, etc., depending on the case.

Author Response

Responses to the reviewer 2 comment's

Manuscript ID: logistics-2796399

Title: Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. Every change in the text is colored in red

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors address a very interesting problem for shipping operators, who are required to make container handling operations increasingly efficient in an increasingly sustainable way. However, much research work in this direction has already been presented in the recent literature, and the authors' work has no innovative aspects, the organization of the article is very confusing, the proposed models have errors, and the results are presented in an unclear way.
For these reasons, the article is to be rejected.

The major critical issues I found are:

1) The abstract is unclearly written. You need to better highlight the objectives of the research, the results obtained, the innovative aspects. Please avoid acronyms and sectioning of the abstract.

2) The initial part of the introduction is very vague and lacks essential information.  The entire section 1 have to be reorganized.

3) The part of the literature, especially that referring to stowage, lacks important citations, while non-core works are cited. Anceh the sequence of citations does not seem to be consistent. Only part 1.1.3 is consistent with the proposed study and should be expanded.

4) In section 2 the flowchart reported in Figure 1 does not provide any added value.

5) In Section 2, releted to the first model, definitions (1) and (2), which express C_ijk as a function of F_ijk, and vice versa, do not make sense. Please, epress the objective function directly in terms of F_ijk and C_ijk.

6) In section 2, related to the second model, how it is possible to express the objective function (19) as a linear combination of to components having different units of measure, that is time and number?

7) In the computational results section the size of the considered instances, expressed in terms of number of variables and constraints, is not given. The assignment problem is quite obvious.

Author Response

Responses to the reviewer 3 comment's

Manuscript ID: logistics-2796399

Title: Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. Every change in the text is colored in red

Author Response File: Author Response.pdf

Reviewer 4 Report

The approached topic is very interesting. I am giving support to the authors. The paper needs some improvement to be accepted for publication.

1. The relevance of the study is poorly illustrated. Introduction section need to be revised, in which readers understand what is the necessity of this study?

2. The authors write “In this context, a significant number of works targeting the seaport system optimization by addressing as an example the assignment of dockworkers [???], the allocation of handling equipment [???], Quay-Court planning and the transfer [???] and storage of containers [???] are addressed in the literature”. Please provide references.

3. In the literature review section, the authors investigate two problems, Berths' Allocation Problem and Container Stowage. The authors should explain this choice in the introduction section.

4. The literature review is not comprehensive enough. There is only 1 paper for 2022 and no references for 2023. Please add relevant references.

5. A table providing an overview of the major articles mentioned in the Literature Overview section would be recommended. It would be a good complement to the section.

6. It is convenient for me as a reader to see the constraint in the model before each formula.

7. How were the values determined? Who were the experts? Please give explanations (Lines 296-297).

8. How many experts attend to this investigation and what their background?

9. Authors should expand the conclusions and focus on the summary and induction of this research rather than a simple repetition of the abstract and Section 1.2.

Best regards

Author Response

Responses to the reviewer 4 comment's

Manuscript ID: logistics-2796399

Title: Mathematical Programming Formulations for the Berth Allocation Problems in Container Seaport Terminals

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. Every change in the text is colored in red

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The paper sounds better

None

Author Response

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. 

Many Thanks

Reviewer 3 Report

I did not notice a significant improvement in the article in this revised version of the paper. The answers to my comments are very vague and do not answer my queries. In particular, only a few changes were made following my comments.
Furthermore, running computational tests in April 2024 based on instances in January 2021 (a period characterised by a disruption in shipping due to the covid-19 pandemic) does not seem very meaningful to me.

Author Response

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. 

We hope that now the manuscript is ok

Many Thanks

Author Response File: Author Response.pdf

Reviewer 4 Report

The authors have responded to all the reviewers' comments. I recommend this manuscript for publication.

Best Regards

Author Response

The authors would like to thank the editor and the anonymous reviewers, whose insightful comments and constructive suggestions helped us to significantly improve the quality of this paper. 

Many Thanks